college-regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "25bb91ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "df <- read.csv(\"E:/Machine Learning/Datasets/College_Regression.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2f98f7a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>387</li><li>16</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 387\n",
       "\\item 16\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 387\n",
       "2. 16\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 387  16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5466b483",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  college_code     division         cutoff         courses      \n",
       " Min.   :1002   Min.   :1.000   Min.   : 2.45   Min.   : 1.000  \n",
       " 1st Qu.:3200   1st Qu.:3.000   1st Qu.:57.92   1st Qu.: 5.000  \n",
       " Median :4649   Median :4.000   Median :75.18   Median : 6.000  \n",
       " Mean   :4543   Mean   :4.253   Mean   :71.75   Mean   : 7.189  \n",
       " 3rd Qu.:6268   3rd Qu.:6.000   3rd Qu.:87.98   3rd Qu.: 9.000  \n",
       " Max.   :6991   Max.   :6.000   Max.   :99.91   Max.   :41.000  \n",
       "                                NA's   :10                      \n",
       "     intake            fees             salary            rating     \n",
       " Min.   :   6.3   Min.   :   3750   Min.   : 120000   Min.   :1.000  \n",
       " 1st Qu.: 240.0   1st Qu.: 240000   1st Qu.: 240000   1st Qu.:3.500  \n",
       " Median : 300.0   Median : 308000   Median : 300000   Median :3.800  \n",
       " Mean   : 382.0   Mean   : 322662   Mean   : 360634   Mean   :3.666  \n",
       " 3rd Qu.: 420.0   3rd Qu.: 372500   3rd Qu.: 390000   3rd Qu.:4.000  \n",
       " Max.   :2274.0   Max.   :1880000   Max.   :1650000   Max.   :5.000  \n",
       " NA's   :13       NA's   :8         NA's   :51        NA's   :28     \n",
       " infrastructure     faculty          crowd          hostel         \n",
       " Min.   :1.000   Min.   :1.000   Min.   :0.500   Length:387        \n",
       " 1st Qu.:3.500   1st Qu.:3.600   1st Qu.:3.500   Class :character  \n",
       " Median :3.900   Median :4.000   Median :3.900   Mode  :character  \n",
       " Mean   :3.804   Mean   :3.822   Mean   :3.756                     \n",
       " 3rd Qu.:4.200   3rd Qu.:4.200   3rd Qu.:4.200                     \n",
       " Max.   :8.000   Max.   :5.000   Max.   :5.000                     \n",
       " NA's   :28      NA's   :31      NA's   :32                        \n",
       "   government        autonomous          rank          new_ban      \n",
       " Min.   :0.00000   Min.   :0.0000   Min.   : 12.0   Min.   :0.0000  \n",
       " 1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:301.0   1st Qu.:0.0000  \n",
       " Median :0.00000   Median :0.0000   Median :301.0   Median :0.0000  \n",
       " Mean   :0.05943   Mean   :0.1473   Mean   :287.5   Mean   :0.2067  \n",
       " 3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:301.0   3rd Qu.:0.0000  \n",
       " Max.   :1.00000   Max.   :1.0000   Max.   :301.0   Max.   :1.0000  \n",
       "                                                                    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6652735",
   "metadata": {},
   "source": [
    "* cutoff, intake, fees, salary, rating, infrastructure, faculty, crowd have missing values\n",
    "* Also courses, salary, cutoff, intake fees have outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55843d0b",
   "metadata": {},
   "source": [
    "# Data Preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ba94d89",
   "metadata": {},
   "source": [
    "### 1. Dummy variable creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9939e246",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Thank you for using fastDummies!\n",
      "\n",
      "To acknowledge our work, please cite the package:\n",
      "\n",
      "Kaplan, J. & Schlegel, B. (2023). fastDummies: Fast Creation of Dummy (Binary) Columns and Rows from Categorical Variables. Version 1.7.1. URL: https://github.com/jacobkap/fastDummies, https://jacobkap.github.io/fastDummies/.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 387 × 19</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>crowd</th><th scope=col>hostel</th><th scope=col>government</th><th scope=col>autonomous</th><th scope=col>rank</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_NONE</th><th scope=col>hostel_ONE</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1002</td><td>1</td><td>96.440</td><td> 8</td><td> 300</td><td>240000</td><td>390000</td><td>3.4</td><td>3.2</td><td>3.5</td><td>3.7</td><td>BOTH</td><td>1</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1005</td><td>1</td><td>61.630</td><td> 4</td><td> 720</td><td>490000</td><td>320000</td><td>3.8</td><td>3.9</td><td>3.9</td><td>3.9</td><td>BOTH</td><td>1</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1012</td><td>1</td><td>86.550</td><td> 5</td><td> 720</td><td> 96000</td><td>300000</td><td>2.8</td><td>2.5</td><td>2.5</td><td>3.0</td><td>BOTH</td><td>1</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1101</td><td>1</td><td>93.170</td><td>11</td><td> 300</td><td>350000</td><td>350000</td><td>3.9</td><td>4.6</td><td>4.0</td><td>3.9</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1105</td><td>1</td><td>88.050</td><td> 8</td><td> 480</td><td>440000</td><td>330000</td><td>3.9</td><td>4.0</td><td>3.9</td><td>4.2</td><td>NONE</td><td>0</td><td>1</td><td>250</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1107</td><td>1</td><td>79.107</td><td> 6</td><td> 720</td><td>400000</td><td>200000</td><td>4.4</td><td>4.4</td><td>4.3</td><td>4.6</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1108</td><td>1</td><td>43.040</td><td> 5</td><td> 300</td><td>310000</td><td>300000</td><td>3.9</td><td>4.0</td><td>4.3</td><td>3.5</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1114</td><td>1</td><td>81.550</td><td> 6</td><td> 300</td><td>320000</td><td>370000</td><td>4.0</td><td>4.4</td><td>3.9</td><td>4.2</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1116</td><td>1</td><td>65.260</td><td> 6</td><td> 340</td><td>420000</td><td>220000</td><td>3.7</td><td>4.0</td><td>4.0</td><td>3.6</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1117</td><td>1</td><td>61.260</td><td> 8</td><td> 540</td><td>340000</td><td>300000</td><td>3.8</td><td>4.5</td><td>4.3</td><td>3.8</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1119</td><td>1</td><td>68.370</td><td> 5</td><td> 540</td><td>290000</td><td>340000</td><td>3.5</td><td>3.8</td><td>4.0</td><td>3.8</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1120</td><td>1</td><td>77.600</td><td> 9</td><td> 420</td><td>280000</td><td>240000</td><td>4.0</td><td>4.4</td><td>4.0</td><td>4.1</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1121</td><td>1</td><td>75.780</td><td> 5</td><td> 300</td><td>280000</td><td>310000</td><td>3.7</td><td>4.0</td><td>4.0</td><td>5.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1122</td><td>1</td><td>41.360</td><td> 5</td><td> 300</td><td>200000</td><td>300000</td><td>2.2</td><td>3.0</td><td>2.0</td><td>3.5</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1123</td><td>1</td><td>66.020</td><td> 4</td><td>1020</td><td>300000</td><td>260000</td><td>4.3</td><td>5.0</td><td>4.0</td><td>4.3</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1124</td><td>1</td><td>49.080</td><td> 5</td><td> 300</td><td>490000</td><td>230000</td><td>3.6</td><td>4.3</td><td>3.6</td><td>3.5</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1125</td><td>1</td><td>52.440</td><td> 5</td><td> 360</td><td> 95900</td><td>180000</td><td>3.2</td><td>3.5</td><td>3.3</td><td>3.4</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1126</td><td>1</td><td>67.710</td><td> 5</td><td> 300</td><td>170000</td><td>490000</td><td>5.0</td><td>5.0</td><td>5.0</td><td>5.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1127</td><td>1</td><td>62.390</td><td> 5</td><td> 150</td><td>330000</td><td>190000</td><td>3.6</td><td>3.0</td><td>3.0</td><td>3.5</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1128</td><td>1</td><td>81.370</td><td> 7</td><td> 480</td><td>320000</td><td>330000</td><td>3.8</td><td>4.0</td><td>4.2</td><td>3.8</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1129</td><td>1</td><td>19.450</td><td> 4</td><td> 240</td><td>210000</td><td>250000</td><td>2.3</td><td>3.5</td><td>2.5</td><td>0.5</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1130</td><td>1</td><td>45.980</td><td> 6</td><td> 480</td><td>180000</td><td>180000</td><td>2.2</td><td>4.0</td><td>2.0</td><td>1.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1180</td><td>1</td><td>49.050</td><td> 5</td><td> 270</td><td>320000</td><td>    NA</td><td>2.6</td><td>3.0</td><td>2.0</td><td>3.0</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1182</td><td>1</td><td>59.680</td><td> 4</td><td> 630</td><td>200000</td><td>450000</td><td>4.2</td><td>4.0</td><td>5.0</td><td>5.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1251</td><td>1</td><td>16.730</td><td> 6</td><td> 300</td><td>284000</td><td>280000</td><td>3.4</td><td>3.2</td><td>3.4</td><td>3.6</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1265</td><td>1</td><td>77.080</td><td> 6</td><td> 300</td><td>230000</td><td>400000</td><td>4.2</td><td>4.3</td><td>4.4</td><td>4.6</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>1267</td><td>1</td><td>    NA</td><td> 4</td><td> 234</td><td> 96000</td><td>    NA</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1268</td><td>1</td><td>48.210</td><td> 6</td><td> 360</td><td>150000</td><td>240000</td><td>2.3</td><td>2.0</td><td>2.5</td><td>2.5</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1276</td><td>1</td><td>56.800</td><td> 5</td><td> 240</td><td>220000</td><td>450000</td><td>4.0</td><td>3.0</td><td>2.0</td><td>3.0</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>1278</td><td>2</td><td>    NA</td><td> 5</td><td> 240</td><td> 58700</td><td>350000</td><td>3.5</td><td>4.2</td><td> NA</td><td> NA</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><td>6766</td><td>6</td><td>63.08</td><td> 5</td><td>300</td><td>260000</td><td>350000</td><td>4.7</td><td>5.0</td><td>5.0</td><td>4.5</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>6767</td><td>6</td><td>72.64</td><td> 7</td><td>420</td><td>260000</td><td>300000</td><td>3.4</td><td>3.9</td><td>3.6</td><td>3.2</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>6768</td><td>6</td><td>77.41</td><td> 4</td><td>255</td><td>190000</td><td>180000</td><td>3.8</td><td>3.8</td><td>3.8</td><td>3.9</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>6769</td><td>6</td><td>84.68</td><td> 5</td><td>480</td><td>    NA</td><td>400000</td><td>3.8</td><td>3.8</td><td>3.8</td><td>3.6</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6770</td><td>6</td><td>77.03</td><td> 5</td><td>300</td><td>410000</td><td>240000</td><td>3.8</td><td>4.1</td><td>3.6</td><td>4.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6771</td><td>6</td><td>   NA</td><td> 7</td><td>420</td><td>250000</td><td>230000</td><td>2.6</td><td>3.1</td><td>3.0</td><td>2.5</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6772</td><td>6</td><td>87.28</td><td> 6</td><td>510</td><td>400000</td><td>290000</td><td>4.0</td><td>4.0</td><td>3.9</td><td>4.4</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6780</td><td>6</td><td>71.76</td><td>11</td><td>420</td><td>250000</td><td>240000</td><td>4.0</td><td>4.0</td><td>4.0</td><td>4.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6781</td><td>6</td><td>54.12</td><td> 4</td><td>300</td><td>210000</td><td>210000</td><td>3.8</td><td>3.0</td><td>4.0</td><td>4.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6782</td><td>6</td><td>28.69</td><td> 4</td><td>105</td><td>170000</td><td>350000</td><td>4.6</td><td>4.0</td><td>4.5</td><td>4.5</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6786</td><td>6</td><td>79.87</td><td> 5</td><td>420</td><td>330000</td><td>350000</td><td>4.2</td><td>4.0</td><td>5.0</td><td>5.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6787</td><td>6</td><td>71.92</td><td> 8</td><td>540</td><td>330000</td><td>250000</td><td>3.6</td><td>4.0</td><td>3.6</td><td>4.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6794</td><td>6</td><td>83.31</td><td> 9</td><td>420</td><td>240000</td><td>240000</td><td>3.6</td><td>3.8</td><td>3.8</td><td>3.6</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6795</td><td>6</td><td>52.82</td><td> 4</td><td>210</td><td>240000</td><td>    NA</td><td>3.0</td><td>3.0</td><td>3.3</td><td>3.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6796</td><td>6</td><td>93.45</td><td> 5</td><td>300</td><td>340000</td><td>450000</td><td>3.6</td><td>3.5</td><td>3.7</td><td>3.7</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6797</td><td>6</td><td>74.20</td><td> 5</td><td>240</td><td>320000</td><td>    NA</td><td>4.1</td><td>4.4</td><td>4.4</td><td>4.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6802</td><td>6</td><td>94.43</td><td> 8</td><td>660</td><td>350000</td><td>380000</td><td>4.0</td><td>4.2</td><td>4.0</td><td>4.1</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6803</td><td>6</td><td>74.51</td><td> 6</td><td>360</td><td>240000</td><td>400000</td><td>4.1</td><td>4.1</td><td>4.2</td><td>4.3</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6805</td><td>6</td><td>   NA</td><td> 4</td><td>300</td><td>200000</td><td>    NA</td><td> NA</td><td> NA</td><td> NA</td><td> NA</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>6808</td><td>6</td><td>74.22</td><td> 4</td><td>360</td><td>290000</td><td>250000</td><td>4.1</td><td>3.9</td><td>4.4</td><td>4.1</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6809</td><td>6</td><td>30.00</td><td> 6</td><td>360</td><td>244000</td><td>400000</td><td>4.5</td><td>4.5</td><td> NA</td><td> NA</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6811</td><td>6</td><td>42.56</td><td>16</td><td>660</td><td>620000</td><td>380000</td><td>4.1</td><td>4.7</td><td>3.9</td><td>4.2</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6815</td><td>6</td><td>69.60</td><td> 4</td><td>120</td><td>190000</td><td>    NA</td><td>2.8</td><td>2.7</td><td>2.7</td><td>3.3</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6822</td><td>6</td><td>96.46</td><td> 9</td><td>480</td><td>400000</td><td>270000</td><td>4.0</td><td>3.6</td><td>4.3</td><td>3.6</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6834</td><td>6</td><td>80.45</td><td> 6</td><td>360</td><td>300000</td><td>300000</td><td>3.0</td><td>3.4</td><td>3.1</td><td>3.2</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6839</td><td>6</td><td>76.27</td><td> 5</td><td>420</td><td>250000</td><td>300000</td><td>3.9</td><td>4.0</td><td>4.0</td><td>4.0</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6878</td><td>6</td><td>55.89</td><td> 5</td><td>300</td><td>180000</td><td>    NA</td><td>1.2</td><td>1.0</td><td>1.0</td><td>2.0</td><td>NONE</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>0</td></tr>\n",
       "\t<tr><td>6901</td><td>6</td><td>54.91</td><td> 4</td><td>240</td><td>340000</td><td>400000</td><td>4.6</td><td>4.7</td><td> NA</td><td> NA</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6938</td><td>6</td><td>46.44</td><td> 8</td><td>540</td><td>250000</td><td>    NA</td><td>3.7</td><td>3.7</td><td>3.8</td><td>3.6</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "\t<tr><td>6991</td><td>6</td><td>78.34</td><td> 4</td><td>360</td><td>344000</td><td>300000</td><td>3.7</td><td>3.8</td><td>3.5</td><td>3.3</td><td>BOTH</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 387 × 19\n",
       "\\begin{tabular}{lllllllllllllllllll}\n",
       " college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & crowd & hostel & government & autonomous & rank & new\\_ban & hostel\\_BOTH & hostel\\_NONE & hostel\\_ONE\\\\\n",
       " <int> & <int> & <dbl> & <int> & <dbl> & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <chr> & <int> & <int> & <int> & <int> & <int> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t 1002 & 1 & 96.440 &  8 &  300 & 240000 & 390000 & 3.4 & 3.2 & 3.5 & 3.7 & BOTH & 1 & 1 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1005 & 1 & 61.630 &  4 &  720 & 490000 & 320000 & 3.8 & 3.9 & 3.9 & 3.9 & BOTH & 1 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1012 & 1 & 86.550 &  5 &  720 &  96000 & 300000 & 2.8 & 2.5 & 2.5 & 3.0 & BOTH & 1 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 1101 & 1 & 93.170 & 11 &  300 & 350000 & 350000 & 3.9 & 4.6 & 4.0 & 3.9 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1105 & 1 & 88.050 &  8 &  480 & 440000 & 330000 & 3.9 & 4.0 & 3.9 & 4.2 & NONE & 0 & 1 & 250 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1107 & 1 & 79.107 &  6 &  720 & 400000 & 200000 & 4.4 & 4.4 & 4.3 & 4.6 & NONE & 0 & 0 & 301 & 1 & 0 & 1 & 0\\\\\n",
       "\t 1108 & 1 & 43.040 &  5 &  300 & 310000 & 300000 & 3.9 & 4.0 & 4.3 & 3.5 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1114 & 1 & 81.550 &  6 &  300 & 320000 & 370000 & 4.0 & 4.4 & 3.9 & 4.2 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1116 & 1 & 65.260 &  6 &  340 & 420000 & 220000 & 3.7 & 4.0 & 4.0 & 3.6 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1117 & 1 & 61.260 &  8 &  540 & 340000 & 300000 & 3.8 & 4.5 & 4.3 & 3.8 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 1119 & 1 & 68.370 &  5 &  540 & 290000 & 340000 & 3.5 & 3.8 & 4.0 & 3.8 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1120 & 1 & 77.600 &  9 &  420 & 280000 & 240000 & 4.0 & 4.4 & 4.0 & 4.1 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1121 & 1 & 75.780 &  5 &  300 & 280000 & 310000 & 3.7 & 4.0 & 4.0 & 5.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1122 & 1 & 41.360 &  5 &  300 & 200000 & 300000 & 2.2 & 3.0 & 2.0 & 3.5 & NONE & 0 & 0 & 301 & 1 & 0 & 1 & 0\\\\\n",
       "\t 1123 & 1 & 66.020 &  4 & 1020 & 300000 & 260000 & 4.3 & 5.0 & 4.0 & 4.3 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1124 & 1 & 49.080 &  5 &  300 & 490000 & 230000 & 3.6 & 4.3 & 3.6 & 3.5 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 1125 & 1 & 52.440 &  5 &  360 &  95900 & 180000 & 3.2 & 3.5 & 3.3 & 3.4 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1126 & 1 & 67.710 &  5 &  300 & 170000 & 490000 & 5.0 & 5.0 & 5.0 & 5.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1127 & 1 & 62.390 &  5 &  150 & 330000 & 190000 & 3.6 & 3.0 & 3.0 & 3.5 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1128 & 1 & 81.370 &  7 &  480 & 320000 & 330000 & 3.8 & 4.0 & 4.2 & 3.8 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1129 & 1 & 19.450 &  4 &  240 & 210000 & 250000 & 2.3 & 3.5 & 2.5 & 0.5 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 1130 & 1 & 45.980 &  6 &  480 & 180000 & 180000 & 2.2 & 4.0 & 2.0 & 1.0 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 1180 & 1 & 49.050 &  5 &  270 & 320000 &     NA & 2.6 & 3.0 & 2.0 & 3.0 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1182 & 1 & 59.680 &  4 &  630 & 200000 & 450000 & 4.2 & 4.0 & 5.0 & 5.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1251 & 1 & 16.730 &  6 &  300 & 284000 & 280000 & 3.4 & 3.2 & 3.4 & 3.6 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 1265 & 1 & 77.080 &  6 &  300 & 230000 & 400000 & 4.2 & 4.3 & 4.4 & 4.6 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 1267 & 1 &     NA &  4 &  234 &  96000 &     NA &  NA &  NA &  NA &  NA & NONE & 0 & 0 & 301 & 1 & 0 & 1 & 0\\\\\n",
       "\t 1268 & 1 & 48.210 &  6 &  360 & 150000 & 240000 & 2.3 & 2.0 & 2.5 & 2.5 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1276 & 1 & 56.800 &  5 &  240 & 220000 & 450000 & 4.0 & 3.0 & 2.0 & 3.0 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 1278 & 2 &     NA &  5 &  240 &  58700 & 350000 & 3.5 & 4.2 &  NA &  NA & NONE & 0 & 0 & 301 & 1 & 0 & 1 & 0\\\\\n",
       "\t ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t 6766 & 6 & 63.08 &  5 & 300 & 260000 & 350000 & 4.7 & 5.0 & 5.0 & 4.5 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 6767 & 6 & 72.64 &  7 & 420 & 260000 & 300000 & 3.4 & 3.9 & 3.6 & 3.2 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 6768 & 6 & 77.41 &  4 & 255 & 190000 & 180000 & 3.8 & 3.8 & 3.8 & 3.9 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 6769 & 6 & 84.68 &  5 & 480 &     NA & 400000 & 3.8 & 3.8 & 3.8 & 3.6 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6770 & 6 & 77.03 &  5 & 300 & 410000 & 240000 & 3.8 & 4.1 & 3.6 & 4.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6771 & 6 &    NA &  7 & 420 & 250000 & 230000 & 2.6 & 3.1 & 3.0 & 2.5 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6772 & 6 & 87.28 &  6 & 510 & 400000 & 290000 & 4.0 & 4.0 & 3.9 & 4.4 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6780 & 6 & 71.76 & 11 & 420 & 250000 & 240000 & 4.0 & 4.0 & 4.0 & 4.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6781 & 6 & 54.12 &  4 & 300 & 210000 & 210000 & 3.8 & 3.0 & 4.0 & 4.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6782 & 6 & 28.69 &  4 & 105 & 170000 & 350000 & 4.6 & 4.0 & 4.5 & 4.5 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6786 & 6 & 79.87 &  5 & 420 & 330000 & 350000 & 4.2 & 4.0 & 5.0 & 5.0 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6787 & 6 & 71.92 &  8 & 540 & 330000 & 250000 & 3.6 & 4.0 & 3.6 & 4.0 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6794 & 6 & 83.31 &  9 & 420 & 240000 & 240000 & 3.6 & 3.8 & 3.8 & 3.6 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6795 & 6 & 52.82 &  4 & 210 & 240000 &     NA & 3.0 & 3.0 & 3.3 & 3.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6796 & 6 & 93.45 &  5 & 300 & 340000 & 450000 & 3.6 & 3.5 & 3.7 & 3.7 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6797 & 6 & 74.20 &  5 & 240 & 320000 &     NA & 4.1 & 4.4 & 4.4 & 4.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6802 & 6 & 94.43 &  8 & 660 & 350000 & 380000 & 4.0 & 4.2 & 4.0 & 4.1 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6803 & 6 & 74.51 &  6 & 360 & 240000 & 400000 & 4.1 & 4.1 & 4.2 & 4.3 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6805 & 6 &    NA &  4 & 300 & 200000 &     NA &  NA &  NA &  NA &  NA & NONE & 0 & 0 & 301 & 1 & 0 & 1 & 0\\\\\n",
       "\t 6808 & 6 & 74.22 &  4 & 360 & 290000 & 250000 & 4.1 & 3.9 & 4.4 & 4.1 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6809 & 6 & 30.00 &  6 & 360 & 244000 & 400000 & 4.5 & 4.5 &  NA &  NA & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6811 & 6 & 42.56 & 16 & 660 & 620000 & 380000 & 4.1 & 4.7 & 3.9 & 4.2 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6815 & 6 & 69.60 &  4 & 120 & 190000 &     NA & 2.8 & 2.7 & 2.7 & 3.3 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6822 & 6 & 96.46 &  9 & 480 & 400000 & 270000 & 4.0 & 3.6 & 4.3 & 3.6 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6834 & 6 & 80.45 &  6 & 360 & 300000 & 300000 & 3.0 & 3.4 & 3.1 & 3.2 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6839 & 6 & 76.27 &  5 & 420 & 250000 & 300000 & 3.9 & 4.0 & 4.0 & 4.0 & BOTH & 0 & 0 & 301 & 0 & 1 & 0 & 0\\\\\n",
       "\t 6878 & 6 & 55.89 &  5 & 300 & 180000 &     NA & 1.2 & 1.0 & 1.0 & 2.0 & NONE & 0 & 0 & 301 & 0 & 0 & 1 & 0\\\\\n",
       "\t 6901 & 6 & 54.91 &  4 & 240 & 340000 & 400000 & 4.6 & 4.7 &  NA &  NA & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6938 & 6 & 46.44 &  8 & 540 & 250000 &     NA & 3.7 & 3.7 & 3.8 & 3.6 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\t 6991 & 6 & 78.34 &  4 & 360 & 344000 & 300000 & 3.7 & 3.8 & 3.5 & 3.3 & BOTH & 0 & 0 & 301 & 1 & 1 & 0 & 0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 387 × 19\n",
       "\n",
       "| college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;int&gt; | intake &lt;dbl&gt; | fees &lt;int&gt; | salary &lt;int&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | crowd &lt;dbl&gt; | hostel &lt;chr&gt; | government &lt;int&gt; | autonomous &lt;int&gt; | rank &lt;int&gt; | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_NONE &lt;int&gt; | hostel_ONE &lt;int&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1002 | 1 | 96.440 |  8 |  300 | 240000 | 390000 | 3.4 | 3.2 | 3.5 | 3.7 | BOTH | 1 | 1 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1005 | 1 | 61.630 |  4 |  720 | 490000 | 320000 | 3.8 | 3.9 | 3.9 | 3.9 | BOTH | 1 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1012 | 1 | 86.550 |  5 |  720 |  96000 | 300000 | 2.8 | 2.5 | 2.5 | 3.0 | BOTH | 1 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 1101 | 1 | 93.170 | 11 |  300 | 350000 | 350000 | 3.9 | 4.6 | 4.0 | 3.9 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1105 | 1 | 88.050 |  8 |  480 | 440000 | 330000 | 3.9 | 4.0 | 3.9 | 4.2 | NONE | 0 | 1 | 250 | 0 | 0 | 1 | 0 |\n",
       "| 1107 | 1 | 79.107 |  6 |  720 | 400000 | 200000 | 4.4 | 4.4 | 4.3 | 4.6 | NONE | 0 | 0 | 301 | 1 | 0 | 1 | 0 |\n",
       "| 1108 | 1 | 43.040 |  5 |  300 | 310000 | 300000 | 3.9 | 4.0 | 4.3 | 3.5 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1114 | 1 | 81.550 |  6 |  300 | 320000 | 370000 | 4.0 | 4.4 | 3.9 | 4.2 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1116 | 1 | 65.260 |  6 |  340 | 420000 | 220000 | 3.7 | 4.0 | 4.0 | 3.6 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 1117 | 1 | 61.260 |  8 |  540 | 340000 | 300000 | 3.8 | 4.5 | 4.3 | 3.8 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 1119 | 1 | 68.370 |  5 |  540 | 290000 | 340000 | 3.5 | 3.8 | 4.0 | 3.8 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1120 | 1 | 77.600 |  9 |  420 | 280000 | 240000 | 4.0 | 4.4 | 4.0 | 4.1 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1121 | 1 | 75.780 |  5 |  300 | 280000 | 310000 | 3.7 | 4.0 | 4.0 | 5.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1122 | 1 | 41.360 |  5 |  300 | 200000 | 300000 | 2.2 | 3.0 | 2.0 | 3.5 | NONE | 0 | 0 | 301 | 1 | 0 | 1 | 0 |\n",
       "| 1123 | 1 | 66.020 |  4 | 1020 | 300000 | 260000 | 4.3 | 5.0 | 4.0 | 4.3 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1124 | 1 | 49.080 |  5 |  300 | 490000 | 230000 | 3.6 | 4.3 | 3.6 | 3.5 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 1125 | 1 | 52.440 |  5 |  360 |  95900 | 180000 | 3.2 | 3.5 | 3.3 | 3.4 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 1126 | 1 | 67.710 |  5 |  300 | 170000 | 490000 | 5.0 | 5.0 | 5.0 | 5.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1127 | 1 | 62.390 |  5 |  150 | 330000 | 190000 | 3.6 | 3.0 | 3.0 | 3.5 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1128 | 1 | 81.370 |  7 |  480 | 320000 | 330000 | 3.8 | 4.0 | 4.2 | 3.8 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1129 | 1 | 19.450 |  4 |  240 | 210000 | 250000 | 2.3 | 3.5 | 2.5 | 0.5 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 1130 | 1 | 45.980 |  6 |  480 | 180000 | 180000 | 2.2 | 4.0 | 2.0 | 1.0 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 1180 | 1 | 49.050 |  5 |  270 | 320000 |     NA | 2.6 | 3.0 | 2.0 | 3.0 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 1182 | 1 | 59.680 |  4 |  630 | 200000 | 450000 | 4.2 | 4.0 | 5.0 | 5.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1251 | 1 | 16.730 |  6 |  300 | 284000 | 280000 | 3.4 | 3.2 | 3.4 | 3.6 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 1265 | 1 | 77.080 |  6 |  300 | 230000 | 400000 | 4.2 | 4.3 | 4.4 | 4.6 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 1267 | 1 |     NA |  4 |  234 |  96000 |     NA |  NA |  NA |  NA |  NA | NONE | 0 | 0 | 301 | 1 | 0 | 1 | 0 |\n",
       "| 1268 | 1 | 48.210 |  6 |  360 | 150000 | 240000 | 2.3 | 2.0 | 2.5 | 2.5 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 1276 | 1 | 56.800 |  5 |  240 | 220000 | 450000 | 4.0 | 3.0 | 2.0 | 3.0 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 1278 | 2 |     NA |  5 |  240 |  58700 | 350000 | 3.5 | 4.2 |  NA |  NA | NONE | 0 | 0 | 301 | 1 | 0 | 1 | 0 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 6766 | 6 | 63.08 |  5 | 300 | 260000 | 350000 | 4.7 | 5.0 | 5.0 | 4.5 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 6767 | 6 | 72.64 |  7 | 420 | 260000 | 300000 | 3.4 | 3.9 | 3.6 | 3.2 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 6768 | 6 | 77.41 |  4 | 255 | 190000 | 180000 | 3.8 | 3.8 | 3.8 | 3.9 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 6769 | 6 | 84.68 |  5 | 480 |     NA | 400000 | 3.8 | 3.8 | 3.8 | 3.6 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6770 | 6 | 77.03 |  5 | 300 | 410000 | 240000 | 3.8 | 4.1 | 3.6 | 4.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6771 | 6 |    NA |  7 | 420 | 250000 | 230000 | 2.6 | 3.1 | 3.0 | 2.5 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6772 | 6 | 87.28 |  6 | 510 | 400000 | 290000 | 4.0 | 4.0 | 3.9 | 4.4 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6780 | 6 | 71.76 | 11 | 420 | 250000 | 240000 | 4.0 | 4.0 | 4.0 | 4.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6781 | 6 | 54.12 |  4 | 300 | 210000 | 210000 | 3.8 | 3.0 | 4.0 | 4.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6782 | 6 | 28.69 |  4 | 105 | 170000 | 350000 | 4.6 | 4.0 | 4.5 | 4.5 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6786 | 6 | 79.87 |  5 | 420 | 330000 | 350000 | 4.2 | 4.0 | 5.0 | 5.0 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6787 | 6 | 71.92 |  8 | 540 | 330000 | 250000 | 3.6 | 4.0 | 3.6 | 4.0 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6794 | 6 | 83.31 |  9 | 420 | 240000 | 240000 | 3.6 | 3.8 | 3.8 | 3.6 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6795 | 6 | 52.82 |  4 | 210 | 240000 |     NA | 3.0 | 3.0 | 3.3 | 3.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6796 | 6 | 93.45 |  5 | 300 | 340000 | 450000 | 3.6 | 3.5 | 3.7 | 3.7 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6797 | 6 | 74.20 |  5 | 240 | 320000 |     NA | 4.1 | 4.4 | 4.4 | 4.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6802 | 6 | 94.43 |  8 | 660 | 350000 | 380000 | 4.0 | 4.2 | 4.0 | 4.1 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6803 | 6 | 74.51 |  6 | 360 | 240000 | 400000 | 4.1 | 4.1 | 4.2 | 4.3 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6805 | 6 |    NA |  4 | 300 | 200000 |     NA |  NA |  NA |  NA |  NA | NONE | 0 | 0 | 301 | 1 | 0 | 1 | 0 |\n",
       "| 6808 | 6 | 74.22 |  4 | 360 | 290000 | 250000 | 4.1 | 3.9 | 4.4 | 4.1 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6809 | 6 | 30.00 |  6 | 360 | 244000 | 400000 | 4.5 | 4.5 |  NA |  NA | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6811 | 6 | 42.56 | 16 | 660 | 620000 | 380000 | 4.1 | 4.7 | 3.9 | 4.2 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6815 | 6 | 69.60 |  4 | 120 | 190000 |     NA | 2.8 | 2.7 | 2.7 | 3.3 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6822 | 6 | 96.46 |  9 | 480 | 400000 | 270000 | 4.0 | 3.6 | 4.3 | 3.6 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6834 | 6 | 80.45 |  6 | 360 | 300000 | 300000 | 3.0 | 3.4 | 3.1 | 3.2 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6839 | 6 | 76.27 |  5 | 420 | 250000 | 300000 | 3.9 | 4.0 | 4.0 | 4.0 | BOTH | 0 | 0 | 301 | 0 | 1 | 0 | 0 |\n",
       "| 6878 | 6 | 55.89 |  5 | 300 | 180000 |     NA | 1.2 | 1.0 | 1.0 | 2.0 | NONE | 0 | 0 | 301 | 0 | 0 | 1 | 0 |\n",
       "| 6901 | 6 | 54.91 |  4 | 240 | 340000 | 400000 | 4.6 | 4.7 |  NA |  NA | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6938 | 6 | 46.44 |  8 | 540 | 250000 |     NA | 3.7 | 3.7 | 3.8 | 3.6 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "| 6991 | 6 | 78.34 |  4 | 360 | 344000 | 300000 | 3.7 | 3.8 | 3.5 | 3.3 | BOTH | 0 | 0 | 301 | 1 | 1 | 0 | 0 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff courses intake fees   salary rating\n",
       "1   1002         1        96.440  8       300   240000 390000 3.4   \n",
       "2   1005         1        61.630  4       720   490000 320000 3.8   \n",
       "3   1012         1        86.550  5       720    96000 300000 2.8   \n",
       "4   1101         1        93.170 11       300   350000 350000 3.9   \n",
       "5   1105         1        88.050  8       480   440000 330000 3.9   \n",
       "6   1107         1        79.107  6       720   400000 200000 4.4   \n",
       "7   1108         1        43.040  5       300   310000 300000 3.9   \n",
       "8   1114         1        81.550  6       300   320000 370000 4.0   \n",
       "9   1116         1        65.260  6       340   420000 220000 3.7   \n",
       "10  1117         1        61.260  8       540   340000 300000 3.8   \n",
       "11  1119         1        68.370  5       540   290000 340000 3.5   \n",
       "12  1120         1        77.600  9       420   280000 240000 4.0   \n",
       "13  1121         1        75.780  5       300   280000 310000 3.7   \n",
       "14  1122         1        41.360  5       300   200000 300000 2.2   \n",
       "15  1123         1        66.020  4      1020   300000 260000 4.3   \n",
       "16  1124         1        49.080  5       300   490000 230000 3.6   \n",
       "17  1125         1        52.440  5       360    95900 180000 3.2   \n",
       "18  1126         1        67.710  5       300   170000 490000 5.0   \n",
       "19  1127         1        62.390  5       150   330000 190000 3.6   \n",
       "20  1128         1        81.370  7       480   320000 330000 3.8   \n",
       "21  1129         1        19.450  4       240   210000 250000 2.3   \n",
       "22  1130         1        45.980  6       480   180000 180000 2.2   \n",
       "23  1180         1        49.050  5       270   320000     NA 2.6   \n",
       "24  1182         1        59.680  4       630   200000 450000 4.2   \n",
       "25  1251         1        16.730  6       300   284000 280000 3.4   \n",
       "26  1265         1        77.080  6       300   230000 400000 4.2   \n",
       "27  1267         1            NA  4       234    96000     NA  NA   \n",
       "28  1268         1        48.210  6       360   150000 240000 2.3   \n",
       "29  1276         1        56.800  5       240   220000 450000 4.0   \n",
       "30  1278         2            NA  5       240    58700 350000 3.5   \n",
       "⋮   ⋮            ⋮        ⋮      ⋮       ⋮      ⋮      ⋮      ⋮     \n",
       "358 6766         6        63.08   5      300    260000 350000 4.7   \n",
       "359 6767         6        72.64   7      420    260000 300000 3.4   \n",
       "360 6768         6        77.41   4      255    190000 180000 3.8   \n",
       "361 6769         6        84.68   5      480        NA 400000 3.8   \n",
       "362 6770         6        77.03   5      300    410000 240000 3.8   \n",
       "363 6771         6           NA   7      420    250000 230000 2.6   \n",
       "364 6772         6        87.28   6      510    400000 290000 4.0   \n",
       "365 6780         6        71.76  11      420    250000 240000 4.0   \n",
       "366 6781         6        54.12   4      300    210000 210000 3.8   \n",
       "367 6782         6        28.69   4      105    170000 350000 4.6   \n",
       "368 6786         6        79.87   5      420    330000 350000 4.2   \n",
       "369 6787         6        71.92   8      540    330000 250000 3.6   \n",
       "370 6794         6        83.31   9      420    240000 240000 3.6   \n",
       "371 6795         6        52.82   4      210    240000     NA 3.0   \n",
       "372 6796         6        93.45   5      300    340000 450000 3.6   \n",
       "373 6797         6        74.20   5      240    320000     NA 4.1   \n",
       "374 6802         6        94.43   8      660    350000 380000 4.0   \n",
       "375 6803         6        74.51   6      360    240000 400000 4.1   \n",
       "376 6805         6           NA   4      300    200000     NA  NA   \n",
       "377 6808         6        74.22   4      360    290000 250000 4.1   \n",
       "378 6809         6        30.00   6      360    244000 400000 4.5   \n",
       "379 6811         6        42.56  16      660    620000 380000 4.1   \n",
       "380 6815         6        69.60   4      120    190000     NA 2.8   \n",
       "381 6822         6        96.46   9      480    400000 270000 4.0   \n",
       "382 6834         6        80.45   6      360    300000 300000 3.0   \n",
       "383 6839         6        76.27   5      420    250000 300000 3.9   \n",
       "384 6878         6        55.89   5      300    180000     NA 1.2   \n",
       "385 6901         6        54.91   4      240    340000 400000 4.6   \n",
       "386 6938         6        46.44   8      540    250000     NA 3.7   \n",
       "387 6991         6        78.34   4      360    344000 300000 3.7   \n",
       "    infrastructure faculty crowd hostel government autonomous rank new_ban\n",
       "1   3.2            3.5     3.7   BOTH   1          1          301  0      \n",
       "2   3.9            3.9     3.9   BOTH   1          0          301  0      \n",
       "3   2.5            2.5     3.0   BOTH   1          0          301  1      \n",
       "4   4.6            4.0     3.9   BOTH   0          0          301  0      \n",
       "5   4.0            3.9     4.2   NONE   0          1          250  0      \n",
       "6   4.4            4.3     4.6   NONE   0          0          301  1      \n",
       "7   4.0            4.3     3.5   BOTH   0          0          301  0      \n",
       "8   4.4            3.9     4.2   BOTH   0          0          301  0      \n",
       "9   4.0            4.0     3.6   NONE   0          0          301  0      \n",
       "10  4.5            4.3     3.8   BOTH   0          0          301  1      \n",
       "11  3.8            4.0     3.8   BOTH   0          0          301  0      \n",
       "12  4.4            4.0     4.1   BOTH   0          0          301  0      \n",
       "13  4.0            4.0     5.0   BOTH   0          0          301  0      \n",
       "14  3.0            2.0     3.5   NONE   0          0          301  1      \n",
       "15  5.0            4.0     4.3   BOTH   0          0          301  0      \n",
       "16  4.3            3.6     3.5   BOTH   0          0          301  1      \n",
       "17  3.5            3.3     3.4   NONE   0          0          301  0      \n",
       "18  5.0            5.0     5.0   BOTH   0          0          301  0      \n",
       "19  3.0            3.0     3.5   BOTH   0          0          301  0      \n",
       "20  4.0            4.2     3.8   BOTH   0          0          301  0      \n",
       "21  3.5            2.5     0.5   BOTH   0          0          301  1      \n",
       "22  4.0            2.0     1.0   BOTH   0          0          301  1      \n",
       "23  3.0            2.0     3.0   NONE   0          0          301  0      \n",
       "24  4.0            5.0     5.0   BOTH   0          0          301  0      \n",
       "25  3.2            3.4     3.6   BOTH   0          0          301  1      \n",
       "26  4.3            4.4     4.6   BOTH   0          0          301  0      \n",
       "27   NA             NA      NA   NONE   0          0          301  1      \n",
       "28  2.0            2.5     2.5   NONE   0          0          301  0      \n",
       "29  3.0            2.0     3.0   NONE   0          0          301  0      \n",
       "30  4.2             NA      NA   NONE   0          0          301  1      \n",
       "⋮   ⋮              ⋮       ⋮     ⋮      ⋮          ⋮          ⋮    ⋮      \n",
       "358 5.0            5.0     4.5   NONE   0          0          301  0      \n",
       "359 3.9            3.6     3.2   NONE   0          0          301  0      \n",
       "360 3.8            3.8     3.9   NONE   0          0          301  0      \n",
       "361 3.8            3.8     3.6   BOTH   0          0          301  0      \n",
       "362 4.1            3.6     4.0   BOTH   0          0          301  0      \n",
       "363 3.1            3.0     2.5   BOTH   0          0          301  1      \n",
       "364 4.0            3.9     4.4   BOTH   0          0          301  0      \n",
       "365 4.0            4.0     4.0   BOTH   0          0          301  0      \n",
       "366 3.0            4.0     4.0   BOTH   0          0          301  0      \n",
       "367 4.0            4.5     4.5   BOTH   0          0          301  0      \n",
       "368 4.0            5.0     5.0   BOTH   0          0          301  1      \n",
       "369 4.0            3.6     4.0   BOTH   0          0          301  1      \n",
       "370 3.8            3.8     3.6   BOTH   0          0          301  0      \n",
       "371 3.0            3.3     3.0   BOTH   0          0          301  0      \n",
       "372 3.5            3.7     3.7   BOTH   0          0          301  0      \n",
       "373 4.4            4.4     4.0   BOTH   0          0          301  0      \n",
       "374 4.2            4.0     4.1   BOTH   0          0          301  0      \n",
       "375 4.1            4.2     4.3   BOTH   0          0          301  0      \n",
       "376  NA             NA      NA   NONE   0          0          301  1      \n",
       "377 3.9            4.4     4.1   BOTH   0          0          301  0      \n",
       "378 4.5             NA      NA   BOTH   0          0          301  1      \n",
       "379 4.7            3.9     4.2   BOTH   0          0          301  1      \n",
       "380 2.7            2.7     3.3   BOTH   0          0          301  1      \n",
       "381 3.6            4.3     3.6   BOTH   0          0          301  0      \n",
       "382 3.4            3.1     3.2   BOTH   0          0          301  0      \n",
       "383 4.0            4.0     4.0   BOTH   0          0          301  0      \n",
       "384 1.0            1.0     2.0   NONE   0          0          301  0      \n",
       "385 4.7             NA      NA   BOTH   0          0          301  1      \n",
       "386 3.7            3.8     3.6   BOTH   0          0          301  1      \n",
       "387 3.8            3.5     3.3   BOTH   0          0          301  1      \n",
       "    hostel_BOTH hostel_NONE hostel_ONE\n",
       "1   1           0           0         \n",
       "2   1           0           0         \n",
       "3   1           0           0         \n",
       "4   1           0           0         \n",
       "5   0           1           0         \n",
       "6   0           1           0         \n",
       "7   1           0           0         \n",
       "8   1           0           0         \n",
       "9   0           1           0         \n",
       "10  1           0           0         \n",
       "11  1           0           0         \n",
       "12  1           0           0         \n",
       "13  1           0           0         \n",
       "14  0           1           0         \n",
       "15  1           0           0         \n",
       "16  1           0           0         \n",
       "17  0           1           0         \n",
       "18  1           0           0         \n",
       "19  1           0           0         \n",
       "20  1           0           0         \n",
       "21  1           0           0         \n",
       "22  1           0           0         \n",
       "23  0           1           0         \n",
       "24  1           0           0         \n",
       "25  1           0           0         \n",
       "26  1           0           0         \n",
       "27  0           1           0         \n",
       "28  0           1           0         \n",
       "29  0           1           0         \n",
       "30  0           1           0         \n",
       "⋮   ⋮           ⋮           ⋮         \n",
       "358 0           1           0         \n",
       "359 0           1           0         \n",
       "360 0           1           0         \n",
       "361 1           0           0         \n",
       "362 1           0           0         \n",
       "363 1           0           0         \n",
       "364 1           0           0         \n",
       "365 1           0           0         \n",
       "366 1           0           0         \n",
       "367 1           0           0         \n",
       "368 1           0           0         \n",
       "369 1           0           0         \n",
       "370 1           0           0         \n",
       "371 1           0           0         \n",
       "372 1           0           0         \n",
       "373 1           0           0         \n",
       "374 1           0           0         \n",
       "375 1           0           0         \n",
       "376 0           1           0         \n",
       "377 1           0           0         \n",
       "378 1           0           0         \n",
       "379 1           0           0         \n",
       "380 1           0           0         \n",
       "381 1           0           0         \n",
       "382 1           0           0         \n",
       "383 1           0           0         \n",
       "384 0           1           0         \n",
       "385 1           0           0         \n",
       "386 1           0           0         \n",
       "387 1           0           0         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating dummy variables for categorical variables\n",
    "library(fastDummies)\n",
    "df <- dummy_cols(df, select_column=\"hostel\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a133ab1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "12"
      ],
      "text/latex": [
       "12"
      ],
      "text/markdown": [
       "12"
      ],
      "text/plain": [
       "[1] 12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "18"
      ],
      "text/latex": [
       "18"
      ],
      "text/markdown": [
       "18"
      ],
      "text/plain": [
       "[1] 18"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Removing the columns \"hostel\" and \"hostelNone\"\n",
    "which(colnames(df) == \"hostel\")\n",
    "which(colnames(df) == \"hostel_NONE\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "67f25feb",
   "metadata": {},
   "outputs": [],
   "source": [
    "df <- df[,-18]\n",
    "df <- df[,-12]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cf237fa",
   "metadata": {},
   "source": [
    "### 2. Missing value imputation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3175ec8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Missing value imputation\n",
    "df$cutoff[is.na(df$cutoff)] <- mean(df$cutoff, na.rm=TRUE)\n",
    "df$intake[is.na(df$intake)] <- mean(df$intake, na.rm=TRUE)\n",
    "df$fees[is.na(df$fees)] <- mean(df$fees, na.rm=TRUE)\n",
    "df$salary[is.na(df$salary)] <- mean(df$salary, na.rm=TRUE)\n",
    "df$rating[is.na(df$rating)] <- mean(df$rating, na.rm=TRUE)\n",
    "df$infrastructure[is.na(df$infrastructure)] <- mean(df$infrastructure, na.rm=TRUE)\n",
    "df$faculty[is.na(df$faculty)] <- mean(df$faculty, na.rm=TRUE)\n",
    "df$crowd[is.na(df$crowd)] <- mean(df$crowd, na.rm=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8b6ca516",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rounding off intake variable upto 1 digit\n",
    "df$intake <- round(df$intake, digits=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3a895cfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YGR6/bpLJiKdC0MuSZKIqxPy0iVixYLKSznbG8aOufXtlrALDa8E0Lyu/3lxCGK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\nz+ZI57CouTc6jHtdbNJ9JqRzWNTcGx3GvS426T4T0jksau6NDuN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OqWJi/ANuyWRXLIxxi4XeDgV0eRuxNEkzUSwlowYnQL+QkIgyHQFI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\nksEggP8DtEwtZRKAozEAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatterplot for outliers\n",
    "pairs(~cutoff+courses+intake+fees+salary, data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08b982e2",
   "metadata": {},
   "source": [
    "* courses, intake, fees and rank have outliers\n",
    "* salary has some functional (logarithmic) relationship with cutoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f47e2222",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TNJEnpS7RWHLfJxW/j7YgJNCCJIBMld1CA99+5uoZuQQ5AIkru4QcqoCQd+Lx+H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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Converting the log relation to linear relation\n",
    "df$salary <- log(1+df$salary)\n",
    "plot(df$cutoff, df$salary)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea710149",
   "metadata": {},
   "source": [
    "### 3. Capping and flooring treatment for outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a8bda1f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  1.000   5.000   6.000   6.935   9.000  13.500 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Capping for courses\n",
    "quantile_value <- quantile(df$courses, 0.75)\n",
    "UV <- 1.5 * quantile_value\n",
    "df$courses[df$courses > UV] <- UV\n",
    "summary(df$courses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ef027b72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  11.70   12.43   12.77   12.71   12.80   14.32 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Capping for salary\n",
    "quantile_value <- quantile(df$salary, 0.75)\n",
    "UV <- 1.5 * quantile_value\n",
    "df$salary[df$salary > UV] <- UV\n",
    "summary(df$salary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d3469091",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  44.34   59.12   74.51   72.95   87.30   99.91 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Flooring for cutoff\n",
    "quantile_value <- quantile(df$cutoff, 0.25)\n",
    "LV <- 0.75 * quantile_value\n",
    "df$cutoff[df$cutoff < LV] <- LV\n",
    "summary(df$cutoff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "325a6e57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "    6.3   262.5   315.0   353.0   420.0   630.0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  196.9   262.5   315.0   360.9   420.0   630.0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Winsorization for intake\n",
    "quantile_value <- quantile(df$intake, 0.75)\n",
    "UV <- 1.5 * quantile_value\n",
    "df$intake[df$intake > UV] <- UV\n",
    "summary(df$intake)\n",
    "\n",
    "quantile_value <- quantile(df$intake, 0.25)\n",
    "LV <- 0.75 * quantile_value\n",
    "df$intake[df$intake < LV] <- LV\n",
    "summary(df$intake)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d18b32da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  196.9   262.5   315.0   360.9   420.0   630.0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  196.9   262.5   315.0   360.9   420.0   630.0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Winsorization for intake\n",
    "quantile_value <- quantile(df$intake, 0.75)\n",
    "UV <- 1.5 * quantile_value\n",
    "df$intake[df$intake > UV] <- UV\n",
    "summary(df$intake)\n",
    "\n",
    "quantile_value <- quantile(df$intake, 0.25)\n",
    "LV <- 0.75 * quantile_value\n",
    "df$intake[df$intake < LV] <- LV\n",
    "summary(df$intake)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b881f29",
   "metadata": {},
   "source": [
    "## Model Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b5ca70a",
   "metadata": {},
   "source": [
    "### Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "655064ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "package 'LiblineaR' successfully unpacked and MD5 sums checked\n",
      "\n",
      "The downloaded binary packages are in\n",
      "\tC:\\Users\\Sharath\\AppData\\Local\\Temp\\RtmpiA1uQo\\downloaded_packages\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = cutoff ~ ., data = df)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-38.449  -9.740   1.009  10.500  35.224 \n",
       "\n",
       "Coefficients:\n",
       "                 Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)    -1.749e+01  2.675e+01  -0.654 0.513739    \n",
       "college_code   -2.002e-03  3.728e-03  -0.537 0.591548    \n",
       "division        2.819e+00  3.989e+00   0.707 0.480177    \n",
       "courses         1.077e+00  2.950e-01   3.649 0.000301 ***\n",
       "intake         -2.095e-03  5.356e-03  -0.391 0.695955    \n",
       "fees            1.499e-05  4.486e-06   3.341 0.000919 ***\n",
       "salary          4.939e+00  1.966e+00   2.511 0.012447 *  \n",
       "rating          1.525e+00  3.548e+00   0.430 0.667542    \n",
       "infrastructure -2.706e+00  1.746e+00  -1.550 0.122068    \n",
       "faculty         2.767e+00  2.321e+00   1.192 0.233841    \n",
       "crowd           2.834e+00  2.070e+00   1.369 0.171917    \n",
       "government      1.314e+01  3.313e+00   3.965 8.81e-05 ***\n",
       "autonomous      8.411e+00  2.479e+00   3.393 0.000765 ***\n",
       "rank           -6.201e-03  1.847e-02  -0.336 0.737227    \n",
       "new_ban        -8.728e+00  1.756e+00  -4.971 1.02e-06 ***\n",
       "hostel_BOTH    -2.334e+00  1.664e+00  -1.402 0.161705    \n",
       "hostel_ONE     -1.035e+00  4.149e+00  -0.249 0.803113    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 13.24 on 370 degrees of freedom\n",
       "Multiple R-squared:  0.4211,\tAdjusted R-squared:  0.396 \n",
       "F-statistic: 16.82 on 16 and 370 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(LiblineaR)\n",
    "linear <- lm(cutoff~., data=df)\n",
    "summary(linear)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f826735f",
   "metadata": {},
   "source": [
    "* 'crowd' and 'new_ban' are more significantly impacting cutoff. \n",
    "* 'government' and 'autonomous' also can be considered for analysis.\n",
    "* 'fees' had some outliers but still it seems to have some relation with cutoff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4c94eccf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IBFhAQI2ElIjOtg1z5CoiNYto+QAMsICRDgIaRLpg4Xu4sYYVwH+1yGdC9UdinP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\nAYQECCAkQMB/0q9x+pXiB1IAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(linear, which = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44331591",
   "metadata": {},
   "source": [
    "### TEST-TRAIN SPLIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "27b454d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "library(caTools)\n",
    "set.seed(0)\n",
    "split <- sample.split(df, SplitRatio=0.7)\n",
    "train <- subset(df, split==TRUE)\n",
    "test <- subset(df, split==FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7a637a5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>251</li><li>17</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 251\n",
       "\\item 17\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 251\n",
       "2. 17\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 251  17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>136</li><li>17</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 136\n",
       "\\item 17\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 136\n",
       "2. 17\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 136  17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(train)\n",
    "dim(test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89a4c3ba",
   "metadata": {},
   "source": [
    "### Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "97683ffc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = cutoff ~ ., data = train)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-28.316  -8.860   0.386   9.526  32.064 \n",
       "\n",
       "Coefficients:\n",
       "                 Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)    -2.705e+01  3.335e+01  -0.811 0.418123    \n",
       "college_code    1.431e-03  4.520e-03   0.317 0.751765    \n",
       "division       -8.431e-01  4.836e+00  -0.174 0.861737    \n",
       "courses         1.119e+00  3.579e-01   3.125 0.002001 ** \n",
       "intake         -4.809e-03  6.706e-03  -0.717 0.474058    \n",
       "fees            1.229e-05  5.238e-06   2.345 0.019840 *  \n",
       "salary          4.876e+00  2.401e+00   2.031 0.043407 *  \n",
       "rating         -7.375e+00  4.370e+00  -1.688 0.092821 .  \n",
       "infrastructure -3.118e-01  2.061e+00  -0.151 0.879886    \n",
       "faculty         6.286e+00  2.812e+00   2.235 0.026360 *  \n",
       "crowd           7.216e+00  2.758e+00   2.616 0.009472 ** \n",
       "government      1.404e+01  4.128e+00   3.401 0.000789 ***\n",
       "autonomous      1.020e+01  3.130e+00   3.258 0.001288 ** \n",
       "rank            5.160e-03  2.467e-02   0.209 0.834511    \n",
       "new_ban        -6.681e+00  2.147e+00  -3.112 0.002091 ** \n",
       "hostel_BOTH     7.041e-02  2.127e+00   0.033 0.973619    \n",
       "hostel_ONE      1.645e+00  5.811e+00   0.283 0.777413    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 13.17 on 234 degrees of freedom\n",
       "Multiple R-squared:  0.4388,\tAdjusted R-squared:  0.4004 \n",
       "F-statistic: 11.43 on 16 and 234 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 136 × 18</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>crowd</th><th scope=col>government</th><th scope=col>autonomous</th><th scope=col>rank</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_ONE</th><th scope=col>linear</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1002</td><td>1</td><td>96.44000</td><td> 8</td><td>300.000</td><td>240000.0</td><td>12.87391</td><td>3.400000</td><td>3.200000</td><td>3.500000</td><td>3.700000</td><td>1</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>95.25097</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1105</td><td>1</td><td>88.05000</td><td> 8</td><td>480.000</td><td>440000.0</td><td>12.70685</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>1</td><td>250</td><td>0</td><td>0</td><td>0</td><td>83.98529</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1108</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>310000.0</td><td>12.61154</td><td>3.900000</td><td>4.000000</td><td>4.300000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.03529</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>1114</td><td>1</td><td>81.55000</td><td> 6</td><td>300.000</td><td>320000.0</td><td>12.82126</td><td>4.000000</td><td>4.400000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.98257</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1122</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>200000.0</td><td>12.61154</td><td>2.200000</td><td>3.000000</td><td>2.000000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>57.34506</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>1124</td><td>1</td><td>49.08000</td><td> 5</td><td>300.000</td><td>490000.0</td><td>12.34584</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.01199</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>1126</td><td>1</td><td>67.71000</td><td> 5</td><td>300.000</td><td>170000.0</td><td>13.10216</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.53221</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>1130</td><td>1</td><td>45.98000</td><td> 6</td><td>480.000</td><td>180000.0</td><td>12.10072</td><td>2.200000</td><td>4.000000</td><td>2.000000</td><td>1.000000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>36.59204</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>1182</td><td>1</td><td>59.68000</td><td> 4</td><td>630.000</td><td>200000.0</td><td>13.01701</td><td>4.200000</td><td>4.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>78.07224</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>1251</td><td>1</td><td>44.34375</td><td> 6</td><td>300.000</td><td>284000.0</td><td>12.54255</td><td>3.400000</td><td>3.200000</td><td>3.400000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>60.02308</td></tr>\n",
       "\t<tr><th scope=row>31</th><td>2008</td><td>2</td><td>97.84000</td><td>10</td><td>540.000</td><td>190000.0</td><td>13.38473</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>3.900000</td><td>1</td><td>1</td><td> 97</td><td>0</td><td>1</td><td>0</td><td>97.83733</td></tr>\n",
       "\t<tr><th scope=row>33</th><td>2021</td><td>2</td><td>72.61000</td><td> 2</td><td>240.000</td><td> 80000.0</td><td>12.70685</td><td>3.800000</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>1</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.88152</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>2111</td><td>2</td><td>65.26000</td><td> 4</td><td>300.000</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>3.700000</td><td>4.300000</td><td>3.700000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.06327</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>2116</td><td>2</td><td>54.60000</td><td>10</td><td>294.000</td><td>200000.0</td><td>12.61154</td><td>3.100000</td><td>3.000000</td><td>3.000000</td><td>3.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>66.33838</td></tr>\n",
       "\t<tr><th scope=row>41</th><td>2127</td><td>2</td><td>80.37000</td><td> 5</td><td>420.000</td><td>350000.0</td><td>12.79386</td><td>3.900000</td><td>4.300000</td><td>4.300000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.52523</td></tr>\n",
       "\t<tr><th scope=row>42</th><td>2128</td><td>2</td><td>44.34375</td><td> 3</td><td>196.875</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>67.18494</td></tr>\n",
       "\t<tr><th scope=row>48</th><td>2134</td><td>2</td><td>72.88000</td><td> 9</td><td>360.000</td><td>240000.0</td><td>12.67608</td><td>3.300000</td><td>3.400000</td><td>3.500000</td><td>3.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>69.44201</td></tr>\n",
       "\t<tr><th scope=row>50</th><td>2136</td><td>2</td><td>44.34375</td><td> 9</td><td>240.000</td><td>480000.0</td><td>13.30469</td><td>4.300000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>89.85680</td></tr>\n",
       "\t<tr><th scope=row>52</th><td>2138</td><td>2</td><td>64.49000</td><td> 4</td><td>270.000</td><td>250000.0</td><td>12.70685</td><td>3.900000</td><td>4.500000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.48739</td></tr>\n",
       "\t<tr><th scope=row>56</th><td>2250</td><td>2</td><td>63.71000</td><td> 6</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>4.000000</td><td>4.000000</td><td>3.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.14808</td></tr>\n",
       "\t<tr><th scope=row>58</th><td>2254</td><td>2</td><td>59.41000</td><td> 5</td><td>196.875</td><td>160000.0</td><td>12.79562</td><td>2.800000</td><td>3.000000</td><td>3.000000</td><td>2.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>56.74210</td></tr>\n",
       "\t<tr><th scope=row>59</th><td>2255</td><td>2</td><td>71.74876</td><td> 3</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>59.76323</td></tr>\n",
       "\t<tr><th scope=row>65</th><td>2641</td><td>2</td><td>71.74876</td><td> 4</td><td>382.000</td><td>322661.9</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>61.80546</td></tr>\n",
       "\t<tr><th scope=row>67</th><td>3014</td><td>3</td><td>98.48000</td><td> 6</td><td>300.000</td><td>340000.0</td><td>13.21768</td><td>4.100000</td><td>3.900000</td><td>4.200000</td><td>4.300000</td><td>1</td><td>1</td><td>150</td><td>0</td><td>1</td><td>0</td><td>99.68131</td></tr>\n",
       "\t<tr><th scope=row>69</th><td>3035</td><td>3</td><td>89.48000</td><td> 7</td><td>196.875</td><td>420000.0</td><td>12.97155</td><td>3.600000</td><td>3.100000</td><td>3.800000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.01919</td></tr>\n",
       "\t<tr><th scope=row>73</th><td>3139</td><td>3</td><td>96.84000</td><td>10</td><td>630.000</td><td>550000.0</td><td>12.76569</td><td>4.300000</td><td>4.700000</td><td>4.300000</td><td>4.300000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>0</td><td>0</td><td>88.69525</td></tr>\n",
       "\t<tr><th scope=row>75</th><td>3147</td><td>3</td><td>83.40000</td><td> 6</td><td>300.000</td><td>264000.0</td><td>12.30139</td><td>2.200000</td><td>2.400000</td><td>2.200000</td><td>2.600000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>53.97024</td></tr>\n",
       "\t<tr><th scope=row>76</th><td>3148</td><td>3</td><td>92.28000</td><td>10</td><td>630.000</td><td>460000.0</td><td>13.30469</td><td>3.800000</td><td>3.700000</td><td>3.700000</td><td>3.900000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>77.37348</td></tr>\n",
       "\t<tr><th scope=row>82</th><td>3182</td><td>3</td><td>98.34000</td><td> 5</td><td>300.000</td><td>600000.0</td><td>14.16617</td><td>3.800000</td><td>3.300000</td><td>3.600000</td><td>4.400000</td><td>0</td><td>0</td><td>250</td><td>0</td><td>0</td><td>0</td><td>82.17729</td></tr>\n",
       "\t<tr><th scope=row>84</th><td>3184</td><td>3</td><td>96.77000</td><td>10</td><td>480.000</td><td>570000.0</td><td>13.12237</td><td>4.000000</td><td>3.900000</td><td>3.900000</td><td>4.100000</td><td>0</td><td>0</td><td>200</td><td>0</td><td>1</td><td>0</td><td>79.32101</td></tr>\n",
       "\t<tr><th scope=row>⋮</th><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><th scope=row>303</th><td>6283</td><td>6</td><td>87.28000</td><td>13.0</td><td>196.875</td><td> 370000</td><td>12.61154</td><td>4.000000</td><td>4.200000</td><td>4.200000</td><td>4.000000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>92.78713</td></tr>\n",
       "\t<tr><th scope=row>305</th><td>6285</td><td>6</td><td>92.61000</td><td> 6.0</td><td>240.000</td><td> 430000</td><td>12.91411</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>4.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.90717</td></tr>\n",
       "\t<tr><th scope=row>307</th><td>6289</td><td>6</td><td>97.98000</td><td> 7.0</td><td>300.000</td><td> 570000</td><td>13.32122</td><td>3.900000</td><td>3.700000</td><td>4.300000</td><td>4.000000</td><td>0</td><td>1</td><td>155</td><td>0</td><td>1</td><td>0</td><td>92.27407</td></tr>\n",
       "\t<tr><th scope=row>311</th><td>6303</td><td>6</td><td>75.18000</td><td> 5.0</td><td>240.000</td><td> 240000</td><td>12.98540</td><td>4.000000</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.50074</td></tr>\n",
       "\t<tr><th scope=row>313</th><td>6305</td><td>6</td><td>46.17000</td><td> 5.0</td><td>210.000</td><td> 192000</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>64.01767</td></tr>\n",
       "\t<tr><th scope=row>314</th><td>6307</td><td>6</td><td>83.32000</td><td>12.0</td><td>255.000</td><td> 370000</td><td>12.76569</td><td>4.100000</td><td>4.200000</td><td>4.200000</td><td>4.100000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.96029</td></tr>\n",
       "\t<tr><th scope=row>320</th><td>6317</td><td>6</td><td>79.53000</td><td>11.0</td><td>630.000</td><td> 310000</td><td>12.54255</td><td>3.500000</td><td>3.300000</td><td>3.700000</td><td>3.400000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>83.93804</td></tr>\n",
       "\t<tr><th scope=row>322</th><td>6319</td><td>6</td><td>63.05000</td><td> 6.0</td><td>360.000</td><td> 308000</td><td>12.76569</td><td>3.600000</td><td>3.900000</td><td>4.000000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.35820</td></tr>\n",
       "\t<tr><th scope=row>324</th><td>6321</td><td>6</td><td>45.67000</td><td> 6.0</td><td>300.000</td><td> 240000</td><td>12.79386</td><td>3.200000</td><td>3.700000</td><td>3.700000</td><td>2.700000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.14082</td></tr>\n",
       "\t<tr><th scope=row>328</th><td>6325</td><td>6</td><td>78.05000</td><td> 5.0</td><td>480.000</td><td> 230000</td><td>13.99783</td><td>3.600000</td><td>3.300000</td><td>4.200000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>79.16464</td></tr>\n",
       "\t<tr><th scope=row>330</th><td>6419</td><td>6</td><td>78.35000</td><td> 6.0</td><td>360.000</td><td> 330000</td><td>12.50618</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.71905</td></tr>\n",
       "\t<tr><th scope=row>331</th><td>6444</td><td>6</td><td>44.34375</td><td> 5.0</td><td>196.875</td><td> 141000</td><td>12.79562</td><td>3.200000</td><td>3.500000</td><td>4.000000</td><td>2.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.30986</td></tr>\n",
       "\t<tr><th scope=row>337</th><td>6620</td><td>6</td><td>73.99000</td><td>13.5</td><td>196.875</td><td>1080000</td><td>13.35348</td><td>3.600000</td><td>4.200000</td><td>3.400000</td><td>3.700000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>85.04649</td></tr>\n",
       "\t<tr><th scope=row>339</th><td>6622</td><td>6</td><td>85.85000</td><td> 6.0</td><td>360.000</td><td> 280000</td><td>12.76569</td><td>3.500000</td><td>3.500000</td><td>3.900000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>73.16798</td></tr>\n",
       "\t<tr><th scope=row>341</th><td>6628</td><td>6</td><td>56.76500</td><td> 5.0</td><td>196.875</td><td> 400000</td><td>12.56025</td><td>3.400000</td><td>3.000000</td><td>4.000000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>75.75998</td></tr>\n",
       "\t<tr><th scope=row>345</th><td>6635</td><td>6</td><td>67.11200</td><td> 9.0</td><td>420.000</td><td> 300000</td><td>12.42922</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.07599</td></tr>\n",
       "\t<tr><th scope=row>347</th><td>6643</td><td>6</td><td>81.98400</td><td> 5.0</td><td>360.000</td><td> 310000</td><td>12.20608</td><td>4.200000</td><td>4.500000</td><td>4.300000</td><td>4.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>73.32382</td></tr>\n",
       "\t<tr><th scope=row>348</th><td>6644</td><td>6</td><td>56.76000</td><td> 7.0</td><td>300.000</td><td> 320000</td><td>12.79386</td><td>3.000000</td><td>3.800000</td><td>3.100000</td><td>2.900000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.82040</td></tr>\n",
       "\t<tr><th scope=row>354</th><td>6757</td><td>6</td><td>60.73000</td><td> 7.0</td><td>360.000</td><td> 310000</td><td>12.76569</td><td>3.800000</td><td>4.000000</td><td>3.700000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>74.10919</td></tr>\n",
       "\t<tr><th scope=row>356</th><td>6759</td><td>6</td><td>68.70000</td><td> 5.0</td><td>270.000</td><td> 270000</td><td>12.61154</td><td>4.600000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>80.30998</td></tr>\n",
       "\t<tr><th scope=row>358</th><td>6766</td><td>6</td><td>63.08000</td><td> 5.0</td><td>300.000</td><td> 260000</td><td>12.76569</td><td>4.700000</td><td>5.000000</td><td>5.000000</td><td>4.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>76.38859</td></tr>\n",
       "\t<tr><th scope=row>362</th><td>6770</td><td>6</td><td>77.03000</td><td> 5.0</td><td>300.000</td><td> 410000</td><td>12.38840</td><td>3.800000</td><td>4.100000</td><td>3.600000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.97872</td></tr>\n",
       "\t<tr><th scope=row>364</th><td>6772</td><td>6</td><td>87.28000</td><td> 6.0</td><td>510.000</td><td> 400000</td><td>12.57764</td><td>4.000000</td><td>4.000000</td><td>3.900000</td><td>4.400000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.21836</td></tr>\n",
       "\t<tr><th scope=row>365</th><td>6780</td><td>6</td><td>71.76000</td><td>11.0</td><td>420.000</td><td> 250000</td><td>12.38840</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.23241</td></tr>\n",
       "\t<tr><th scope=row>371</th><td>6795</td><td>6</td><td>52.82000</td><td> 4.0</td><td>210.000</td><td> 240000</td><td>12.79562</td><td>3.000000</td><td>3.000000</td><td>3.300000</td><td>3.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.36720</td></tr>\n",
       "\t<tr><th scope=row>373</th><td>6797</td><td>6</td><td>74.20000</td><td> 5.0</td><td>240.000</td><td> 320000</td><td>12.79562</td><td>4.100000</td><td>4.400000</td><td>4.400000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.90800</td></tr>\n",
       "\t<tr><th scope=row>375</th><td>6803</td><td>6</td><td>74.51000</td><td> 6.0</td><td>360.000</td><td> 240000</td><td>12.89922</td><td>4.100000</td><td>4.100000</td><td>4.200000</td><td>4.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.98160</td></tr>\n",
       "\t<tr><th scope=row>379</th><td>6811</td><td>6</td><td>44.34375</td><td>13.5</td><td>630.000</td><td> 620000</td><td>12.84793</td><td>4.100000</td><td>4.700000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>78.02752</td></tr>\n",
       "\t<tr><th scope=row>381</th><td>6822</td><td>6</td><td>96.46000</td><td> 9.0</td><td>480.000</td><td> 400000</td><td>12.50618</td><td>4.000000</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.30797</td></tr>\n",
       "\t<tr><th scope=row>382</th><td>6834</td><td>6</td><td>80.45000</td><td> 6.0</td><td>360.000</td><td> 300000</td><td>12.61154</td><td>3.000000</td><td>3.400000</td><td>3.100000</td><td>3.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.83997</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 136 × 18\n",
       "\\begin{tabular}{r|llllllllllllllllll}\n",
       "  & college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & crowd & government & autonomous & rank & new\\_ban & hostel\\_BOTH & hostel\\_ONE & linear\\\\\n",
       "  & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <int> & <int> & <int> & <int> & <int> & <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1002 & 1 & 96.44000 &  8 & 300.000 & 240000.0 & 12.87391 & 3.400000 & 3.200000 & 3.500000 & 3.700000 & 1 & 1 & 301 & 0 & 1 & 0 & 95.25097\\\\\n",
       "\t5 & 1105 & 1 & 88.05000 &  8 & 480.000 & 440000.0 & 12.70685 & 3.900000 & 4.000000 & 3.900000 & 4.200000 & 0 & 1 & 250 & 0 & 0 & 0 & 83.98529\\\\\n",
       "\t7 & 1108 & 1 & 44.34375 &  5 & 300.000 & 310000.0 & 12.61154 & 3.900000 & 4.000000 & 4.300000 & 3.500000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.03529\\\\\n",
       "\t8 & 1114 & 1 & 81.55000 &  6 & 300.000 & 320000.0 & 12.82126 & 4.000000 & 4.400000 & 3.900000 & 4.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.98257\\\\\n",
       "\t14 & 1122 & 1 & 44.34375 &  5 & 300.000 & 200000.0 & 12.61154 & 2.200000 & 3.000000 & 2.000000 & 3.500000 & 0 & 0 & 301 & 1 & 0 & 0 & 57.34506\\\\\n",
       "\t16 & 1124 & 1 & 49.08000 &  5 & 300.000 & 490000.0 & 12.34584 & 3.600000 & 4.300000 & 3.600000 & 3.500000 & 0 & 0 & 301 & 1 & 1 & 0 & 59.01199\\\\\n",
       "\t18 & 1126 & 1 & 67.71000 &  5 & 300.000 & 170000.0 & 13.10216 & 5.000000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.53221\\\\\n",
       "\t22 & 1130 & 1 & 45.98000 &  6 & 480.000 & 180000.0 & 12.10072 & 2.200000 & 4.000000 & 2.000000 & 1.000000 & 0 & 0 & 301 & 1 & 1 & 0 & 36.59204\\\\\n",
       "\t24 & 1182 & 1 & 59.68000 &  4 & 630.000 & 200000.0 & 13.01701 & 4.200000 & 4.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 78.07224\\\\\n",
       "\t25 & 1251 & 1 & 44.34375 &  6 & 300.000 & 284000.0 & 12.54255 & 3.400000 & 3.200000 & 3.400000 & 3.600000 & 0 & 0 & 301 & 1 & 1 & 0 & 60.02308\\\\\n",
       "\t31 & 2008 & 2 & 97.84000 & 10 & 540.000 & 190000.0 & 13.38473 & 3.900000 & 3.800000 & 3.900000 & 3.900000 & 1 & 1 &  97 & 0 & 1 & 0 & 97.83733\\\\\n",
       "\t33 & 2021 & 2 & 72.61000 &  2 & 240.000 &  80000.0 & 12.70685 & 3.800000 & 3.900000 & 4.000000 & 3.900000 & 1 & 0 & 301 & 0 & 1 & 0 & 77.88152\\\\\n",
       "\t35 & 2111 & 2 & 65.26000 &  4 & 300.000 & 170000.0 & 12.61154 & 3.800000 & 3.700000 & 4.300000 & 3.700000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.06327\\\\\n",
       "\t39 & 2116 & 2 & 54.60000 & 10 & 294.000 & 200000.0 & 12.61154 & 3.100000 & 3.000000 & 3.000000 & 3.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 66.33838\\\\\n",
       "\t41 & 2127 & 2 & 80.37000 &  5 & 420.000 & 350000.0 & 12.79386 & 3.900000 & 4.300000 & 4.300000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.52523\\\\\n",
       "\t42 & 2128 & 2 & 44.34375 &  3 & 196.875 & 170000.0 & 12.61154 & 3.800000 & 4.000000 & 4.000000 & 5.000000 & 0 & 0 & 301 & 1 & 1 & 0 & 67.18494\\\\\n",
       "\t48 & 2134 & 2 & 72.88000 &  9 & 360.000 & 240000.0 & 12.67608 & 3.300000 & 3.400000 & 3.500000 & 3.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 69.44201\\\\\n",
       "\t50 & 2136 & 2 & 44.34375 &  9 & 240.000 & 480000.0 & 13.30469 & 4.300000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 89.85680\\\\\n",
       "\t52 & 2138 & 2 & 64.49000 &  4 & 270.000 & 250000.0 & 12.70685 & 3.900000 & 4.500000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 81.48739\\\\\n",
       "\t56 & 2250 & 2 & 63.71000 &  6 & 196.875 & 220000.0 & 12.79562 & 4.000000 & 4.000000 & 3.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 71.14808\\\\\n",
       "\t58 & 2254 & 2 & 59.41000 &  5 & 196.875 & 160000.0 & 12.79562 & 2.800000 & 3.000000 & 3.000000 & 2.000000 & 0 & 0 & 301 & 0 & 0 & 0 & 56.74210\\\\\n",
       "\t59 & 2255 & 2 & 71.74876 &  3 & 196.875 & 220000.0 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 59.76323\\\\\n",
       "\t65 & 2641 & 2 & 71.74876 &  4 & 382.000 & 322661.9 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 61.80546\\\\\n",
       "\t67 & 3014 & 3 & 98.48000 &  6 & 300.000 & 340000.0 & 13.21768 & 4.100000 & 3.900000 & 4.200000 & 4.300000 & 1 & 1 & 150 & 0 & 1 & 0 & 99.68131\\\\\n",
       "\t69 & 3035 & 3 & 89.48000 &  7 & 196.875 & 420000.0 & 12.97155 & 3.600000 & 3.100000 & 3.800000 & 3.600000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.01919\\\\\n",
       "\t73 & 3139 & 3 & 96.84000 & 10 & 630.000 & 550000.0 & 12.76569 & 4.300000 & 4.700000 & 4.300000 & 4.300000 & 0 & 1 & 301 & 0 & 0 & 0 & 88.69525\\\\\n",
       "\t75 & 3147 & 3 & 83.40000 &  6 & 300.000 & 264000.0 & 12.30139 & 2.200000 & 2.400000 & 2.200000 & 2.600000 & 0 & 0 & 301 & 1 & 1 & 0 & 53.97024\\\\\n",
       "\t76 & 3148 & 3 & 92.28000 & 10 & 630.000 & 460000.0 & 13.30469 & 3.800000 & 3.700000 & 3.700000 & 3.900000 & 0 & 0 & 301 & 0 & 0 & 0 & 77.37348\\\\\n",
       "\t82 & 3182 & 3 & 98.34000 &  5 & 300.000 & 600000.0 & 14.16617 & 3.800000 & 3.300000 & 3.600000 & 4.400000 & 0 & 0 & 250 & 0 & 0 & 0 & 82.17729\\\\\n",
       "\t84 & 3184 & 3 & 96.77000 & 10 & 480.000 & 570000.0 & 13.12237 & 4.000000 & 3.900000 & 3.900000 & 4.100000 & 0 & 0 & 200 & 0 & 1 & 0 & 79.32101\\\\\n",
       "\t⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t303 & 6283 & 6 & 87.28000 & 13.0 & 196.875 &  370000 & 12.61154 & 4.000000 & 4.200000 & 4.200000 & 4.000000 & 0 & 1 & 301 & 0 & 1 & 0 & 92.78713\\\\\n",
       "\t305 & 6285 & 6 & 92.61000 &  6.0 & 240.000 &  430000 & 12.91411 & 3.900000 & 3.800000 & 3.900000 & 4.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 77.90717\\\\\n",
       "\t307 & 6289 & 6 & 97.98000 &  7.0 & 300.000 &  570000 & 13.32122 & 3.900000 & 3.700000 & 4.300000 & 4.000000 & 0 & 1 & 155 & 0 & 1 & 0 & 92.27407\\\\\n",
       "\t311 & 6303 & 6 & 75.18000 &  5.0 & 240.000 &  240000 & 12.98540 & 4.000000 & 4.200000 & 4.100000 & 4.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.50074\\\\\n",
       "\t313 & 6305 & 6 & 46.17000 &  5.0 & 210.000 &  192000 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 64.01767\\\\\n",
       "\t314 & 6307 & 6 & 83.32000 & 12.0 & 255.000 &  370000 & 12.76569 & 4.100000 & 4.200000 & 4.200000 & 4.100000 & 0 & 0 & 301 & 0 & 1 & 0 & 81.96029\\\\\n",
       "\t320 & 6317 & 6 & 79.53000 & 11.0 & 630.000 &  310000 & 12.54255 & 3.500000 & 3.300000 & 3.700000 & 3.400000 & 0 & 1 & 301 & 0 & 1 & 0 & 83.93804\\\\\n",
       "\t322 & 6319 & 6 & 63.05000 &  6.0 & 360.000 &  308000 & 12.76569 & 3.600000 & 3.900000 & 4.000000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.35820\\\\\n",
       "\t324 & 6321 & 6 & 45.67000 &  6.0 & 300.000 &  240000 & 12.79386 & 3.200000 & 3.700000 & 3.700000 & 2.700000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.14082\\\\\n",
       "\t328 & 6325 & 6 & 78.05000 &  5.0 & 480.000 &  230000 & 13.99783 & 3.600000 & 3.300000 & 4.200000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 79.16464\\\\\n",
       "\t330 & 6419 & 6 & 78.35000 &  6.0 & 360.000 &  330000 & 12.50618 & 4.200000 & 4.100000 & 4.200000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 71.71905\\\\\n",
       "\t331 & 6444 & 6 & 44.34375 &  5.0 & 196.875 &  141000 & 12.79562 & 3.200000 & 3.500000 & 4.000000 & 2.500000 & 0 & 0 & 301 & 1 & 1 & 0 & 59.30986\\\\\n",
       "\t337 & 6620 & 6 & 73.99000 & 13.5 & 196.875 & 1080000 & 13.35348 & 3.600000 & 4.200000 & 3.400000 & 3.700000 & 0 & 0 & 301 & 1 & 1 & 0 & 85.04649\\\\\n",
       "\t339 & 6622 & 6 & 85.85000 &  6.0 & 360.000 &  280000 & 12.76569 & 3.500000 & 3.500000 & 3.900000 & 3.600000 & 0 & 0 & 301 & 0 & 0 & 0 & 73.16798\\\\\n",
       "\t341 & 6628 & 6 & 56.76500 &  5.0 & 196.875 &  400000 & 12.56025 & 3.400000 & 3.000000 & 4.000000 & 3.500000 & 0 & 0 & 301 & 0 & 0 & 1 & 75.75998\\\\\n",
       "\t345 & 6635 & 6 & 67.11200 &  9.0 & 420.000 &  300000 & 12.42922 & 3.800000 & 4.000000 & 4.000000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 76.07599\\\\\n",
       "\t347 & 6643 & 6 & 81.98400 &  5.0 & 360.000 &  310000 & 12.20608 & 4.200000 & 4.500000 & 4.300000 & 4.500000 & 0 & 0 & 301 & 0 & 1 & 0 & 73.32382\\\\\n",
       "\t348 & 6644 & 6 & 56.76000 &  7.0 & 300.000 &  320000 & 12.79386 & 3.000000 & 3.800000 & 3.100000 & 2.900000 & 0 & 0 & 301 & 0 & 1 & 0 & 68.82040\\\\\n",
       "\t354 & 6757 & 6 & 60.73000 &  7.0 & 360.000 &  310000 & 12.76569 & 3.800000 & 4.000000 & 3.700000 & 4.000000 & 0 & 0 & 301 & 0 & 0 & 0 & 74.10919\\\\\n",
       "\t356 & 6759 & 6 & 68.70000 &  5.0 & 270.000 &  270000 & 12.61154 & 4.600000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 80.30998\\\\\n",
       "\t358 & 6766 & 6 & 63.08000 &  5.0 & 300.000 &  260000 & 12.76569 & 4.700000 & 5.000000 & 5.000000 & 4.500000 & 0 & 0 & 301 & 0 & 0 & 0 & 76.38859\\\\\n",
       "\t362 & 6770 & 6 & 77.03000 &  5.0 & 300.000 &  410000 & 12.38840 & 3.800000 & 4.100000 & 3.600000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.97872\\\\\n",
       "\t364 & 6772 & 6 & 87.28000 &  6.0 & 510.000 &  400000 & 12.57764 & 4.000000 & 4.000000 & 3.900000 & 4.400000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.21836\\\\\n",
       "\t365 & 6780 & 6 & 71.76000 & 11.0 & 420.000 &  250000 & 12.38840 & 4.000000 & 4.000000 & 4.000000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 76.23241\\\\\n",
       "\t371 & 6795 & 6 & 52.82000 &  4.0 & 210.000 &  240000 & 12.79562 & 3.000000 & 3.000000 & 3.300000 & 3.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.36720\\\\\n",
       "\t373 & 6797 & 6 & 74.20000 &  5.0 & 240.000 &  320000 & 12.79562 & 4.100000 & 4.400000 & 4.400000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.90800\\\\\n",
       "\t375 & 6803 & 6 & 74.51000 &  6.0 & 360.000 &  240000 & 12.89922 & 4.100000 & 4.100000 & 4.200000 & 4.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.98160\\\\\n",
       "\t379 & 6811 & 6 & 44.34375 & 13.5 & 630.000 &  620000 & 12.84793 & 4.100000 & 4.700000 & 3.900000 & 4.200000 & 0 & 0 & 301 & 1 & 1 & 0 & 78.02752\\\\\n",
       "\t381 & 6822 & 6 & 96.46000 &  9.0 & 480.000 &  400000 & 12.50618 & 4.000000 & 3.600000 & 4.300000 & 3.600000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.30797\\\\\n",
       "\t382 & 6834 & 6 & 80.45000 &  6.0 & 360.000 &  300000 & 12.61154 & 3.000000 & 3.400000 & 3.100000 & 3.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 68.83997\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 136 × 18\n",
       "\n",
       "| <!--/--> | college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;dbl&gt; | intake &lt;dbl&gt; | fees &lt;dbl&gt; | salary &lt;dbl&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | crowd &lt;dbl&gt; | government &lt;int&gt; | autonomous &lt;int&gt; | rank &lt;int&gt; | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_ONE &lt;int&gt; | linear &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1002 | 1 | 96.44000 |  8 | 300.000 | 240000.0 | 12.87391 | 3.400000 | 3.200000 | 3.500000 | 3.700000 | 1 | 1 | 301 | 0 | 1 | 0 | 95.25097 |\n",
       "| 5 | 1105 | 1 | 88.05000 |  8 | 480.000 | 440000.0 | 12.70685 | 3.900000 | 4.000000 | 3.900000 | 4.200000 | 0 | 1 | 250 | 0 | 0 | 0 | 83.98529 |\n",
       "| 7 | 1108 | 1 | 44.34375 |  5 | 300.000 | 310000.0 | 12.61154 | 3.900000 | 4.000000 | 4.300000 | 3.500000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.03529 |\n",
       "| 8 | 1114 | 1 | 81.55000 |  6 | 300.000 | 320000.0 | 12.82126 | 4.000000 | 4.400000 | 3.900000 | 4.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.98257 |\n",
       "| 14 | 1122 | 1 | 44.34375 |  5 | 300.000 | 200000.0 | 12.61154 | 2.200000 | 3.000000 | 2.000000 | 3.500000 | 0 | 0 | 301 | 1 | 0 | 0 | 57.34506 |\n",
       "| 16 | 1124 | 1 | 49.08000 |  5 | 300.000 | 490000.0 | 12.34584 | 3.600000 | 4.300000 | 3.600000 | 3.500000 | 0 | 0 | 301 | 1 | 1 | 0 | 59.01199 |\n",
       "| 18 | 1126 | 1 | 67.71000 |  5 | 300.000 | 170000.0 | 13.10216 | 5.000000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.53221 |\n",
       "| 22 | 1130 | 1 | 45.98000 |  6 | 480.000 | 180000.0 | 12.10072 | 2.200000 | 4.000000 | 2.000000 | 1.000000 | 0 | 0 | 301 | 1 | 1 | 0 | 36.59204 |\n",
       "| 24 | 1182 | 1 | 59.68000 |  4 | 630.000 | 200000.0 | 13.01701 | 4.200000 | 4.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 78.07224 |\n",
       "| 25 | 1251 | 1 | 44.34375 |  6 | 300.000 | 284000.0 | 12.54255 | 3.400000 | 3.200000 | 3.400000 | 3.600000 | 0 | 0 | 301 | 1 | 1 | 0 | 60.02308 |\n",
       "| 31 | 2008 | 2 | 97.84000 | 10 | 540.000 | 190000.0 | 13.38473 | 3.900000 | 3.800000 | 3.900000 | 3.900000 | 1 | 1 |  97 | 0 | 1 | 0 | 97.83733 |\n",
       "| 33 | 2021 | 2 | 72.61000 |  2 | 240.000 |  80000.0 | 12.70685 | 3.800000 | 3.900000 | 4.000000 | 3.900000 | 1 | 0 | 301 | 0 | 1 | 0 | 77.88152 |\n",
       "| 35 | 2111 | 2 | 65.26000 |  4 | 300.000 | 170000.0 | 12.61154 | 3.800000 | 3.700000 | 4.300000 | 3.700000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.06327 |\n",
       "| 39 | 2116 | 2 | 54.60000 | 10 | 294.000 | 200000.0 | 12.61154 | 3.100000 | 3.000000 | 3.000000 | 3.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 66.33838 |\n",
       "| 41 | 2127 | 2 | 80.37000 |  5 | 420.000 | 350000.0 | 12.79386 | 3.900000 | 4.300000 | 4.300000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.52523 |\n",
       "| 42 | 2128 | 2 | 44.34375 |  3 | 196.875 | 170000.0 | 12.61154 | 3.800000 | 4.000000 | 4.000000 | 5.000000 | 0 | 0 | 301 | 1 | 1 | 0 | 67.18494 |\n",
       "| 48 | 2134 | 2 | 72.88000 |  9 | 360.000 | 240000.0 | 12.67608 | 3.300000 | 3.400000 | 3.500000 | 3.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 69.44201 |\n",
       "| 50 | 2136 | 2 | 44.34375 |  9 | 240.000 | 480000.0 | 13.30469 | 4.300000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 89.85680 |\n",
       "| 52 | 2138 | 2 | 64.49000 |  4 | 270.000 | 250000.0 | 12.70685 | 3.900000 | 4.500000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 81.48739 |\n",
       "| 56 | 2250 | 2 | 63.71000 |  6 | 196.875 | 220000.0 | 12.79562 | 4.000000 | 4.000000 | 3.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 71.14808 |\n",
       "| 58 | 2254 | 2 | 59.41000 |  5 | 196.875 | 160000.0 | 12.79562 | 2.800000 | 3.000000 | 3.000000 | 2.000000 | 0 | 0 | 301 | 0 | 0 | 0 | 56.74210 |\n",
       "| 59 | 2255 | 2 | 71.74876 |  3 | 196.875 | 220000.0 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 59.76323 |\n",
       "| 65 | 2641 | 2 | 71.74876 |  4 | 382.000 | 322661.9 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 61.80546 |\n",
       "| 67 | 3014 | 3 | 98.48000 |  6 | 300.000 | 340000.0 | 13.21768 | 4.100000 | 3.900000 | 4.200000 | 4.300000 | 1 | 1 | 150 | 0 | 1 | 0 | 99.68131 |\n",
       "| 69 | 3035 | 3 | 89.48000 |  7 | 196.875 | 420000.0 | 12.97155 | 3.600000 | 3.100000 | 3.800000 | 3.600000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.01919 |\n",
       "| 73 | 3139 | 3 | 96.84000 | 10 | 630.000 | 550000.0 | 12.76569 | 4.300000 | 4.700000 | 4.300000 | 4.300000 | 0 | 1 | 301 | 0 | 0 | 0 | 88.69525 |\n",
       "| 75 | 3147 | 3 | 83.40000 |  6 | 300.000 | 264000.0 | 12.30139 | 2.200000 | 2.400000 | 2.200000 | 2.600000 | 0 | 0 | 301 | 1 | 1 | 0 | 53.97024 |\n",
       "| 76 | 3148 | 3 | 92.28000 | 10 | 630.000 | 460000.0 | 13.30469 | 3.800000 | 3.700000 | 3.700000 | 3.900000 | 0 | 0 | 301 | 0 | 0 | 0 | 77.37348 |\n",
       "| 82 | 3182 | 3 | 98.34000 |  5 | 300.000 | 600000.0 | 14.16617 | 3.800000 | 3.300000 | 3.600000 | 4.400000 | 0 | 0 | 250 | 0 | 0 | 0 | 82.17729 |\n",
       "| 84 | 3184 | 3 | 96.77000 | 10 | 480.000 | 570000.0 | 13.12237 | 4.000000 | 3.900000 | 3.900000 | 4.100000 | 0 | 0 | 200 | 0 | 1 | 0 | 79.32101 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 303 | 6283 | 6 | 87.28000 | 13.0 | 196.875 |  370000 | 12.61154 | 4.000000 | 4.200000 | 4.200000 | 4.000000 | 0 | 1 | 301 | 0 | 1 | 0 | 92.78713 |\n",
       "| 305 | 6285 | 6 | 92.61000 |  6.0 | 240.000 |  430000 | 12.91411 | 3.900000 | 3.800000 | 3.900000 | 4.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 77.90717 |\n",
       "| 307 | 6289 | 6 | 97.98000 |  7.0 | 300.000 |  570000 | 13.32122 | 3.900000 | 3.700000 | 4.300000 | 4.000000 | 0 | 1 | 155 | 0 | 1 | 0 | 92.27407 |\n",
       "| 311 | 6303 | 6 | 75.18000 |  5.0 | 240.000 |  240000 | 12.98540 | 4.000000 | 4.200000 | 4.100000 | 4.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.50074 |\n",
       "| 313 | 6305 | 6 | 46.17000 |  5.0 | 210.000 |  192000 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 64.01767 |\n",
       "| 314 | 6307 | 6 | 83.32000 | 12.0 | 255.000 |  370000 | 12.76569 | 4.100000 | 4.200000 | 4.200000 | 4.100000 | 0 | 0 | 301 | 0 | 1 | 0 | 81.96029 |\n",
       "| 320 | 6317 | 6 | 79.53000 | 11.0 | 630.000 |  310000 | 12.54255 | 3.500000 | 3.300000 | 3.700000 | 3.400000 | 0 | 1 | 301 | 0 | 1 | 0 | 83.93804 |\n",
       "| 322 | 6319 | 6 | 63.05000 |  6.0 | 360.000 |  308000 | 12.76569 | 3.600000 | 3.900000 | 4.000000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.35820 |\n",
       "| 324 | 6321 | 6 | 45.67000 |  6.0 | 300.000 |  240000 | 12.79386 | 3.200000 | 3.700000 | 3.700000 | 2.700000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.14082 |\n",
       "| 328 | 6325 | 6 | 78.05000 |  5.0 | 480.000 |  230000 | 13.99783 | 3.600000 | 3.300000 | 4.200000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 79.16464 |\n",
       "| 330 | 6419 | 6 | 78.35000 |  6.0 | 360.000 |  330000 | 12.50618 | 4.200000 | 4.100000 | 4.200000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 71.71905 |\n",
       "| 331 | 6444 | 6 | 44.34375 |  5.0 | 196.875 |  141000 | 12.79562 | 3.200000 | 3.500000 | 4.000000 | 2.500000 | 0 | 0 | 301 | 1 | 1 | 0 | 59.30986 |\n",
       "| 337 | 6620 | 6 | 73.99000 | 13.5 | 196.875 | 1080000 | 13.35348 | 3.600000 | 4.200000 | 3.400000 | 3.700000 | 0 | 0 | 301 | 1 | 1 | 0 | 85.04649 |\n",
       "| 339 | 6622 | 6 | 85.85000 |  6.0 | 360.000 |  280000 | 12.76569 | 3.500000 | 3.500000 | 3.900000 | 3.600000 | 0 | 0 | 301 | 0 | 0 | 0 | 73.16798 |\n",
       "| 341 | 6628 | 6 | 56.76500 |  5.0 | 196.875 |  400000 | 12.56025 | 3.400000 | 3.000000 | 4.000000 | 3.500000 | 0 | 0 | 301 | 0 | 0 | 1 | 75.75998 |\n",
       "| 345 | 6635 | 6 | 67.11200 |  9.0 | 420.000 |  300000 | 12.42922 | 3.800000 | 4.000000 | 4.000000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 76.07599 |\n",
       "| 347 | 6643 | 6 | 81.98400 |  5.0 | 360.000 |  310000 | 12.20608 | 4.200000 | 4.500000 | 4.300000 | 4.500000 | 0 | 0 | 301 | 0 | 1 | 0 | 73.32382 |\n",
       "| 348 | 6644 | 6 | 56.76000 |  7.0 | 300.000 |  320000 | 12.79386 | 3.000000 | 3.800000 | 3.100000 | 2.900000 | 0 | 0 | 301 | 0 | 1 | 0 | 68.82040 |\n",
       "| 354 | 6757 | 6 | 60.73000 |  7.0 | 360.000 |  310000 | 12.76569 | 3.800000 | 4.000000 | 3.700000 | 4.000000 | 0 | 0 | 301 | 0 | 0 | 0 | 74.10919 |\n",
       "| 356 | 6759 | 6 | 68.70000 |  5.0 | 270.000 |  270000 | 12.61154 | 4.600000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 80.30998 |\n",
       "| 358 | 6766 | 6 | 63.08000 |  5.0 | 300.000 |  260000 | 12.76569 | 4.700000 | 5.000000 | 5.000000 | 4.500000 | 0 | 0 | 301 | 0 | 0 | 0 | 76.38859 |\n",
       "| 362 | 6770 | 6 | 77.03000 |  5.0 | 300.000 |  410000 | 12.38840 | 3.800000 | 4.100000 | 3.600000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.97872 |\n",
       "| 364 | 6772 | 6 | 87.28000 |  6.0 | 510.000 |  400000 | 12.57764 | 4.000000 | 4.000000 | 3.900000 | 4.400000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.21836 |\n",
       "| 365 | 6780 | 6 | 71.76000 | 11.0 | 420.000 |  250000 | 12.38840 | 4.000000 | 4.000000 | 4.000000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 76.23241 |\n",
       "| 371 | 6795 | 6 | 52.82000 |  4.0 | 210.000 |  240000 | 12.79562 | 3.000000 | 3.000000 | 3.300000 | 3.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.36720 |\n",
       "| 373 | 6797 | 6 | 74.20000 |  5.0 | 240.000 |  320000 | 12.79562 | 4.100000 | 4.400000 | 4.400000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.90800 |\n",
       "| 375 | 6803 | 6 | 74.51000 |  6.0 | 360.000 |  240000 | 12.89922 | 4.100000 | 4.100000 | 4.200000 | 4.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.98160 |\n",
       "| 379 | 6811 | 6 | 44.34375 | 13.5 | 630.000 |  620000 | 12.84793 | 4.100000 | 4.700000 | 3.900000 | 4.200000 | 0 | 0 | 301 | 1 | 1 | 0 | 78.02752 |\n",
       "| 381 | 6822 | 6 | 96.46000 |  9.0 | 480.000 |  400000 | 12.50618 | 4.000000 | 3.600000 | 4.300000 | 3.600000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.30797 |\n",
       "| 382 | 6834 | 6 | 80.45000 |  6.0 | 360.000 |  300000 | 12.61154 | 3.000000 | 3.400000 | 3.100000 | 3.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 68.83997 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff   courses intake  fees     salary   rating  \n",
       "1   1002         1        96.44000  8      300.000 240000.0 12.87391 3.400000\n",
       "5   1105         1        88.05000  8      480.000 440000.0 12.70685 3.900000\n",
       "7   1108         1        44.34375  5      300.000 310000.0 12.61154 3.900000\n",
       "8   1114         1        81.55000  6      300.000 320000.0 12.82126 4.000000\n",
       "14  1122         1        44.34375  5      300.000 200000.0 12.61154 2.200000\n",
       "16  1124         1        49.08000  5      300.000 490000.0 12.34584 3.600000\n",
       "18  1126         1        67.71000  5      300.000 170000.0 13.10216 5.000000\n",
       "22  1130         1        45.98000  6      480.000 180000.0 12.10072 2.200000\n",
       "24  1182         1        59.68000  4      630.000 200000.0 13.01701 4.200000\n",
       "25  1251         1        44.34375  6      300.000 284000.0 12.54255 3.400000\n",
       "31  2008         2        97.84000 10      540.000 190000.0 13.38473 3.900000\n",
       "33  2021         2        72.61000  2      240.000  80000.0 12.70685 3.800000\n",
       "35  2111         2        65.26000  4      300.000 170000.0 12.61154 3.800000\n",
       "39  2116         2        54.60000 10      294.000 200000.0 12.61154 3.100000\n",
       "41  2127         2        80.37000  5      420.000 350000.0 12.79386 3.900000\n",
       "42  2128         2        44.34375  3      196.875 170000.0 12.61154 3.800000\n",
       "48  2134         2        72.88000  9      360.000 240000.0 12.67608 3.300000\n",
       "50  2136         2        44.34375  9      240.000 480000.0 13.30469 4.300000\n",
       "52  2138         2        64.49000  4      270.000 250000.0 12.70685 3.900000\n",
       "56  2250         2        63.71000  6      196.875 220000.0 12.79562 4.000000\n",
       "58  2254         2        59.41000  5      196.875 160000.0 12.79562 2.800000\n",
       "59  2255         2        71.74876  3      196.875 220000.0 12.79562 3.666295\n",
       "65  2641         2        71.74876  4      382.000 322661.9 12.79562 3.666295\n",
       "67  3014         3        98.48000  6      300.000 340000.0 13.21768 4.100000\n",
       "69  3035         3        89.48000  7      196.875 420000.0 12.97155 3.600000\n",
       "73  3139         3        96.84000 10      630.000 550000.0 12.76569 4.300000\n",
       "75  3147         3        83.40000  6      300.000 264000.0 12.30139 2.200000\n",
       "76  3148         3        92.28000 10      630.000 460000.0 13.30469 3.800000\n",
       "82  3182         3        98.34000  5      300.000 600000.0 14.16617 3.800000\n",
       "84  3184         3        96.77000 10      480.000 570000.0 13.12237 4.000000\n",
       "⋮   ⋮            ⋮        ⋮        ⋮       ⋮       ⋮        ⋮        ⋮       \n",
       "303 6283         6        87.28000 13.0    196.875  370000  12.61154 4.000000\n",
       "305 6285         6        92.61000  6.0    240.000  430000  12.91411 3.900000\n",
       "307 6289         6        97.98000  7.0    300.000  570000  13.32122 3.900000\n",
       "311 6303         6        75.18000  5.0    240.000  240000  12.98540 4.000000\n",
       "313 6305         6        46.17000  5.0    210.000  192000  12.79562 3.666295\n",
       "314 6307         6        83.32000 12.0    255.000  370000  12.76569 4.100000\n",
       "320 6317         6        79.53000 11.0    630.000  310000  12.54255 3.500000\n",
       "322 6319         6        63.05000  6.0    360.000  308000  12.76569 3.600000\n",
       "324 6321         6        45.67000  6.0    300.000  240000  12.79386 3.200000\n",
       "328 6325         6        78.05000  5.0    480.000  230000  13.99783 3.600000\n",
       "330 6419         6        78.35000  6.0    360.000  330000  12.50618 4.200000\n",
       "331 6444         6        44.34375  5.0    196.875  141000  12.79562 3.200000\n",
       "337 6620         6        73.99000 13.5    196.875 1080000  13.35348 3.600000\n",
       "339 6622         6        85.85000  6.0    360.000  280000  12.76569 3.500000\n",
       "341 6628         6        56.76500  5.0    196.875  400000  12.56025 3.400000\n",
       "345 6635         6        67.11200  9.0    420.000  300000  12.42922 3.800000\n",
       "347 6643         6        81.98400  5.0    360.000  310000  12.20608 4.200000\n",
       "348 6644         6        56.76000  7.0    300.000  320000  12.79386 3.000000\n",
       "354 6757         6        60.73000  7.0    360.000  310000  12.76569 3.800000\n",
       "356 6759         6        68.70000  5.0    270.000  270000  12.61154 4.600000\n",
       "358 6766         6        63.08000  5.0    300.000  260000  12.76569 4.700000\n",
       "362 6770         6        77.03000  5.0    300.000  410000  12.38840 3.800000\n",
       "364 6772         6        87.28000  6.0    510.000  400000  12.57764 4.000000\n",
       "365 6780         6        71.76000 11.0    420.000  250000  12.38840 4.000000\n",
       "371 6795         6        52.82000  4.0    210.000  240000  12.79562 3.000000\n",
       "373 6797         6        74.20000  5.0    240.000  320000  12.79562 4.100000\n",
       "375 6803         6        74.51000  6.0    360.000  240000  12.89922 4.100000\n",
       "379 6811         6        44.34375 13.5    630.000  620000  12.84793 4.100000\n",
       "381 6822         6        96.46000  9.0    480.000  400000  12.50618 4.000000\n",
       "382 6834         6        80.45000  6.0    360.000  300000  12.61154 3.000000\n",
       "    infrastructure faculty  crowd    government autonomous rank new_ban\n",
       "1   3.200000       3.500000 3.700000 1          1          301  0      \n",
       "5   4.000000       3.900000 4.200000 0          1          250  0      \n",
       "7   4.000000       4.300000 3.500000 0          0          301  0      \n",
       "8   4.400000       3.900000 4.200000 0          0          301  0      \n",
       "14  3.000000       2.000000 3.500000 0          0          301  1      \n",
       "16  4.300000       3.600000 3.500000 0          0          301  1      \n",
       "18  5.000000       5.000000 5.000000 0          0          301  0      \n",
       "22  4.000000       2.000000 1.000000 0          0          301  1      \n",
       "24  4.000000       5.000000 5.000000 0          0          301  0      \n",
       "25  3.200000       3.400000 3.600000 0          0          301  1      \n",
       "31  3.800000       3.900000 3.900000 1          1           97  0      \n",
       "33  3.900000       4.000000 3.900000 1          0          301  0      \n",
       "35  3.700000       4.300000 3.700000 0          0          301  0      \n",
       "39  3.000000       3.000000 3.000000 0          0          301  0      \n",
       "41  4.300000       4.300000 3.800000 0          0          301  0      \n",
       "42  4.000000       4.000000 5.000000 0          0          301  1      \n",
       "48  3.400000       3.500000 3.300000 0          0          301  0      \n",
       "50  5.000000       5.000000 5.000000 0          0          301  0      \n",
       "52  4.500000       5.000000 5.000000 0          0          301  0      \n",
       "56  4.000000       3.000000 5.000000 0          0          301  0      \n",
       "58  3.000000       3.000000 2.000000 0          0          301  0      \n",
       "59  3.804457       3.822472 3.756056 0          0          301  1      \n",
       "65  3.804457       3.822472 3.756056 0          0          301  1      \n",
       "67  3.900000       4.200000 4.300000 1          1          150  0      \n",
       "69  3.100000       3.800000 3.600000 0          0          301  0      \n",
       "73  4.700000       4.300000 4.300000 0          1          301  0      \n",
       "75  2.400000       2.200000 2.600000 0          0          301  1      \n",
       "76  3.700000       3.700000 3.900000 0          0          301  0      \n",
       "82  3.300000       3.600000 4.400000 0          0          250  0      \n",
       "84  3.900000       3.900000 4.100000 0          0          200  0      \n",
       "⋮   ⋮              ⋮        ⋮        ⋮          ⋮          ⋮    ⋮      \n",
       "303 4.200000       4.200000 4.000000 0          1          301  0      \n",
       "305 3.800000       3.900000 4.300000 0          0          301  0      \n",
       "307 3.700000       4.300000 4.000000 0          1          155  0      \n",
       "311 4.200000       4.100000 4.200000 0          0          301  0      \n",
       "313 3.804457       3.822472 3.756056 0          0          301  1      \n",
       "314 4.200000       4.200000 4.100000 0          0          301  0      \n",
       "320 3.300000       3.700000 3.400000 0          1          301  0      \n",
       "322 3.900000       4.000000 3.800000 0          0          301  0      \n",
       "324 3.700000       3.700000 2.700000 0          0          301  0      \n",
       "328 3.300000       4.200000 3.800000 0          0          301  0      \n",
       "330 4.100000       4.200000 4.000000 0          0          301  0      \n",
       "331 3.500000       4.000000 2.500000 0          0          301  1      \n",
       "337 4.200000       3.400000 3.700000 0          0          301  1      \n",
       "339 3.500000       3.900000 3.600000 0          0          301  0      \n",
       "341 3.000000       4.000000 3.500000 0          0          301  0      \n",
       "345 4.000000       4.000000 4.000000 0          0          301  0      \n",
       "347 4.500000       4.300000 4.500000 0          0          301  0      \n",
       "348 3.800000       3.100000 2.900000 0          0          301  0      \n",
       "354 4.000000       3.700000 4.000000 0          0          301  0      \n",
       "356 5.000000       5.000000 5.000000 0          0          301  0      \n",
       "358 5.000000       5.000000 4.500000 0          0          301  0      \n",
       "362 4.100000       3.600000 4.000000 0          0          301  0      \n",
       "364 4.000000       3.900000 4.400000 0          0          301  0      \n",
       "365 4.000000       4.000000 4.000000 0          0          301  0      \n",
       "371 3.000000       3.300000 3.000000 0          0          301  0      \n",
       "373 4.400000       4.400000 4.000000 0          0          301  0      \n",
       "375 4.100000       4.200000 4.300000 0          0          301  0      \n",
       "379 4.700000       3.900000 4.200000 0          0          301  1      \n",
       "381 3.600000       4.300000 3.600000 0          0          301  0      \n",
       "382 3.400000       3.100000 3.200000 0          0          301  0      \n",
       "    hostel_BOTH hostel_ONE linear  \n",
       "1   1           0          95.25097\n",
       "5   0           0          83.98529\n",
       "7   1           0          67.03529\n",
       "8   1           0          70.98257\n",
       "14  0           0          57.34506\n",
       "16  1           0          59.01199\n",
       "18  1           0          74.53221\n",
       "22  1           0          36.59204\n",
       "24  1           0          78.07224\n",
       "25  1           0          60.02308\n",
       "31  1           0          97.83733\n",
       "33  1           0          77.88152\n",
       "35  1           0          67.06327\n",
       "39  1           0          66.33838\n",
       "41  1           0          70.52523\n",
       "42  1           0          67.18494\n",
       "48  1           0          69.44201\n",
       "50  1           0          89.85680\n",
       "52  1           0          81.48739\n",
       "56  1           0          71.14808\n",
       "58  0           0          56.74210\n",
       "59  0           0          59.76323\n",
       "65  0           0          61.80546\n",
       "67  1           0          99.68131\n",
       "69  1           0          74.01919\n",
       "73  0           0          88.69525\n",
       "75  1           0          53.97024\n",
       "76  0           0          77.37348\n",
       "82  0           0          82.17729\n",
       "84  1           0          79.32101\n",
       "⋮   ⋮           ⋮          ⋮       \n",
       "303 1           0          92.78713\n",
       "305 1           0          77.90717\n",
       "307 1           0          92.27407\n",
       "311 1           0          74.50074\n",
       "313 0           0          64.01767\n",
       "314 1           0          81.96029\n",
       "320 1           0          83.93804\n",
       "322 1           0          74.35820\n",
       "324 1           0          67.14082\n",
       "328 1           0          79.16464\n",
       "330 1           0          71.71905\n",
       "331 1           0          59.30986\n",
       "337 1           0          85.04649\n",
       "339 0           0          73.16798\n",
       "341 0           1          75.75998\n",
       "345 1           0          76.07599\n",
       "347 1           0          73.32382\n",
       "348 1           0          68.82040\n",
       "354 0           0          74.10919\n",
       "356 1           0          80.30998\n",
       "358 0           0          76.38859\n",
       "362 1           0          70.97872\n",
       "364 1           0          75.21836\n",
       "365 1           0          76.23241\n",
       "371 1           0          67.36720\n",
       "373 1           0          74.90800\n",
       "375 1           0          75.98160\n",
       "379 1           0          78.02752\n",
       "381 1           0          75.30797\n",
       "382 1           0          68.83997"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear <- lm(cutoff~., data=train)\n",
    "summary(linear)\n",
    "test$linear <- predict(linear, test)\n",
    "View(test)\n",
    "MSELinear <- mean((test$cutoff-test$linear)^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d4e7407f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "197.636323200128"
      ],
      "text/latex": [
       "197.636323200128"
      ],
      "text/markdown": [
       "197.636323200128"
      ],
      "text/plain": [
       "[1] 197.6363"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSELinear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "fbb43cc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Subset selection object\n",
       "Call: regsubsets.formula(cutoff ~ . - college_code, data = df, nvmax = 15)\n",
       "15 Variables  (and intercept)\n",
       "               Forced in Forced out\n",
       "division           FALSE      FALSE\n",
       "courses            FALSE      FALSE\n",
       "intake             FALSE      FALSE\n",
       "fees               FALSE      FALSE\n",
       "salary             FALSE      FALSE\n",
       "rating             FALSE      FALSE\n",
       "infrastructure     FALSE      FALSE\n",
       "faculty            FALSE      FALSE\n",
       "crowd              FALSE      FALSE\n",
       "government         FALSE      FALSE\n",
       "autonomous         FALSE      FALSE\n",
       "rank               FALSE      FALSE\n",
       "new_ban            FALSE      FALSE\n",
       "hostel_BOTH        FALSE      FALSE\n",
       "hostel_ONE         FALSE      FALSE\n",
       "1 subsets of each size up to 15\n",
       "Selection Algorithm: exhaustive\n",
       "          division courses intake fees salary rating infrastructure faculty\n",
       "1  ( 1 )  \" \"      \" \"     \" \"    \" \"  \" \"    \" \"    \" \"            \" \"    \n",
       "2  ( 1 )  \" \"      \" \"     \" \"    \" \"  \" \"    \" \"    \" \"            \" \"    \n",
       "3  ( 1 )  \" \"      \" \"     \" \"    \" \"  \"*\"    \" \"    \" \"            \" \"    \n",
       "4  ( 1 )  \" \"      \"*\"     \" \"    \" \"  \"*\"    \" \"    \" \"            \" \"    \n",
       "5  ( 1 )  \" \"      \"*\"     \" \"    \" \"  \"*\"    \" \"    \" \"            \" \"    \n",
       "6  ( 1 )  \" \"      \"*\"     \" \"    \"*\"  \" \"    \" \"    \" \"            \" \"    \n",
       "7  ( 1 )  \" \"      \"*\"     \" \"    \"*\"  \"*\"    \" \"    \" \"            \" \"    \n",
       "8  ( 1 )  \"*\"      \"*\"     \" \"    \"*\"  \"*\"    \" \"    \" \"            \" \"    \n",
       "9  ( 1 )  \"*\"      \"*\"     \" \"    \"*\"  \"*\"    \" \"    \" \"            \" \"    \n",
       "10  ( 1 ) \"*\"      \"*\"     \" \"    \"*\"  \"*\"    \" \"    \"*\"            \"*\"    \n",
       "11  ( 1 ) \"*\"      \"*\"     \" \"    \"*\"  \"*\"    \" \"    \"*\"            \"*\"    \n",
       "12  ( 1 ) \"*\"      \"*\"     \"*\"    \"*\"  \"*\"    \" \"    \"*\"            \"*\"    \n",
       "13  ( 1 ) \"*\"      \"*\"     \"*\"    \"*\"  \"*\"    \"*\"    \"*\"            \"*\"    \n",
       "14  ( 1 ) \"*\"      \"*\"     \"*\"    \"*\"  \"*\"    \"*\"    \"*\"            \"*\"    \n",
       "15  ( 1 ) \"*\"      \"*\"     \"*\"    \"*\"  \"*\"    \"*\"    \"*\"            \"*\"    \n",
       "          crowd government autonomous rank new_ban hostel_BOTH hostel_ONE\n",
       "1  ( 1 )  \" \"   \" \"        \"*\"        \" \"  \" \"     \" \"         \" \"       \n",
       "2  ( 1 )  \" \"   \" \"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "3  ( 1 )  \" \"   \" \"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "4  ( 1 )  \" \"   \" \"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "5  ( 1 )  \"*\"   \" \"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "6  ( 1 )  \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "7  ( 1 )  \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "8  ( 1 )  \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "9  ( 1 )  \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \"*\"         \" \"       \n",
       "10  ( 1 ) \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \" \"         \" \"       \n",
       "11  ( 1 ) \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \"*\"         \" \"       \n",
       "12  ( 1 ) \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \"*\"         \" \"       \n",
       "13  ( 1 ) \"*\"   \"*\"        \"*\"        \" \"  \"*\"     \"*\"         \" \"       \n",
       "14  ( 1 ) \"*\"   \"*\"        \"*\"        \"*\"  \"*\"     \"*\"         \" \"       \n",
       "15  ( 1 ) \"*\"   \"*\"        \"*\"        \"*\"  \"*\"     \"*\"         \"*\"       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(leaps)\n",
    "lm_subset <- regsubsets(cutoff~ .-college_code, data = df, nvmax = 15) # Creates 2^p subsets for p variables. Here there are 15 variables and the regsubset can hold upto 8 variables, so nvmax is used for p>8\n",
    "summary(lm_subset)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4275efc2",
   "metadata": {},
   "source": [
    "The best model is autonomous, followed by new_ban, salary, courses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0847b801",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0.199662451223764</li><li>0.267129776855678</li><li>0.307583186413824</li><li>0.33914884696318</li><li>0.363175314748338</li><li>0.381857664113497</li><li>0.395657010715734</li><li>0.398514597389286</li><li>0.399902363568869</li><li>0.401372000499621</li><li>0.402787882023513</li><li>0.401588387416481</li><li>0.400194536743259</li><li>0.398764335078486</li><li>0.397195005327999</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.199662451223764\n",
       "\\item 0.267129776855678\n",
       "\\item 0.307583186413824\n",
       "\\item 0.33914884696318\n",
       "\\item 0.363175314748338\n",
       "\\item 0.381857664113497\n",
       "\\item 0.395657010715734\n",
       "\\item 0.398514597389286\n",
       "\\item 0.399902363568869\n",
       "\\item 0.401372000499621\n",
       "\\item 0.402787882023513\n",
       "\\item 0.401588387416481\n",
       "\\item 0.400194536743259\n",
       "\\item 0.398764335078486\n",
       "\\item 0.397195005327999\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.199662451223764\n",
       "2. 0.267129776855678\n",
       "3. 0.307583186413824\n",
       "4. 0.33914884696318\n",
       "5. 0.363175314748338\n",
       "6. 0.381857664113497\n",
       "7. 0.395657010715734\n",
       "8. 0.398514597389286\n",
       "9. 0.399902363568869\n",
       "10. 0.401372000499621\n",
       "11. 0.402787882023513\n",
       "12. 0.401588387416481\n",
       "13. 0.400194536743259\n",
       "14. 0.398764335078486\n",
       "15. 0.397195005327999\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0.1996625 0.2671298 0.3075832 0.3391488 0.3631753 0.3818577 0.3956570\n",
       " [8] 0.3985146 0.3999024 0.4013720 0.4027879 0.4015884 0.4001945 0.3987643\n",
       "[15] 0.3971950"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm_subset)$adjr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "cc4a5946",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "11"
      ],
      "text/latex": [
       "11"
      ],
      "text/markdown": [
       "11"
      ],
      "text/plain": [
       "[1] 11"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "which.max(summary(lm_subset)$adjr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "75f14474",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>-24.0275658250263</dd><dt>division</dt><dd>0.713067734814331</dd><dt>courses</dt><dd>1.0822388621291</dd><dt>fees</dt><dd>1.50284203949869e-05</dd><dt>salary</dt><dd>5.26390716554967</dd><dt>infrastructure</dt><dd>-2.41290160029372</dd><dt>faculty</dt><dd>3.28729722254168</dd><dt>crowd</dt><dd>3.33730752895674</dd><dt>government</dt><dd>13.9183061091077</dd><dt>autonomous</dt><dd>9.12103049803126</dd><dt>new_ban</dt><dd>-8.85974228193013</dd><dt>hostel_BOTH</dt><dd>-2.16882722144797</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] -24.0275658250263\n",
       "\\item[division] 0.713067734814331\n",
       "\\item[courses] 1.0822388621291\n",
       "\\item[fees] 1.50284203949869e-05\n",
       "\\item[salary] 5.26390716554967\n",
       "\\item[infrastructure] -2.41290160029372\n",
       "\\item[faculty] 3.28729722254168\n",
       "\\item[crowd] 3.33730752895674\n",
       "\\item[government] 13.9183061091077\n",
       "\\item[autonomous] 9.12103049803126\n",
       "\\item[new\\textbackslash{}\\_ban] -8.85974228193013\n",
       "\\item[hostel\\textbackslash{}\\_BOTH] -2.16882722144797\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   -24.0275658250263division\n",
       ":   0.713067734814331courses\n",
       ":   1.0822388621291fees\n",
       ":   1.50284203949869e-05salary\n",
       ":   5.26390716554967infrastructure\n",
       ":   -2.41290160029372faculty\n",
       ":   3.28729722254168crowd\n",
       ":   3.33730752895674government\n",
       ":   13.9183061091077autonomous\n",
       ":   9.12103049803126new_ban\n",
       ":   -8.85974228193013hostel_BOTH\n",
       ":   -2.16882722144797\n",
       "\n"
      ],
      "text/plain": [
       "   (Intercept)       division        courses           fees         salary \n",
       " -2.402757e+01   7.130677e-01   1.082239e+00   1.502842e-05   5.263907e+00 \n",
       "infrastructure        faculty          crowd     government     autonomous \n",
       " -2.412902e+00   3.287297e+00   3.337308e+00   1.391831e+01   9.121030e+00 \n",
       "       new_ban    hostel_BOTH \n",
       " -8.859742e+00  -2.168827e+00 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef(lm_subset, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a5b14db",
   "metadata": {},
   "source": [
    "We get our best model with these 11 variables. These variables significantly impact cutoff"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c6702af",
   "metadata": {},
   "source": [
    "## Regularization Techniques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "4c956b63",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: Matrix\n",
      "\n",
      "Loaded glmnet 4.1-8\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1e+10</li><li>3856620421.16347</li><li>1487352107.29351</li><li>573615251.044868</li><li>221221629.107045</li><li>85316785.2417281</li><li>32903445.6231267</li><li>12689610.0316792</li><li>4893900.9184775</li><li>1887391.8221351</li><li>727895.384398315</li><li>280721.620394118</li><li>108263.673387405</li><li>41753.189365604</li><li>16102.6202756094</li><li>6210.16941891562</li><li>2395.02661998749</li><li>923.670857187387</li><li>356.224789026244</li><li>137.382379588326</li><li>52.983169062837</li><li>20.4335971785694</li><li>7.8804628156699</li><li>3.03919538231319</li><li>1.17210229753348</li><li>0.452035365636024</li><li>0.174332882219999</li><li>0.0672335753649933</li><li>0.0259294379740467</li><li>0.01</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1e+10\n",
       "\\item 3856620421.16347\n",
       "\\item 1487352107.29351\n",
       "\\item 573615251.044868\n",
       "\\item 221221629.107045\n",
       "\\item 85316785.2417281\n",
       "\\item 32903445.6231267\n",
       "\\item 12689610.0316792\n",
       "\\item 4893900.9184775\n",
       "\\item 1887391.8221351\n",
       "\\item 727895.384398315\n",
       "\\item 280721.620394118\n",
       "\\item 108263.673387405\n",
       "\\item 41753.189365604\n",
       "\\item 16102.6202756094\n",
       "\\item 6210.16941891562\n",
       "\\item 2395.02661998749\n",
       "\\item 923.670857187387\n",
       "\\item 356.224789026244\n",
       "\\item 137.382379588326\n",
       "\\item 52.983169062837\n",
       "\\item 20.4335971785694\n",
       "\\item 7.8804628156699\n",
       "\\item 3.03919538231319\n",
       "\\item 1.17210229753348\n",
       "\\item 0.452035365636024\n",
       "\\item 0.174332882219999\n",
       "\\item 0.0672335753649933\n",
       "\\item 0.0259294379740467\n",
       "\\item 0.01\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1e+10\n",
       "2. 3856620421.16347\n",
       "3. 1487352107.29351\n",
       "4. 573615251.044868\n",
       "5. 221221629.107045\n",
       "6. 85316785.2417281\n",
       "7. 32903445.6231267\n",
       "8. 12689610.0316792\n",
       "9. 4893900.9184775\n",
       "10. 1887391.8221351\n",
       "11. 727895.384398315\n",
       "12. 280721.620394118\n",
       "13. 108263.673387405\n",
       "14. 41753.189365604\n",
       "15. 16102.6202756094\n",
       "16. 6210.16941891562\n",
       "17. 2395.02661998749\n",
       "18. 923.670857187387\n",
       "19. 356.224789026244\n",
       "20. 137.382379588326\n",
       "21. 52.983169062837\n",
       "22. 20.4335971785694\n",
       "23. 7.8804628156699\n",
       "24. 3.03919538231319\n",
       "25. 1.17210229753348\n",
       "26. 0.452035365636024\n",
       "27. 0.174332882219999\n",
       "28. 0.0672335753649933\n",
       "29. 0.0259294379740467\n",
       "30. 0.01\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 1.000000e+10 3.856620e+09 1.487352e+09 5.736153e+08 2.212216e+08\n",
       " [6] 8.531679e+07 3.290345e+07 1.268961e+07 4.893901e+06 1.887392e+06\n",
       "[11] 7.278954e+05 2.807216e+05 1.082637e+05 4.175319e+04 1.610262e+04\n",
       "[16] 6.210169e+03 2.395027e+03 9.236709e+02 3.562248e+02 1.373824e+02\n",
       "[21] 5.298317e+01 2.043360e+01 7.880463e+00 3.039195e+00 1.172102e+00\n",
       "[26] 4.520354e-01 1.743329e-01 6.723358e-02 2.592944e-02 1.000000e-02"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(glmnet)\n",
    "x <- model.matrix(cutoff~.-college_code, data = df)[, -1]\n",
    "y <- df$cutoff\n",
    "grid <- 10^seq(10, -2, length = 30)\n",
    "grid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71e9a1e0",
   "metadata": {},
   "source": [
    "### 1. Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d3028c86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Length Class     Mode   \n",
       "a0         30    -none-    numeric\n",
       "beta      450    dgCMatrix S4     \n",
       "df         30    -none-    numeric\n",
       "dim         2    -none-    numeric\n",
       "lambda     30    -none-    numeric\n",
       "dev.ratio  30    -none-    numeric\n",
       "nulldev     1    -none-    numeric\n",
       "npasses     1    -none-    numeric\n",
       "jerr        1    -none-    numeric\n",
       "offset      1    -none-    logical\n",
       "call        5    -none-    call   \n",
       "nobs        1    -none-    numeric"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KS8Q2JpByEwpI3rRh/Sxr2zR2i/7i+H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\nDBASYICQAAOEBBj4H/PKeaHnKlGbAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm_ridge <- glmnet(x, y, alpha = 0, lambda = grid)\n",
    "summary(lm_ridge)\n",
    "cv_fit <- cv.glmnet(x, y, alpha = 0, lambda = grid)\n",
    "plot(cv_fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "fe6ff259",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.03919538231319"
      ],
      "text/latex": [
       "3.03919538231319"
      ],
      "text/markdown": [
       "3.03919538231319"
      ],
      "text/plain": [
       "[1] 3.039195"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "opt_lambda <- cv_fit$lambda.min\n",
    "opt_lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "eff393fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.03220938345949"
      ],
      "text/latex": [
       "1.03220938345949"
      ],
      "text/markdown": [
       "1.03220938345949"
      ],
      "text/plain": [
       "[1] 1.032209"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tss <- sum(y - mean(y)^2)\n",
    "y_a <- predict(lm_ridge, s = opt_lambda, newx = x)\n",
    "rss <- sum((y - y_a)^2)\n",
    "rsq <- 1 - rss/tss\n",
    "rsq"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2494ad8f",
   "metadata": {},
   "source": [
    "### 2. Lasso Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "2dffd8b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Length Class     Mode   \n",
       "a0         30    -none-    numeric\n",
       "beta      450    dgCMatrix S4     \n",
       "df         30    -none-    numeric\n",
       "dim         2    -none-    numeric\n",
       "lambda     30    -none-    numeric\n",
       "dev.ratio  30    -none-    numeric\n",
       "nulldev     1    -none-    numeric\n",
       "npasses     1    -none-    numeric\n",
       "jerr        1    -none-    numeric\n",
       "offset      1    -none-    logical\n",
       "call        5    -none-    call   \n",
       "nobs        1    -none-    numeric"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NzWTEJKNJKZ25pJSIlGMnNbMwkp0UhmbmsmISUaycxtzSQkYJsICTBASIABQgIM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\nH7iZkCrUrM+hAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm_lasso <- glmnet(x, y, alpha = 1, lambda = grid)\n",
    "summary(lm_lasso)\n",
    "cv_fit <- cv.glmnet(x, y, alpha = 1, lambda = grid)\n",
    "plot(cv_fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "2f0153e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.452035365636024"
      ],
      "text/latex": [
       "0.452035365636024"
      ],
      "text/markdown": [
       "0.452035365636024"
      ],
      "text/plain": [
       "[1] 0.4520354"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "opt_lambda <- cv_fit$lambda.min\n",
    "opt_lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "74a36b2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.03247168369483"
      ],
      "text/latex": [
       "1.03247168369483"
      ],
      "text/markdown": [
       "1.03247168369483"
      ],
      "text/plain": [
       "[1] 1.032472"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tss <- sum(y - mean(y)^2)\n",
    "y_a <- predict(lm_lasso, s = opt_lambda, newx = x)\n",
    "rss <- sum((y - y_a)^2)\n",
    "rsq <- 1 - rss/tss\n",
    "rsq"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e55550f",
   "metadata": {},
   "source": [
    "Here, Ridge Regression is best suited among the two to avoid overfitting and for shrinkage of coefficients towards zero"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa51e982",
   "metadata": {},
   "source": [
    "### Decision Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "3442e790",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Regression tree:\n",
      "rpart(formula = cutoff ~ . - college_code, data = train, control = rpart.control(maxdepth = 10))\n",
      "\n",
      "Variables actually used in tree construction:\n",
      " [1] autonomous     courses        crowd          division       faculty       \n",
      " [6] fees           infrastructure intake         rank           rating        \n",
      "[11] salary        \n",
      "\n",
      "Root node error: 72335/251 = 288.19\n",
      "\n",
      "n= 251 \n",
      "\n",
      "         CP nsplit rel error  xerror     xstd\n",
      "1  0.223238      0   1.00000 1.00341 0.058817\n",
      "2  0.123613      1   0.77676 0.90145 0.066194\n",
      "3  0.036390      2   0.65315 0.81939 0.062797\n",
      "4  0.035734      3   0.61676 0.73716 0.058982\n",
      "5  0.035188      4   0.58102 0.74346 0.062550\n",
      "6  0.024599      5   0.54584 0.73241 0.065095\n",
      "7  0.021179      6   0.52124 0.72749 0.067760\n",
      "8  0.019829      7   0.50006 0.72664 0.068409\n",
      "9  0.017260      8   0.48023 0.75142 0.074823\n",
      "10 0.012416      9   0.46297 0.75251 0.075898\n",
      "11 0.011018     11   0.43814 0.79084 0.078074\n",
      "12 0.010765     12   0.42712 0.80079 0.079101\n",
      "13 0.010000     13   0.41636 0.80079 0.079101\n"
     ]
    },
    {
     "data": {
      "image/png": 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kgASaQ6kIwLvif+ikN/8/nWIe9Mjou8\nRxeEt6MSASTB6g+LxrM8Y5DSo1LerRUoBz5OkPSoBJBEagDSBEcAKZrsA6PRYoPeDJBky2bI\n/Ze4AFJM0W83PL/JKuolvZihJLKJXdMmMk/EkvpLXGSU/xinZcERv/R52O7ka3/6VZ+c7T4S\ne0ACSJ9o3UVCmTdWpFZdJBR1BwCkT7SGpNzbKlMrSIq7AwDSR/InKfumCpU3SZF3AED6TPhn\nzFvLk6TYOwAgfSoPlIBRTJEHSvH3AED6XMO/ujWkaB+tFCyaZynJHgBILKJpbR3aMTSzA9Ls\nAYAEQQwCSBDEIIAEQQwCSBDEIIAEQQwCSBDEIIAEQQwCSBDEIIAEQQwCSBDEIIAEQQwCSFCu\nWnEV3Vfz0ceJiqve9i440w8g8cu1g2/WPvzaZ8MTaxGk56V9fl2ajz6aS1j1XjizXs4KkPhl\n7qBuX96afWjvV2ilXlXqX15t/51fbT/35VdxOtG7fNNJfVx3M7XMXOhWw9S9XX21AaStdC+a\nL7RmrzUzhdOjLE/0Kn+qfdTswp+iuPc7SO/LCz3K52C/Qit1qr+Mzs1QQnVf173Yl4m+rnQv\n792Q875Wg8+zNbyUHUjVg+LsSU+AtJWaucGt22vdTOFRftNPNVf7qmD6rnajcQeMuS/Letd9\ntYXLmtk9pEXVgNPpVfdg14td+Vq+71UPf1UwVbpScXubpl3h2r5dUfnNuxeOC9LcrWCTer7a\nr79qr1Vfhtdqv5yrHXmpviyLahe+qm3fFVhtswb78qTnHO1+DfKfupNEqerY860uPL/PGiRd\nrrr6Xe2FQnf+1QHSlW5d4bxqsWJZBwYpwETNzZqvxuZV/VBNzelC7xaxepbu3JfVCPY1rChB\nzHvS7XKqjzPv9K1HJLNcT/Tu9dyvlj0d0DPsH72B+YsJIK0xIfO5fmygudK1mnBf68m53lbL\n2JeXojTxAUihqnuuoNdDwWOW6zHrVE0JOr0vww4/q3kdQGJUgO8zPV7V7EHvlnZqVx8sFfWR\n8ENt01XrfflVbb/Xpp1vgBSgZmHh0i46FKRmA325PYh99AZq+bt7+6rg6bofU7utfDfLC1dz\nr1VHTWX9tVgf5BZ623j5+9lsvpmDWaKYd6T3V7f8XU3wXtV+aJa/jXLZDDRO02ZzAZBiKMS3\nXv5uXnXL3/V4cyt/2iOge1H8uHZQ/dmfEiBF1rk/Dk0sgJSTcow5qYyjoMQCSDkpx5hTyrwM\nK7XrRDaxa8rLd6hyjPkgAkg5KceYDyKAlJNyjPkgAkg5KceYWcXaAZtXBpC2Uo4xs2rz3Get\nDCBtpRxjZtXmuc9aGUDaSjnGzKrNc5+1MoC0lXKMmVWb5z5rZQBpK+UYM6s2z33WygDSVsox\nZlZtnvuslQGkrZRjzKzaPPdZKwNIWynHmFm1ee6zVgaQtlKOMbNq89xnrQwgbaUcY2bV5rnP\nWhlA2ko5xsyqzXOftTKAtJVyjJlVm+c+a2UAaSvlGDOrNs991soA0lbKMWZWbZ77rJUBpK2U\nY8ys2jz3WSsDSFspx5hZtXnus1YGkLZSjjGzavPcZ60MIG2lHGNm1ea5z1pZtiBl+G8e8K8p\nLH3a5ni9eRyQqr76b1oi87IK6p8ZiYw5rj5qcNVfv6b1YW8eBaRZihRLyaLx0jxFiqWto0yr\nD5o7S5FiKW1k+YHkgZE4lDwwOh5KwY31wOgzlA4Bkh9GDUppAvKQJ0c1SluHmlChbfXDqEEp\nYWS5geTPkRyS/Dk6FEmBTfXnKJikA4C0hiMpJK3h6EgkhbV0DUehJAEkgJSRAFLsmmZ8rOJI\nBknrODoQSUENXcdRIEnHAqk589Y9kbGJJIPUnk1q49Rb7FNMEmJOoo9Bov5kEpkbAdKyDxMS\nn3KCmJZkQdL9/mM8j8pbB5xKn4JEPUE9PGRRBZAmXKzkSAJIk7xMlAHSrM0vF0j0azwyAaQ5\nF+OZ3TxIAkhaDdJhSGIDiX5NgxRE0rFA6qmZ5kgcSP2h0SRHAGnOxmKkOx6yQBpehAeQXC7+\nGyg3kPpjJIDENiKZh0U0PEYCSE4XuYPUYwOQuEAy1hx+2S8A0qQL59RuhiOxIM1wBJDmbBwg\ntQJIa1wMkFkckACSYPGt2mFEWuvCYkSt2pHBkGyQ/tHnXs0lB4C0wsZiZHBCluxtAGnaxX9r\ntX1Srr1CCCDN2vxaK4DkcgGQdiSAFLumaRcAaUcCSLFrmnYBkHYkgBS7pmkXAGlHAkixa5p2\nAZB2JIAUu6ZpFwBpRwJIsWuadqH5aB+tu/jUtr4sDKT2pJFxF58qk306afuY0+gjkNR9SMap\nJHUJq31SFiC5XCg8HNcH6W1knpbdPikNbP6xz8Cqsv4BSMs2mppfFi7WJaxkvgGQXC7U2DMG\nqd8mFCT6ByDZ+gAkGl8LBJDWuLCncY4SaaSEgUT/zINkHEptH3MafT61I8dFQmTeMAuQJlwM\n8Jk4RhIOEg1AajYAJD+b4QBkXbZK6gEgLbhYHJHUqETCQOpHI6LhiKQ4I4C0bGMvNpilenDq\noepHqlSRBdjErmnGhx9IelSSkJPDGZ3z0m/qD5MkxJxEQQ11/P2t4YFSN7ejYI6OBhK5QTLX\nGyQkZf+H7GgSJHO9QULMSfQ5SO4VB2u9ASC5fWQKkjW9s3gCSCuNhiCZG4yZHUBacGIvLJin\nX637++RwZC6Ad8dI/SKDeZsfHYyjz/72d39Ctl9psG43/4CjA4HkKRlJue4iIRkxp9BHIHkK\nIE16yY6jdSRJiTmBApu6hqRQF4lsYtc06wUg7UUAKXZN826y42gNSXJijq/QtvqTFOwhkU3s\nmhb8+KEk6h8be5IkKuboCm4s/hkzl6dllKSlJHmgJC3m2PqguR4ofdKbRwGp7sgFJYzFU4sh\nC4w5rj5qcNTePA5I0A4kN2EAEpSR5CYMQIIyktyEAUhQRpKbMAAJykhyEwYgQRlJbsIAJCgj\nyU0YgARlJLkJA5CgjCQ3YQASlJHkJgxAgjKS3IQBSFBGkpswAAnKSHITJjeQrEt07wWdJz73\nvEzXMffepB4nKq5d+XUh+i7V5cQBlUXRu1ChyIqLU0uNslpt7Wfv/lA7tyy/qDX06szcQLLN\np+3nmr7ULZfneNuj6c6WpFdRl7/Lp4SE7bPlrEIREVccrWqU1QWu/nDtaLVzG6BK/87MDaS6\nSUTV8HB+td8V1eOrODXNrjaVryqdLvZbTS80D9UIdi31e7q2+kPl/USnh/JR1VDq+1eabRe6\n1TA15WtVy5Mu5U+17WO1MTUjXuN/EFfXnj4+vaFRt7dr3U6qyBKXTPmMSHZ6qMSo3zkXr8Ud\nrXZuSe0Xk29n5glSrbMmguir/jomqng4jd/SqdmMKrcxSPWH2hGn/YZ6Xqux5z0Eqf74qSmf\nurCvVE33bl1Yn+imRrxHOYyra08fn9pQ610H2n2rPulJVlyfBBSwK9PID6S2i9qWqMRois9y\ncUernVte2l1h7OSPIuOy4aqp7alLOzp0SXct3/Vbr3bTW3+ue0unZtWRr65PrYStP1R38rNK\n3Fbv726csHSle1t3caXiu4aro+CDLlExnSt/1xqQQVyqPTo+taGJp7jpF6dvPXsx4gpT7iCZ\n6VHqxPhqdt/SjlY7t6vMuzPzBOmtCqXOrOd3MxR/V99Ft9J6y0jNvg5za/uhWkXnpe3fwdfz\nVXVnu/m7vBTPauQ/hTXEaI8V0yCuvj1dfGpDE1BxVSBdz31dRlyBQYWbRpYfSGZ6qMRQ49DS\njlY7t1QgeXZmniANC9XMl76bL57ydjk1M9z+rUWQ2m19X7pG/Pqr6acrFc2XmlkZD0jvceOM\n9qhYug21jKndaE6W+g95pJEfSGZBJUY1v2u6bWlHGzu378LdLjYMC3X7Xw8zKS2QHtWXdzO1\ne7zq76LuvW5r+6EzPQ0fl3c51Lmb15X1suizmS6cqiruH45IKiZjamfFpdpjxme89VaLDfY0\nX8cVpj2BpBKj+r3Ufbi0o9XO7erw7sy9gFQfgxdNwlE9R676Ty0ztJv0YsO1e09vbT/UHoO2\n3/SuVdGr8fFnN/q3x/OPsIZ0UjHpY+BBXKo9Or5zH2cj42SJ6g4jrjDtBKRCrdYUar9dlne0\n2rldHd6duReQXtXA/aoPz7/aNc1HQRf11plO93aYb48sm/f01u5r/Mc44epQYeb349wu5NwK\ntZIa3iXD5e9BXKo9Oj69wd03zUMfV5h2AlK7n7vEqDc0Q9LCjtY7V+0Bz87MDSSh2k1DGslt\nzb4iA0gj7aYhjeS2Zl+RAaSRdtOQRnJbs6/IANJIu2lII7mt2VdkOYGUqH1yd3CI5LYm0a6R\n6yZ6TZweANLWAUxKboYDJBYbuakXIrmtkZvhAInFRm7qhUhua+RmOEBisZGbeiGS2xq5GQ6Q\nWGzkpl6I5LZGboYDJBYbuakXIrmtkZvhAInFRm7qhUhua+RmOEBisZGbeiGS2xq5GQ6QWGzk\npl6I5LZGboYDJBYbuakXIrmtkZvhAInFRm7qhUhua+RmOEBisZGbeiGS2xq5GQ6QWGzkpl6I\n5LZGboYDJBYbuakXIrmtkZvhAInFRm7qhUhua+RmOEBisZGbeiGS2xq5GQ6QWGzkpl6I5LZG\nboYDJBYbuakXIrmtkZvhAInFRm7qhUhua+RmOEBisZGbej6iBW0dXy+5GQ6QWGwE5dpqEf29\nIDkoyc1wgMRiIybT1msRowalraPsJDfDARKLjZREWy8vjsQMSnIzHCCx2MhIswB5ciRlUJKb\n4QCJxUZElgXInyMZJMnNcIDEYiMhyQK0hiMRJMnNcIDEYiMgx0IEkHJzE70mTg+HAWkdRxJI\nkpvhAInFZvsUC5EBUnvmtSuY7AAkUW6i18Tp4YggKWrIpocAkiw30Wvi9HAUkBwcDUAijEjC\n3ESvidMDQBqMUABJjJvoNXF6OChI9DdAEu8mek2cHgDSYIQCSGLcRK+J0wNAGrwGSGLcRK+J\n08MxQRrRQ3pJHCCJcRO9Jk4PAGm4FSBJcRO9Jk4PRwZJn5AlgCTRTfSaOD0cEyQPbd9KuRkO\nkFhstk+xAAGk/NxEr4nTA0ACSFLdRK+J0wNAAkhS3USvidMDQAJIUt1Er4nTA0ACSFLdRK+J\n0wNAAkhS3USvidPDwUDSly/0lzEYt/k1LwGSFDfRa+L0cCyQNCrDa1TJ+AFIQtxEr4nTwzFB\nmrg7CSCJchO9Jk4PxwLp7yWQjBvPt45YcIYDJBab7VMsQMYRUQONdam3Omz6GyBJchO9Jk4P\nRwOpG3rsYyQavgWQJLiJXhOnh6OAVFrYDP9+UF/Qo9L2rZSb4QCJxWb7FAuRdU/s8O8HWYgB\nJCFuotfE6QEgASSpbqLXxOnhMCB1JKlb+cxb+sgEiqRwJDjDARKLjYAcC9G6i4QENFJuhgMk\nFhsBORakNSRJaKPcDAdILDYSkixEACkzN9Fr4vRwIJDwry8zcxO9Jk4PRwIJ/4w5LzfRa+L0\ncCiQSvJASQhGkjMcILHYSEm0INGito5QS26GAyQWGzmptm/JzXCAxGIDkNJIboYDJBYbgJRG\ncjMcILHYAKQ0kpvhAInFBiClkdwMB0gsNgApjeRmOEBisQFIaSQ3wwESiw1ASiO5GQ6QWGwA\nUhrJzXCAxGIDkNJIboYDJBYbgJRGcjMcILHYAKQ0kpvhAInFBiClkdwMB0gsNjmBVF/MbV3Q\nbb7wu9L7dSH6Zg7LS3IzHCCx2OQGUqCel+bpVdT3VmxBktwMB0gsNrmA9FMU925EetBXteGL\nHg1ZrzPR5dVR9jjR6VHWL6rS+aWM63GoKVzpWj7pskH8cjMcILHYbA7S8s15te7qPr3691QH\nTYV6Uenclh/Nhx6q0nPr4X0luj6b4onWOGVtZhITwW6i18TpIUuQvD51ruZj3wqkb/opf+oJ\nWrvh3dZD9aeu1aDTUHWpqWreuFJxeytnRfXKd2YHkFhtYtfE6WG/INW4vBVI74qVc81PSxWd\nb6WxEqHp6kG6apBoxTESQGK1iV0Tp4c9g1T2IJWXaqp37raWt8upPurpKTOJqmVM7Qp6VsdI\nnm0GSKw2sWvi9LBfkNpJm0KkPmK6lz0q6g1jame8W6GkFhu+KpBeAGkLN9Fr4vSwX5Ae5mJD\nPbIUjW0DD5EakdpPPUcg6eXvJ6Z2W7mJXhOnh/2CVN6L4qcHqV7GLrup3Jdz+bu0QVJ6nKm4\n8UYWrTLBGQCQWNywavMAJgWQWG1i18TpAVePK94AAB1fSURBVCBxCiCx2sSuidMDQOIUQGK1\niV0TpweAxCmAxGoTuyZODwCJUwCJ1SZ2TZweABKnABKrTeyaOD0AJE4BJFab2DVxegBInAJI\nrDaxa+L0AJA4BZBYbWLXxOkBIHEKILHaxK6J0wNA4hRAYrWJXROnB4DEKYDEahO7Jk4PAIlT\nAInVJnZNnB4AEqcAEqtN7Jo4PQAkTgEkVpvYNXF6AEicAkisNrFr4vQAkDgFkFhtYtfE6QEg\ncQogsdrEronTA0DiFEBitYldE6cHgMQpgMRqE7smTg8AiVMAidUmdk2cHgASpwASq03smjg9\nACROASRWm9g1cXoASJwCSKw2sWvi9JABSGn/mYqcyORmOEBisUmbt0R/FrUNSkS/F/VJZHIz\nHCCx2CTNWg+MNkLJA6PPUJKb4QCJxSZlznpyVKOUMKomMj+OapRCPSQxEewmek2cHmSD5M9R\napL8OQomSW6GAyQWG4BUAqQkNrFr4vQgGqQ1HKUlaQ1HoSTJzXCAxGKTLGHXcQSQRGcAQGJx\nE6SVICUkaR1HgSTJzXCAxGKTKl9tjqg5odSe5uw30eYgtRGpgrERIH1sE7smTg+5gETd75/+\nmYzyxiMSdb/GS/M1QAJITG5CRAOOhuXtQFrgCCAx2cSuidNDxiCN30gUmBskc2YHkFhsYtfE\n6SEbkPTxkLF5q2MkGnNkw4NjJBab2DVxesgFpP4YabAGIQUks4QRiccmdk2cHnIBqYcGILGa\nCHYTvSZOD9mBRI5t24JEI3gAEo9N7Jo4PQCkkMgmQMJiA69N7Jo4PWQCUn/y1Vhy2OyErAsk\nvcBAv7HYwGQTuyZOD7mA5KPNlr8XBZAAEo+bEAGkFCaC3USvidMDQAqJDCAlsYldE6cHgBQS\nGUBKYhO7Jk4PACkkMoCUxCZ2TZweAFJIZAApiU3smjg9AKSQyABSEpvYNXF6kA+SOltknjVS\nt/eRdVI2PUjduVjrrJHa1pcBUqBN7Jo4PYgHSaFiI6OfyLi4ITlIBi09W+olmRuDvCQxEewm\nek2cHrIEyeBpS5DIdQPFb4DEZhO7Jk4P4kEakmPN7JoblTY8Rhpd921wRea2IC9JTAS7iV4T\np4eMQDL+6ol6IHNA2g6kiWMkgPShTeyaOD1kARKNCvZxEm0MkrtE6oAJIAXaxK6J00MOIDmI\nMkHSo1IykPrVhnmQ9KgEkAASj5sQ2QdGo8UGvXlrkMgNkrneAJAAEo+bII1uQLJuRvoDkDhM\nBLuJXhOnB/EgUX/ytT/9at/mR6k5MhbA24UF8/Srdbv5BxwJznCAxGKT8Iv/zxptAJKnABJA\nYnITqDUkpeRoHUmBkcnNcIDEYpP0m18oR2tICo1MboYDJBabpCnrSRL+GXOoiWA30Wvi9CAd\npJI8UNoAoyaymBhJznCAxGKTfBI1zxJtg1EX2TxFH0UmN8MBEovNBnlLM0ofTaLI5GY4QGKx\n2Th1DyO5GQ6QWGwAUhrJzXCAxGIDkNJIboYDJBYbgJRGcjMcILHYAKQ0kpvhAInFBiClkdwM\nB0gsNgApjeRmOEBisQFIaSQ3wwESiw1ASiO5GQ6QWGwAUhrJzXCAxGIDkNJIboYDJBabKA25\nF3SecVn5fF6m37+dqLh25WvRll8Xom/OEFNLboYDJBabKA2Zv8Szftf1iQ6uW3ONaFu+NuVr\n+Srq509Jmud7pEcHtIJZvb6f6HR3PM9KboYDJBabGA1pr5auB5Hzq2zy91p27HQQNZ840bt8\n06kzqj/eFC70KJ9dmejZlK9VDU+aGcU84/L6WAf0o4NYwaxeP5vn5+h5wXdAuOtNBLuJXhOn\nB1EgnRtYuoS8OUC60r28UzuJe1fpeu2T8UlfzfOpSdRT9cwWVjOAPOrXqvCqIr281KcMoG91\n7Bpm9fqrgetr9LzgPCDe9SaC3USvidODEJD0V/+rLpzp+aqBMkFqfu9NFjaToisVt3dvf1Lj\n1OtUw/gqqzkVFZ/O7FqQHmoA0YXah5rzGUBfmnhPGmb1umiei9HzgvOAeNebCHYTvSZOD1uD\nZN8G9/w+m4dDI5DeKgsbkK4GSFWSt9/wz/rYqHgO77gLDq9suG4HPF0g0q4HQJf1oKlgVq9V\nO4bPC74Dwl1vIthN9Jo4PWwOknquC3f6fs2CVKXy3TUSFKU2UqNB0U2vPou5i6BWYRS+q/Ho\n1n5iAPS1npIqmNVrgASQmNwsVtakVUGvRzu1e7zaxH3UB+4GSN906lfi3urYpD7muHdTJXV8\n8lU9vzhBIqNQ3i4ntZBhHatd6KfsYVavMbUDSExuFitr0rOeEdVJ9mgXu9rFBwVR9S3/1bzz\n6K271bJ2Faz96lcrZu2274Gb1eGpqV2js7nS1o8oGuh6wGzf6kbD7jUWGwASk5vFyppUrI4t\nLq+aoG75+3Wm012B9CjqMcB9uPM40emnq6U+OVvz8zhXRy+fxtx4e6jTVLpw7s9bNXqa57B6\nmNVrtUgxfPbrmjXhrjcR7CZ6TZwepIDkq/PiFzmLG23XGP6oCydU4f1lLn9rFWoE7WDWr3FC\nFiDxuGGrrJssxXYjQXIzHCCx2GwJUn9JXVQ3IiQ3wwESi82mI5JsN6ySm+EAicUGIKWR3AwH\nSCw2ACmN5GY4QGKxOTxIcvtZbmQAicdNmsoSuZHbz3IjA0g8btJUlsiN3H6WGxlA4nGTprJE\nbuT2s9zIABKPmzSVJXIjt5/lRgaQeNykqSyRG7n9LDcygMTjJk1lidzI7We5kQEkHjdpKkvk\nRm4/y40MIPG4SVNZIjdy+1luZACJx02ayhK5kdvPciMDSDxu0lSWyI3cfpYbGUDicZOmskRu\n5Paz3MgAEo+bNJUlciO3n+VGBpB43KSpLJEbuf0sNzKAxOMmTWWJ3MjtZ7mRASQeN2kqS+RG\nbj/LjQwg8bhJU1kiN3L7WW5kAInHTZrKErmR289yIwNIPG7SVJbIjdx+lhsZQOJxM6zCpc+r\nXfbB4kluP8uNDCDxuLHsif51iZOlqq6/p/WhJ7n9LDcygMTjxrB2U6RY+qju3scMRYqlD6pP\nYyM3wwESi81n3+YzGDGh5IHRZyjJ7We5kQEkHjfadoGjGqUPqm9ceGHUoBTqIY2N3AwHSCw2\nn0yKljn6lCR/joJJktvPciMDSDxuOksfjj4jaQ1HoSTJ7We5kQEkHjedJUASZyLYTfSaOD2k\nBMmTo09IWsdRIEly+1luZACJx01rCJDkmQh2E70mTg+bgNSdkqX+1Gx7xQErSG2VXcHYDJBy\ncRO9Jk4PCUHqOWl/SZXN7Z+BNBqQqCNHv0EAKRs30Wvi9LABSNYzOTjiA4n+HoBEgxEpiCS5\n/Sw3MoDE46axGwGTHqTh1A4gCXYTvSZOD5uAZB4OOZEK9DAEiewHgJSXm+g1cXrYAiTqsXEO\nSAApoYlgN9Fr4vSw1dSORrM8gLSJiWA30Wvi9LApSBMccYFEA5oAUl5uotfE6WFLkKZWHQBS\nQhPBbqLXxOlhk/NI7WKDPgk7Hp0CPThB0idkCSDl5SZ6TZwetgBpUXwnZBcFkOS6iV4TpweA\nFOAljY3cDAdILDYAKY2N3AwHSCw2ACmNjdwMB0gsNgApjY3cDAdILDYAKY2N3AwHSCw2H4Jk\n3Xik70xqHvlAGhWMu5Ps90O8pLGRm+EAicXmM5BMZFRZ/3CBRKOCokr/ACTxbqLXxOlhlyDp\nu47s24/ob4CUk5voNXF6kAMS60Wr+ioGJ0jmnechXtLYyM1wgMRiE+kYKTpIpCd7ACkLN9Fr\n4vQgYkRSAxPxgqTvjzVB6vgigCTeTfSaOD0kBKkc3T9hl/tRKbyryIBmcNm3CZIelYI8ye1n\nuZEBJB43reEMSNZ6AxNIesl7PCABpAzcRK+J08OOQbILACk7N9Fr4vSQEqTS+rOQZJT/NU7L\nsvzt7/HB0t8WY/QBR4L7WW5kAInHTWf5r5cYQPIUQJLsJnpNnB6SgoT/jyTPRLCb6DVxegBI\nAS7S2MjNcIDEYvPRzCs2R2tICj4hlsZGboYDJBabjxqyRBL+GXNiE8FuotfE6SE1SCXNocSA\nUesjIkaS+1luZACJx41lP8ESMWHU+Zil6LNRNY2N3AwHSCw2DA0hlz6vdtkHiye5/Sw3MoDE\n42ZXktvPciMDSDxudiW5/Sw3MoDE42ZXktvPciMDSDxudiW5/Sw3MoDE42ZXktvPciMDSDxu\ndiW5/Sw3MoDE42ZXktvPciMDSDxudiW5/Sw3MoDE42ZXktvPciMDSDxudiW5/Sw3MoDE42ZX\nktvPciMDSB+aPC+1xSqT24mKa1d+XYi+B9s2l8R+DjYR7CZ6TZweYnfjPEOX53jbrbmu9NKU\nX0Vd/ra2ccu8jtXvmlaJ/RxsIthN9Jo4PfB3I9GrODVDyfnVZmZDE9HjVG8py5/i9OqytYLj\n1T73GXyhR/nsyle6VuWLtY1Lz5bLp+H6CZAkuYleE6eHGCARfZXn+ulkgVTrXJaP6qlQmXsl\nur5tkJrtVQ21ToYvtU3pXlAz2av4PD3KbuxrPTUknztK7937ekOjGvSm8EM3XaVZDu8ALhu5\nGQ6QWGwWQbqW77rwarO6VOl9qRkqK8S+q5FGVfL+7ngwVaV+V1dxpeLb3tap5rHO++a5GrBM\nTzXJJ4NbomepNzRea4DbaeWVqsOvjh+zHN4BXDZyMxwgsdgsgtRg9Pw+D0B694X3AKThiPTo\nRp9287e1rdOZnq+arXNlfq0BMTzVJHdh1J9rBzO1oayBKW7qxYU6Igfl8A7gspGb4QCJxWYR\npPrxTt/DEakcg+Sa2l0KXUlZNBSQtc1yM+WgLL+r4edWqqqLfkPZgHTVIBXPakp3GpXDO4DL\nRm6GAyQWGy+QCno93CCZU7tqvvce2n9VA8q9zvym/GxmiOY2y037/B57Ksvb5VSv8/WMdhtq\nGVM7q7JhOagDuGzkZjhAYrHxAunULCnUQFXTKivP66Xskxp9HMvfTzW/qj7z7KZ2z/Gc60yP\nV42WMbV7tID2JLTcOoF5q8WGU2V270YhsxzeAVw2cjMcILHYeIH0qr79X1WOP4pqFLBAMpe/\nnaqX4X66Dz/O7dG/2mZ8qkbraiwmnNXQ09Z97s48PdQpKLVBqVv+vhmLFbr8UQdw2cjNcIDE\nYvNhQ4heVXYXyx9c0HD5+3Wm070H6f3VrXb/dBdF6A0D3Yp++VyVF1oQEC1ACrCJXROnh/Qg\ntUtjYq73CZDcfpYbGUDicWOqGhnkXDcXIrn9LDcygMTjZleS289yIwNIPG52Jbn9LDcygJST\nG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6\nACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu\n5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgA\ngJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmR\nGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMA\nUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZu\nZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBI\nGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mR\noQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl\n5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaG\nDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSR\nG7mRoQMAUkZu5EaGDgBIGbmRGxk6ACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6\nACBl5EZuZOgAgJSRG7mRoQMAUkZu5EaGDgBIGbmRGxk6QDhINC02m5nPh5lxtibAZHs3W0Y2\n8/lAM84O8FEEkIj+m9Zkj/yZlsOG6N9FOc0CIvtnWm6b2eAm3fw1rSk3qyOrbH5NijOy39Ny\n7pb/LcppNt2Y6dascuEvfpDmMJpI2FmMGpSGn1/GqEnaoVlAZDPJ2iSsowNCAJ9J1iZhHW6W\nIluZee7kC4psBiMXSh4YufJ8oTHu1qym1VfsIC1xVCfs0GQBoyFJnhgNSQqJbCFZXST5jJVD\nk4VkdeVrQGhLmVcnH0dkCxzVKFmf9+OozvNPW7PSxRpxg+SRrcN89eDIIsmfIytlAyLzydZh\nunpFN+iA5Wwd5atPZIPQPDJvlHs+oQ1NljmySPLnyErzgNZ4eQoFAiDNRbY+W/cFUlBkAIlB\nXtlq56sXRwZJazgyUjYgMr9stdM14OjNK1sH+eoXmRWaV+YNcs8vNNvEhyODpDUcGWke0Brf\nQzFXXi8LIM1E5petdromASkosoDU84vMDg0gMcgzW8189eRIk7SOI52yAZGFpKt3dEYHeGbr\nXwGRGaF5Zp6VewEgeXKkSVrHkU7zgNZ4ewpDIg5Izfmt7tncRON07UGidhW8+Vy/iWZAaj7a\nPZvb5kAyQzNjc0Q2TMp2LZxotCZu2BhhDKOxIhuD1HZQV/jL3DhKV5qNySr3Njq1SK2C99nY\nb7NSzzcyM7QOk0ZdQbNjlF0g1e+bz13RWrMegKQCNxtgNswFUlfjsGoauFipSCAZT+ZYMAcS\nGb/GJv3aBZLx5Ci7QRqGMghzEiRqf0mVZ0Gi9nc6sokRiZqf7sF4ngDJFROZ8Y1Bov6Bfo22\nOUFajGwMUstK89M92GUXSNQ9kJXWw7LVGhW41YBfNAuSVX1fNUkCaZikQ5D64hik4fMIpI4k\nAxIzaydBalN2jqNBmP00fMSRfp4Cibwjc6cr/WWnqz23GkXmiokmIhtBQ7/cIPW5FxKZzdEi\nSCNeHCBZczKyWuMEieZHJLN6gyOzHJT7IUaTlQ2mT86v/iWQzOncAkhqZrcGJMfMzo6NE6R/\nJyObBsksWPMnZpB+fQbSRGQDkH5vANLC1M4JEv1PJkju734Tqd5G89ICNBiFDKjcI1I3gdKH\nH8NjJNeIRF6zziFI7bFH87sMkorC/xjJSlJzw/hIhAYxmcdI5D5Gch0PWSA5DpKGkY1GJEdk\nI47mj5FsSMbHSEOOBiCFHCO1x0ejAUkkSGZmOgckF0jm8dFofucESdNUZ6jniGQFMj9YDkDq\nKaLlEYmMKPxHJHKUZkFyHCPpOFeMSHUezo9II5CmInMMSB+OSHMghYxINaf/G4BE/xMPkvNL\nf3JqFwjSZLp6g+QKzTG1G86ppkekNCD94wDJis8TJHt8mopsJyD1lTrXHySBRPbDOFlnQDKB\n8llsWAmSe2rnDI0BpHWLDfTXMF0Xp3aJQPKPbEDP54sNg9M/nCBZC+L04bJdNJBGHK0AyTlK\nuUEyf31BMn9HkS2BZM2cUoC0tNjAABLZafhJZPJB6qdxg7FO4IikznCSXiNbBkmffNXPRnli\naqcO3/WRvbFtAiR98lU/T54rHg47/YH9gKMxSGZk5IxsGiR92nN4CnQMkhmTBoho3WJDu9Lg\nyr2QyBxrDRqgtYsNoxNKI5BGiw2joXbiGMlEZ7wUHpT7IUaTlf3nKwdIi3IfIy3KcYzkF5r3\ndTgOkPyiam3+8tVHkf3ylnP52zey375ygOQjWtmaiamdh4+1uR9iNFkZQAJIAOlzASSABJAY\nBJAAEkBiEEACSACJQQAJIAEkBgEkgASQGKQurzPPyujTNs3jJEjmRd/9GaXm0Q2SviZ0dIMS\nOU59uq6qWwrNOBujC/q8jb1Zm/yroxpeROuKqrXpctE6L9Odr1m6soH8I+vyiozLO/uTMM3j\nBEitiW9kPSgmNM3D7AnZ8Q1C6nwPWaeTTJCsxvxaaEx/QpbMM0oOF2JAMvPSuCKH/jOvbett\nOkqMkad70D8ukIy8NM5y9vfTDU59midk//MMzUhSEygyfqZAGqI9EVVr85fOSfOibzJ+JkAy\nLrJYjsz8ljaeyPiZGZG8I9OcmFfddXcmkYmXDZI+R2pfY0fGz8SIZF7kMNcY5cq4PtW4lELk\n1d8hILlu55sDif51gET/LoNEo7sOF0HqL/b2BGk8Rq4DycjaOZDMCd4akBzX1yyBROPneZDI\numZ1EaT+cmzXEDUHEo2fZ0GauCYpL5Bmrv42Z3Z/TJDMkar9vJmhVkndmaQxc4BkILMYWv9l\n7wTJyOMhSMPLlGgiqtZmHiRzWLAjmwTJGdkYJCvxvC4R8ohMz+XM2/o0SOYw1X7ewY0DpGGS\nL4A0c4nQJEjmnDIo90OMJitTs6fR/KmZUc2B5BqWiP4EgNRM8FaANBnaGCTrSGQGJNew5Iqq\ntennTBok40hkDiQaTTqnI3NzpO/pmwXJKCxFNglSM8FbBZJxADMJklEwjpFmQZo4RhIIkmtE\nUklMw2wthwdHdpHUksM0SOYGkykyU9YIZ3yvx0Ro/ff+KF07vmiUrjY8DtKtqFqbLhdJf8eT\ncWk19XyNQHIcI01HNjkg6S9yGuaeA6TFyPTiQj/Js8r62GkRJPtgRh9E2a0xlhr6V87GKJAc\nx0gDFwJAKkc3Itnl/qt/ASTjTwvpUakzGYLkvH+C+gMSmohsKjQjsmGGDtK1/+43bBwg2cdw\naj2iNzG+2I2nfnTSdzHYkU3ePDERmQsk8wtdXzo9jswujCMb/BWhyXsnyBiq1H6ZHpHMLNdD\nBtmtcd0dYjbGPbVzgjR0sVLpQLIO6uendmZhASTrxgXjdgo3SOYNExOhDUFqNUpX66h+ANJw\nCcQYkNaCZB7Ve4I0Fdk8R3MgDY6VxpENQWrVrdgZ5d9hIJmLATZIg3GWRo3xBcnhYqUEgTTm\naBmkwRlQGqesCdJ/RmTLINl/Pm4mXU0TFcWYo3mQzBvlFkEaD5ZBIFlp6ACpNMH2jcw4NPo9\nKAOkFdWpL359RKJGAOPcp5WtxrKdPigyXuhjJOe5Gj0KWeOTcQLU8be/50OzIvtnCJAenIyT\nnxZIpQ5LoUPGi/4YyTJpk5HMVQfjhToSGUemlz78IrNyj8zzmcaZTNff/jaenJE5//b3aH5n\nnpYd/+1vG6TmQIbMv/VDgySnQWP6+xXNxjj+9rdeYFh0sU4xQFrWGKRFuQ7oPTQGyT8y/DcK\nv9Bsk99eGoLkKddyvm9rPD3JAAn/H8kruoGb1dkaFJpX7jFEtoqjdSSZZgGticgR/vXlfGSr\nOfKKbuRmdbYGheaReyyRreJoDUm2WUBr4nGEf8a8FNlajpZJwj9jHu4XT4yGZksYuVqzzsUK\n8YO0QJLb4TxJjh4J4GgptInI1nK0FNyEm7XZGhTZfPLxReY/HLWf9+JoXWOmWhNlOCqjgDT3\nzT+J/Myg5LRZHpQmzAIiW/OlvxTcjJvpZJ10szqyuUGJNTLv4aj7/NrhaLEx062JwlEUkOpo\nJ8RoM/n5MDPe1qToANFu1ppMfj7QjLcDPBQHJAg6mAASBDEIIEEQgwASBDEIIEEQgwASBDEI\nIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEI\nIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEI\nIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEI\nIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDEIIEEQgwASBDHo/4TKqNSWWPBm\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(rpart)\n",
    "library(rpart.plot)\n",
    "regtree <- rpart(cutoff~.-college_code, data=train, control=rpart.control(maxdepth = 10))\n",
    "rpart.plot(regtree, digits=-3)\n",
    "printcp(regtree)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4deda587",
   "metadata": {},
   "source": [
    "Our decision tree can scale upto a maximum depth of 7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "0d1a8def",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 136 × 19</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>crowd</th><th scope=col>government</th><th scope=col>autonomous</th><th scope=col>rank</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_ONE</th><th scope=col>linear</th><th scope=col>decision</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1002</td><td>1</td><td>96.44000</td><td> 8</td><td>300.000</td><td>240000.0</td><td>12.87391</td><td>3.400000</td><td>3.200000</td><td>3.500000</td><td>3.700000</td><td>1</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>95.25097</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1105</td><td>1</td><td>88.05000</td><td> 8</td><td>480.000</td><td>440000.0</td><td>12.70685</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>1</td><td>250</td><td>0</td><td>0</td><td>0</td><td>83.98529</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1108</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>310000.0</td><td>12.61154</td><td>3.900000</td><td>4.000000</td><td>4.300000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.03529</td><td>63.77202</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>1114</td><td>1</td><td>81.55000</td><td> 6</td><td>300.000</td><td>320000.0</td><td>12.82126</td><td>4.000000</td><td>4.400000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.98257</td><td>73.49375</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1122</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>200000.0</td><td>12.61154</td><td>2.200000</td><td>3.000000</td><td>2.000000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>57.34506</td><td>69.04323</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>1124</td><td>1</td><td>49.08000</td><td> 5</td><td>300.000</td><td>490000.0</td><td>12.34584</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.01199</td><td>70.52405</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>1126</td><td>1</td><td>67.71000</td><td> 5</td><td>300.000</td><td>170000.0</td><td>13.10216</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.53221</td><td>63.77202</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>1130</td><td>1</td><td>45.98000</td><td> 6</td><td>480.000</td><td>180000.0</td><td>12.10072</td><td>2.200000</td><td>4.000000</td><td>2.000000</td><td>1.000000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>36.59204</td><td>52.71238</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>1182</td><td>1</td><td>59.68000</td><td> 4</td><td>630.000</td><td>200000.0</td><td>13.01701</td><td>4.200000</td><td>4.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>78.07224</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>1251</td><td>1</td><td>44.34375</td><td> 6</td><td>300.000</td><td>284000.0</td><td>12.54255</td><td>3.400000</td><td>3.200000</td><td>3.400000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>60.02308</td><td>69.04323</td></tr>\n",
       "\t<tr><th scope=row>31</th><td>2008</td><td>2</td><td>97.84000</td><td>10</td><td>540.000</td><td>190000.0</td><td>13.38473</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>3.900000</td><td>1</td><td>1</td><td> 97</td><td>0</td><td>1</td><td>0</td><td>97.83733</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>33</th><td>2021</td><td>2</td><td>72.61000</td><td> 2</td><td>240.000</td><td> 80000.0</td><td>12.70685</td><td>3.800000</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>1</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.88152</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>2111</td><td>2</td><td>65.26000</td><td> 4</td><td>300.000</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>3.700000</td><td>4.300000</td><td>3.700000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.06327</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>2116</td><td>2</td><td>54.60000</td><td>10</td><td>294.000</td><td>200000.0</td><td>12.61154</td><td>3.100000</td><td>3.000000</td><td>3.000000</td><td>3.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>66.33838</td><td>52.71238</td></tr>\n",
       "\t<tr><th scope=row>41</th><td>2127</td><td>2</td><td>80.37000</td><td> 5</td><td>420.000</td><td>350000.0</td><td>12.79386</td><td>3.900000</td><td>4.300000</td><td>4.300000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.52523</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>42</th><td>2128</td><td>2</td><td>44.34375</td><td> 3</td><td>196.875</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>67.18494</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>48</th><td>2134</td><td>2</td><td>72.88000</td><td> 9</td><td>360.000</td><td>240000.0</td><td>12.67608</td><td>3.300000</td><td>3.400000</td><td>3.500000</td><td>3.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>69.44201</td><td>69.04323</td></tr>\n",
       "\t<tr><th scope=row>50</th><td>2136</td><td>2</td><td>44.34375</td><td> 9</td><td>240.000</td><td>480000.0</td><td>13.30469</td><td>4.300000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>89.85680</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>52</th><td>2138</td><td>2</td><td>64.49000</td><td> 4</td><td>270.000</td><td>250000.0</td><td>12.70685</td><td>3.900000</td><td>4.500000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.48739</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>56</th><td>2250</td><td>2</td><td>63.71000</td><td> 6</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>4.000000</td><td>4.000000</td><td>3.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.14808</td><td>55.15813</td></tr>\n",
       "\t<tr><th scope=row>58</th><td>2254</td><td>2</td><td>59.41000</td><td> 5</td><td>196.875</td><td>160000.0</td><td>12.79562</td><td>2.800000</td><td>3.000000</td><td>3.000000</td><td>2.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>56.74210</td><td>52.71238</td></tr>\n",
       "\t<tr><th scope=row>59</th><td>2255</td><td>2</td><td>71.74876</td><td> 3</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>59.76323</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>65</th><td>2641</td><td>2</td><td>71.74876</td><td> 4</td><td>382.000</td><td>322661.9</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>61.80546</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>67</th><td>3014</td><td>3</td><td>98.48000</td><td> 6</td><td>300.000</td><td>340000.0</td><td>13.21768</td><td>4.100000</td><td>3.900000</td><td>4.200000</td><td>4.300000</td><td>1</td><td>1</td><td>150</td><td>0</td><td>1</td><td>0</td><td>99.68131</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>69</th><td>3035</td><td>3</td><td>89.48000</td><td> 7</td><td>196.875</td><td>420000.0</td><td>12.97155</td><td>3.600000</td><td>3.100000</td><td>3.800000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.01919</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>73</th><td>3139</td><td>3</td><td>96.84000</td><td>10</td><td>630.000</td><td>550000.0</td><td>12.76569</td><td>4.300000</td><td>4.700000</td><td>4.300000</td><td>4.300000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>0</td><td>0</td><td>88.69525</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>75</th><td>3147</td><td>3</td><td>83.40000</td><td> 6</td><td>300.000</td><td>264000.0</td><td>12.30139</td><td>2.200000</td><td>2.400000</td><td>2.200000</td><td>2.600000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>53.97024</td><td>65.30064</td></tr>\n",
       "\t<tr><th scope=row>76</th><td>3148</td><td>3</td><td>92.28000</td><td>10</td><td>630.000</td><td>460000.0</td><td>13.30469</td><td>3.800000</td><td>3.700000</td><td>3.700000</td><td>3.900000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>77.37348</td><td>73.75159</td></tr>\n",
       "\t<tr><th scope=row>82</th><td>3182</td><td>3</td><td>98.34000</td><td> 5</td><td>300.000</td><td>600000.0</td><td>14.16617</td><td>3.800000</td><td>3.300000</td><td>3.600000</td><td>4.400000</td><td>0</td><td>0</td><td>250</td><td>0</td><td>0</td><td>0</td><td>82.17729</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>84</th><td>3184</td><td>3</td><td>96.77000</td><td>10</td><td>480.000</td><td>570000.0</td><td>13.12237</td><td>4.000000</td><td>3.900000</td><td>3.900000</td><td>4.100000</td><td>0</td><td>0</td><td>200</td><td>0</td><td>1</td><td>0</td><td>79.32101</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>⋮</th><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><th scope=row>303</th><td>6283</td><td>6</td><td>87.28000</td><td>13.0</td><td>196.875</td><td> 370000</td><td>12.61154</td><td>4.000000</td><td>4.200000</td><td>4.200000</td><td>4.000000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>92.78713</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>305</th><td>6285</td><td>6</td><td>92.61000</td><td> 6.0</td><td>240.000</td><td> 430000</td><td>12.91411</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>4.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.90717</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>307</th><td>6289</td><td>6</td><td>97.98000</td><td> 7.0</td><td>300.000</td><td> 570000</td><td>13.32122</td><td>3.900000</td><td>3.700000</td><td>4.300000</td><td>4.000000</td><td>0</td><td>1</td><td>155</td><td>0</td><td>1</td><td>0</td><td>92.27407</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>311</th><td>6303</td><td>6</td><td>75.18000</td><td> 5.0</td><td>240.000</td><td> 240000</td><td>12.98540</td><td>4.000000</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.50074</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>313</th><td>6305</td><td>6</td><td>46.17000</td><td> 5.0</td><td>210.000</td><td> 192000</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>64.01767</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>314</th><td>6307</td><td>6</td><td>83.32000</td><td>12.0</td><td>255.000</td><td> 370000</td><td>12.76569</td><td>4.100000</td><td>4.200000</td><td>4.200000</td><td>4.100000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.96029</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>320</th><td>6317</td><td>6</td><td>79.53000</td><td>11.0</td><td>630.000</td><td> 310000</td><td>12.54255</td><td>3.500000</td><td>3.300000</td><td>3.700000</td><td>3.400000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>83.93804</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>322</th><td>6319</td><td>6</td><td>63.05000</td><td> 6.0</td><td>360.000</td><td> 308000</td><td>12.76569</td><td>3.600000</td><td>3.900000</td><td>4.000000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.35820</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>324</th><td>6321</td><td>6</td><td>45.67000</td><td> 6.0</td><td>300.000</td><td> 240000</td><td>12.79386</td><td>3.200000</td><td>3.700000</td><td>3.700000</td><td>2.700000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.14082</td><td>52.71238</td></tr>\n",
       "\t<tr><th scope=row>328</th><td>6325</td><td>6</td><td>78.05000</td><td> 5.0</td><td>480.000</td><td> 230000</td><td>13.99783</td><td>3.600000</td><td>3.300000</td><td>4.200000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>79.16464</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>330</th><td>6419</td><td>6</td><td>78.35000</td><td> 6.0</td><td>360.000</td><td> 330000</td><td>12.50618</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.71905</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>331</th><td>6444</td><td>6</td><td>44.34375</td><td> 5.0</td><td>196.875</td><td> 141000</td><td>12.79562</td><td>3.200000</td><td>3.500000</td><td>4.000000</td><td>2.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.30986</td><td>52.71238</td></tr>\n",
       "\t<tr><th scope=row>337</th><td>6620</td><td>6</td><td>73.99000</td><td>13.5</td><td>196.875</td><td>1080000</td><td>13.35348</td><td>3.600000</td><td>4.200000</td><td>3.400000</td><td>3.700000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>85.04649</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>339</th><td>6622</td><td>6</td><td>85.85000</td><td> 6.0</td><td>360.000</td><td> 280000</td><td>12.76569</td><td>3.500000</td><td>3.500000</td><td>3.900000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>73.16798</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>341</th><td>6628</td><td>6</td><td>56.76500</td><td> 5.0</td><td>196.875</td><td> 400000</td><td>12.56025</td><td>3.400000</td><td>3.000000</td><td>4.000000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>75.75998</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>345</th><td>6635</td><td>6</td><td>67.11200</td><td> 9.0</td><td>420.000</td><td> 300000</td><td>12.42922</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.07599</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>347</th><td>6643</td><td>6</td><td>81.98400</td><td> 5.0</td><td>360.000</td><td> 310000</td><td>12.20608</td><td>4.200000</td><td>4.500000</td><td>4.300000</td><td>4.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>73.32382</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>348</th><td>6644</td><td>6</td><td>56.76000</td><td> 7.0</td><td>300.000</td><td> 320000</td><td>12.79386</td><td>3.000000</td><td>3.800000</td><td>3.100000</td><td>2.900000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.82040</td><td>52.71238</td></tr>\n",
       "\t<tr><th scope=row>354</th><td>6757</td><td>6</td><td>60.73000</td><td> 7.0</td><td>360.000</td><td> 310000</td><td>12.76569</td><td>3.800000</td><td>4.000000</td><td>3.700000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>74.10919</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>356</th><td>6759</td><td>6</td><td>68.70000</td><td> 5.0</td><td>270.000</td><td> 270000</td><td>12.61154</td><td>4.600000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>80.30998</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>358</th><td>6766</td><td>6</td><td>63.08000</td><td> 5.0</td><td>300.000</td><td> 260000</td><td>12.76569</td><td>4.700000</td><td>5.000000</td><td>5.000000</td><td>4.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>76.38859</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>362</th><td>6770</td><td>6</td><td>77.03000</td><td> 5.0</td><td>300.000</td><td> 410000</td><td>12.38840</td><td>3.800000</td><td>4.100000</td><td>3.600000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.97872</td><td>70.52405</td></tr>\n",
       "\t<tr><th scope=row>364</th><td>6772</td><td>6</td><td>87.28000</td><td> 6.0</td><td>510.000</td><td> 400000</td><td>12.57764</td><td>4.000000</td><td>4.000000</td><td>3.900000</td><td>4.400000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.21836</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>365</th><td>6780</td><td>6</td><td>71.76000</td><td>11.0</td><td>420.000</td><td> 250000</td><td>12.38840</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.23241</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>371</th><td>6795</td><td>6</td><td>52.82000</td><td> 4.0</td><td>210.000</td><td> 240000</td><td>12.79562</td><td>3.000000</td><td>3.000000</td><td>3.300000</td><td>3.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.36720</td><td>52.71238</td></tr>\n",
       "\t<tr><th scope=row>373</th><td>6797</td><td>6</td><td>74.20000</td><td> 5.0</td><td>240.000</td><td> 320000</td><td>12.79562</td><td>4.100000</td><td>4.400000</td><td>4.400000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.90800</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>375</th><td>6803</td><td>6</td><td>74.51000</td><td> 6.0</td><td>360.000</td><td> 240000</td><td>12.89922</td><td>4.100000</td><td>4.100000</td><td>4.200000</td><td>4.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.98160</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>379</th><td>6811</td><td>6</td><td>44.34375</td><td>13.5</td><td>630.000</td><td> 620000</td><td>12.84793</td><td>4.100000</td><td>4.700000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>78.02752</td><td>73.75159</td></tr>\n",
       "\t<tr><th scope=row>381</th><td>6822</td><td>6</td><td>96.46000</td><td> 9.0</td><td>480.000</td><td> 400000</td><td>12.50618</td><td>4.000000</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.30797</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>382</th><td>6834</td><td>6</td><td>80.45000</td><td> 6.0</td><td>360.000</td><td> 300000</td><td>12.61154</td><td>3.000000</td><td>3.400000</td><td>3.100000</td><td>3.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.83997</td><td>81.86522</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 136 × 19\n",
       "\\begin{tabular}{r|lllllllllllllllllll}\n",
       "  & college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & crowd & government & autonomous & rank & new\\_ban & hostel\\_BOTH & hostel\\_ONE & linear & decision\\\\\n",
       "  & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <int> & <int> & <int> & <int> & <int> & <int> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1002 & 1 & 96.44000 &  8 & 300.000 & 240000.0 & 12.87391 & 3.400000 & 3.200000 & 3.500000 & 3.700000 & 1 & 1 & 301 & 0 & 1 & 0 & 95.25097 & 88.05211\\\\\n",
       "\t5 & 1105 & 1 & 88.05000 &  8 & 480.000 & 440000.0 & 12.70685 & 3.900000 & 4.000000 & 3.900000 & 4.200000 & 0 & 1 & 250 & 0 & 0 & 0 & 83.98529 & 97.36824\\\\\n",
       "\t7 & 1108 & 1 & 44.34375 &  5 & 300.000 & 310000.0 & 12.61154 & 3.900000 & 4.000000 & 4.300000 & 3.500000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.03529 & 63.77202\\\\\n",
       "\t8 & 1114 & 1 & 81.55000 &  6 & 300.000 & 320000.0 & 12.82126 & 4.000000 & 4.400000 & 3.900000 & 4.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.98257 & 73.49375\\\\\n",
       "\t14 & 1122 & 1 & 44.34375 &  5 & 300.000 & 200000.0 & 12.61154 & 2.200000 & 3.000000 & 2.000000 & 3.500000 & 0 & 0 & 301 & 1 & 0 & 0 & 57.34506 & 69.04323\\\\\n",
       "\t16 & 1124 & 1 & 49.08000 &  5 & 300.000 & 490000.0 & 12.34584 & 3.600000 & 4.300000 & 3.600000 & 3.500000 & 0 & 0 & 301 & 1 & 1 & 0 & 59.01199 & 70.52405\\\\\n",
       "\t18 & 1126 & 1 & 67.71000 &  5 & 300.000 & 170000.0 & 13.10216 & 5.000000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.53221 & 63.77202\\\\\n",
       "\t22 & 1130 & 1 & 45.98000 &  6 & 480.000 & 180000.0 & 12.10072 & 2.200000 & 4.000000 & 2.000000 & 1.000000 & 0 & 0 & 301 & 1 & 1 & 0 & 36.59204 & 52.71238\\\\\n",
       "\t24 & 1182 & 1 & 59.68000 &  4 & 630.000 & 200000.0 & 13.01701 & 4.200000 & 4.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 78.07224 & 59.83230\\\\\n",
       "\t25 & 1251 & 1 & 44.34375 &  6 & 300.000 & 284000.0 & 12.54255 & 3.400000 & 3.200000 & 3.400000 & 3.600000 & 0 & 0 & 301 & 1 & 1 & 0 & 60.02308 & 69.04323\\\\\n",
       "\t31 & 2008 & 2 & 97.84000 & 10 & 540.000 & 190000.0 & 13.38473 & 3.900000 & 3.800000 & 3.900000 & 3.900000 & 1 & 1 &  97 & 0 & 1 & 0 & 97.83733 & 97.36824\\\\\n",
       "\t33 & 2021 & 2 & 72.61000 &  2 & 240.000 &  80000.0 & 12.70685 & 3.800000 & 3.900000 & 4.000000 & 3.900000 & 1 & 0 & 301 & 0 & 1 & 0 & 77.88152 & 59.83230\\\\\n",
       "\t35 & 2111 & 2 & 65.26000 &  4 & 300.000 & 170000.0 & 12.61154 & 3.800000 & 3.700000 & 4.300000 & 3.700000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.06327 & 59.83230\\\\\n",
       "\t39 & 2116 & 2 & 54.60000 & 10 & 294.000 & 200000.0 & 12.61154 & 3.100000 & 3.000000 & 3.000000 & 3.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 66.33838 & 52.71238\\\\\n",
       "\t41 & 2127 & 2 & 80.37000 &  5 & 420.000 & 350000.0 & 12.79386 & 3.900000 & 4.300000 & 4.300000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.52523 & 88.68862\\\\\n",
       "\t42 & 2128 & 2 & 44.34375 &  3 & 196.875 & 170000.0 & 12.61154 & 3.800000 & 4.000000 & 4.000000 & 5.000000 & 0 & 0 & 301 & 1 & 1 & 0 & 67.18494 & 59.83230\\\\\n",
       "\t48 & 2134 & 2 & 72.88000 &  9 & 360.000 & 240000.0 & 12.67608 & 3.300000 & 3.400000 & 3.500000 & 3.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 69.44201 & 69.04323\\\\\n",
       "\t50 & 2136 & 2 & 44.34375 &  9 & 240.000 & 480000.0 & 13.30469 & 4.300000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 89.85680 & 88.68862\\\\\n",
       "\t52 & 2138 & 2 & 64.49000 &  4 & 270.000 & 250000.0 & 12.70685 & 3.900000 & 4.500000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 81.48739 & 59.83230\\\\\n",
       "\t56 & 2250 & 2 & 63.71000 &  6 & 196.875 & 220000.0 & 12.79562 & 4.000000 & 4.000000 & 3.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 71.14808 & 55.15813\\\\\n",
       "\t58 & 2254 & 2 & 59.41000 &  5 & 196.875 & 160000.0 & 12.79562 & 2.800000 & 3.000000 & 3.000000 & 2.000000 & 0 & 0 & 301 & 0 & 0 & 0 & 56.74210 & 52.71238\\\\\n",
       "\t59 & 2255 & 2 & 71.74876 &  3 & 196.875 & 220000.0 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 59.76323 & 59.83230\\\\\n",
       "\t65 & 2641 & 2 & 71.74876 &  4 & 382.000 & 322661.9 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 61.80546 & 59.83230\\\\\n",
       "\t67 & 3014 & 3 & 98.48000 &  6 & 300.000 & 340000.0 & 13.21768 & 4.100000 & 3.900000 & 4.200000 & 4.300000 & 1 & 1 & 150 & 0 & 1 & 0 & 99.68131 & 97.36824\\\\\n",
       "\t69 & 3035 & 3 & 89.48000 &  7 & 196.875 & 420000.0 & 12.97155 & 3.600000 & 3.100000 & 3.800000 & 3.600000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.01919 & 88.68862\\\\\n",
       "\t73 & 3139 & 3 & 96.84000 & 10 & 630.000 & 550000.0 & 12.76569 & 4.300000 & 4.700000 & 4.300000 & 4.300000 & 0 & 1 & 301 & 0 & 0 & 0 & 88.69525 & 88.05211\\\\\n",
       "\t75 & 3147 & 3 & 83.40000 &  6 & 300.000 & 264000.0 & 12.30139 & 2.200000 & 2.400000 & 2.200000 & 2.600000 & 0 & 0 & 301 & 1 & 1 & 0 & 53.97024 & 65.30064\\\\\n",
       "\t76 & 3148 & 3 & 92.28000 & 10 & 630.000 & 460000.0 & 13.30469 & 3.800000 & 3.700000 & 3.700000 & 3.900000 & 0 & 0 & 301 & 0 & 0 & 0 & 77.37348 & 73.75159\\\\\n",
       "\t82 & 3182 & 3 & 98.34000 &  5 & 300.000 & 600000.0 & 14.16617 & 3.800000 & 3.300000 & 3.600000 & 4.400000 & 0 & 0 & 250 & 0 & 0 & 0 & 82.17729 & 88.68862\\\\\n",
       "\t84 & 3184 & 3 & 96.77000 & 10 & 480.000 & 570000.0 & 13.12237 & 4.000000 & 3.900000 & 3.900000 & 4.100000 & 0 & 0 & 200 & 0 & 1 & 0 & 79.32101 & 88.68862\\\\\n",
       "\t⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t303 & 6283 & 6 & 87.28000 & 13.0 & 196.875 &  370000 & 12.61154 & 4.000000 & 4.200000 & 4.200000 & 4.000000 & 0 & 1 & 301 & 0 & 1 & 0 & 92.78713 & 88.05211\\\\\n",
       "\t305 & 6285 & 6 & 92.61000 &  6.0 & 240.000 &  430000 & 12.91411 & 3.900000 & 3.800000 & 3.900000 & 4.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 77.90717 & 88.68862\\\\\n",
       "\t307 & 6289 & 6 & 97.98000 &  7.0 & 300.000 &  570000 & 13.32122 & 3.900000 & 3.700000 & 4.300000 & 4.000000 & 0 & 1 & 155 & 0 & 1 & 0 & 92.27407 & 97.36824\\\\\n",
       "\t311 & 6303 & 6 & 75.18000 &  5.0 & 240.000 &  240000 & 12.98540 & 4.000000 & 4.200000 & 4.100000 & 4.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.50074 & 68.62492\\\\\n",
       "\t313 & 6305 & 6 & 46.17000 &  5.0 & 210.000 &  192000 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 64.01767 & 68.62492\\\\\n",
       "\t314 & 6307 & 6 & 83.32000 & 12.0 & 255.000 &  370000 & 12.76569 & 4.100000 & 4.200000 & 4.200000 & 4.100000 & 0 & 0 & 301 & 0 & 1 & 0 & 81.96029 & 88.68862\\\\\n",
       "\t320 & 6317 & 6 & 79.53000 & 11.0 & 630.000 &  310000 & 12.54255 & 3.500000 & 3.300000 & 3.700000 & 3.400000 & 0 & 1 & 301 & 0 & 1 & 0 & 83.93804 & 88.05211\\\\\n",
       "\t322 & 6319 & 6 & 63.05000 &  6.0 & 360.000 &  308000 & 12.76569 & 3.600000 & 3.900000 & 4.000000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.35820 & 81.86522\\\\\n",
       "\t324 & 6321 & 6 & 45.67000 &  6.0 & 300.000 &  240000 & 12.79386 & 3.200000 & 3.700000 & 3.700000 & 2.700000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.14082 & 52.71238\\\\\n",
       "\t328 & 6325 & 6 & 78.05000 &  5.0 & 480.000 &  230000 & 13.99783 & 3.600000 & 3.300000 & 4.200000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 79.16464 & 68.62492\\\\\n",
       "\t330 & 6419 & 6 & 78.35000 &  6.0 & 360.000 &  330000 & 12.50618 & 4.200000 & 4.100000 & 4.200000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 71.71905 & 81.86522\\\\\n",
       "\t331 & 6444 & 6 & 44.34375 &  5.0 & 196.875 &  141000 & 12.79562 & 3.200000 & 3.500000 & 4.000000 & 2.500000 & 0 & 0 & 301 & 1 & 1 & 0 & 59.30986 & 52.71238\\\\\n",
       "\t337 & 6620 & 6 & 73.99000 & 13.5 & 196.875 & 1080000 & 13.35348 & 3.600000 & 4.200000 & 3.400000 & 3.700000 & 0 & 0 & 301 & 1 & 1 & 0 & 85.04649 & 88.68862\\\\\n",
       "\t339 & 6622 & 6 & 85.85000 &  6.0 & 360.000 &  280000 & 12.76569 & 3.500000 & 3.500000 & 3.900000 & 3.600000 & 0 & 0 & 301 & 0 & 0 & 0 & 73.16798 & 68.62492\\\\\n",
       "\t341 & 6628 & 6 & 56.76500 &  5.0 & 196.875 &  400000 & 12.56025 & 3.400000 & 3.000000 & 4.000000 & 3.500000 & 0 & 0 & 301 & 0 & 0 & 1 & 75.75998 & 88.68862\\\\\n",
       "\t345 & 6635 & 6 & 67.11200 &  9.0 & 420.000 &  300000 & 12.42922 & 3.800000 & 4.000000 & 4.000000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 76.07599 & 81.86522\\\\\n",
       "\t347 & 6643 & 6 & 81.98400 &  5.0 & 360.000 &  310000 & 12.20608 & 4.200000 & 4.500000 & 4.300000 & 4.500000 & 0 & 0 & 301 & 0 & 1 & 0 & 73.32382 & 81.86522\\\\\n",
       "\t348 & 6644 & 6 & 56.76000 &  7.0 & 300.000 &  320000 & 12.79386 & 3.000000 & 3.800000 & 3.100000 & 2.900000 & 0 & 0 & 301 & 0 & 1 & 0 & 68.82040 & 52.71238\\\\\n",
       "\t354 & 6757 & 6 & 60.73000 &  7.0 & 360.000 &  310000 & 12.76569 & 3.800000 & 4.000000 & 3.700000 & 4.000000 & 0 & 0 & 301 & 0 & 0 & 0 & 74.10919 & 81.86522\\\\\n",
       "\t356 & 6759 & 6 & 68.70000 &  5.0 & 270.000 &  270000 & 12.61154 & 4.600000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 80.30998 & 68.62492\\\\\n",
       "\t358 & 6766 & 6 & 63.08000 &  5.0 & 300.000 &  260000 & 12.76569 & 4.700000 & 5.000000 & 5.000000 & 4.500000 & 0 & 0 & 301 & 0 & 0 & 0 & 76.38859 & 68.62492\\\\\n",
       "\t362 & 6770 & 6 & 77.03000 &  5.0 & 300.000 &  410000 & 12.38840 & 3.800000 & 4.100000 & 3.600000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.97872 & 70.52405\\\\\n",
       "\t364 & 6772 & 6 & 87.28000 &  6.0 & 510.000 &  400000 & 12.57764 & 4.000000 & 4.000000 & 3.900000 & 4.400000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.21836 & 88.68862\\\\\n",
       "\t365 & 6780 & 6 & 71.76000 & 11.0 & 420.000 &  250000 & 12.38840 & 4.000000 & 4.000000 & 4.000000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 76.23241 & 68.62492\\\\\n",
       "\t371 & 6795 & 6 & 52.82000 &  4.0 & 210.000 &  240000 & 12.79562 & 3.000000 & 3.000000 & 3.300000 & 3.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.36720 & 52.71238\\\\\n",
       "\t373 & 6797 & 6 & 74.20000 &  5.0 & 240.000 &  320000 & 12.79562 & 4.100000 & 4.400000 & 4.400000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.90800 & 81.86522\\\\\n",
       "\t375 & 6803 & 6 & 74.51000 &  6.0 & 360.000 &  240000 & 12.89922 & 4.100000 & 4.100000 & 4.200000 & 4.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.98160 & 68.62492\\\\\n",
       "\t379 & 6811 & 6 & 44.34375 & 13.5 & 630.000 &  620000 & 12.84793 & 4.100000 & 4.700000 & 3.900000 & 4.200000 & 0 & 0 & 301 & 1 & 1 & 0 & 78.02752 & 73.75159\\\\\n",
       "\t381 & 6822 & 6 & 96.46000 &  9.0 & 480.000 &  400000 & 12.50618 & 4.000000 & 3.600000 & 4.300000 & 3.600000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.30797 & 88.68862\\\\\n",
       "\t382 & 6834 & 6 & 80.45000 &  6.0 & 360.000 &  300000 & 12.61154 & 3.000000 & 3.400000 & 3.100000 & 3.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 68.83997 & 81.86522\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 136 × 19\n",
       "\n",
       "| <!--/--> | college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;dbl&gt; | intake &lt;dbl&gt; | fees &lt;dbl&gt; | salary &lt;dbl&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | crowd &lt;dbl&gt; | government &lt;int&gt; | autonomous &lt;int&gt; | rank &lt;int&gt; | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_ONE &lt;int&gt; | linear &lt;dbl&gt; | decision &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1002 | 1 | 96.44000 |  8 | 300.000 | 240000.0 | 12.87391 | 3.400000 | 3.200000 | 3.500000 | 3.700000 | 1 | 1 | 301 | 0 | 1 | 0 | 95.25097 | 88.05211 |\n",
       "| 5 | 1105 | 1 | 88.05000 |  8 | 480.000 | 440000.0 | 12.70685 | 3.900000 | 4.000000 | 3.900000 | 4.200000 | 0 | 1 | 250 | 0 | 0 | 0 | 83.98529 | 97.36824 |\n",
       "| 7 | 1108 | 1 | 44.34375 |  5 | 300.000 | 310000.0 | 12.61154 | 3.900000 | 4.000000 | 4.300000 | 3.500000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.03529 | 63.77202 |\n",
       "| 8 | 1114 | 1 | 81.55000 |  6 | 300.000 | 320000.0 | 12.82126 | 4.000000 | 4.400000 | 3.900000 | 4.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.98257 | 73.49375 |\n",
       "| 14 | 1122 | 1 | 44.34375 |  5 | 300.000 | 200000.0 | 12.61154 | 2.200000 | 3.000000 | 2.000000 | 3.500000 | 0 | 0 | 301 | 1 | 0 | 0 | 57.34506 | 69.04323 |\n",
       "| 16 | 1124 | 1 | 49.08000 |  5 | 300.000 | 490000.0 | 12.34584 | 3.600000 | 4.300000 | 3.600000 | 3.500000 | 0 | 0 | 301 | 1 | 1 | 0 | 59.01199 | 70.52405 |\n",
       "| 18 | 1126 | 1 | 67.71000 |  5 | 300.000 | 170000.0 | 13.10216 | 5.000000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.53221 | 63.77202 |\n",
       "| 22 | 1130 | 1 | 45.98000 |  6 | 480.000 | 180000.0 | 12.10072 | 2.200000 | 4.000000 | 2.000000 | 1.000000 | 0 | 0 | 301 | 1 | 1 | 0 | 36.59204 | 52.71238 |\n",
       "| 24 | 1182 | 1 | 59.68000 |  4 | 630.000 | 200000.0 | 13.01701 | 4.200000 | 4.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 78.07224 | 59.83230 |\n",
       "| 25 | 1251 | 1 | 44.34375 |  6 | 300.000 | 284000.0 | 12.54255 | 3.400000 | 3.200000 | 3.400000 | 3.600000 | 0 | 0 | 301 | 1 | 1 | 0 | 60.02308 | 69.04323 |\n",
       "| 31 | 2008 | 2 | 97.84000 | 10 | 540.000 | 190000.0 | 13.38473 | 3.900000 | 3.800000 | 3.900000 | 3.900000 | 1 | 1 |  97 | 0 | 1 | 0 | 97.83733 | 97.36824 |\n",
       "| 33 | 2021 | 2 | 72.61000 |  2 | 240.000 |  80000.0 | 12.70685 | 3.800000 | 3.900000 | 4.000000 | 3.900000 | 1 | 0 | 301 | 0 | 1 | 0 | 77.88152 | 59.83230 |\n",
       "| 35 | 2111 | 2 | 65.26000 |  4 | 300.000 | 170000.0 | 12.61154 | 3.800000 | 3.700000 | 4.300000 | 3.700000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.06327 | 59.83230 |\n",
       "| 39 | 2116 | 2 | 54.60000 | 10 | 294.000 | 200000.0 | 12.61154 | 3.100000 | 3.000000 | 3.000000 | 3.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 66.33838 | 52.71238 |\n",
       "| 41 | 2127 | 2 | 80.37000 |  5 | 420.000 | 350000.0 | 12.79386 | 3.900000 | 4.300000 | 4.300000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.52523 | 88.68862 |\n",
       "| 42 | 2128 | 2 | 44.34375 |  3 | 196.875 | 170000.0 | 12.61154 | 3.800000 | 4.000000 | 4.000000 | 5.000000 | 0 | 0 | 301 | 1 | 1 | 0 | 67.18494 | 59.83230 |\n",
       "| 48 | 2134 | 2 | 72.88000 |  9 | 360.000 | 240000.0 | 12.67608 | 3.300000 | 3.400000 | 3.500000 | 3.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 69.44201 | 69.04323 |\n",
       "| 50 | 2136 | 2 | 44.34375 |  9 | 240.000 | 480000.0 | 13.30469 | 4.300000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 89.85680 | 88.68862 |\n",
       "| 52 | 2138 | 2 | 64.49000 |  4 | 270.000 | 250000.0 | 12.70685 | 3.900000 | 4.500000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 81.48739 | 59.83230 |\n",
       "| 56 | 2250 | 2 | 63.71000 |  6 | 196.875 | 220000.0 | 12.79562 | 4.000000 | 4.000000 | 3.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 71.14808 | 55.15813 |\n",
       "| 58 | 2254 | 2 | 59.41000 |  5 | 196.875 | 160000.0 | 12.79562 | 2.800000 | 3.000000 | 3.000000 | 2.000000 | 0 | 0 | 301 | 0 | 0 | 0 | 56.74210 | 52.71238 |\n",
       "| 59 | 2255 | 2 | 71.74876 |  3 | 196.875 | 220000.0 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 59.76323 | 59.83230 |\n",
       "| 65 | 2641 | 2 | 71.74876 |  4 | 382.000 | 322661.9 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 61.80546 | 59.83230 |\n",
       "| 67 | 3014 | 3 | 98.48000 |  6 | 300.000 | 340000.0 | 13.21768 | 4.100000 | 3.900000 | 4.200000 | 4.300000 | 1 | 1 | 150 | 0 | 1 | 0 | 99.68131 | 97.36824 |\n",
       "| 69 | 3035 | 3 | 89.48000 |  7 | 196.875 | 420000.0 | 12.97155 | 3.600000 | 3.100000 | 3.800000 | 3.600000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.01919 | 88.68862 |\n",
       "| 73 | 3139 | 3 | 96.84000 | 10 | 630.000 | 550000.0 | 12.76569 | 4.300000 | 4.700000 | 4.300000 | 4.300000 | 0 | 1 | 301 | 0 | 0 | 0 | 88.69525 | 88.05211 |\n",
       "| 75 | 3147 | 3 | 83.40000 |  6 | 300.000 | 264000.0 | 12.30139 | 2.200000 | 2.400000 | 2.200000 | 2.600000 | 0 | 0 | 301 | 1 | 1 | 0 | 53.97024 | 65.30064 |\n",
       "| 76 | 3148 | 3 | 92.28000 | 10 | 630.000 | 460000.0 | 13.30469 | 3.800000 | 3.700000 | 3.700000 | 3.900000 | 0 | 0 | 301 | 0 | 0 | 0 | 77.37348 | 73.75159 |\n",
       "| 82 | 3182 | 3 | 98.34000 |  5 | 300.000 | 600000.0 | 14.16617 | 3.800000 | 3.300000 | 3.600000 | 4.400000 | 0 | 0 | 250 | 0 | 0 | 0 | 82.17729 | 88.68862 |\n",
       "| 84 | 3184 | 3 | 96.77000 | 10 | 480.000 | 570000.0 | 13.12237 | 4.000000 | 3.900000 | 3.900000 | 4.100000 | 0 | 0 | 200 | 0 | 1 | 0 | 79.32101 | 88.68862 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 303 | 6283 | 6 | 87.28000 | 13.0 | 196.875 |  370000 | 12.61154 | 4.000000 | 4.200000 | 4.200000 | 4.000000 | 0 | 1 | 301 | 0 | 1 | 0 | 92.78713 | 88.05211 |\n",
       "| 305 | 6285 | 6 | 92.61000 |  6.0 | 240.000 |  430000 | 12.91411 | 3.900000 | 3.800000 | 3.900000 | 4.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 77.90717 | 88.68862 |\n",
       "| 307 | 6289 | 6 | 97.98000 |  7.0 | 300.000 |  570000 | 13.32122 | 3.900000 | 3.700000 | 4.300000 | 4.000000 | 0 | 1 | 155 | 0 | 1 | 0 | 92.27407 | 97.36824 |\n",
       "| 311 | 6303 | 6 | 75.18000 |  5.0 | 240.000 |  240000 | 12.98540 | 4.000000 | 4.200000 | 4.100000 | 4.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.50074 | 68.62492 |\n",
       "| 313 | 6305 | 6 | 46.17000 |  5.0 | 210.000 |  192000 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 64.01767 | 68.62492 |\n",
       "| 314 | 6307 | 6 | 83.32000 | 12.0 | 255.000 |  370000 | 12.76569 | 4.100000 | 4.200000 | 4.200000 | 4.100000 | 0 | 0 | 301 | 0 | 1 | 0 | 81.96029 | 88.68862 |\n",
       "| 320 | 6317 | 6 | 79.53000 | 11.0 | 630.000 |  310000 | 12.54255 | 3.500000 | 3.300000 | 3.700000 | 3.400000 | 0 | 1 | 301 | 0 | 1 | 0 | 83.93804 | 88.05211 |\n",
       "| 322 | 6319 | 6 | 63.05000 |  6.0 | 360.000 |  308000 | 12.76569 | 3.600000 | 3.900000 | 4.000000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.35820 | 81.86522 |\n",
       "| 324 | 6321 | 6 | 45.67000 |  6.0 | 300.000 |  240000 | 12.79386 | 3.200000 | 3.700000 | 3.700000 | 2.700000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.14082 | 52.71238 |\n",
       "| 328 | 6325 | 6 | 78.05000 |  5.0 | 480.000 |  230000 | 13.99783 | 3.600000 | 3.300000 | 4.200000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 79.16464 | 68.62492 |\n",
       "| 330 | 6419 | 6 | 78.35000 |  6.0 | 360.000 |  330000 | 12.50618 | 4.200000 | 4.100000 | 4.200000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 71.71905 | 81.86522 |\n",
       "| 331 | 6444 | 6 | 44.34375 |  5.0 | 196.875 |  141000 | 12.79562 | 3.200000 | 3.500000 | 4.000000 | 2.500000 | 0 | 0 | 301 | 1 | 1 | 0 | 59.30986 | 52.71238 |\n",
       "| 337 | 6620 | 6 | 73.99000 | 13.5 | 196.875 | 1080000 | 13.35348 | 3.600000 | 4.200000 | 3.400000 | 3.700000 | 0 | 0 | 301 | 1 | 1 | 0 | 85.04649 | 88.68862 |\n",
       "| 339 | 6622 | 6 | 85.85000 |  6.0 | 360.000 |  280000 | 12.76569 | 3.500000 | 3.500000 | 3.900000 | 3.600000 | 0 | 0 | 301 | 0 | 0 | 0 | 73.16798 | 68.62492 |\n",
       "| 341 | 6628 | 6 | 56.76500 |  5.0 | 196.875 |  400000 | 12.56025 | 3.400000 | 3.000000 | 4.000000 | 3.500000 | 0 | 0 | 301 | 0 | 0 | 1 | 75.75998 | 88.68862 |\n",
       "| 345 | 6635 | 6 | 67.11200 |  9.0 | 420.000 |  300000 | 12.42922 | 3.800000 | 4.000000 | 4.000000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 76.07599 | 81.86522 |\n",
       "| 347 | 6643 | 6 | 81.98400 |  5.0 | 360.000 |  310000 | 12.20608 | 4.200000 | 4.500000 | 4.300000 | 4.500000 | 0 | 0 | 301 | 0 | 1 | 0 | 73.32382 | 81.86522 |\n",
       "| 348 | 6644 | 6 | 56.76000 |  7.0 | 300.000 |  320000 | 12.79386 | 3.000000 | 3.800000 | 3.100000 | 2.900000 | 0 | 0 | 301 | 0 | 1 | 0 | 68.82040 | 52.71238 |\n",
       "| 354 | 6757 | 6 | 60.73000 |  7.0 | 360.000 |  310000 | 12.76569 | 3.800000 | 4.000000 | 3.700000 | 4.000000 | 0 | 0 | 301 | 0 | 0 | 0 | 74.10919 | 81.86522 |\n",
       "| 356 | 6759 | 6 | 68.70000 |  5.0 | 270.000 |  270000 | 12.61154 | 4.600000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 80.30998 | 68.62492 |\n",
       "| 358 | 6766 | 6 | 63.08000 |  5.0 | 300.000 |  260000 | 12.76569 | 4.700000 | 5.000000 | 5.000000 | 4.500000 | 0 | 0 | 301 | 0 | 0 | 0 | 76.38859 | 68.62492 |\n",
       "| 362 | 6770 | 6 | 77.03000 |  5.0 | 300.000 |  410000 | 12.38840 | 3.800000 | 4.100000 | 3.600000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.97872 | 70.52405 |\n",
       "| 364 | 6772 | 6 | 87.28000 |  6.0 | 510.000 |  400000 | 12.57764 | 4.000000 | 4.000000 | 3.900000 | 4.400000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.21836 | 88.68862 |\n",
       "| 365 | 6780 | 6 | 71.76000 | 11.0 | 420.000 |  250000 | 12.38840 | 4.000000 | 4.000000 | 4.000000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 76.23241 | 68.62492 |\n",
       "| 371 | 6795 | 6 | 52.82000 |  4.0 | 210.000 |  240000 | 12.79562 | 3.000000 | 3.000000 | 3.300000 | 3.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.36720 | 52.71238 |\n",
       "| 373 | 6797 | 6 | 74.20000 |  5.0 | 240.000 |  320000 | 12.79562 | 4.100000 | 4.400000 | 4.400000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.90800 | 81.86522 |\n",
       "| 375 | 6803 | 6 | 74.51000 |  6.0 | 360.000 |  240000 | 12.89922 | 4.100000 | 4.100000 | 4.200000 | 4.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.98160 | 68.62492 |\n",
       "| 379 | 6811 | 6 | 44.34375 | 13.5 | 630.000 |  620000 | 12.84793 | 4.100000 | 4.700000 | 3.900000 | 4.200000 | 0 | 0 | 301 | 1 | 1 | 0 | 78.02752 | 73.75159 |\n",
       "| 381 | 6822 | 6 | 96.46000 |  9.0 | 480.000 |  400000 | 12.50618 | 4.000000 | 3.600000 | 4.300000 | 3.600000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.30797 | 88.68862 |\n",
       "| 382 | 6834 | 6 | 80.45000 |  6.0 | 360.000 |  300000 | 12.61154 | 3.000000 | 3.400000 | 3.100000 | 3.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 68.83997 | 81.86522 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff   courses intake  fees     salary   rating  \n",
       "1   1002         1        96.44000  8      300.000 240000.0 12.87391 3.400000\n",
       "5   1105         1        88.05000  8      480.000 440000.0 12.70685 3.900000\n",
       "7   1108         1        44.34375  5      300.000 310000.0 12.61154 3.900000\n",
       "8   1114         1        81.55000  6      300.000 320000.0 12.82126 4.000000\n",
       "14  1122         1        44.34375  5      300.000 200000.0 12.61154 2.200000\n",
       "16  1124         1        49.08000  5      300.000 490000.0 12.34584 3.600000\n",
       "18  1126         1        67.71000  5      300.000 170000.0 13.10216 5.000000\n",
       "22  1130         1        45.98000  6      480.000 180000.0 12.10072 2.200000\n",
       "24  1182         1        59.68000  4      630.000 200000.0 13.01701 4.200000\n",
       "25  1251         1        44.34375  6      300.000 284000.0 12.54255 3.400000\n",
       "31  2008         2        97.84000 10      540.000 190000.0 13.38473 3.900000\n",
       "33  2021         2        72.61000  2      240.000  80000.0 12.70685 3.800000\n",
       "35  2111         2        65.26000  4      300.000 170000.0 12.61154 3.800000\n",
       "39  2116         2        54.60000 10      294.000 200000.0 12.61154 3.100000\n",
       "41  2127         2        80.37000  5      420.000 350000.0 12.79386 3.900000\n",
       "42  2128         2        44.34375  3      196.875 170000.0 12.61154 3.800000\n",
       "48  2134         2        72.88000  9      360.000 240000.0 12.67608 3.300000\n",
       "50  2136         2        44.34375  9      240.000 480000.0 13.30469 4.300000\n",
       "52  2138         2        64.49000  4      270.000 250000.0 12.70685 3.900000\n",
       "56  2250         2        63.71000  6      196.875 220000.0 12.79562 4.000000\n",
       "58  2254         2        59.41000  5      196.875 160000.0 12.79562 2.800000\n",
       "59  2255         2        71.74876  3      196.875 220000.0 12.79562 3.666295\n",
       "65  2641         2        71.74876  4      382.000 322661.9 12.79562 3.666295\n",
       "67  3014         3        98.48000  6      300.000 340000.0 13.21768 4.100000\n",
       "69  3035         3        89.48000  7      196.875 420000.0 12.97155 3.600000\n",
       "73  3139         3        96.84000 10      630.000 550000.0 12.76569 4.300000\n",
       "75  3147         3        83.40000  6      300.000 264000.0 12.30139 2.200000\n",
       "76  3148         3        92.28000 10      630.000 460000.0 13.30469 3.800000\n",
       "82  3182         3        98.34000  5      300.000 600000.0 14.16617 3.800000\n",
       "84  3184         3        96.77000 10      480.000 570000.0 13.12237 4.000000\n",
       "⋮   ⋮            ⋮        ⋮        ⋮       ⋮       ⋮        ⋮        ⋮       \n",
       "303 6283         6        87.28000 13.0    196.875  370000  12.61154 4.000000\n",
       "305 6285         6        92.61000  6.0    240.000  430000  12.91411 3.900000\n",
       "307 6289         6        97.98000  7.0    300.000  570000  13.32122 3.900000\n",
       "311 6303         6        75.18000  5.0    240.000  240000  12.98540 4.000000\n",
       "313 6305         6        46.17000  5.0    210.000  192000  12.79562 3.666295\n",
       "314 6307         6        83.32000 12.0    255.000  370000  12.76569 4.100000\n",
       "320 6317         6        79.53000 11.0    630.000  310000  12.54255 3.500000\n",
       "322 6319         6        63.05000  6.0    360.000  308000  12.76569 3.600000\n",
       "324 6321         6        45.67000  6.0    300.000  240000  12.79386 3.200000\n",
       "328 6325         6        78.05000  5.0    480.000  230000  13.99783 3.600000\n",
       "330 6419         6        78.35000  6.0    360.000  330000  12.50618 4.200000\n",
       "331 6444         6        44.34375  5.0    196.875  141000  12.79562 3.200000\n",
       "337 6620         6        73.99000 13.5    196.875 1080000  13.35348 3.600000\n",
       "339 6622         6        85.85000  6.0    360.000  280000  12.76569 3.500000\n",
       "341 6628         6        56.76500  5.0    196.875  400000  12.56025 3.400000\n",
       "345 6635         6        67.11200  9.0    420.000  300000  12.42922 3.800000\n",
       "347 6643         6        81.98400  5.0    360.000  310000  12.20608 4.200000\n",
       "348 6644         6        56.76000  7.0    300.000  320000  12.79386 3.000000\n",
       "354 6757         6        60.73000  7.0    360.000  310000  12.76569 3.800000\n",
       "356 6759         6        68.70000  5.0    270.000  270000  12.61154 4.600000\n",
       "358 6766         6        63.08000  5.0    300.000  260000  12.76569 4.700000\n",
       "362 6770         6        77.03000  5.0    300.000  410000  12.38840 3.800000\n",
       "364 6772         6        87.28000  6.0    510.000  400000  12.57764 4.000000\n",
       "365 6780         6        71.76000 11.0    420.000  250000  12.38840 4.000000\n",
       "371 6795         6        52.82000  4.0    210.000  240000  12.79562 3.000000\n",
       "373 6797         6        74.20000  5.0    240.000  320000  12.79562 4.100000\n",
       "375 6803         6        74.51000  6.0    360.000  240000  12.89922 4.100000\n",
       "379 6811         6        44.34375 13.5    630.000  620000  12.84793 4.100000\n",
       "381 6822         6        96.46000  9.0    480.000  400000  12.50618 4.000000\n",
       "382 6834         6        80.45000  6.0    360.000  300000  12.61154 3.000000\n",
       "    infrastructure faculty  crowd    government autonomous rank new_ban\n",
       "1   3.200000       3.500000 3.700000 1          1          301  0      \n",
       "5   4.000000       3.900000 4.200000 0          1          250  0      \n",
       "7   4.000000       4.300000 3.500000 0          0          301  0      \n",
       "8   4.400000       3.900000 4.200000 0          0          301  0      \n",
       "14  3.000000       2.000000 3.500000 0          0          301  1      \n",
       "16  4.300000       3.600000 3.500000 0          0          301  1      \n",
       "18  5.000000       5.000000 5.000000 0          0          301  0      \n",
       "22  4.000000       2.000000 1.000000 0          0          301  1      \n",
       "24  4.000000       5.000000 5.000000 0          0          301  0      \n",
       "25  3.200000       3.400000 3.600000 0          0          301  1      \n",
       "31  3.800000       3.900000 3.900000 1          1           97  0      \n",
       "33  3.900000       4.000000 3.900000 1          0          301  0      \n",
       "35  3.700000       4.300000 3.700000 0          0          301  0      \n",
       "39  3.000000       3.000000 3.000000 0          0          301  0      \n",
       "41  4.300000       4.300000 3.800000 0          0          301  0      \n",
       "42  4.000000       4.000000 5.000000 0          0          301  1      \n",
       "48  3.400000       3.500000 3.300000 0          0          301  0      \n",
       "50  5.000000       5.000000 5.000000 0          0          301  0      \n",
       "52  4.500000       5.000000 5.000000 0          0          301  0      \n",
       "56  4.000000       3.000000 5.000000 0          0          301  0      \n",
       "58  3.000000       3.000000 2.000000 0          0          301  0      \n",
       "59  3.804457       3.822472 3.756056 0          0          301  1      \n",
       "65  3.804457       3.822472 3.756056 0          0          301  1      \n",
       "67  3.900000       4.200000 4.300000 1          1          150  0      \n",
       "69  3.100000       3.800000 3.600000 0          0          301  0      \n",
       "73  4.700000       4.300000 4.300000 0          1          301  0      \n",
       "75  2.400000       2.200000 2.600000 0          0          301  1      \n",
       "76  3.700000       3.700000 3.900000 0          0          301  0      \n",
       "82  3.300000       3.600000 4.400000 0          0          250  0      \n",
       "84  3.900000       3.900000 4.100000 0          0          200  0      \n",
       "⋮   ⋮              ⋮        ⋮        ⋮          ⋮          ⋮    ⋮      \n",
       "303 4.200000       4.200000 4.000000 0          1          301  0      \n",
       "305 3.800000       3.900000 4.300000 0          0          301  0      \n",
       "307 3.700000       4.300000 4.000000 0          1          155  0      \n",
       "311 4.200000       4.100000 4.200000 0          0          301  0      \n",
       "313 3.804457       3.822472 3.756056 0          0          301  1      \n",
       "314 4.200000       4.200000 4.100000 0          0          301  0      \n",
       "320 3.300000       3.700000 3.400000 0          1          301  0      \n",
       "322 3.900000       4.000000 3.800000 0          0          301  0      \n",
       "324 3.700000       3.700000 2.700000 0          0          301  0      \n",
       "328 3.300000       4.200000 3.800000 0          0          301  0      \n",
       "330 4.100000       4.200000 4.000000 0          0          301  0      \n",
       "331 3.500000       4.000000 2.500000 0          0          301  1      \n",
       "337 4.200000       3.400000 3.700000 0          0          301  1      \n",
       "339 3.500000       3.900000 3.600000 0          0          301  0      \n",
       "341 3.000000       4.000000 3.500000 0          0          301  0      \n",
       "345 4.000000       4.000000 4.000000 0          0          301  0      \n",
       "347 4.500000       4.300000 4.500000 0          0          301  0      \n",
       "348 3.800000       3.100000 2.900000 0          0          301  0      \n",
       "354 4.000000       3.700000 4.000000 0          0          301  0      \n",
       "356 5.000000       5.000000 5.000000 0          0          301  0      \n",
       "358 5.000000       5.000000 4.500000 0          0          301  0      \n",
       "362 4.100000       3.600000 4.000000 0          0          301  0      \n",
       "364 4.000000       3.900000 4.400000 0          0          301  0      \n",
       "365 4.000000       4.000000 4.000000 0          0          301  0      \n",
       "371 3.000000       3.300000 3.000000 0          0          301  0      \n",
       "373 4.400000       4.400000 4.000000 0          0          301  0      \n",
       "375 4.100000       4.200000 4.300000 0          0          301  0      \n",
       "379 4.700000       3.900000 4.200000 0          0          301  1      \n",
       "381 3.600000       4.300000 3.600000 0          0          301  0      \n",
       "382 3.400000       3.100000 3.200000 0          0          301  0      \n",
       "    hostel_BOTH hostel_ONE linear   decision\n",
       "1   1           0          95.25097 88.05211\n",
       "5   0           0          83.98529 97.36824\n",
       "7   1           0          67.03529 63.77202\n",
       "8   1           0          70.98257 73.49375\n",
       "14  0           0          57.34506 69.04323\n",
       "16  1           0          59.01199 70.52405\n",
       "18  1           0          74.53221 63.77202\n",
       "22  1           0          36.59204 52.71238\n",
       "24  1           0          78.07224 59.83230\n",
       "25  1           0          60.02308 69.04323\n",
       "31  1           0          97.83733 97.36824\n",
       "33  1           0          77.88152 59.83230\n",
       "35  1           0          67.06327 59.83230\n",
       "39  1           0          66.33838 52.71238\n",
       "41  1           0          70.52523 88.68862\n",
       "42  1           0          67.18494 59.83230\n",
       "48  1           0          69.44201 69.04323\n",
       "50  1           0          89.85680 88.68862\n",
       "52  1           0          81.48739 59.83230\n",
       "56  1           0          71.14808 55.15813\n",
       "58  0           0          56.74210 52.71238\n",
       "59  0           0          59.76323 59.83230\n",
       "65  0           0          61.80546 59.83230\n",
       "67  1           0          99.68131 97.36824\n",
       "69  1           0          74.01919 88.68862\n",
       "73  0           0          88.69525 88.05211\n",
       "75  1           0          53.97024 65.30064\n",
       "76  0           0          77.37348 73.75159\n",
       "82  0           0          82.17729 88.68862\n",
       "84  1           0          79.32101 88.68862\n",
       "⋮   ⋮           ⋮          ⋮        ⋮       \n",
       "303 1           0          92.78713 88.05211\n",
       "305 1           0          77.90717 88.68862\n",
       "307 1           0          92.27407 97.36824\n",
       "311 1           0          74.50074 68.62492\n",
       "313 0           0          64.01767 68.62492\n",
       "314 1           0          81.96029 88.68862\n",
       "320 1           0          83.93804 88.05211\n",
       "322 1           0          74.35820 81.86522\n",
       "324 1           0          67.14082 52.71238\n",
       "328 1           0          79.16464 68.62492\n",
       "330 1           0          71.71905 81.86522\n",
       "331 1           0          59.30986 52.71238\n",
       "337 1           0          85.04649 88.68862\n",
       "339 0           0          73.16798 68.62492\n",
       "341 0           1          75.75998 88.68862\n",
       "345 1           0          76.07599 81.86522\n",
       "347 1           0          73.32382 81.86522\n",
       "348 1           0          68.82040 52.71238\n",
       "354 0           0          74.10919 81.86522\n",
       "356 1           0          80.30998 68.62492\n",
       "358 0           0          76.38859 68.62492\n",
       "362 1           0          70.97872 70.52405\n",
       "364 1           0          75.21836 88.68862\n",
       "365 1           0          76.23241 68.62492\n",
       "371 1           0          67.36720 52.71238\n",
       "373 1           0          74.90800 81.86522\n",
       "375 1           0          75.98160 68.62492\n",
       "379 1           0          78.02752 73.75159\n",
       "381 1           0          75.30797 88.68862\n",
       "382 1           0          68.83997 81.86522"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Predicting values on test set\n",
    "test$decision <- predict(regtree, test, type=\"vector\")\n",
    "View(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ef26ad64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "201.325050522112"
      ],
      "text/latex": [
       "201.325050522112"
      ],
      "text/markdown": [
       "201.325050522112"
      ],
      "text/plain": [
       "[1] 201.3251"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSEdecision <- mean((test$decision - test$cutoff)^2)\n",
    "MSEdecision"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8a4ac2d",
   "metadata": {},
   "source": [
    "### Full Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "838d2a46",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Regression tree:\n",
      "rpart(formula = cutoff ~ . - college_code, data = train, control = rpart.control(cp = 0))\n",
      "\n",
      "Variables actually used in tree construction:\n",
      " [1] autonomous     courses        crowd          division       faculty       \n",
      " [6] fees           infrastructure intake         rank           rating        \n",
      "[11] salary        \n",
      "\n",
      "Root node error: 72335/251 = 288.19\n",
      "\n",
      "n= 251 \n",
      "\n",
      "           CP nsplit rel error  xerror     xstd\n",
      "1  0.22323757      0   1.00000 1.00702 0.058989\n",
      "2  0.12361298      1   0.77676 0.91900 0.063660\n",
      "3  0.03639029      2   0.65315 0.80328 0.057237\n",
      "4  0.03573425      3   0.61676 0.76081 0.056978\n",
      "5  0.03518788      4   0.58102 0.76256 0.057996\n",
      "6  0.02459872      5   0.54584 0.75383 0.062012\n",
      "7  0.02117882      6   0.52124 0.74177 0.064901\n",
      "8  0.01982892      7   0.50006 0.75154 0.065503\n",
      "9  0.01726013      8   0.48023 0.74176 0.065437\n",
      "10 0.01241569      9   0.46297 0.72422 0.066751\n",
      "11 0.01101776     11   0.43814 0.73033 0.066521\n",
      "12 0.01076526     12   0.42712 0.73444 0.066916\n",
      "13 0.00878253     13   0.41636 0.74146 0.067494\n",
      "14 0.00394656     14   0.40757 0.74965 0.068018\n",
      "15 0.00332275     15   0.40363 0.76074 0.069471\n",
      "16 0.00328216     16   0.40030 0.76457 0.070321\n",
      "17 0.00067328     17   0.39702 0.75870 0.068615\n",
      "18 0.00000000     18   0.39635 0.75668 0.068405\n"
     ]
    },
    {
     "data": {
      "image/png": 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bE2KFFM53fafX0VCN2bFhMlcARJZ6xqIq1qXRc7nSJYVTnqjOOFtWnPFSAtt1pz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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fulltree <- rpart(cutoff~.-college_code, data=train, control=rpart.control(cp=0))\n",
    "rpart.plot(fulltree, digits=-3) \n",
    "printcp(fulltree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "57b2f52a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 136 × 20</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>crowd</th><th scope=col>government</th><th scope=col>autonomous</th><th scope=col>rank</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_ONE</th><th scope=col>linear</th><th scope=col>decision</th><th scope=col>fulltree</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1002</td><td>1</td><td>96.44000</td><td> 8</td><td>300.000</td><td>240000.0</td><td>12.87391</td><td>3.400000</td><td>3.200000</td><td>3.500000</td><td>3.700000</td><td>1</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>95.25097</td><td>88.05211</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1105</td><td>1</td><td>88.05000</td><td> 8</td><td>480.000</td><td>440000.0</td><td>12.70685</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>1</td><td>250</td><td>0</td><td>0</td><td>0</td><td>83.98529</td><td>97.36824</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1108</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>310000.0</td><td>12.61154</td><td>3.900000</td><td>4.000000</td><td>4.300000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.03529</td><td>63.77202</td><td>63.77202</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>1114</td><td>1</td><td>81.55000</td><td> 6</td><td>300.000</td><td>320000.0</td><td>12.82126</td><td>4.000000</td><td>4.400000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.98257</td><td>73.49375</td><td>70.32917</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1122</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>200000.0</td><td>12.61154</td><td>2.200000</td><td>3.000000</td><td>2.000000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>57.34506</td><td>69.04323</td><td>69.04323</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>1124</td><td>1</td><td>49.08000</td><td> 5</td><td>300.000</td><td>490000.0</td><td>12.34584</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.01199</td><td>70.52405</td><td>70.52405</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>1126</td><td>1</td><td>67.71000</td><td> 5</td><td>300.000</td><td>170000.0</td><td>13.10216</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.53221</td><td>63.77202</td><td>63.77202</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>1130</td><td>1</td><td>45.98000</td><td> 6</td><td>480.000</td><td>180000.0</td><td>12.10072</td><td>2.200000</td><td>4.000000</td><td>2.000000</td><td>1.000000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>36.59204</td><td>52.71238</td><td>56.88917</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>1182</td><td>1</td><td>59.68000</td><td> 4</td><td>630.000</td><td>200000.0</td><td>13.01701</td><td>4.200000</td><td>4.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>78.07224</td><td>59.83230</td><td>56.23467</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>1251</td><td>1</td><td>44.34375</td><td> 6</td><td>300.000</td><td>284000.0</td><td>12.54255</td><td>3.400000</td><td>3.200000</td><td>3.400000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>60.02308</td><td>69.04323</td><td>69.04323</td></tr>\n",
       "\t<tr><th scope=row>31</th><td>2008</td><td>2</td><td>97.84000</td><td>10</td><td>540.000</td><td>190000.0</td><td>13.38473</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>3.900000</td><td>1</td><td>1</td><td> 97</td><td>0</td><td>1</td><td>0</td><td>97.83733</td><td>97.36824</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>33</th><td>2021</td><td>2</td><td>72.61000</td><td> 2</td><td>240.000</td><td> 80000.0</td><td>12.70685</td><td>3.800000</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>1</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.88152</td><td>59.83230</td><td>56.23467</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>2111</td><td>2</td><td>65.26000</td><td> 4</td><td>300.000</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>3.700000</td><td>4.300000</td><td>3.700000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.06327</td><td>59.83230</td><td>56.23467</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>2116</td><td>2</td><td>54.60000</td><td>10</td><td>294.000</td><td>200000.0</td><td>12.61154</td><td>3.100000</td><td>3.000000</td><td>3.000000</td><td>3.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>66.33838</td><td>52.71238</td><td>56.88917</td></tr>\n",
       "\t<tr><th scope=row>41</th><td>2127</td><td>2</td><td>80.37000</td><td> 5</td><td>420.000</td><td>350000.0</td><td>12.79386</td><td>3.900000</td><td>4.300000</td><td>4.300000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.52523</td><td>88.68862</td><td>84.42333</td></tr>\n",
       "\t<tr><th scope=row>42</th><td>2128</td><td>2</td><td>44.34375</td><td> 3</td><td>196.875</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>67.18494</td><td>59.83230</td><td>56.23467</td></tr>\n",
       "\t<tr><th scope=row>48</th><td>2134</td><td>2</td><td>72.88000</td><td> 9</td><td>360.000</td><td>240000.0</td><td>12.67608</td><td>3.300000</td><td>3.400000</td><td>3.500000</td><td>3.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>69.44201</td><td>69.04323</td><td>69.04323</td></tr>\n",
       "\t<tr><th scope=row>50</th><td>2136</td><td>2</td><td>44.34375</td><td> 9</td><td>240.000</td><td>480000.0</td><td>13.30469</td><td>4.300000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>89.85680</td><td>88.68862</td><td>88.48143</td></tr>\n",
       "\t<tr><th scope=row>52</th><td>2138</td><td>2</td><td>64.49000</td><td> 4</td><td>270.000</td><td>250000.0</td><td>12.70685</td><td>3.900000</td><td>4.500000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.48739</td><td>59.83230</td><td>56.23467</td></tr>\n",
       "\t<tr><th scope=row>56</th><td>2250</td><td>2</td><td>63.71000</td><td> 6</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>4.000000</td><td>4.000000</td><td>3.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.14808</td><td>55.15813</td><td>55.15813</td></tr>\n",
       "\t<tr><th scope=row>58</th><td>2254</td><td>2</td><td>59.41000</td><td> 5</td><td>196.875</td><td>160000.0</td><td>12.79562</td><td>2.800000</td><td>3.000000</td><td>3.000000</td><td>2.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>56.74210</td><td>52.71238</td><td>49.29500</td></tr>\n",
       "\t<tr><th scope=row>59</th><td>2255</td><td>2</td><td>71.74876</td><td> 3</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>59.76323</td><td>59.83230</td><td>56.23467</td></tr>\n",
       "\t<tr><th scope=row>65</th><td>2641</td><td>2</td><td>71.74876</td><td> 4</td><td>382.000</td><td>322661.9</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>61.80546</td><td>59.83230</td><td>65.52854</td></tr>\n",
       "\t<tr><th scope=row>67</th><td>3014</td><td>3</td><td>98.48000</td><td> 6</td><td>300.000</td><td>340000.0</td><td>13.21768</td><td>4.100000</td><td>3.900000</td><td>4.200000</td><td>4.300000</td><td>1</td><td>1</td><td>150</td><td>0</td><td>1</td><td>0</td><td>99.68131</td><td>97.36824</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>69</th><td>3035</td><td>3</td><td>89.48000</td><td> 7</td><td>196.875</td><td>420000.0</td><td>12.97155</td><td>3.600000</td><td>3.100000</td><td>3.800000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.01919</td><td>88.68862</td><td>91.75308</td></tr>\n",
       "\t<tr><th scope=row>73</th><td>3139</td><td>3</td><td>96.84000</td><td>10</td><td>630.000</td><td>550000.0</td><td>12.76569</td><td>4.300000</td><td>4.700000</td><td>4.300000</td><td>4.300000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>0</td><td>0</td><td>88.69525</td><td>88.05211</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>75</th><td>3147</td><td>3</td><td>83.40000</td><td> 6</td><td>300.000</td><td>264000.0</td><td>12.30139</td><td>2.200000</td><td>2.400000</td><td>2.200000</td><td>2.600000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>53.97024</td><td>65.30064</td><td>65.30064</td></tr>\n",
       "\t<tr><th scope=row>76</th><td>3148</td><td>3</td><td>92.28000</td><td>10</td><td>630.000</td><td>460000.0</td><td>13.30469</td><td>3.800000</td><td>3.700000</td><td>3.700000</td><td>3.900000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>77.37348</td><td>73.75159</td><td>73.75159</td></tr>\n",
       "\t<tr><th scope=row>82</th><td>3182</td><td>3</td><td>98.34000</td><td> 5</td><td>300.000</td><td>600000.0</td><td>14.16617</td><td>3.800000</td><td>3.300000</td><td>3.600000</td><td>4.400000</td><td>0</td><td>0</td><td>250</td><td>0</td><td>0</td><td>0</td><td>82.17729</td><td>88.68862</td><td>91.75308</td></tr>\n",
       "\t<tr><th scope=row>84</th><td>3184</td><td>3</td><td>96.77000</td><td>10</td><td>480.000</td><td>570000.0</td><td>13.12237</td><td>4.000000</td><td>3.900000</td><td>3.900000</td><td>4.100000</td><td>0</td><td>0</td><td>200</td><td>0</td><td>1</td><td>0</td><td>79.32101</td><td>88.68862</td><td>88.48143</td></tr>\n",
       "\t<tr><th scope=row>⋮</th><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><th scope=row>303</th><td>6283</td><td>6</td><td>87.28000</td><td>13.0</td><td>196.875</td><td> 370000</td><td>12.61154</td><td>4.000000</td><td>4.200000</td><td>4.200000</td><td>4.000000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>92.78713</td><td>88.05211</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>305</th><td>6285</td><td>6</td><td>92.61000</td><td> 6.0</td><td>240.000</td><td> 430000</td><td>12.91411</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>4.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.90717</td><td>88.68862</td><td>91.75308</td></tr>\n",
       "\t<tr><th scope=row>307</th><td>6289</td><td>6</td><td>97.98000</td><td> 7.0</td><td>300.000</td><td> 570000</td><td>13.32122</td><td>3.900000</td><td>3.700000</td><td>4.300000</td><td>4.000000</td><td>0</td><td>1</td><td>155</td><td>0</td><td>1</td><td>0</td><td>92.27407</td><td>97.36824</td><td>97.36824</td></tr>\n",
       "\t<tr><th scope=row>311</th><td>6303</td><td>6</td><td>75.18000</td><td> 5.0</td><td>240.000</td><td> 240000</td><td>12.98540</td><td>4.000000</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.50074</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>313</th><td>6305</td><td>6</td><td>46.17000</td><td> 5.0</td><td>210.000</td><td> 192000</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>3.756056</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>64.01767</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>314</th><td>6307</td><td>6</td><td>83.32000</td><td>12.0</td><td>255.000</td><td> 370000</td><td>12.76569</td><td>4.100000</td><td>4.200000</td><td>4.200000</td><td>4.100000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.96029</td><td>88.68862</td><td>88.48143</td></tr>\n",
       "\t<tr><th scope=row>320</th><td>6317</td><td>6</td><td>79.53000</td><td>11.0</td><td>630.000</td><td> 310000</td><td>12.54255</td><td>3.500000</td><td>3.300000</td><td>3.700000</td><td>3.400000</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>83.93804</td><td>88.05211</td><td>88.05211</td></tr>\n",
       "\t<tr><th scope=row>322</th><td>6319</td><td>6</td><td>63.05000</td><td> 6.0</td><td>360.000</td><td> 308000</td><td>12.76569</td><td>3.600000</td><td>3.900000</td><td>4.000000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.35820</td><td>81.86522</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>324</th><td>6321</td><td>6</td><td>45.67000</td><td> 6.0</td><td>300.000</td><td> 240000</td><td>12.79386</td><td>3.200000</td><td>3.700000</td><td>3.700000</td><td>2.700000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.14082</td><td>52.71238</td><td>56.88917</td></tr>\n",
       "\t<tr><th scope=row>328</th><td>6325</td><td>6</td><td>78.05000</td><td> 5.0</td><td>480.000</td><td> 230000</td><td>13.99783</td><td>3.600000</td><td>3.300000</td><td>4.200000</td><td>3.800000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>79.16464</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>330</th><td>6419</td><td>6</td><td>78.35000</td><td> 6.0</td><td>360.000</td><td> 330000</td><td>12.50618</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.71905</td><td>81.86522</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>331</th><td>6444</td><td>6</td><td>44.34375</td><td> 5.0</td><td>196.875</td><td> 141000</td><td>12.79562</td><td>3.200000</td><td>3.500000</td><td>4.000000</td><td>2.500000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.30986</td><td>52.71238</td><td>49.29500</td></tr>\n",
       "\t<tr><th scope=row>337</th><td>6620</td><td>6</td><td>73.99000</td><td>13.5</td><td>196.875</td><td>1080000</td><td>13.35348</td><td>3.600000</td><td>4.200000</td><td>3.400000</td><td>3.700000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>85.04649</td><td>88.68862</td><td>91.75308</td></tr>\n",
       "\t<tr><th scope=row>339</th><td>6622</td><td>6</td><td>85.85000</td><td> 6.0</td><td>360.000</td><td> 280000</td><td>12.76569</td><td>3.500000</td><td>3.500000</td><td>3.900000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>73.16798</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>341</th><td>6628</td><td>6</td><td>56.76500</td><td> 5.0</td><td>196.875</td><td> 400000</td><td>12.56025</td><td>3.400000</td><td>3.000000</td><td>4.000000</td><td>3.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>75.75998</td><td>88.68862</td><td>91.75308</td></tr>\n",
       "\t<tr><th scope=row>345</th><td>6635</td><td>6</td><td>67.11200</td><td> 9.0</td><td>420.000</td><td> 300000</td><td>12.42922</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.07599</td><td>81.86522</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>347</th><td>6643</td><td>6</td><td>81.98400</td><td> 5.0</td><td>360.000</td><td> 310000</td><td>12.20608</td><td>4.200000</td><td>4.500000</td><td>4.300000</td><td>4.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>73.32382</td><td>81.86522</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>348</th><td>6644</td><td>6</td><td>56.76000</td><td> 7.0</td><td>300.000</td><td> 320000</td><td>12.79386</td><td>3.000000</td><td>3.800000</td><td>3.100000</td><td>2.900000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.82040</td><td>52.71238</td><td>56.88917</td></tr>\n",
       "\t<tr><th scope=row>354</th><td>6757</td><td>6</td><td>60.73000</td><td> 7.0</td><td>360.000</td><td> 310000</td><td>12.76569</td><td>3.800000</td><td>4.000000</td><td>3.700000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>74.10919</td><td>81.86522</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>356</th><td>6759</td><td>6</td><td>68.70000</td><td> 5.0</td><td>270.000</td><td> 270000</td><td>12.61154</td><td>4.600000</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>80.30998</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>358</th><td>6766</td><td>6</td><td>63.08000</td><td> 5.0</td><td>300.000</td><td> 260000</td><td>12.76569</td><td>4.700000</td><td>5.000000</td><td>5.000000</td><td>4.500000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>76.38859</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>362</th><td>6770</td><td>6</td><td>77.03000</td><td> 5.0</td><td>300.000</td><td> 410000</td><td>12.38840</td><td>3.800000</td><td>4.100000</td><td>3.600000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.97872</td><td>70.52405</td><td>70.52405</td></tr>\n",
       "\t<tr><th scope=row>364</th><td>6772</td><td>6</td><td>87.28000</td><td> 6.0</td><td>510.000</td><td> 400000</td><td>12.57764</td><td>4.000000</td><td>4.000000</td><td>3.900000</td><td>4.400000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.21836</td><td>88.68862</td><td>88.48143</td></tr>\n",
       "\t<tr><th scope=row>365</th><td>6780</td><td>6</td><td>71.76000</td><td>11.0</td><td>420.000</td><td> 250000</td><td>12.38840</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.23241</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>371</th><td>6795</td><td>6</td><td>52.82000</td><td> 4.0</td><td>210.000</td><td> 240000</td><td>12.79562</td><td>3.000000</td><td>3.000000</td><td>3.300000</td><td>3.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.36720</td><td>52.71238</td><td>49.29500</td></tr>\n",
       "\t<tr><th scope=row>373</th><td>6797</td><td>6</td><td>74.20000</td><td> 5.0</td><td>240.000</td><td> 320000</td><td>12.79562</td><td>4.100000</td><td>4.400000</td><td>4.400000</td><td>4.000000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.90800</td><td>81.86522</td><td>81.86522</td></tr>\n",
       "\t<tr><th scope=row>375</th><td>6803</td><td>6</td><td>74.51000</td><td> 6.0</td><td>360.000</td><td> 240000</td><td>12.89922</td><td>4.100000</td><td>4.100000</td><td>4.200000</td><td>4.300000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.98160</td><td>68.62492</td><td>68.62492</td></tr>\n",
       "\t<tr><th scope=row>379</th><td>6811</td><td>6</td><td>44.34375</td><td>13.5</td><td>630.000</td><td> 620000</td><td>12.84793</td><td>4.100000</td><td>4.700000</td><td>3.900000</td><td>4.200000</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>78.02752</td><td>73.75159</td><td>73.75159</td></tr>\n",
       "\t<tr><th scope=row>381</th><td>6822</td><td>6</td><td>96.46000</td><td> 9.0</td><td>480.000</td><td> 400000</td><td>12.50618</td><td>4.000000</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.30797</td><td>88.68862</td><td>88.48143</td></tr>\n",
       "\t<tr><th scope=row>382</th><td>6834</td><td>6</td><td>80.45000</td><td> 6.0</td><td>360.000</td><td> 300000</td><td>12.61154</td><td>3.000000</td><td>3.400000</td><td>3.100000</td><td>3.200000</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.83997</td><td>81.86522</td><td>81.86522</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 136 × 20\n",
       "\\begin{tabular}{r|llllllllllllllllllll}\n",
       "  & college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & crowd & government & autonomous & rank & new\\_ban & hostel\\_BOTH & hostel\\_ONE & linear & decision & fulltree\\\\\n",
       "  & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <int> & <int> & <int> & <int> & <int> & <int> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1002 & 1 & 96.44000 &  8 & 300.000 & 240000.0 & 12.87391 & 3.400000 & 3.200000 & 3.500000 & 3.700000 & 1 & 1 & 301 & 0 & 1 & 0 & 95.25097 & 88.05211 & 88.05211\\\\\n",
       "\t5 & 1105 & 1 & 88.05000 &  8 & 480.000 & 440000.0 & 12.70685 & 3.900000 & 4.000000 & 3.900000 & 4.200000 & 0 & 1 & 250 & 0 & 0 & 0 & 83.98529 & 97.36824 & 97.36824\\\\\n",
       "\t7 & 1108 & 1 & 44.34375 &  5 & 300.000 & 310000.0 & 12.61154 & 3.900000 & 4.000000 & 4.300000 & 3.500000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.03529 & 63.77202 & 63.77202\\\\\n",
       "\t8 & 1114 & 1 & 81.55000 &  6 & 300.000 & 320000.0 & 12.82126 & 4.000000 & 4.400000 & 3.900000 & 4.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.98257 & 73.49375 & 70.32917\\\\\n",
       "\t14 & 1122 & 1 & 44.34375 &  5 & 300.000 & 200000.0 & 12.61154 & 2.200000 & 3.000000 & 2.000000 & 3.500000 & 0 & 0 & 301 & 1 & 0 & 0 & 57.34506 & 69.04323 & 69.04323\\\\\n",
       "\t16 & 1124 & 1 & 49.08000 &  5 & 300.000 & 490000.0 & 12.34584 & 3.600000 & 4.300000 & 3.600000 & 3.500000 & 0 & 0 & 301 & 1 & 1 & 0 & 59.01199 & 70.52405 & 70.52405\\\\\n",
       "\t18 & 1126 & 1 & 67.71000 &  5 & 300.000 & 170000.0 & 13.10216 & 5.000000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.53221 & 63.77202 & 63.77202\\\\\n",
       "\t22 & 1130 & 1 & 45.98000 &  6 & 480.000 & 180000.0 & 12.10072 & 2.200000 & 4.000000 & 2.000000 & 1.000000 & 0 & 0 & 301 & 1 & 1 & 0 & 36.59204 & 52.71238 & 56.88917\\\\\n",
       "\t24 & 1182 & 1 & 59.68000 &  4 & 630.000 & 200000.0 & 13.01701 & 4.200000 & 4.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 78.07224 & 59.83230 & 56.23467\\\\\n",
       "\t25 & 1251 & 1 & 44.34375 &  6 & 300.000 & 284000.0 & 12.54255 & 3.400000 & 3.200000 & 3.400000 & 3.600000 & 0 & 0 & 301 & 1 & 1 & 0 & 60.02308 & 69.04323 & 69.04323\\\\\n",
       "\t31 & 2008 & 2 & 97.84000 & 10 & 540.000 & 190000.0 & 13.38473 & 3.900000 & 3.800000 & 3.900000 & 3.900000 & 1 & 1 &  97 & 0 & 1 & 0 & 97.83733 & 97.36824 & 97.36824\\\\\n",
       "\t33 & 2021 & 2 & 72.61000 &  2 & 240.000 &  80000.0 & 12.70685 & 3.800000 & 3.900000 & 4.000000 & 3.900000 & 1 & 0 & 301 & 0 & 1 & 0 & 77.88152 & 59.83230 & 56.23467\\\\\n",
       "\t35 & 2111 & 2 & 65.26000 &  4 & 300.000 & 170000.0 & 12.61154 & 3.800000 & 3.700000 & 4.300000 & 3.700000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.06327 & 59.83230 & 56.23467\\\\\n",
       "\t39 & 2116 & 2 & 54.60000 & 10 & 294.000 & 200000.0 & 12.61154 & 3.100000 & 3.000000 & 3.000000 & 3.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 66.33838 & 52.71238 & 56.88917\\\\\n",
       "\t41 & 2127 & 2 & 80.37000 &  5 & 420.000 & 350000.0 & 12.79386 & 3.900000 & 4.300000 & 4.300000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.52523 & 88.68862 & 84.42333\\\\\n",
       "\t42 & 2128 & 2 & 44.34375 &  3 & 196.875 & 170000.0 & 12.61154 & 3.800000 & 4.000000 & 4.000000 & 5.000000 & 0 & 0 & 301 & 1 & 1 & 0 & 67.18494 & 59.83230 & 56.23467\\\\\n",
       "\t48 & 2134 & 2 & 72.88000 &  9 & 360.000 & 240000.0 & 12.67608 & 3.300000 & 3.400000 & 3.500000 & 3.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 69.44201 & 69.04323 & 69.04323\\\\\n",
       "\t50 & 2136 & 2 & 44.34375 &  9 & 240.000 & 480000.0 & 13.30469 & 4.300000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 89.85680 & 88.68862 & 88.48143\\\\\n",
       "\t52 & 2138 & 2 & 64.49000 &  4 & 270.000 & 250000.0 & 12.70685 & 3.900000 & 4.500000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 81.48739 & 59.83230 & 56.23467\\\\\n",
       "\t56 & 2250 & 2 & 63.71000 &  6 & 196.875 & 220000.0 & 12.79562 & 4.000000 & 4.000000 & 3.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 71.14808 & 55.15813 & 55.15813\\\\\n",
       "\t58 & 2254 & 2 & 59.41000 &  5 & 196.875 & 160000.0 & 12.79562 & 2.800000 & 3.000000 & 3.000000 & 2.000000 & 0 & 0 & 301 & 0 & 0 & 0 & 56.74210 & 52.71238 & 49.29500\\\\\n",
       "\t59 & 2255 & 2 & 71.74876 &  3 & 196.875 & 220000.0 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 59.76323 & 59.83230 & 56.23467\\\\\n",
       "\t65 & 2641 & 2 & 71.74876 &  4 & 382.000 & 322661.9 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 61.80546 & 59.83230 & 65.52854\\\\\n",
       "\t67 & 3014 & 3 & 98.48000 &  6 & 300.000 & 340000.0 & 13.21768 & 4.100000 & 3.900000 & 4.200000 & 4.300000 & 1 & 1 & 150 & 0 & 1 & 0 & 99.68131 & 97.36824 & 97.36824\\\\\n",
       "\t69 & 3035 & 3 & 89.48000 &  7 & 196.875 & 420000.0 & 12.97155 & 3.600000 & 3.100000 & 3.800000 & 3.600000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.01919 & 88.68862 & 91.75308\\\\\n",
       "\t73 & 3139 & 3 & 96.84000 & 10 & 630.000 & 550000.0 & 12.76569 & 4.300000 & 4.700000 & 4.300000 & 4.300000 & 0 & 1 & 301 & 0 & 0 & 0 & 88.69525 & 88.05211 & 88.05211\\\\\n",
       "\t75 & 3147 & 3 & 83.40000 &  6 & 300.000 & 264000.0 & 12.30139 & 2.200000 & 2.400000 & 2.200000 & 2.600000 & 0 & 0 & 301 & 1 & 1 & 0 & 53.97024 & 65.30064 & 65.30064\\\\\n",
       "\t76 & 3148 & 3 & 92.28000 & 10 & 630.000 & 460000.0 & 13.30469 & 3.800000 & 3.700000 & 3.700000 & 3.900000 & 0 & 0 & 301 & 0 & 0 & 0 & 77.37348 & 73.75159 & 73.75159\\\\\n",
       "\t82 & 3182 & 3 & 98.34000 &  5 & 300.000 & 600000.0 & 14.16617 & 3.800000 & 3.300000 & 3.600000 & 4.400000 & 0 & 0 & 250 & 0 & 0 & 0 & 82.17729 & 88.68862 & 91.75308\\\\\n",
       "\t84 & 3184 & 3 & 96.77000 & 10 & 480.000 & 570000.0 & 13.12237 & 4.000000 & 3.900000 & 3.900000 & 4.100000 & 0 & 0 & 200 & 0 & 1 & 0 & 79.32101 & 88.68862 & 88.48143\\\\\n",
       "\t⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t303 & 6283 & 6 & 87.28000 & 13.0 & 196.875 &  370000 & 12.61154 & 4.000000 & 4.200000 & 4.200000 & 4.000000 & 0 & 1 & 301 & 0 & 1 & 0 & 92.78713 & 88.05211 & 88.05211\\\\\n",
       "\t305 & 6285 & 6 & 92.61000 &  6.0 & 240.000 &  430000 & 12.91411 & 3.900000 & 3.800000 & 3.900000 & 4.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 77.90717 & 88.68862 & 91.75308\\\\\n",
       "\t307 & 6289 & 6 & 97.98000 &  7.0 & 300.000 &  570000 & 13.32122 & 3.900000 & 3.700000 & 4.300000 & 4.000000 & 0 & 1 & 155 & 0 & 1 & 0 & 92.27407 & 97.36824 & 97.36824\\\\\n",
       "\t311 & 6303 & 6 & 75.18000 &  5.0 & 240.000 &  240000 & 12.98540 & 4.000000 & 4.200000 & 4.100000 & 4.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.50074 & 68.62492 & 68.62492\\\\\n",
       "\t313 & 6305 & 6 & 46.17000 &  5.0 & 210.000 &  192000 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & 3.756056 & 0 & 0 & 301 & 1 & 0 & 0 & 64.01767 & 68.62492 & 68.62492\\\\\n",
       "\t314 & 6307 & 6 & 83.32000 & 12.0 & 255.000 &  370000 & 12.76569 & 4.100000 & 4.200000 & 4.200000 & 4.100000 & 0 & 0 & 301 & 0 & 1 & 0 & 81.96029 & 88.68862 & 88.48143\\\\\n",
       "\t320 & 6317 & 6 & 79.53000 & 11.0 & 630.000 &  310000 & 12.54255 & 3.500000 & 3.300000 & 3.700000 & 3.400000 & 0 & 1 & 301 & 0 & 1 & 0 & 83.93804 & 88.05211 & 88.05211\\\\\n",
       "\t322 & 6319 & 6 & 63.05000 &  6.0 & 360.000 &  308000 & 12.76569 & 3.600000 & 3.900000 & 4.000000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.35820 & 81.86522 & 81.86522\\\\\n",
       "\t324 & 6321 & 6 & 45.67000 &  6.0 & 300.000 &  240000 & 12.79386 & 3.200000 & 3.700000 & 3.700000 & 2.700000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.14082 & 52.71238 & 56.88917\\\\\n",
       "\t328 & 6325 & 6 & 78.05000 &  5.0 & 480.000 &  230000 & 13.99783 & 3.600000 & 3.300000 & 4.200000 & 3.800000 & 0 & 0 & 301 & 0 & 1 & 0 & 79.16464 & 68.62492 & 68.62492\\\\\n",
       "\t330 & 6419 & 6 & 78.35000 &  6.0 & 360.000 &  330000 & 12.50618 & 4.200000 & 4.100000 & 4.200000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 71.71905 & 81.86522 & 81.86522\\\\\n",
       "\t331 & 6444 & 6 & 44.34375 &  5.0 & 196.875 &  141000 & 12.79562 & 3.200000 & 3.500000 & 4.000000 & 2.500000 & 0 & 0 & 301 & 1 & 1 & 0 & 59.30986 & 52.71238 & 49.29500\\\\\n",
       "\t337 & 6620 & 6 & 73.99000 & 13.5 & 196.875 & 1080000 & 13.35348 & 3.600000 & 4.200000 & 3.400000 & 3.700000 & 0 & 0 & 301 & 1 & 1 & 0 & 85.04649 & 88.68862 & 91.75308\\\\\n",
       "\t339 & 6622 & 6 & 85.85000 &  6.0 & 360.000 &  280000 & 12.76569 & 3.500000 & 3.500000 & 3.900000 & 3.600000 & 0 & 0 & 301 & 0 & 0 & 0 & 73.16798 & 68.62492 & 68.62492\\\\\n",
       "\t341 & 6628 & 6 & 56.76500 &  5.0 & 196.875 &  400000 & 12.56025 & 3.400000 & 3.000000 & 4.000000 & 3.500000 & 0 & 0 & 301 & 0 & 0 & 1 & 75.75998 & 88.68862 & 91.75308\\\\\n",
       "\t345 & 6635 & 6 & 67.11200 &  9.0 & 420.000 &  300000 & 12.42922 & 3.800000 & 4.000000 & 4.000000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 76.07599 & 81.86522 & 81.86522\\\\\n",
       "\t347 & 6643 & 6 & 81.98400 &  5.0 & 360.000 &  310000 & 12.20608 & 4.200000 & 4.500000 & 4.300000 & 4.500000 & 0 & 0 & 301 & 0 & 1 & 0 & 73.32382 & 81.86522 & 81.86522\\\\\n",
       "\t348 & 6644 & 6 & 56.76000 &  7.0 & 300.000 &  320000 & 12.79386 & 3.000000 & 3.800000 & 3.100000 & 2.900000 & 0 & 0 & 301 & 0 & 1 & 0 & 68.82040 & 52.71238 & 56.88917\\\\\n",
       "\t354 & 6757 & 6 & 60.73000 &  7.0 & 360.000 &  310000 & 12.76569 & 3.800000 & 4.000000 & 3.700000 & 4.000000 & 0 & 0 & 301 & 0 & 0 & 0 & 74.10919 & 81.86522 & 81.86522\\\\\n",
       "\t356 & 6759 & 6 & 68.70000 &  5.0 & 270.000 &  270000 & 12.61154 & 4.600000 & 5.000000 & 5.000000 & 5.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 80.30998 & 68.62492 & 68.62492\\\\\n",
       "\t358 & 6766 & 6 & 63.08000 &  5.0 & 300.000 &  260000 & 12.76569 & 4.700000 & 5.000000 & 5.000000 & 4.500000 & 0 & 0 & 301 & 0 & 0 & 0 & 76.38859 & 68.62492 & 68.62492\\\\\n",
       "\t362 & 6770 & 6 & 77.03000 &  5.0 & 300.000 &  410000 & 12.38840 & 3.800000 & 4.100000 & 3.600000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 70.97872 & 70.52405 & 70.52405\\\\\n",
       "\t364 & 6772 & 6 & 87.28000 &  6.0 & 510.000 &  400000 & 12.57764 & 4.000000 & 4.000000 & 3.900000 & 4.400000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.21836 & 88.68862 & 88.48143\\\\\n",
       "\t365 & 6780 & 6 & 71.76000 & 11.0 & 420.000 &  250000 & 12.38840 & 4.000000 & 4.000000 & 4.000000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 76.23241 & 68.62492 & 68.62492\\\\\n",
       "\t371 & 6795 & 6 & 52.82000 &  4.0 & 210.000 &  240000 & 12.79562 & 3.000000 & 3.000000 & 3.300000 & 3.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 67.36720 & 52.71238 & 49.29500\\\\\n",
       "\t373 & 6797 & 6 & 74.20000 &  5.0 & 240.000 &  320000 & 12.79562 & 4.100000 & 4.400000 & 4.400000 & 4.000000 & 0 & 0 & 301 & 0 & 1 & 0 & 74.90800 & 81.86522 & 81.86522\\\\\n",
       "\t375 & 6803 & 6 & 74.51000 &  6.0 & 360.000 &  240000 & 12.89922 & 4.100000 & 4.100000 & 4.200000 & 4.300000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.98160 & 68.62492 & 68.62492\\\\\n",
       "\t379 & 6811 & 6 & 44.34375 & 13.5 & 630.000 &  620000 & 12.84793 & 4.100000 & 4.700000 & 3.900000 & 4.200000 & 0 & 0 & 301 & 1 & 1 & 0 & 78.02752 & 73.75159 & 73.75159\\\\\n",
       "\t381 & 6822 & 6 & 96.46000 &  9.0 & 480.000 &  400000 & 12.50618 & 4.000000 & 3.600000 & 4.300000 & 3.600000 & 0 & 0 & 301 & 0 & 1 & 0 & 75.30797 & 88.68862 & 88.48143\\\\\n",
       "\t382 & 6834 & 6 & 80.45000 &  6.0 & 360.000 &  300000 & 12.61154 & 3.000000 & 3.400000 & 3.100000 & 3.200000 & 0 & 0 & 301 & 0 & 1 & 0 & 68.83997 & 81.86522 & 81.86522\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 136 × 20\n",
       "\n",
       "| <!--/--> | college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;dbl&gt; | intake &lt;dbl&gt; | fees &lt;dbl&gt; | salary &lt;dbl&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | crowd &lt;dbl&gt; | government &lt;int&gt; | autonomous &lt;int&gt; | rank &lt;int&gt; | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_ONE &lt;int&gt; | linear &lt;dbl&gt; | decision &lt;dbl&gt; | fulltree &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1002 | 1 | 96.44000 |  8 | 300.000 | 240000.0 | 12.87391 | 3.400000 | 3.200000 | 3.500000 | 3.700000 | 1 | 1 | 301 | 0 | 1 | 0 | 95.25097 | 88.05211 | 88.05211 |\n",
       "| 5 | 1105 | 1 | 88.05000 |  8 | 480.000 | 440000.0 | 12.70685 | 3.900000 | 4.000000 | 3.900000 | 4.200000 | 0 | 1 | 250 | 0 | 0 | 0 | 83.98529 | 97.36824 | 97.36824 |\n",
       "| 7 | 1108 | 1 | 44.34375 |  5 | 300.000 | 310000.0 | 12.61154 | 3.900000 | 4.000000 | 4.300000 | 3.500000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.03529 | 63.77202 | 63.77202 |\n",
       "| 8 | 1114 | 1 | 81.55000 |  6 | 300.000 | 320000.0 | 12.82126 | 4.000000 | 4.400000 | 3.900000 | 4.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.98257 | 73.49375 | 70.32917 |\n",
       "| 14 | 1122 | 1 | 44.34375 |  5 | 300.000 | 200000.0 | 12.61154 | 2.200000 | 3.000000 | 2.000000 | 3.500000 | 0 | 0 | 301 | 1 | 0 | 0 | 57.34506 | 69.04323 | 69.04323 |\n",
       "| 16 | 1124 | 1 | 49.08000 |  5 | 300.000 | 490000.0 | 12.34584 | 3.600000 | 4.300000 | 3.600000 | 3.500000 | 0 | 0 | 301 | 1 | 1 | 0 | 59.01199 | 70.52405 | 70.52405 |\n",
       "| 18 | 1126 | 1 | 67.71000 |  5 | 300.000 | 170000.0 | 13.10216 | 5.000000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.53221 | 63.77202 | 63.77202 |\n",
       "| 22 | 1130 | 1 | 45.98000 |  6 | 480.000 | 180000.0 | 12.10072 | 2.200000 | 4.000000 | 2.000000 | 1.000000 | 0 | 0 | 301 | 1 | 1 | 0 | 36.59204 | 52.71238 | 56.88917 |\n",
       "| 24 | 1182 | 1 | 59.68000 |  4 | 630.000 | 200000.0 | 13.01701 | 4.200000 | 4.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 78.07224 | 59.83230 | 56.23467 |\n",
       "| 25 | 1251 | 1 | 44.34375 |  6 | 300.000 | 284000.0 | 12.54255 | 3.400000 | 3.200000 | 3.400000 | 3.600000 | 0 | 0 | 301 | 1 | 1 | 0 | 60.02308 | 69.04323 | 69.04323 |\n",
       "| 31 | 2008 | 2 | 97.84000 | 10 | 540.000 | 190000.0 | 13.38473 | 3.900000 | 3.800000 | 3.900000 | 3.900000 | 1 | 1 |  97 | 0 | 1 | 0 | 97.83733 | 97.36824 | 97.36824 |\n",
       "| 33 | 2021 | 2 | 72.61000 |  2 | 240.000 |  80000.0 | 12.70685 | 3.800000 | 3.900000 | 4.000000 | 3.900000 | 1 | 0 | 301 | 0 | 1 | 0 | 77.88152 | 59.83230 | 56.23467 |\n",
       "| 35 | 2111 | 2 | 65.26000 |  4 | 300.000 | 170000.0 | 12.61154 | 3.800000 | 3.700000 | 4.300000 | 3.700000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.06327 | 59.83230 | 56.23467 |\n",
       "| 39 | 2116 | 2 | 54.60000 | 10 | 294.000 | 200000.0 | 12.61154 | 3.100000 | 3.000000 | 3.000000 | 3.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 66.33838 | 52.71238 | 56.88917 |\n",
       "| 41 | 2127 | 2 | 80.37000 |  5 | 420.000 | 350000.0 | 12.79386 | 3.900000 | 4.300000 | 4.300000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.52523 | 88.68862 | 84.42333 |\n",
       "| 42 | 2128 | 2 | 44.34375 |  3 | 196.875 | 170000.0 | 12.61154 | 3.800000 | 4.000000 | 4.000000 | 5.000000 | 0 | 0 | 301 | 1 | 1 | 0 | 67.18494 | 59.83230 | 56.23467 |\n",
       "| 48 | 2134 | 2 | 72.88000 |  9 | 360.000 | 240000.0 | 12.67608 | 3.300000 | 3.400000 | 3.500000 | 3.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 69.44201 | 69.04323 | 69.04323 |\n",
       "| 50 | 2136 | 2 | 44.34375 |  9 | 240.000 | 480000.0 | 13.30469 | 4.300000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 89.85680 | 88.68862 | 88.48143 |\n",
       "| 52 | 2138 | 2 | 64.49000 |  4 | 270.000 | 250000.0 | 12.70685 | 3.900000 | 4.500000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 81.48739 | 59.83230 | 56.23467 |\n",
       "| 56 | 2250 | 2 | 63.71000 |  6 | 196.875 | 220000.0 | 12.79562 | 4.000000 | 4.000000 | 3.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 71.14808 | 55.15813 | 55.15813 |\n",
       "| 58 | 2254 | 2 | 59.41000 |  5 | 196.875 | 160000.0 | 12.79562 | 2.800000 | 3.000000 | 3.000000 | 2.000000 | 0 | 0 | 301 | 0 | 0 | 0 | 56.74210 | 52.71238 | 49.29500 |\n",
       "| 59 | 2255 | 2 | 71.74876 |  3 | 196.875 | 220000.0 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 59.76323 | 59.83230 | 56.23467 |\n",
       "| 65 | 2641 | 2 | 71.74876 |  4 | 382.000 | 322661.9 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 61.80546 | 59.83230 | 65.52854 |\n",
       "| 67 | 3014 | 3 | 98.48000 |  6 | 300.000 | 340000.0 | 13.21768 | 4.100000 | 3.900000 | 4.200000 | 4.300000 | 1 | 1 | 150 | 0 | 1 | 0 | 99.68131 | 97.36824 | 97.36824 |\n",
       "| 69 | 3035 | 3 | 89.48000 |  7 | 196.875 | 420000.0 | 12.97155 | 3.600000 | 3.100000 | 3.800000 | 3.600000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.01919 | 88.68862 | 91.75308 |\n",
       "| 73 | 3139 | 3 | 96.84000 | 10 | 630.000 | 550000.0 | 12.76569 | 4.300000 | 4.700000 | 4.300000 | 4.300000 | 0 | 1 | 301 | 0 | 0 | 0 | 88.69525 | 88.05211 | 88.05211 |\n",
       "| 75 | 3147 | 3 | 83.40000 |  6 | 300.000 | 264000.0 | 12.30139 | 2.200000 | 2.400000 | 2.200000 | 2.600000 | 0 | 0 | 301 | 1 | 1 | 0 | 53.97024 | 65.30064 | 65.30064 |\n",
       "| 76 | 3148 | 3 | 92.28000 | 10 | 630.000 | 460000.0 | 13.30469 | 3.800000 | 3.700000 | 3.700000 | 3.900000 | 0 | 0 | 301 | 0 | 0 | 0 | 77.37348 | 73.75159 | 73.75159 |\n",
       "| 82 | 3182 | 3 | 98.34000 |  5 | 300.000 | 600000.0 | 14.16617 | 3.800000 | 3.300000 | 3.600000 | 4.400000 | 0 | 0 | 250 | 0 | 0 | 0 | 82.17729 | 88.68862 | 91.75308 |\n",
       "| 84 | 3184 | 3 | 96.77000 | 10 | 480.000 | 570000.0 | 13.12237 | 4.000000 | 3.900000 | 3.900000 | 4.100000 | 0 | 0 | 200 | 0 | 1 | 0 | 79.32101 | 88.68862 | 88.48143 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 303 | 6283 | 6 | 87.28000 | 13.0 | 196.875 |  370000 | 12.61154 | 4.000000 | 4.200000 | 4.200000 | 4.000000 | 0 | 1 | 301 | 0 | 1 | 0 | 92.78713 | 88.05211 | 88.05211 |\n",
       "| 305 | 6285 | 6 | 92.61000 |  6.0 | 240.000 |  430000 | 12.91411 | 3.900000 | 3.800000 | 3.900000 | 4.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 77.90717 | 88.68862 | 91.75308 |\n",
       "| 307 | 6289 | 6 | 97.98000 |  7.0 | 300.000 |  570000 | 13.32122 | 3.900000 | 3.700000 | 4.300000 | 4.000000 | 0 | 1 | 155 | 0 | 1 | 0 | 92.27407 | 97.36824 | 97.36824 |\n",
       "| 311 | 6303 | 6 | 75.18000 |  5.0 | 240.000 |  240000 | 12.98540 | 4.000000 | 4.200000 | 4.100000 | 4.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.50074 | 68.62492 | 68.62492 |\n",
       "| 313 | 6305 | 6 | 46.17000 |  5.0 | 210.000 |  192000 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | 3.756056 | 0 | 0 | 301 | 1 | 0 | 0 | 64.01767 | 68.62492 | 68.62492 |\n",
       "| 314 | 6307 | 6 | 83.32000 | 12.0 | 255.000 |  370000 | 12.76569 | 4.100000 | 4.200000 | 4.200000 | 4.100000 | 0 | 0 | 301 | 0 | 1 | 0 | 81.96029 | 88.68862 | 88.48143 |\n",
       "| 320 | 6317 | 6 | 79.53000 | 11.0 | 630.000 |  310000 | 12.54255 | 3.500000 | 3.300000 | 3.700000 | 3.400000 | 0 | 1 | 301 | 0 | 1 | 0 | 83.93804 | 88.05211 | 88.05211 |\n",
       "| 322 | 6319 | 6 | 63.05000 |  6.0 | 360.000 |  308000 | 12.76569 | 3.600000 | 3.900000 | 4.000000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.35820 | 81.86522 | 81.86522 |\n",
       "| 324 | 6321 | 6 | 45.67000 |  6.0 | 300.000 |  240000 | 12.79386 | 3.200000 | 3.700000 | 3.700000 | 2.700000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.14082 | 52.71238 | 56.88917 |\n",
       "| 328 | 6325 | 6 | 78.05000 |  5.0 | 480.000 |  230000 | 13.99783 | 3.600000 | 3.300000 | 4.200000 | 3.800000 | 0 | 0 | 301 | 0 | 1 | 0 | 79.16464 | 68.62492 | 68.62492 |\n",
       "| 330 | 6419 | 6 | 78.35000 |  6.0 | 360.000 |  330000 | 12.50618 | 4.200000 | 4.100000 | 4.200000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 71.71905 | 81.86522 | 81.86522 |\n",
       "| 331 | 6444 | 6 | 44.34375 |  5.0 | 196.875 |  141000 | 12.79562 | 3.200000 | 3.500000 | 4.000000 | 2.500000 | 0 | 0 | 301 | 1 | 1 | 0 | 59.30986 | 52.71238 | 49.29500 |\n",
       "| 337 | 6620 | 6 | 73.99000 | 13.5 | 196.875 | 1080000 | 13.35348 | 3.600000 | 4.200000 | 3.400000 | 3.700000 | 0 | 0 | 301 | 1 | 1 | 0 | 85.04649 | 88.68862 | 91.75308 |\n",
       "| 339 | 6622 | 6 | 85.85000 |  6.0 | 360.000 |  280000 | 12.76569 | 3.500000 | 3.500000 | 3.900000 | 3.600000 | 0 | 0 | 301 | 0 | 0 | 0 | 73.16798 | 68.62492 | 68.62492 |\n",
       "| 341 | 6628 | 6 | 56.76500 |  5.0 | 196.875 |  400000 | 12.56025 | 3.400000 | 3.000000 | 4.000000 | 3.500000 | 0 | 0 | 301 | 0 | 0 | 1 | 75.75998 | 88.68862 | 91.75308 |\n",
       "| 345 | 6635 | 6 | 67.11200 |  9.0 | 420.000 |  300000 | 12.42922 | 3.800000 | 4.000000 | 4.000000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 76.07599 | 81.86522 | 81.86522 |\n",
       "| 347 | 6643 | 6 | 81.98400 |  5.0 | 360.000 |  310000 | 12.20608 | 4.200000 | 4.500000 | 4.300000 | 4.500000 | 0 | 0 | 301 | 0 | 1 | 0 | 73.32382 | 81.86522 | 81.86522 |\n",
       "| 348 | 6644 | 6 | 56.76000 |  7.0 | 300.000 |  320000 | 12.79386 | 3.000000 | 3.800000 | 3.100000 | 2.900000 | 0 | 0 | 301 | 0 | 1 | 0 | 68.82040 | 52.71238 | 56.88917 |\n",
       "| 354 | 6757 | 6 | 60.73000 |  7.0 | 360.000 |  310000 | 12.76569 | 3.800000 | 4.000000 | 3.700000 | 4.000000 | 0 | 0 | 301 | 0 | 0 | 0 | 74.10919 | 81.86522 | 81.86522 |\n",
       "| 356 | 6759 | 6 | 68.70000 |  5.0 | 270.000 |  270000 | 12.61154 | 4.600000 | 5.000000 | 5.000000 | 5.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 80.30998 | 68.62492 | 68.62492 |\n",
       "| 358 | 6766 | 6 | 63.08000 |  5.0 | 300.000 |  260000 | 12.76569 | 4.700000 | 5.000000 | 5.000000 | 4.500000 | 0 | 0 | 301 | 0 | 0 | 0 | 76.38859 | 68.62492 | 68.62492 |\n",
       "| 362 | 6770 | 6 | 77.03000 |  5.0 | 300.000 |  410000 | 12.38840 | 3.800000 | 4.100000 | 3.600000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 70.97872 | 70.52405 | 70.52405 |\n",
       "| 364 | 6772 | 6 | 87.28000 |  6.0 | 510.000 |  400000 | 12.57764 | 4.000000 | 4.000000 | 3.900000 | 4.400000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.21836 | 88.68862 | 88.48143 |\n",
       "| 365 | 6780 | 6 | 71.76000 | 11.0 | 420.000 |  250000 | 12.38840 | 4.000000 | 4.000000 | 4.000000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 76.23241 | 68.62492 | 68.62492 |\n",
       "| 371 | 6795 | 6 | 52.82000 |  4.0 | 210.000 |  240000 | 12.79562 | 3.000000 | 3.000000 | 3.300000 | 3.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 67.36720 | 52.71238 | 49.29500 |\n",
       "| 373 | 6797 | 6 | 74.20000 |  5.0 | 240.000 |  320000 | 12.79562 | 4.100000 | 4.400000 | 4.400000 | 4.000000 | 0 | 0 | 301 | 0 | 1 | 0 | 74.90800 | 81.86522 | 81.86522 |\n",
       "| 375 | 6803 | 6 | 74.51000 |  6.0 | 360.000 |  240000 | 12.89922 | 4.100000 | 4.100000 | 4.200000 | 4.300000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.98160 | 68.62492 | 68.62492 |\n",
       "| 379 | 6811 | 6 | 44.34375 | 13.5 | 630.000 |  620000 | 12.84793 | 4.100000 | 4.700000 | 3.900000 | 4.200000 | 0 | 0 | 301 | 1 | 1 | 0 | 78.02752 | 73.75159 | 73.75159 |\n",
       "| 381 | 6822 | 6 | 96.46000 |  9.0 | 480.000 |  400000 | 12.50618 | 4.000000 | 3.600000 | 4.300000 | 3.600000 | 0 | 0 | 301 | 0 | 1 | 0 | 75.30797 | 88.68862 | 88.48143 |\n",
       "| 382 | 6834 | 6 | 80.45000 |  6.0 | 360.000 |  300000 | 12.61154 | 3.000000 | 3.400000 | 3.100000 | 3.200000 | 0 | 0 | 301 | 0 | 1 | 0 | 68.83997 | 81.86522 | 81.86522 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff   courses intake  fees     salary   rating  \n",
       "1   1002         1        96.44000  8      300.000 240000.0 12.87391 3.400000\n",
       "5   1105         1        88.05000  8      480.000 440000.0 12.70685 3.900000\n",
       "7   1108         1        44.34375  5      300.000 310000.0 12.61154 3.900000\n",
       "8   1114         1        81.55000  6      300.000 320000.0 12.82126 4.000000\n",
       "14  1122         1        44.34375  5      300.000 200000.0 12.61154 2.200000\n",
       "16  1124         1        49.08000  5      300.000 490000.0 12.34584 3.600000\n",
       "18  1126         1        67.71000  5      300.000 170000.0 13.10216 5.000000\n",
       "22  1130         1        45.98000  6      480.000 180000.0 12.10072 2.200000\n",
       "24  1182         1        59.68000  4      630.000 200000.0 13.01701 4.200000\n",
       "25  1251         1        44.34375  6      300.000 284000.0 12.54255 3.400000\n",
       "31  2008         2        97.84000 10      540.000 190000.0 13.38473 3.900000\n",
       "33  2021         2        72.61000  2      240.000  80000.0 12.70685 3.800000\n",
       "35  2111         2        65.26000  4      300.000 170000.0 12.61154 3.800000\n",
       "39  2116         2        54.60000 10      294.000 200000.0 12.61154 3.100000\n",
       "41  2127         2        80.37000  5      420.000 350000.0 12.79386 3.900000\n",
       "42  2128         2        44.34375  3      196.875 170000.0 12.61154 3.800000\n",
       "48  2134         2        72.88000  9      360.000 240000.0 12.67608 3.300000\n",
       "50  2136         2        44.34375  9      240.000 480000.0 13.30469 4.300000\n",
       "52  2138         2        64.49000  4      270.000 250000.0 12.70685 3.900000\n",
       "56  2250         2        63.71000  6      196.875 220000.0 12.79562 4.000000\n",
       "58  2254         2        59.41000  5      196.875 160000.0 12.79562 2.800000\n",
       "59  2255         2        71.74876  3      196.875 220000.0 12.79562 3.666295\n",
       "65  2641         2        71.74876  4      382.000 322661.9 12.79562 3.666295\n",
       "67  3014         3        98.48000  6      300.000 340000.0 13.21768 4.100000\n",
       "69  3035         3        89.48000  7      196.875 420000.0 12.97155 3.600000\n",
       "73  3139         3        96.84000 10      630.000 550000.0 12.76569 4.300000\n",
       "75  3147         3        83.40000  6      300.000 264000.0 12.30139 2.200000\n",
       "76  3148         3        92.28000 10      630.000 460000.0 13.30469 3.800000\n",
       "82  3182         3        98.34000  5      300.000 600000.0 14.16617 3.800000\n",
       "84  3184         3        96.77000 10      480.000 570000.0 13.12237 4.000000\n",
       "⋮   ⋮            ⋮        ⋮        ⋮       ⋮       ⋮        ⋮        ⋮       \n",
       "303 6283         6        87.28000 13.0    196.875  370000  12.61154 4.000000\n",
       "305 6285         6        92.61000  6.0    240.000  430000  12.91411 3.900000\n",
       "307 6289         6        97.98000  7.0    300.000  570000  13.32122 3.900000\n",
       "311 6303         6        75.18000  5.0    240.000  240000  12.98540 4.000000\n",
       "313 6305         6        46.17000  5.0    210.000  192000  12.79562 3.666295\n",
       "314 6307         6        83.32000 12.0    255.000  370000  12.76569 4.100000\n",
       "320 6317         6        79.53000 11.0    630.000  310000  12.54255 3.500000\n",
       "322 6319         6        63.05000  6.0    360.000  308000  12.76569 3.600000\n",
       "324 6321         6        45.67000  6.0    300.000  240000  12.79386 3.200000\n",
       "328 6325         6        78.05000  5.0    480.000  230000  13.99783 3.600000\n",
       "330 6419         6        78.35000  6.0    360.000  330000  12.50618 4.200000\n",
       "331 6444         6        44.34375  5.0    196.875  141000  12.79562 3.200000\n",
       "337 6620         6        73.99000 13.5    196.875 1080000  13.35348 3.600000\n",
       "339 6622         6        85.85000  6.0    360.000  280000  12.76569 3.500000\n",
       "341 6628         6        56.76500  5.0    196.875  400000  12.56025 3.400000\n",
       "345 6635         6        67.11200  9.0    420.000  300000  12.42922 3.800000\n",
       "347 6643         6        81.98400  5.0    360.000  310000  12.20608 4.200000\n",
       "348 6644         6        56.76000  7.0    300.000  320000  12.79386 3.000000\n",
       "354 6757         6        60.73000  7.0    360.000  310000  12.76569 3.800000\n",
       "356 6759         6        68.70000  5.0    270.000  270000  12.61154 4.600000\n",
       "358 6766         6        63.08000  5.0    300.000  260000  12.76569 4.700000\n",
       "362 6770         6        77.03000  5.0    300.000  410000  12.38840 3.800000\n",
       "364 6772         6        87.28000  6.0    510.000  400000  12.57764 4.000000\n",
       "365 6780         6        71.76000 11.0    420.000  250000  12.38840 4.000000\n",
       "371 6795         6        52.82000  4.0    210.000  240000  12.79562 3.000000\n",
       "373 6797         6        74.20000  5.0    240.000  320000  12.79562 4.100000\n",
       "375 6803         6        74.51000  6.0    360.000  240000  12.89922 4.100000\n",
       "379 6811         6        44.34375 13.5    630.000  620000  12.84793 4.100000\n",
       "381 6822         6        96.46000  9.0    480.000  400000  12.50618 4.000000\n",
       "382 6834         6        80.45000  6.0    360.000  300000  12.61154 3.000000\n",
       "    infrastructure faculty  crowd    government autonomous rank new_ban\n",
       "1   3.200000       3.500000 3.700000 1          1          301  0      \n",
       "5   4.000000       3.900000 4.200000 0          1          250  0      \n",
       "7   4.000000       4.300000 3.500000 0          0          301  0      \n",
       "8   4.400000       3.900000 4.200000 0          0          301  0      \n",
       "14  3.000000       2.000000 3.500000 0          0          301  1      \n",
       "16  4.300000       3.600000 3.500000 0          0          301  1      \n",
       "18  5.000000       5.000000 5.000000 0          0          301  0      \n",
       "22  4.000000       2.000000 1.000000 0          0          301  1      \n",
       "24  4.000000       5.000000 5.000000 0          0          301  0      \n",
       "25  3.200000       3.400000 3.600000 0          0          301  1      \n",
       "31  3.800000       3.900000 3.900000 1          1           97  0      \n",
       "33  3.900000       4.000000 3.900000 1          0          301  0      \n",
       "35  3.700000       4.300000 3.700000 0          0          301  0      \n",
       "39  3.000000       3.000000 3.000000 0          0          301  0      \n",
       "41  4.300000       4.300000 3.800000 0          0          301  0      \n",
       "42  4.000000       4.000000 5.000000 0          0          301  1      \n",
       "48  3.400000       3.500000 3.300000 0          0          301  0      \n",
       "50  5.000000       5.000000 5.000000 0          0          301  0      \n",
       "52  4.500000       5.000000 5.000000 0          0          301  0      \n",
       "56  4.000000       3.000000 5.000000 0          0          301  0      \n",
       "58  3.000000       3.000000 2.000000 0          0          301  0      \n",
       "59  3.804457       3.822472 3.756056 0          0          301  1      \n",
       "65  3.804457       3.822472 3.756056 0          0          301  1      \n",
       "67  3.900000       4.200000 4.300000 1          1          150  0      \n",
       "69  3.100000       3.800000 3.600000 0          0          301  0      \n",
       "73  4.700000       4.300000 4.300000 0          1          301  0      \n",
       "75  2.400000       2.200000 2.600000 0          0          301  1      \n",
       "76  3.700000       3.700000 3.900000 0          0          301  0      \n",
       "82  3.300000       3.600000 4.400000 0          0          250  0      \n",
       "84  3.900000       3.900000 4.100000 0          0          200  0      \n",
       "⋮   ⋮              ⋮        ⋮        ⋮          ⋮          ⋮    ⋮      \n",
       "303 4.200000       4.200000 4.000000 0          1          301  0      \n",
       "305 3.800000       3.900000 4.300000 0          0          301  0      \n",
       "307 3.700000       4.300000 4.000000 0          1          155  0      \n",
       "311 4.200000       4.100000 4.200000 0          0          301  0      \n",
       "313 3.804457       3.822472 3.756056 0          0          301  1      \n",
       "314 4.200000       4.200000 4.100000 0          0          301  0      \n",
       "320 3.300000       3.700000 3.400000 0          1          301  0      \n",
       "322 3.900000       4.000000 3.800000 0          0          301  0      \n",
       "324 3.700000       3.700000 2.700000 0          0          301  0      \n",
       "328 3.300000       4.200000 3.800000 0          0          301  0      \n",
       "330 4.100000       4.200000 4.000000 0          0          301  0      \n",
       "331 3.500000       4.000000 2.500000 0          0          301  1      \n",
       "337 4.200000       3.400000 3.700000 0          0          301  1      \n",
       "339 3.500000       3.900000 3.600000 0          0          301  0      \n",
       "341 3.000000       4.000000 3.500000 0          0          301  0      \n",
       "345 4.000000       4.000000 4.000000 0          0          301  0      \n",
       "347 4.500000       4.300000 4.500000 0          0          301  0      \n",
       "348 3.800000       3.100000 2.900000 0          0          301  0      \n",
       "354 4.000000       3.700000 4.000000 0          0          301  0      \n",
       "356 5.000000       5.000000 5.000000 0          0          301  0      \n",
       "358 5.000000       5.000000 4.500000 0          0          301  0      \n",
       "362 4.100000       3.600000 4.000000 0          0          301  0      \n",
       "364 4.000000       3.900000 4.400000 0          0          301  0      \n",
       "365 4.000000       4.000000 4.000000 0          0          301  0      \n",
       "371 3.000000       3.300000 3.000000 0          0          301  0      \n",
       "373 4.400000       4.400000 4.000000 0          0          301  0      \n",
       "375 4.100000       4.200000 4.300000 0          0          301  0      \n",
       "379 4.700000       3.900000 4.200000 0          0          301  1      \n",
       "381 3.600000       4.300000 3.600000 0          0          301  0      \n",
       "382 3.400000       3.100000 3.200000 0          0          301  0      \n",
       "    hostel_BOTH hostel_ONE linear   decision fulltree\n",
       "1   1           0          95.25097 88.05211 88.05211\n",
       "5   0           0          83.98529 97.36824 97.36824\n",
       "7   1           0          67.03529 63.77202 63.77202\n",
       "8   1           0          70.98257 73.49375 70.32917\n",
       "14  0           0          57.34506 69.04323 69.04323\n",
       "16  1           0          59.01199 70.52405 70.52405\n",
       "18  1           0          74.53221 63.77202 63.77202\n",
       "22  1           0          36.59204 52.71238 56.88917\n",
       "24  1           0          78.07224 59.83230 56.23467\n",
       "25  1           0          60.02308 69.04323 69.04323\n",
       "31  1           0          97.83733 97.36824 97.36824\n",
       "33  1           0          77.88152 59.83230 56.23467\n",
       "35  1           0          67.06327 59.83230 56.23467\n",
       "39  1           0          66.33838 52.71238 56.88917\n",
       "41  1           0          70.52523 88.68862 84.42333\n",
       "42  1           0          67.18494 59.83230 56.23467\n",
       "48  1           0          69.44201 69.04323 69.04323\n",
       "50  1           0          89.85680 88.68862 88.48143\n",
       "52  1           0          81.48739 59.83230 56.23467\n",
       "56  1           0          71.14808 55.15813 55.15813\n",
       "58  0           0          56.74210 52.71238 49.29500\n",
       "59  0           0          59.76323 59.83230 56.23467\n",
       "65  0           0          61.80546 59.83230 65.52854\n",
       "67  1           0          99.68131 97.36824 97.36824\n",
       "69  1           0          74.01919 88.68862 91.75308\n",
       "73  0           0          88.69525 88.05211 88.05211\n",
       "75  1           0          53.97024 65.30064 65.30064\n",
       "76  0           0          77.37348 73.75159 73.75159\n",
       "82  0           0          82.17729 88.68862 91.75308\n",
       "84  1           0          79.32101 88.68862 88.48143\n",
       "⋮   ⋮           ⋮          ⋮        ⋮        ⋮       \n",
       "303 1           0          92.78713 88.05211 88.05211\n",
       "305 1           0          77.90717 88.68862 91.75308\n",
       "307 1           0          92.27407 97.36824 97.36824\n",
       "311 1           0          74.50074 68.62492 68.62492\n",
       "313 0           0          64.01767 68.62492 68.62492\n",
       "314 1           0          81.96029 88.68862 88.48143\n",
       "320 1           0          83.93804 88.05211 88.05211\n",
       "322 1           0          74.35820 81.86522 81.86522\n",
       "324 1           0          67.14082 52.71238 56.88917\n",
       "328 1           0          79.16464 68.62492 68.62492\n",
       "330 1           0          71.71905 81.86522 81.86522\n",
       "331 1           0          59.30986 52.71238 49.29500\n",
       "337 1           0          85.04649 88.68862 91.75308\n",
       "339 0           0          73.16798 68.62492 68.62492\n",
       "341 0           1          75.75998 88.68862 91.75308\n",
       "345 1           0          76.07599 81.86522 81.86522\n",
       "347 1           0          73.32382 81.86522 81.86522\n",
       "348 1           0          68.82040 52.71238 56.88917\n",
       "354 0           0          74.10919 81.86522 81.86522\n",
       "356 1           0          80.30998 68.62492 68.62492\n",
       "358 0           0          76.38859 68.62492 68.62492\n",
       "362 1           0          70.97872 70.52405 70.52405\n",
       "364 1           0          75.21836 88.68862 88.48143\n",
       "365 1           0          76.23241 68.62492 68.62492\n",
       "371 1           0          67.36720 52.71238 49.29500\n",
       "373 1           0          74.90800 81.86522 81.86522\n",
       "375 1           0          75.98160 68.62492 68.62492\n",
       "379 1           0          78.02752 73.75159 73.75159\n",
       "381 1           0          75.30797 88.68862 88.48143\n",
       "382 1           0          68.83997 81.86522 81.86522"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test$fulltree <- predict(fulltree, test, type=\"vector\")\n",
    "View(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "243b6856",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "201.134184296388"
      ],
      "text/latex": [
       "201.134184296388"
      ],
      "text/markdown": [
       "201.134184296388"
      ],
      "text/plain": [
       "[1] 201.1342"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSEfull <- mean((test$fulltree - test$cutoff)^2)\n",
    "MSEfull"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fc22152",
   "metadata": {},
   "source": [
    "### Pruned Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "38b344d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.019828923642447"
      ],
      "text/latex": [
       "0.019828923642447"
      ],
      "text/markdown": [
       "0.019828923642447"
      ],
      "text/plain": [
       "[1] 0.01982892"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ept1fYYHt8LG6R4sMG0kBCvhAMRJC+l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\nRp/PcQZPtYcAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mincp <- regtree$cptable[which.min(regtree$cptable[,\"xerror\"]), \"CP\"]\n",
    "mincp\n",
    "prunedtree<-prune(fulltree, cp= mincp )\n",
    "rpart.plot(prunedtree, digits=-3) # FIG 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "c47fe826",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 136 × 21</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>⋯</th><th scope=col>government</th><th scope=col>autonomous</th><th scope=col>rank</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_ONE</th><th scope=col>linear</th><th scope=col>decision</th><th scope=col>fulltree</th><th scope=col>pruned</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>⋯</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1002</td><td>1</td><td>96.44000</td><td> 8</td><td>300.000</td><td>240000.0</td><td>12.87391</td><td>3.400000</td><td>3.200000</td><td>3.500000</td><td>⋯</td><td>1</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>95.25097</td><td>88.05211</td><td>88.05211</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1105</td><td>1</td><td>88.05000</td><td> 8</td><td>480.000</td><td>440000.0</td><td>12.70685</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>0</td><td>1</td><td>250</td><td>0</td><td>0</td><td>0</td><td>83.98529</td><td>97.36824</td><td>97.36824</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1108</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>310000.0</td><td>12.61154</td><td>3.900000</td><td>4.000000</td><td>4.300000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.03529</td><td>63.77202</td><td>63.77202</td><td>67.33875</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>1114</td><td>1</td><td>81.55000</td><td> 6</td><td>300.000</td><td>320000.0</td><td>12.82126</td><td>4.000000</td><td>4.400000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.98257</td><td>73.49375</td><td>70.32917</td><td>67.33875</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1122</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>200000.0</td><td>12.61154</td><td>2.200000</td><td>3.000000</td><td>2.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>57.34506</td><td>69.04323</td><td>69.04323</td><td>67.33875</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>1124</td><td>1</td><td>49.08000</td><td> 5</td><td>300.000</td><td>490000.0</td><td>12.34584</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.01199</td><td>70.52405</td><td>70.52405</td><td>70.52405</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>1126</td><td>1</td><td>67.71000</td><td> 5</td><td>300.000</td><td>170000.0</td><td>13.10216</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.53221</td><td>63.77202</td><td>63.77202</td><td>67.33875</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>1130</td><td>1</td><td>45.98000</td><td> 6</td><td>480.000</td><td>180000.0</td><td>12.10072</td><td>2.200000</td><td>4.000000</td><td>2.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>36.59204</td><td>52.71238</td><td>56.88917</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>1182</td><td>1</td><td>59.68000</td><td> 4</td><td>630.000</td><td>200000.0</td><td>13.01701</td><td>4.200000</td><td>4.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>78.07224</td><td>59.83230</td><td>56.23467</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>1251</td><td>1</td><td>44.34375</td><td> 6</td><td>300.000</td><td>284000.0</td><td>12.54255</td><td>3.400000</td><td>3.200000</td><td>3.400000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>60.02308</td><td>69.04323</td><td>69.04323</td><td>67.33875</td></tr>\n",
       "\t<tr><th scope=row>31</th><td>2008</td><td>2</td><td>97.84000</td><td>10</td><td>540.000</td><td>190000.0</td><td>13.38473</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td>1</td><td>1</td><td> 97</td><td>0</td><td>1</td><td>0</td><td>97.83733</td><td>97.36824</td><td>97.36824</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>33</th><td>2021</td><td>2</td><td>72.61000</td><td> 2</td><td>240.000</td><td> 80000.0</td><td>12.70685</td><td>3.800000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>1</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.88152</td><td>59.83230</td><td>56.23467</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>2111</td><td>2</td><td>65.26000</td><td> 4</td><td>300.000</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.06327</td><td>59.83230</td><td>56.23467</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>2116</td><td>2</td><td>54.60000</td><td>10</td><td>294.000</td><td>200000.0</td><td>12.61154</td><td>3.100000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>66.33838</td><td>52.71238</td><td>56.88917</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>41</th><td>2127</td><td>2</td><td>80.37000</td><td> 5</td><td>420.000</td><td>350000.0</td><td>12.79386</td><td>3.900000</td><td>4.300000</td><td>4.300000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.52523</td><td>88.68862</td><td>84.42333</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>42</th><td>2128</td><td>2</td><td>44.34375</td><td> 3</td><td>196.875</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>67.18494</td><td>59.83230</td><td>56.23467</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>48</th><td>2134</td><td>2</td><td>72.88000</td><td> 9</td><td>360.000</td><td>240000.0</td><td>12.67608</td><td>3.300000</td><td>3.400000</td><td>3.500000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>69.44201</td><td>69.04323</td><td>69.04323</td><td>67.33875</td></tr>\n",
       "\t<tr><th scope=row>50</th><td>2136</td><td>2</td><td>44.34375</td><td> 9</td><td>240.000</td><td>480000.0</td><td>13.30469</td><td>4.300000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>89.85680</td><td>88.68862</td><td>88.48143</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>52</th><td>2138</td><td>2</td><td>64.49000</td><td> 4</td><td>270.000</td><td>250000.0</td><td>12.70685</td><td>3.900000</td><td>4.500000</td><td>5.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.48739</td><td>59.83230</td><td>56.23467</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>56</th><td>2250</td><td>2</td><td>63.71000</td><td> 6</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>4.000000</td><td>4.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.14808</td><td>55.15813</td><td>55.15813</td><td>67.33875</td></tr>\n",
       "\t<tr><th scope=row>58</th><td>2254</td><td>2</td><td>59.41000</td><td> 5</td><td>196.875</td><td>160000.0</td><td>12.79562</td><td>2.800000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>56.74210</td><td>52.71238</td><td>49.29500</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>59</th><td>2255</td><td>2</td><td>71.74876</td><td> 3</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>59.76323</td><td>59.83230</td><td>56.23467</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>65</th><td>2641</td><td>2</td><td>71.74876</td><td> 4</td><td>382.000</td><td>322661.9</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>61.80546</td><td>59.83230</td><td>65.52854</td><td>59.83230</td></tr>\n",
       "\t<tr><th scope=row>67</th><td>3014</td><td>3</td><td>98.48000</td><td> 6</td><td>300.000</td><td>340000.0</td><td>13.21768</td><td>4.100000</td><td>3.900000</td><td>4.200000</td><td>⋯</td><td>1</td><td>1</td><td>150</td><td>0</td><td>1</td><td>0</td><td>99.68131</td><td>97.36824</td><td>97.36824</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>69</th><td>3035</td><td>3</td><td>89.48000</td><td> 7</td><td>196.875</td><td>420000.0</td><td>12.97155</td><td>3.600000</td><td>3.100000</td><td>3.800000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.01919</td><td>88.68862</td><td>91.75308</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>73</th><td>3139</td><td>3</td><td>96.84000</td><td>10</td><td>630.000</td><td>550000.0</td><td>12.76569</td><td>4.300000</td><td>4.700000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>301</td><td>0</td><td>0</td><td>0</td><td>88.69525</td><td>88.05211</td><td>88.05211</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>75</th><td>3147</td><td>3</td><td>83.40000</td><td> 6</td><td>300.000</td><td>264000.0</td><td>12.30139</td><td>2.200000</td><td>2.400000</td><td>2.200000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>53.97024</td><td>65.30064</td><td>65.30064</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>76</th><td>3148</td><td>3</td><td>92.28000</td><td>10</td><td>630.000</td><td>460000.0</td><td>13.30469</td><td>3.800000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>77.37348</td><td>73.75159</td><td>73.75159</td><td>73.75159</td></tr>\n",
       "\t<tr><th scope=row>82</th><td>3182</td><td>3</td><td>98.34000</td><td> 5</td><td>300.000</td><td>600000.0</td><td>14.16617</td><td>3.800000</td><td>3.300000</td><td>3.600000</td><td>⋯</td><td>0</td><td>0</td><td>250</td><td>0</td><td>0</td><td>0</td><td>82.17729</td><td>88.68862</td><td>91.75308</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>84</th><td>3184</td><td>3</td><td>96.77000</td><td>10</td><td>480.000</td><td>570000.0</td><td>13.12237</td><td>4.000000</td><td>3.900000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>200</td><td>0</td><td>1</td><td>0</td><td>79.32101</td><td>88.68862</td><td>88.48143</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>⋮</th><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋱</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><th scope=row>303</th><td>6283</td><td>6</td><td>87.28000</td><td>13.0</td><td>196.875</td><td> 370000</td><td>12.61154</td><td>4.000000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>92.78713</td><td>88.05211</td><td>88.05211</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>305</th><td>6285</td><td>6</td><td>92.61000</td><td> 6.0</td><td>240.000</td><td> 430000</td><td>12.91411</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.90717</td><td>88.68862</td><td>91.75308</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>307</th><td>6289</td><td>6</td><td>97.98000</td><td> 7.0</td><td>300.000</td><td> 570000</td><td>13.32122</td><td>3.900000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>155</td><td>0</td><td>1</td><td>0</td><td>92.27407</td><td>97.36824</td><td>97.36824</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>311</th><td>6303</td><td>6</td><td>75.18000</td><td> 5.0</td><td>240.000</td><td> 240000</td><td>12.98540</td><td>4.000000</td><td>4.200000</td><td>4.100000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.50074</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>313</th><td>6305</td><td>6</td><td>46.17000</td><td> 5.0</td><td>210.000</td><td> 192000</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>64.01767</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>314</th><td>6307</td><td>6</td><td>83.32000</td><td>12.0</td><td>255.000</td><td> 370000</td><td>12.76569</td><td>4.100000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.96029</td><td>88.68862</td><td>88.48143</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>320</th><td>6317</td><td>6</td><td>79.53000</td><td>11.0</td><td>630.000</td><td> 310000</td><td>12.54255</td><td>3.500000</td><td>3.300000</td><td>3.700000</td><td>⋯</td><td>0</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>83.93804</td><td>88.05211</td><td>88.05211</td><td>92.45139</td></tr>\n",
       "\t<tr><th scope=row>322</th><td>6319</td><td>6</td><td>63.05000</td><td> 6.0</td><td>360.000</td><td> 308000</td><td>12.76569</td><td>3.600000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.35820</td><td>81.86522</td><td>81.86522</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>324</th><td>6321</td><td>6</td><td>45.67000</td><td> 6.0</td><td>300.000</td><td> 240000</td><td>12.79386</td><td>3.200000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.14082</td><td>52.71238</td><td>56.88917</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>328</th><td>6325</td><td>6</td><td>78.05000</td><td> 5.0</td><td>480.000</td><td> 230000</td><td>13.99783</td><td>3.600000</td><td>3.300000</td><td>4.200000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>79.16464</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>330</th><td>6419</td><td>6</td><td>78.35000</td><td> 6.0</td><td>360.000</td><td> 330000</td><td>12.50618</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.71905</td><td>81.86522</td><td>81.86522</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>331</th><td>6444</td><td>6</td><td>44.34375</td><td> 5.0</td><td>196.875</td><td> 141000</td><td>12.79562</td><td>3.200000</td><td>3.500000</td><td>4.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.30986</td><td>52.71238</td><td>49.29500</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>337</th><td>6620</td><td>6</td><td>73.99000</td><td>13.5</td><td>196.875</td><td>1080000</td><td>13.35348</td><td>3.600000</td><td>4.200000</td><td>3.400000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>85.04649</td><td>88.68862</td><td>91.75308</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>339</th><td>6622</td><td>6</td><td>85.85000</td><td> 6.0</td><td>360.000</td><td> 280000</td><td>12.76569</td><td>3.500000</td><td>3.500000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>73.16798</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>341</th><td>6628</td><td>6</td><td>56.76500</td><td> 5.0</td><td>196.875</td><td> 400000</td><td>12.56025</td><td>3.400000</td><td>3.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>75.75998</td><td>88.68862</td><td>91.75308</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>345</th><td>6635</td><td>6</td><td>67.11200</td><td> 9.0</td><td>420.000</td><td> 300000</td><td>12.42922</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.07599</td><td>81.86522</td><td>81.86522</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>347</th><td>6643</td><td>6</td><td>81.98400</td><td> 5.0</td><td>360.000</td><td> 310000</td><td>12.20608</td><td>4.200000</td><td>4.500000</td><td>4.300000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>73.32382</td><td>81.86522</td><td>81.86522</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>348</th><td>6644</td><td>6</td><td>56.76000</td><td> 7.0</td><td>300.000</td><td> 320000</td><td>12.79386</td><td>3.000000</td><td>3.800000</td><td>3.100000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.82040</td><td>52.71238</td><td>56.88917</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>354</th><td>6757</td><td>6</td><td>60.73000</td><td> 7.0</td><td>360.000</td><td> 310000</td><td>12.76569</td><td>3.800000</td><td>4.000000</td><td>3.700000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>74.10919</td><td>81.86522</td><td>81.86522</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>356</th><td>6759</td><td>6</td><td>68.70000</td><td> 5.0</td><td>270.000</td><td> 270000</td><td>12.61154</td><td>4.600000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>80.30998</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>358</th><td>6766</td><td>6</td><td>63.08000</td><td> 5.0</td><td>300.000</td><td> 260000</td><td>12.76569</td><td>4.700000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>76.38859</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>362</th><td>6770</td><td>6</td><td>77.03000</td><td> 5.0</td><td>300.000</td><td> 410000</td><td>12.38840</td><td>3.800000</td><td>4.100000</td><td>3.600000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.97872</td><td>70.52405</td><td>70.52405</td><td>70.52405</td></tr>\n",
       "\t<tr><th scope=row>364</th><td>6772</td><td>6</td><td>87.28000</td><td> 6.0</td><td>510.000</td><td> 400000</td><td>12.57764</td><td>4.000000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.21836</td><td>88.68862</td><td>88.48143</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>365</th><td>6780</td><td>6</td><td>71.76000</td><td>11.0</td><td>420.000</td><td> 250000</td><td>12.38840</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.23241</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>371</th><td>6795</td><td>6</td><td>52.82000</td><td> 4.0</td><td>210.000</td><td> 240000</td><td>12.79562</td><td>3.000000</td><td>3.000000</td><td>3.300000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.36720</td><td>52.71238</td><td>49.29500</td><td>57.67139</td></tr>\n",
       "\t<tr><th scope=row>373</th><td>6797</td><td>6</td><td>74.20000</td><td> 5.0</td><td>240.000</td><td> 320000</td><td>12.79562</td><td>4.100000</td><td>4.400000</td><td>4.400000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.90800</td><td>81.86522</td><td>81.86522</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>375</th><td>6803</td><td>6</td><td>74.51000</td><td> 6.0</td><td>360.000</td><td> 240000</td><td>12.89922</td><td>4.100000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.98160</td><td>68.62492</td><td>68.62492</td><td>75.84690</td></tr>\n",
       "\t<tr><th scope=row>379</th><td>6811</td><td>6</td><td>44.34375</td><td>13.5</td><td>630.000</td><td> 620000</td><td>12.84793</td><td>4.100000</td><td>4.700000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>78.02752</td><td>73.75159</td><td>73.75159</td><td>73.75159</td></tr>\n",
       "\t<tr><th scope=row>381</th><td>6822</td><td>6</td><td>96.46000</td><td> 9.0</td><td>480.000</td><td> 400000</td><td>12.50618</td><td>4.000000</td><td>3.600000</td><td>4.300000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.30797</td><td>88.68862</td><td>88.48143</td><td>88.68862</td></tr>\n",
       "\t<tr><th scope=row>382</th><td>6834</td><td>6</td><td>80.45000</td><td> 6.0</td><td>360.000</td><td> 300000</td><td>12.61154</td><td>3.000000</td><td>3.400000</td><td>3.100000</td><td>⋯</td><td>0</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.83997</td><td>81.86522</td><td>81.86522</td><td>75.84690</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 136 × 21\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & ⋯ & government & autonomous & rank & new\\_ban & hostel\\_BOTH & hostel\\_ONE & linear & decision & fulltree & pruned\\\\\n",
       "  & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ⋯ & <int> & <int> & <int> & <int> & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1002 & 1 & 96.44000 &  8 & 300.000 & 240000.0 & 12.87391 & 3.400000 & 3.200000 & 3.500000 & ⋯ & 1 & 1 & 301 & 0 & 1 & 0 & 95.25097 & 88.05211 & 88.05211 & 92.45139\\\\\n",
       "\t5 & 1105 & 1 & 88.05000 &  8 & 480.000 & 440000.0 & 12.70685 & 3.900000 & 4.000000 & 3.900000 & ⋯ & 0 & 1 & 250 & 0 & 0 & 0 & 83.98529 & 97.36824 & 97.36824 & 92.45139\\\\\n",
       "\t7 & 1108 & 1 & 44.34375 &  5 & 300.000 & 310000.0 & 12.61154 & 3.900000 & 4.000000 & 4.300000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 67.03529 & 63.77202 & 63.77202 & 67.33875\\\\\n",
       "\t8 & 1114 & 1 & 81.55000 &  6 & 300.000 & 320000.0 & 12.82126 & 4.000000 & 4.400000 & 3.900000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 70.98257 & 73.49375 & 70.32917 & 67.33875\\\\\n",
       "\t14 & 1122 & 1 & 44.34375 &  5 & 300.000 & 200000.0 & 12.61154 & 2.200000 & 3.000000 & 2.000000 & ⋯ & 0 & 0 & 301 & 1 & 0 & 0 & 57.34506 & 69.04323 & 69.04323 & 67.33875\\\\\n",
       "\t16 & 1124 & 1 & 49.08000 &  5 & 300.000 & 490000.0 & 12.34584 & 3.600000 & 4.300000 & 3.600000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 59.01199 & 70.52405 & 70.52405 & 70.52405\\\\\n",
       "\t18 & 1126 & 1 & 67.71000 &  5 & 300.000 & 170000.0 & 13.10216 & 5.000000 & 5.000000 & 5.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 74.53221 & 63.77202 & 63.77202 & 67.33875\\\\\n",
       "\t22 & 1130 & 1 & 45.98000 &  6 & 480.000 & 180000.0 & 12.10072 & 2.200000 & 4.000000 & 2.000000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 36.59204 & 52.71238 & 56.88917 & 57.67139\\\\\n",
       "\t24 & 1182 & 1 & 59.68000 &  4 & 630.000 & 200000.0 & 13.01701 & 4.200000 & 4.000000 & 5.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 78.07224 & 59.83230 & 56.23467 & 59.83230\\\\\n",
       "\t25 & 1251 & 1 & 44.34375 &  6 & 300.000 & 284000.0 & 12.54255 & 3.400000 & 3.200000 & 3.400000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 60.02308 & 69.04323 & 69.04323 & 67.33875\\\\\n",
       "\t31 & 2008 & 2 & 97.84000 & 10 & 540.000 & 190000.0 & 13.38473 & 3.900000 & 3.800000 & 3.900000 & ⋯ & 1 & 1 &  97 & 0 & 1 & 0 & 97.83733 & 97.36824 & 97.36824 & 92.45139\\\\\n",
       "\t33 & 2021 & 2 & 72.61000 &  2 & 240.000 &  80000.0 & 12.70685 & 3.800000 & 3.900000 & 4.000000 & ⋯ & 1 & 0 & 301 & 0 & 1 & 0 & 77.88152 & 59.83230 & 56.23467 & 59.83230\\\\\n",
       "\t35 & 2111 & 2 & 65.26000 &  4 & 300.000 & 170000.0 & 12.61154 & 3.800000 & 3.700000 & 4.300000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 67.06327 & 59.83230 & 56.23467 & 59.83230\\\\\n",
       "\t39 & 2116 & 2 & 54.60000 & 10 & 294.000 & 200000.0 & 12.61154 & 3.100000 & 3.000000 & 3.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 66.33838 & 52.71238 & 56.88917 & 57.67139\\\\\n",
       "\t41 & 2127 & 2 & 80.37000 &  5 & 420.000 & 350000.0 & 12.79386 & 3.900000 & 4.300000 & 4.300000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 70.52523 & 88.68862 & 84.42333 & 88.68862\\\\\n",
       "\t42 & 2128 & 2 & 44.34375 &  3 & 196.875 & 170000.0 & 12.61154 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 67.18494 & 59.83230 & 56.23467 & 59.83230\\\\\n",
       "\t48 & 2134 & 2 & 72.88000 &  9 & 360.000 & 240000.0 & 12.67608 & 3.300000 & 3.400000 & 3.500000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 69.44201 & 69.04323 & 69.04323 & 67.33875\\\\\n",
       "\t50 & 2136 & 2 & 44.34375 &  9 & 240.000 & 480000.0 & 13.30469 & 4.300000 & 5.000000 & 5.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 89.85680 & 88.68862 & 88.48143 & 88.68862\\\\\n",
       "\t52 & 2138 & 2 & 64.49000 &  4 & 270.000 & 250000.0 & 12.70685 & 3.900000 & 4.500000 & 5.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 81.48739 & 59.83230 & 56.23467 & 59.83230\\\\\n",
       "\t56 & 2250 & 2 & 63.71000 &  6 & 196.875 & 220000.0 & 12.79562 & 4.000000 & 4.000000 & 3.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 71.14808 & 55.15813 & 55.15813 & 67.33875\\\\\n",
       "\t58 & 2254 & 2 & 59.41000 &  5 & 196.875 & 160000.0 & 12.79562 & 2.800000 & 3.000000 & 3.000000 & ⋯ & 0 & 0 & 301 & 0 & 0 & 0 & 56.74210 & 52.71238 & 49.29500 & 57.67139\\\\\n",
       "\t59 & 2255 & 2 & 71.74876 &  3 & 196.875 & 220000.0 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 0 & 0 & 301 & 1 & 0 & 0 & 59.76323 & 59.83230 & 56.23467 & 59.83230\\\\\n",
       "\t65 & 2641 & 2 & 71.74876 &  4 & 382.000 & 322661.9 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 0 & 0 & 301 & 1 & 0 & 0 & 61.80546 & 59.83230 & 65.52854 & 59.83230\\\\\n",
       "\t67 & 3014 & 3 & 98.48000 &  6 & 300.000 & 340000.0 & 13.21768 & 4.100000 & 3.900000 & 4.200000 & ⋯ & 1 & 1 & 150 & 0 & 1 & 0 & 99.68131 & 97.36824 & 97.36824 & 92.45139\\\\\n",
       "\t69 & 3035 & 3 & 89.48000 &  7 & 196.875 & 420000.0 & 12.97155 & 3.600000 & 3.100000 & 3.800000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 74.01919 & 88.68862 & 91.75308 & 88.68862\\\\\n",
       "\t73 & 3139 & 3 & 96.84000 & 10 & 630.000 & 550000.0 & 12.76569 & 4.300000 & 4.700000 & 4.300000 & ⋯ & 0 & 1 & 301 & 0 & 0 & 0 & 88.69525 & 88.05211 & 88.05211 & 92.45139\\\\\n",
       "\t75 & 3147 & 3 & 83.40000 &  6 & 300.000 & 264000.0 & 12.30139 & 2.200000 & 2.400000 & 2.200000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 53.97024 & 65.30064 & 65.30064 & 57.67139\\\\\n",
       "\t76 & 3148 & 3 & 92.28000 & 10 & 630.000 & 460000.0 & 13.30469 & 3.800000 & 3.700000 & 3.700000 & ⋯ & 0 & 0 & 301 & 0 & 0 & 0 & 77.37348 & 73.75159 & 73.75159 & 73.75159\\\\\n",
       "\t82 & 3182 & 3 & 98.34000 &  5 & 300.000 & 600000.0 & 14.16617 & 3.800000 & 3.300000 & 3.600000 & ⋯ & 0 & 0 & 250 & 0 & 0 & 0 & 82.17729 & 88.68862 & 91.75308 & 88.68862\\\\\n",
       "\t84 & 3184 & 3 & 96.77000 & 10 & 480.000 & 570000.0 & 13.12237 & 4.000000 & 3.900000 & 3.900000 & ⋯ & 0 & 0 & 200 & 0 & 1 & 0 & 79.32101 & 88.68862 & 88.48143 & 88.68862\\\\\n",
       "\t⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋱ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t303 & 6283 & 6 & 87.28000 & 13.0 & 196.875 &  370000 & 12.61154 & 4.000000 & 4.200000 & 4.200000 & ⋯ & 0 & 1 & 301 & 0 & 1 & 0 & 92.78713 & 88.05211 & 88.05211 & 92.45139\\\\\n",
       "\t305 & 6285 & 6 & 92.61000 &  6.0 & 240.000 &  430000 & 12.91411 & 3.900000 & 3.800000 & 3.900000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 77.90717 & 88.68862 & 91.75308 & 88.68862\\\\\n",
       "\t307 & 6289 & 6 & 97.98000 &  7.0 & 300.000 &  570000 & 13.32122 & 3.900000 & 3.700000 & 4.300000 & ⋯ & 0 & 1 & 155 & 0 & 1 & 0 & 92.27407 & 97.36824 & 97.36824 & 92.45139\\\\\n",
       "\t311 & 6303 & 6 & 75.18000 &  5.0 & 240.000 &  240000 & 12.98540 & 4.000000 & 4.200000 & 4.100000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 74.50074 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t313 & 6305 & 6 & 46.17000 &  5.0 & 210.000 &  192000 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 0 & 0 & 301 & 1 & 0 & 0 & 64.01767 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t314 & 6307 & 6 & 83.32000 & 12.0 & 255.000 &  370000 & 12.76569 & 4.100000 & 4.200000 & 4.200000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 81.96029 & 88.68862 & 88.48143 & 88.68862\\\\\n",
       "\t320 & 6317 & 6 & 79.53000 & 11.0 & 630.000 &  310000 & 12.54255 & 3.500000 & 3.300000 & 3.700000 & ⋯ & 0 & 1 & 301 & 0 & 1 & 0 & 83.93804 & 88.05211 & 88.05211 & 92.45139\\\\\n",
       "\t322 & 6319 & 6 & 63.05000 &  6.0 & 360.000 &  308000 & 12.76569 & 3.600000 & 3.900000 & 4.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 74.35820 & 81.86522 & 81.86522 & 75.84690\\\\\n",
       "\t324 & 6321 & 6 & 45.67000 &  6.0 & 300.000 &  240000 & 12.79386 & 3.200000 & 3.700000 & 3.700000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 67.14082 & 52.71238 & 56.88917 & 57.67139\\\\\n",
       "\t328 & 6325 & 6 & 78.05000 &  5.0 & 480.000 &  230000 & 13.99783 & 3.600000 & 3.300000 & 4.200000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 79.16464 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t330 & 6419 & 6 & 78.35000 &  6.0 & 360.000 &  330000 & 12.50618 & 4.200000 & 4.100000 & 4.200000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 71.71905 & 81.86522 & 81.86522 & 75.84690\\\\\n",
       "\t331 & 6444 & 6 & 44.34375 &  5.0 & 196.875 &  141000 & 12.79562 & 3.200000 & 3.500000 & 4.000000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 59.30986 & 52.71238 & 49.29500 & 57.67139\\\\\n",
       "\t337 & 6620 & 6 & 73.99000 & 13.5 & 196.875 & 1080000 & 13.35348 & 3.600000 & 4.200000 & 3.400000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 85.04649 & 88.68862 & 91.75308 & 88.68862\\\\\n",
       "\t339 & 6622 & 6 & 85.85000 &  6.0 & 360.000 &  280000 & 12.76569 & 3.500000 & 3.500000 & 3.900000 & ⋯ & 0 & 0 & 301 & 0 & 0 & 0 & 73.16798 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t341 & 6628 & 6 & 56.76500 &  5.0 & 196.875 &  400000 & 12.56025 & 3.400000 & 3.000000 & 4.000000 & ⋯ & 0 & 0 & 301 & 0 & 0 & 1 & 75.75998 & 88.68862 & 91.75308 & 88.68862\\\\\n",
       "\t345 & 6635 & 6 & 67.11200 &  9.0 & 420.000 &  300000 & 12.42922 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 76.07599 & 81.86522 & 81.86522 & 75.84690\\\\\n",
       "\t347 & 6643 & 6 & 81.98400 &  5.0 & 360.000 &  310000 & 12.20608 & 4.200000 & 4.500000 & 4.300000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 73.32382 & 81.86522 & 81.86522 & 75.84690\\\\\n",
       "\t348 & 6644 & 6 & 56.76000 &  7.0 & 300.000 &  320000 & 12.79386 & 3.000000 & 3.800000 & 3.100000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 68.82040 & 52.71238 & 56.88917 & 57.67139\\\\\n",
       "\t354 & 6757 & 6 & 60.73000 &  7.0 & 360.000 &  310000 & 12.76569 & 3.800000 & 4.000000 & 3.700000 & ⋯ & 0 & 0 & 301 & 0 & 0 & 0 & 74.10919 & 81.86522 & 81.86522 & 75.84690\\\\\n",
       "\t356 & 6759 & 6 & 68.70000 &  5.0 & 270.000 &  270000 & 12.61154 & 4.600000 & 5.000000 & 5.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 80.30998 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t358 & 6766 & 6 & 63.08000 &  5.0 & 300.000 &  260000 & 12.76569 & 4.700000 & 5.000000 & 5.000000 & ⋯ & 0 & 0 & 301 & 0 & 0 & 0 & 76.38859 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t362 & 6770 & 6 & 77.03000 &  5.0 & 300.000 &  410000 & 12.38840 & 3.800000 & 4.100000 & 3.600000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 70.97872 & 70.52405 & 70.52405 & 70.52405\\\\\n",
       "\t364 & 6772 & 6 & 87.28000 &  6.0 & 510.000 &  400000 & 12.57764 & 4.000000 & 4.000000 & 3.900000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 75.21836 & 88.68862 & 88.48143 & 88.68862\\\\\n",
       "\t365 & 6780 & 6 & 71.76000 & 11.0 & 420.000 &  250000 & 12.38840 & 4.000000 & 4.000000 & 4.000000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 76.23241 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t371 & 6795 & 6 & 52.82000 &  4.0 & 210.000 &  240000 & 12.79562 & 3.000000 & 3.000000 & 3.300000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 67.36720 & 52.71238 & 49.29500 & 57.67139\\\\\n",
       "\t373 & 6797 & 6 & 74.20000 &  5.0 & 240.000 &  320000 & 12.79562 & 4.100000 & 4.400000 & 4.400000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 74.90800 & 81.86522 & 81.86522 & 75.84690\\\\\n",
       "\t375 & 6803 & 6 & 74.51000 &  6.0 & 360.000 &  240000 & 12.89922 & 4.100000 & 4.100000 & 4.200000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 75.98160 & 68.62492 & 68.62492 & 75.84690\\\\\n",
       "\t379 & 6811 & 6 & 44.34375 & 13.5 & 630.000 &  620000 & 12.84793 & 4.100000 & 4.700000 & 3.900000 & ⋯ & 0 & 0 & 301 & 1 & 1 & 0 & 78.02752 & 73.75159 & 73.75159 & 73.75159\\\\\n",
       "\t381 & 6822 & 6 & 96.46000 &  9.0 & 480.000 &  400000 & 12.50618 & 4.000000 & 3.600000 & 4.300000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 75.30797 & 88.68862 & 88.48143 & 88.68862\\\\\n",
       "\t382 & 6834 & 6 & 80.45000 &  6.0 & 360.000 &  300000 & 12.61154 & 3.000000 & 3.400000 & 3.100000 & ⋯ & 0 & 0 & 301 & 0 & 1 & 0 & 68.83997 & 81.86522 & 81.86522 & 75.84690\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 136 × 21\n",
       "\n",
       "| <!--/--> | college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;dbl&gt; | intake &lt;dbl&gt; | fees &lt;dbl&gt; | salary &lt;dbl&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | ⋯ ⋯ | government &lt;int&gt; | autonomous &lt;int&gt; | rank &lt;int&gt; | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_ONE &lt;int&gt; | linear &lt;dbl&gt; | decision &lt;dbl&gt; | fulltree &lt;dbl&gt; | pruned &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1002 | 1 | 96.44000 |  8 | 300.000 | 240000.0 | 12.87391 | 3.400000 | 3.200000 | 3.500000 | ⋯ | 1 | 1 | 301 | 0 | 1 | 0 | 95.25097 | 88.05211 | 88.05211 | 92.45139 |\n",
       "| 5 | 1105 | 1 | 88.05000 |  8 | 480.000 | 440000.0 | 12.70685 | 3.900000 | 4.000000 | 3.900000 | ⋯ | 0 | 1 | 250 | 0 | 0 | 0 | 83.98529 | 97.36824 | 97.36824 | 92.45139 |\n",
       "| 7 | 1108 | 1 | 44.34375 |  5 | 300.000 | 310000.0 | 12.61154 | 3.900000 | 4.000000 | 4.300000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 67.03529 | 63.77202 | 63.77202 | 67.33875 |\n",
       "| 8 | 1114 | 1 | 81.55000 |  6 | 300.000 | 320000.0 | 12.82126 | 4.000000 | 4.400000 | 3.900000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 70.98257 | 73.49375 | 70.32917 | 67.33875 |\n",
       "| 14 | 1122 | 1 | 44.34375 |  5 | 300.000 | 200000.0 | 12.61154 | 2.200000 | 3.000000 | 2.000000 | ⋯ | 0 | 0 | 301 | 1 | 0 | 0 | 57.34506 | 69.04323 | 69.04323 | 67.33875 |\n",
       "| 16 | 1124 | 1 | 49.08000 |  5 | 300.000 | 490000.0 | 12.34584 | 3.600000 | 4.300000 | 3.600000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 59.01199 | 70.52405 | 70.52405 | 70.52405 |\n",
       "| 18 | 1126 | 1 | 67.71000 |  5 | 300.000 | 170000.0 | 13.10216 | 5.000000 | 5.000000 | 5.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 74.53221 | 63.77202 | 63.77202 | 67.33875 |\n",
       "| 22 | 1130 | 1 | 45.98000 |  6 | 480.000 | 180000.0 | 12.10072 | 2.200000 | 4.000000 | 2.000000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 36.59204 | 52.71238 | 56.88917 | 57.67139 |\n",
       "| 24 | 1182 | 1 | 59.68000 |  4 | 630.000 | 200000.0 | 13.01701 | 4.200000 | 4.000000 | 5.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 78.07224 | 59.83230 | 56.23467 | 59.83230 |\n",
       "| 25 | 1251 | 1 | 44.34375 |  6 | 300.000 | 284000.0 | 12.54255 | 3.400000 | 3.200000 | 3.400000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 60.02308 | 69.04323 | 69.04323 | 67.33875 |\n",
       "| 31 | 2008 | 2 | 97.84000 | 10 | 540.000 | 190000.0 | 13.38473 | 3.900000 | 3.800000 | 3.900000 | ⋯ | 1 | 1 |  97 | 0 | 1 | 0 | 97.83733 | 97.36824 | 97.36824 | 92.45139 |\n",
       "| 33 | 2021 | 2 | 72.61000 |  2 | 240.000 |  80000.0 | 12.70685 | 3.800000 | 3.900000 | 4.000000 | ⋯ | 1 | 0 | 301 | 0 | 1 | 0 | 77.88152 | 59.83230 | 56.23467 | 59.83230 |\n",
       "| 35 | 2111 | 2 | 65.26000 |  4 | 300.000 | 170000.0 | 12.61154 | 3.800000 | 3.700000 | 4.300000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 67.06327 | 59.83230 | 56.23467 | 59.83230 |\n",
       "| 39 | 2116 | 2 | 54.60000 | 10 | 294.000 | 200000.0 | 12.61154 | 3.100000 | 3.000000 | 3.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 66.33838 | 52.71238 | 56.88917 | 57.67139 |\n",
       "| 41 | 2127 | 2 | 80.37000 |  5 | 420.000 | 350000.0 | 12.79386 | 3.900000 | 4.300000 | 4.300000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 70.52523 | 88.68862 | 84.42333 | 88.68862 |\n",
       "| 42 | 2128 | 2 | 44.34375 |  3 | 196.875 | 170000.0 | 12.61154 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 67.18494 | 59.83230 | 56.23467 | 59.83230 |\n",
       "| 48 | 2134 | 2 | 72.88000 |  9 | 360.000 | 240000.0 | 12.67608 | 3.300000 | 3.400000 | 3.500000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 69.44201 | 69.04323 | 69.04323 | 67.33875 |\n",
       "| 50 | 2136 | 2 | 44.34375 |  9 | 240.000 | 480000.0 | 13.30469 | 4.300000 | 5.000000 | 5.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 89.85680 | 88.68862 | 88.48143 | 88.68862 |\n",
       "| 52 | 2138 | 2 | 64.49000 |  4 | 270.000 | 250000.0 | 12.70685 | 3.900000 | 4.500000 | 5.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 81.48739 | 59.83230 | 56.23467 | 59.83230 |\n",
       "| 56 | 2250 | 2 | 63.71000 |  6 | 196.875 | 220000.0 | 12.79562 | 4.000000 | 4.000000 | 3.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 71.14808 | 55.15813 | 55.15813 | 67.33875 |\n",
       "| 58 | 2254 | 2 | 59.41000 |  5 | 196.875 | 160000.0 | 12.79562 | 2.800000 | 3.000000 | 3.000000 | ⋯ | 0 | 0 | 301 | 0 | 0 | 0 | 56.74210 | 52.71238 | 49.29500 | 57.67139 |\n",
       "| 59 | 2255 | 2 | 71.74876 |  3 | 196.875 | 220000.0 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 0 | 0 | 301 | 1 | 0 | 0 | 59.76323 | 59.83230 | 56.23467 | 59.83230 |\n",
       "| 65 | 2641 | 2 | 71.74876 |  4 | 382.000 | 322661.9 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 0 | 0 | 301 | 1 | 0 | 0 | 61.80546 | 59.83230 | 65.52854 | 59.83230 |\n",
       "| 67 | 3014 | 3 | 98.48000 |  6 | 300.000 | 340000.0 | 13.21768 | 4.100000 | 3.900000 | 4.200000 | ⋯ | 1 | 1 | 150 | 0 | 1 | 0 | 99.68131 | 97.36824 | 97.36824 | 92.45139 |\n",
       "| 69 | 3035 | 3 | 89.48000 |  7 | 196.875 | 420000.0 | 12.97155 | 3.600000 | 3.100000 | 3.800000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 74.01919 | 88.68862 | 91.75308 | 88.68862 |\n",
       "| 73 | 3139 | 3 | 96.84000 | 10 | 630.000 | 550000.0 | 12.76569 | 4.300000 | 4.700000 | 4.300000 | ⋯ | 0 | 1 | 301 | 0 | 0 | 0 | 88.69525 | 88.05211 | 88.05211 | 92.45139 |\n",
       "| 75 | 3147 | 3 | 83.40000 |  6 | 300.000 | 264000.0 | 12.30139 | 2.200000 | 2.400000 | 2.200000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 53.97024 | 65.30064 | 65.30064 | 57.67139 |\n",
       "| 76 | 3148 | 3 | 92.28000 | 10 | 630.000 | 460000.0 | 13.30469 | 3.800000 | 3.700000 | 3.700000 | ⋯ | 0 | 0 | 301 | 0 | 0 | 0 | 77.37348 | 73.75159 | 73.75159 | 73.75159 |\n",
       "| 82 | 3182 | 3 | 98.34000 |  5 | 300.000 | 600000.0 | 14.16617 | 3.800000 | 3.300000 | 3.600000 | ⋯ | 0 | 0 | 250 | 0 | 0 | 0 | 82.17729 | 88.68862 | 91.75308 | 88.68862 |\n",
       "| 84 | 3184 | 3 | 96.77000 | 10 | 480.000 | 570000.0 | 13.12237 | 4.000000 | 3.900000 | 3.900000 | ⋯ | 0 | 0 | 200 | 0 | 1 | 0 | 79.32101 | 88.68862 | 88.48143 | 88.68862 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 303 | 6283 | 6 | 87.28000 | 13.0 | 196.875 |  370000 | 12.61154 | 4.000000 | 4.200000 | 4.200000 | ⋯ | 0 | 1 | 301 | 0 | 1 | 0 | 92.78713 | 88.05211 | 88.05211 | 92.45139 |\n",
       "| 305 | 6285 | 6 | 92.61000 |  6.0 | 240.000 |  430000 | 12.91411 | 3.900000 | 3.800000 | 3.900000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 77.90717 | 88.68862 | 91.75308 | 88.68862 |\n",
       "| 307 | 6289 | 6 | 97.98000 |  7.0 | 300.000 |  570000 | 13.32122 | 3.900000 | 3.700000 | 4.300000 | ⋯ | 0 | 1 | 155 | 0 | 1 | 0 | 92.27407 | 97.36824 | 97.36824 | 92.45139 |\n",
       "| 311 | 6303 | 6 | 75.18000 |  5.0 | 240.000 |  240000 | 12.98540 | 4.000000 | 4.200000 | 4.100000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 74.50074 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 313 | 6305 | 6 | 46.17000 |  5.0 | 210.000 |  192000 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 0 | 0 | 301 | 1 | 0 | 0 | 64.01767 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 314 | 6307 | 6 | 83.32000 | 12.0 | 255.000 |  370000 | 12.76569 | 4.100000 | 4.200000 | 4.200000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 81.96029 | 88.68862 | 88.48143 | 88.68862 |\n",
       "| 320 | 6317 | 6 | 79.53000 | 11.0 | 630.000 |  310000 | 12.54255 | 3.500000 | 3.300000 | 3.700000 | ⋯ | 0 | 1 | 301 | 0 | 1 | 0 | 83.93804 | 88.05211 | 88.05211 | 92.45139 |\n",
       "| 322 | 6319 | 6 | 63.05000 |  6.0 | 360.000 |  308000 | 12.76569 | 3.600000 | 3.900000 | 4.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 74.35820 | 81.86522 | 81.86522 | 75.84690 |\n",
       "| 324 | 6321 | 6 | 45.67000 |  6.0 | 300.000 |  240000 | 12.79386 | 3.200000 | 3.700000 | 3.700000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 67.14082 | 52.71238 | 56.88917 | 57.67139 |\n",
       "| 328 | 6325 | 6 | 78.05000 |  5.0 | 480.000 |  230000 | 13.99783 | 3.600000 | 3.300000 | 4.200000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 79.16464 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 330 | 6419 | 6 | 78.35000 |  6.0 | 360.000 |  330000 | 12.50618 | 4.200000 | 4.100000 | 4.200000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 71.71905 | 81.86522 | 81.86522 | 75.84690 |\n",
       "| 331 | 6444 | 6 | 44.34375 |  5.0 | 196.875 |  141000 | 12.79562 | 3.200000 | 3.500000 | 4.000000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 59.30986 | 52.71238 | 49.29500 | 57.67139 |\n",
       "| 337 | 6620 | 6 | 73.99000 | 13.5 | 196.875 | 1080000 | 13.35348 | 3.600000 | 4.200000 | 3.400000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 85.04649 | 88.68862 | 91.75308 | 88.68862 |\n",
       "| 339 | 6622 | 6 | 85.85000 |  6.0 | 360.000 |  280000 | 12.76569 | 3.500000 | 3.500000 | 3.900000 | ⋯ | 0 | 0 | 301 | 0 | 0 | 0 | 73.16798 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 341 | 6628 | 6 | 56.76500 |  5.0 | 196.875 |  400000 | 12.56025 | 3.400000 | 3.000000 | 4.000000 | ⋯ | 0 | 0 | 301 | 0 | 0 | 1 | 75.75998 | 88.68862 | 91.75308 | 88.68862 |\n",
       "| 345 | 6635 | 6 | 67.11200 |  9.0 | 420.000 |  300000 | 12.42922 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 76.07599 | 81.86522 | 81.86522 | 75.84690 |\n",
       "| 347 | 6643 | 6 | 81.98400 |  5.0 | 360.000 |  310000 | 12.20608 | 4.200000 | 4.500000 | 4.300000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 73.32382 | 81.86522 | 81.86522 | 75.84690 |\n",
       "| 348 | 6644 | 6 | 56.76000 |  7.0 | 300.000 |  320000 | 12.79386 | 3.000000 | 3.800000 | 3.100000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 68.82040 | 52.71238 | 56.88917 | 57.67139 |\n",
       "| 354 | 6757 | 6 | 60.73000 |  7.0 | 360.000 |  310000 | 12.76569 | 3.800000 | 4.000000 | 3.700000 | ⋯ | 0 | 0 | 301 | 0 | 0 | 0 | 74.10919 | 81.86522 | 81.86522 | 75.84690 |\n",
       "| 356 | 6759 | 6 | 68.70000 |  5.0 | 270.000 |  270000 | 12.61154 | 4.600000 | 5.000000 | 5.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 80.30998 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 358 | 6766 | 6 | 63.08000 |  5.0 | 300.000 |  260000 | 12.76569 | 4.700000 | 5.000000 | 5.000000 | ⋯ | 0 | 0 | 301 | 0 | 0 | 0 | 76.38859 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 362 | 6770 | 6 | 77.03000 |  5.0 | 300.000 |  410000 | 12.38840 | 3.800000 | 4.100000 | 3.600000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 70.97872 | 70.52405 | 70.52405 | 70.52405 |\n",
       "| 364 | 6772 | 6 | 87.28000 |  6.0 | 510.000 |  400000 | 12.57764 | 4.000000 | 4.000000 | 3.900000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 75.21836 | 88.68862 | 88.48143 | 88.68862 |\n",
       "| 365 | 6780 | 6 | 71.76000 | 11.0 | 420.000 |  250000 | 12.38840 | 4.000000 | 4.000000 | 4.000000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 76.23241 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 371 | 6795 | 6 | 52.82000 |  4.0 | 210.000 |  240000 | 12.79562 | 3.000000 | 3.000000 | 3.300000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 67.36720 | 52.71238 | 49.29500 | 57.67139 |\n",
       "| 373 | 6797 | 6 | 74.20000 |  5.0 | 240.000 |  320000 | 12.79562 | 4.100000 | 4.400000 | 4.400000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 74.90800 | 81.86522 | 81.86522 | 75.84690 |\n",
       "| 375 | 6803 | 6 | 74.51000 |  6.0 | 360.000 |  240000 | 12.89922 | 4.100000 | 4.100000 | 4.200000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 75.98160 | 68.62492 | 68.62492 | 75.84690 |\n",
       "| 379 | 6811 | 6 | 44.34375 | 13.5 | 630.000 |  620000 | 12.84793 | 4.100000 | 4.700000 | 3.900000 | ⋯ | 0 | 0 | 301 | 1 | 1 | 0 | 78.02752 | 73.75159 | 73.75159 | 73.75159 |\n",
       "| 381 | 6822 | 6 | 96.46000 |  9.0 | 480.000 |  400000 | 12.50618 | 4.000000 | 3.600000 | 4.300000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 75.30797 | 88.68862 | 88.48143 | 88.68862 |\n",
       "| 382 | 6834 | 6 | 80.45000 |  6.0 | 360.000 |  300000 | 12.61154 | 3.000000 | 3.400000 | 3.100000 | ⋯ | 0 | 0 | 301 | 0 | 1 | 0 | 68.83997 | 81.86522 | 81.86522 | 75.84690 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff   courses intake  fees     salary   rating  \n",
       "1   1002         1        96.44000  8      300.000 240000.0 12.87391 3.400000\n",
       "5   1105         1        88.05000  8      480.000 440000.0 12.70685 3.900000\n",
       "7   1108         1        44.34375  5      300.000 310000.0 12.61154 3.900000\n",
       "8   1114         1        81.55000  6      300.000 320000.0 12.82126 4.000000\n",
       "14  1122         1        44.34375  5      300.000 200000.0 12.61154 2.200000\n",
       "16  1124         1        49.08000  5      300.000 490000.0 12.34584 3.600000\n",
       "18  1126         1        67.71000  5      300.000 170000.0 13.10216 5.000000\n",
       "22  1130         1        45.98000  6      480.000 180000.0 12.10072 2.200000\n",
       "24  1182         1        59.68000  4      630.000 200000.0 13.01701 4.200000\n",
       "25  1251         1        44.34375  6      300.000 284000.0 12.54255 3.400000\n",
       "31  2008         2        97.84000 10      540.000 190000.0 13.38473 3.900000\n",
       "33  2021         2        72.61000  2      240.000  80000.0 12.70685 3.800000\n",
       "35  2111         2        65.26000  4      300.000 170000.0 12.61154 3.800000\n",
       "39  2116         2        54.60000 10      294.000 200000.0 12.61154 3.100000\n",
       "41  2127         2        80.37000  5      420.000 350000.0 12.79386 3.900000\n",
       "42  2128         2        44.34375  3      196.875 170000.0 12.61154 3.800000\n",
       "48  2134         2        72.88000  9      360.000 240000.0 12.67608 3.300000\n",
       "50  2136         2        44.34375  9      240.000 480000.0 13.30469 4.300000\n",
       "52  2138         2        64.49000  4      270.000 250000.0 12.70685 3.900000\n",
       "56  2250         2        63.71000  6      196.875 220000.0 12.79562 4.000000\n",
       "58  2254         2        59.41000  5      196.875 160000.0 12.79562 2.800000\n",
       "59  2255         2        71.74876  3      196.875 220000.0 12.79562 3.666295\n",
       "65  2641         2        71.74876  4      382.000 322661.9 12.79562 3.666295\n",
       "67  3014         3        98.48000  6      300.000 340000.0 13.21768 4.100000\n",
       "69  3035         3        89.48000  7      196.875 420000.0 12.97155 3.600000\n",
       "73  3139         3        96.84000 10      630.000 550000.0 12.76569 4.300000\n",
       "75  3147         3        83.40000  6      300.000 264000.0 12.30139 2.200000\n",
       "76  3148         3        92.28000 10      630.000 460000.0 13.30469 3.800000\n",
       "82  3182         3        98.34000  5      300.000 600000.0 14.16617 3.800000\n",
       "84  3184         3        96.77000 10      480.000 570000.0 13.12237 4.000000\n",
       "⋮   ⋮            ⋮        ⋮        ⋮       ⋮       ⋮        ⋮        ⋮       \n",
       "303 6283         6        87.28000 13.0    196.875  370000  12.61154 4.000000\n",
       "305 6285         6        92.61000  6.0    240.000  430000  12.91411 3.900000\n",
       "307 6289         6        97.98000  7.0    300.000  570000  13.32122 3.900000\n",
       "311 6303         6        75.18000  5.0    240.000  240000  12.98540 4.000000\n",
       "313 6305         6        46.17000  5.0    210.000  192000  12.79562 3.666295\n",
       "314 6307         6        83.32000 12.0    255.000  370000  12.76569 4.100000\n",
       "320 6317         6        79.53000 11.0    630.000  310000  12.54255 3.500000\n",
       "322 6319         6        63.05000  6.0    360.000  308000  12.76569 3.600000\n",
       "324 6321         6        45.67000  6.0    300.000  240000  12.79386 3.200000\n",
       "328 6325         6        78.05000  5.0    480.000  230000  13.99783 3.600000\n",
       "330 6419         6        78.35000  6.0    360.000  330000  12.50618 4.200000\n",
       "331 6444         6        44.34375  5.0    196.875  141000  12.79562 3.200000\n",
       "337 6620         6        73.99000 13.5    196.875 1080000  13.35348 3.600000\n",
       "339 6622         6        85.85000  6.0    360.000  280000  12.76569 3.500000\n",
       "341 6628         6        56.76500  5.0    196.875  400000  12.56025 3.400000\n",
       "345 6635         6        67.11200  9.0    420.000  300000  12.42922 3.800000\n",
       "347 6643         6        81.98400  5.0    360.000  310000  12.20608 4.200000\n",
       "348 6644         6        56.76000  7.0    300.000  320000  12.79386 3.000000\n",
       "354 6757         6        60.73000  7.0    360.000  310000  12.76569 3.800000\n",
       "356 6759         6        68.70000  5.0    270.000  270000  12.61154 4.600000\n",
       "358 6766         6        63.08000  5.0    300.000  260000  12.76569 4.700000\n",
       "362 6770         6        77.03000  5.0    300.000  410000  12.38840 3.800000\n",
       "364 6772         6        87.28000  6.0    510.000  400000  12.57764 4.000000\n",
       "365 6780         6        71.76000 11.0    420.000  250000  12.38840 4.000000\n",
       "371 6795         6        52.82000  4.0    210.000  240000  12.79562 3.000000\n",
       "373 6797         6        74.20000  5.0    240.000  320000  12.79562 4.100000\n",
       "375 6803         6        74.51000  6.0    360.000  240000  12.89922 4.100000\n",
       "379 6811         6        44.34375 13.5    630.000  620000  12.84793 4.100000\n",
       "381 6822         6        96.46000  9.0    480.000  400000  12.50618 4.000000\n",
       "382 6834         6        80.45000  6.0    360.000  300000  12.61154 3.000000\n",
       "    infrastructure faculty  ⋯ government autonomous rank new_ban hostel_BOTH\n",
       "1   3.200000       3.500000 ⋯ 1          1          301  0       1          \n",
       "5   4.000000       3.900000 ⋯ 0          1          250  0       0          \n",
       "7   4.000000       4.300000 ⋯ 0          0          301  0       1          \n",
       "8   4.400000       3.900000 ⋯ 0          0          301  0       1          \n",
       "14  3.000000       2.000000 ⋯ 0          0          301  1       0          \n",
       "16  4.300000       3.600000 ⋯ 0          0          301  1       1          \n",
       "18  5.000000       5.000000 ⋯ 0          0          301  0       1          \n",
       "22  4.000000       2.000000 ⋯ 0          0          301  1       1          \n",
       "24  4.000000       5.000000 ⋯ 0          0          301  0       1          \n",
       "25  3.200000       3.400000 ⋯ 0          0          301  1       1          \n",
       "31  3.800000       3.900000 ⋯ 1          1           97  0       1          \n",
       "33  3.900000       4.000000 ⋯ 1          0          301  0       1          \n",
       "35  3.700000       4.300000 ⋯ 0          0          301  0       1          \n",
       "39  3.000000       3.000000 ⋯ 0          0          301  0       1          \n",
       "41  4.300000       4.300000 ⋯ 0          0          301  0       1          \n",
       "42  4.000000       4.000000 ⋯ 0          0          301  1       1          \n",
       "48  3.400000       3.500000 ⋯ 0          0          301  0       1          \n",
       "50  5.000000       5.000000 ⋯ 0          0          301  0       1          \n",
       "52  4.500000       5.000000 ⋯ 0          0          301  0       1          \n",
       "56  4.000000       3.000000 ⋯ 0          0          301  0       1          \n",
       "58  3.000000       3.000000 ⋯ 0          0          301  0       0          \n",
       "59  3.804457       3.822472 ⋯ 0          0          301  1       0          \n",
       "65  3.804457       3.822472 ⋯ 0          0          301  1       0          \n",
       "67  3.900000       4.200000 ⋯ 1          1          150  0       1          \n",
       "69  3.100000       3.800000 ⋯ 0          0          301  0       1          \n",
       "73  4.700000       4.300000 ⋯ 0          1          301  0       0          \n",
       "75  2.400000       2.200000 ⋯ 0          0          301  1       1          \n",
       "76  3.700000       3.700000 ⋯ 0          0          301  0       0          \n",
       "82  3.300000       3.600000 ⋯ 0          0          250  0       0          \n",
       "84  3.900000       3.900000 ⋯ 0          0          200  0       1          \n",
       "⋮   ⋮              ⋮        ⋱ ⋮          ⋮          ⋮    ⋮       ⋮          \n",
       "303 4.200000       4.200000 ⋯ 0          1          301  0       1          \n",
       "305 3.800000       3.900000 ⋯ 0          0          301  0       1          \n",
       "307 3.700000       4.300000 ⋯ 0          1          155  0       1          \n",
       "311 4.200000       4.100000 ⋯ 0          0          301  0       1          \n",
       "313 3.804457       3.822472 ⋯ 0          0          301  1       0          \n",
       "314 4.200000       4.200000 ⋯ 0          0          301  0       1          \n",
       "320 3.300000       3.700000 ⋯ 0          1          301  0       1          \n",
       "322 3.900000       4.000000 ⋯ 0          0          301  0       1          \n",
       "324 3.700000       3.700000 ⋯ 0          0          301  0       1          \n",
       "328 3.300000       4.200000 ⋯ 0          0          301  0       1          \n",
       "330 4.100000       4.200000 ⋯ 0          0          301  0       1          \n",
       "331 3.500000       4.000000 ⋯ 0          0          301  1       1          \n",
       "337 4.200000       3.400000 ⋯ 0          0          301  1       1          \n",
       "339 3.500000       3.900000 ⋯ 0          0          301  0       0          \n",
       "341 3.000000       4.000000 ⋯ 0          0          301  0       0          \n",
       "345 4.000000       4.000000 ⋯ 0          0          301  0       1          \n",
       "347 4.500000       4.300000 ⋯ 0          0          301  0       1          \n",
       "348 3.800000       3.100000 ⋯ 0          0          301  0       1          \n",
       "354 4.000000       3.700000 ⋯ 0          0          301  0       0          \n",
       "356 5.000000       5.000000 ⋯ 0          0          301  0       1          \n",
       "358 5.000000       5.000000 ⋯ 0          0          301  0       0          \n",
       "362 4.100000       3.600000 ⋯ 0          0          301  0       1          \n",
       "364 4.000000       3.900000 ⋯ 0          0          301  0       1          \n",
       "365 4.000000       4.000000 ⋯ 0          0          301  0       1          \n",
       "371 3.000000       3.300000 ⋯ 0          0          301  0       1          \n",
       "373 4.400000       4.400000 ⋯ 0          0          301  0       1          \n",
       "375 4.100000       4.200000 ⋯ 0          0          301  0       1          \n",
       "379 4.700000       3.900000 ⋯ 0          0          301  1       1          \n",
       "381 3.600000       4.300000 ⋯ 0          0          301  0       1          \n",
       "382 3.400000       3.100000 ⋯ 0          0          301  0       1          \n",
       "    hostel_ONE linear   decision fulltree pruned  \n",
       "1   0          95.25097 88.05211 88.05211 92.45139\n",
       "5   0          83.98529 97.36824 97.36824 92.45139\n",
       "7   0          67.03529 63.77202 63.77202 67.33875\n",
       "8   0          70.98257 73.49375 70.32917 67.33875\n",
       "14  0          57.34506 69.04323 69.04323 67.33875\n",
       "16  0          59.01199 70.52405 70.52405 70.52405\n",
       "18  0          74.53221 63.77202 63.77202 67.33875\n",
       "22  0          36.59204 52.71238 56.88917 57.67139\n",
       "24  0          78.07224 59.83230 56.23467 59.83230\n",
       "25  0          60.02308 69.04323 69.04323 67.33875\n",
       "31  0          97.83733 97.36824 97.36824 92.45139\n",
       "33  0          77.88152 59.83230 56.23467 59.83230\n",
       "35  0          67.06327 59.83230 56.23467 59.83230\n",
       "39  0          66.33838 52.71238 56.88917 57.67139\n",
       "41  0          70.52523 88.68862 84.42333 88.68862\n",
       "42  0          67.18494 59.83230 56.23467 59.83230\n",
       "48  0          69.44201 69.04323 69.04323 67.33875\n",
       "50  0          89.85680 88.68862 88.48143 88.68862\n",
       "52  0          81.48739 59.83230 56.23467 59.83230\n",
       "56  0          71.14808 55.15813 55.15813 67.33875\n",
       "58  0          56.74210 52.71238 49.29500 57.67139\n",
       "59  0          59.76323 59.83230 56.23467 59.83230\n",
       "65  0          61.80546 59.83230 65.52854 59.83230\n",
       "67  0          99.68131 97.36824 97.36824 92.45139\n",
       "69  0          74.01919 88.68862 91.75308 88.68862\n",
       "73  0          88.69525 88.05211 88.05211 92.45139\n",
       "75  0          53.97024 65.30064 65.30064 57.67139\n",
       "76  0          77.37348 73.75159 73.75159 73.75159\n",
       "82  0          82.17729 88.68862 91.75308 88.68862\n",
       "84  0          79.32101 88.68862 88.48143 88.68862\n",
       "⋮   ⋮          ⋮        ⋮        ⋮        ⋮       \n",
       "303 0          92.78713 88.05211 88.05211 92.45139\n",
       "305 0          77.90717 88.68862 91.75308 88.68862\n",
       "307 0          92.27407 97.36824 97.36824 92.45139\n",
       "311 0          74.50074 68.62492 68.62492 75.84690\n",
       "313 0          64.01767 68.62492 68.62492 75.84690\n",
       "314 0          81.96029 88.68862 88.48143 88.68862\n",
       "320 0          83.93804 88.05211 88.05211 92.45139\n",
       "322 0          74.35820 81.86522 81.86522 75.84690\n",
       "324 0          67.14082 52.71238 56.88917 57.67139\n",
       "328 0          79.16464 68.62492 68.62492 75.84690\n",
       "330 0          71.71905 81.86522 81.86522 75.84690\n",
       "331 0          59.30986 52.71238 49.29500 57.67139\n",
       "337 0          85.04649 88.68862 91.75308 88.68862\n",
       "339 0          73.16798 68.62492 68.62492 75.84690\n",
       "341 1          75.75998 88.68862 91.75308 88.68862\n",
       "345 0          76.07599 81.86522 81.86522 75.84690\n",
       "347 0          73.32382 81.86522 81.86522 75.84690\n",
       "348 0          68.82040 52.71238 56.88917 57.67139\n",
       "354 0          74.10919 81.86522 81.86522 75.84690\n",
       "356 0          80.30998 68.62492 68.62492 75.84690\n",
       "358 0          76.38859 68.62492 68.62492 75.84690\n",
       "362 0          70.97872 70.52405 70.52405 70.52405\n",
       "364 0          75.21836 88.68862 88.48143 88.68862\n",
       "365 0          76.23241 68.62492 68.62492 75.84690\n",
       "371 0          67.36720 52.71238 49.29500 57.67139\n",
       "373 0          74.90800 81.86522 81.86522 75.84690\n",
       "375 0          75.98160 68.62492 68.62492 75.84690\n",
       "379 0          78.02752 73.75159 73.75159 73.75159\n",
       "381 0          75.30797 88.68862 88.48143 88.68862\n",
       "382 0          68.83997 81.86522 81.86522 75.84690"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test$pruned <- predict(prunedtree, test, type=\"vector\")\n",
    "View(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "2fb86729",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "195.373477100332"
      ],
      "text/latex": [
       "195.373477100332"
      ],
      "text/markdown": [
       "195.373477100332"
      ],
      "text/plain": [
       "[1] 195.3735"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSEpruned <- mean((test$pruned - test$cutoff)^2)\n",
    "MSEpruned"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edcbac47",
   "metadata": {},
   "source": [
    "Pruning the full tree helps us to avoid overfitting  by removing the unnecessary nodes and hence reduce the mean squared error. We'll consider the MSE of the pruned tree as the optimum value for our decision tree model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ae6ee93",
   "metadata": {},
   "source": [
    "### Bagging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "ea05ca8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "randomForest 4.7-1.1\n",
      "\n",
      "Type rfNews() to see new features/changes/bug fixes.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 136 × 22</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>⋯</th><th scope=col>autonomous</th><th scope=col>rank</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_ONE</th><th scope=col>linear</th><th scope=col>decision</th><th scope=col>fulltree</th><th scope=col>pruned</th><th scope=col>bagging</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>⋯</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1002</td><td>1</td><td>96.44000</td><td> 8</td><td>300.000</td><td>240000.0</td><td>12.87391</td><td>3.400000</td><td>3.200000</td><td>3.500000</td><td>⋯</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>95.25097</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>87.14085</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1105</td><td>1</td><td>88.05000</td><td> 8</td><td>480.000</td><td>440000.0</td><td>12.70685</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>1</td><td>250</td><td>0</td><td>0</td><td>0</td><td>83.98529</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>91.94186</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1108</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>310000.0</td><td>12.61154</td><td>3.900000</td><td>4.000000</td><td>4.300000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.03529</td><td>63.77202</td><td>63.77202</td><td>67.33875</td><td>70.91037</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>1114</td><td>1</td><td>81.55000</td><td> 6</td><td>300.000</td><td>320000.0</td><td>12.82126</td><td>4.000000</td><td>4.400000</td><td>3.900000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.98257</td><td>73.49375</td><td>70.32917</td><td>67.33875</td><td>73.05704</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1122</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>200000.0</td><td>12.61154</td><td>2.200000</td><td>3.000000</td><td>2.000000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>57.34506</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>54.54966</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>1124</td><td>1</td><td>49.08000</td><td> 5</td><td>300.000</td><td>490000.0</td><td>12.34584</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.01199</td><td>70.52405</td><td>70.52405</td><td>70.52405</td><td>69.83709</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>1126</td><td>1</td><td>67.71000</td><td> 5</td><td>300.000</td><td>170000.0</td><td>13.10216</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.53221</td><td>63.77202</td><td>63.77202</td><td>67.33875</td><td>57.85599</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>1130</td><td>1</td><td>45.98000</td><td> 6</td><td>480.000</td><td>180000.0</td><td>12.10072</td><td>2.200000</td><td>4.000000</td><td>2.000000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>36.59204</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>56.40356</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>1182</td><td>1</td><td>59.68000</td><td> 4</td><td>630.000</td><td>200000.0</td><td>13.01701</td><td>4.200000</td><td>4.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>78.07224</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>61.11015</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>1251</td><td>1</td><td>44.34375</td><td> 6</td><td>300.000</td><td>284000.0</td><td>12.54255</td><td>3.400000</td><td>3.200000</td><td>3.400000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>60.02308</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>63.24937</td></tr>\n",
       "\t<tr><th scope=row>31</th><td>2008</td><td>2</td><td>97.84000</td><td>10</td><td>540.000</td><td>190000.0</td><td>13.38473</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td>1</td><td> 97</td><td>0</td><td>1</td><td>0</td><td>97.83733</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>93.19946</td></tr>\n",
       "\t<tr><th scope=row>33</th><td>2021</td><td>2</td><td>72.61000</td><td> 2</td><td>240.000</td><td> 80000.0</td><td>12.70685</td><td>3.800000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.88152</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>73.75753</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>2111</td><td>2</td><td>65.26000</td><td> 4</td><td>300.000</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.06327</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>59.49070</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>2116</td><td>2</td><td>54.60000</td><td>10</td><td>294.000</td><td>200000.0</td><td>12.61154</td><td>3.100000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>66.33838</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>55.81445</td></tr>\n",
       "\t<tr><th scope=row>41</th><td>2127</td><td>2</td><td>80.37000</td><td> 5</td><td>420.000</td><td>350000.0</td><td>12.79386</td><td>3.900000</td><td>4.300000</td><td>4.300000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.52523</td><td>88.68862</td><td>84.42333</td><td>88.68862</td><td>78.27550</td></tr>\n",
       "\t<tr><th scope=row>42</th><td>2128</td><td>2</td><td>44.34375</td><td> 3</td><td>196.875</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>67.18494</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>59.67666</td></tr>\n",
       "\t<tr><th scope=row>48</th><td>2134</td><td>2</td><td>72.88000</td><td> 9</td><td>360.000</td><td>240000.0</td><td>12.67608</td><td>3.300000</td><td>3.400000</td><td>3.500000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>69.44201</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>64.49678</td></tr>\n",
       "\t<tr><th scope=row>50</th><td>2136</td><td>2</td><td>44.34375</td><td> 9</td><td>240.000</td><td>480000.0</td><td>13.30469</td><td>4.300000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>89.85680</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>84.47547</td></tr>\n",
       "\t<tr><th scope=row>52</th><td>2138</td><td>2</td><td>64.49000</td><td> 4</td><td>270.000</td><td>250000.0</td><td>12.70685</td><td>3.900000</td><td>4.500000</td><td>5.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.48739</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>63.52538</td></tr>\n",
       "\t<tr><th scope=row>56</th><td>2250</td><td>2</td><td>63.71000</td><td> 6</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>4.000000</td><td>4.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.14808</td><td>55.15813</td><td>55.15813</td><td>67.33875</td><td>62.93025</td></tr>\n",
       "\t<tr><th scope=row>58</th><td>2254</td><td>2</td><td>59.41000</td><td> 5</td><td>196.875</td><td>160000.0</td><td>12.79562</td><td>2.800000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>56.74210</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>51.01997</td></tr>\n",
       "\t<tr><th scope=row>59</th><td>2255</td><td>2</td><td>71.74876</td><td> 3</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>59.76323</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>60.48674</td></tr>\n",
       "\t<tr><th scope=row>65</th><td>2641</td><td>2</td><td>71.74876</td><td> 4</td><td>382.000</td><td>322661.9</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>61.80546</td><td>59.83230</td><td>65.52854</td><td>59.83230</td><td>66.70431</td></tr>\n",
       "\t<tr><th scope=row>67</th><td>3014</td><td>3</td><td>98.48000</td><td> 6</td><td>300.000</td><td>340000.0</td><td>13.21768</td><td>4.100000</td><td>3.900000</td><td>4.200000</td><td>⋯</td><td>1</td><td>150</td><td>0</td><td>1</td><td>0</td><td>99.68131</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>95.94890</td></tr>\n",
       "\t<tr><th scope=row>69</th><td>3035</td><td>3</td><td>89.48000</td><td> 7</td><td>196.875</td><td>420000.0</td><td>12.97155</td><td>3.600000</td><td>3.100000</td><td>3.800000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.01919</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>87.07321</td></tr>\n",
       "\t<tr><th scope=row>73</th><td>3139</td><td>3</td><td>96.84000</td><td>10</td><td>630.000</td><td>550000.0</td><td>12.76569</td><td>4.300000</td><td>4.700000</td><td>4.300000</td><td>⋯</td><td>1</td><td>301</td><td>0</td><td>0</td><td>0</td><td>88.69525</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>84.10130</td></tr>\n",
       "\t<tr><th scope=row>75</th><td>3147</td><td>3</td><td>83.40000</td><td> 6</td><td>300.000</td><td>264000.0</td><td>12.30139</td><td>2.200000</td><td>2.400000</td><td>2.200000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>53.97024</td><td>65.30064</td><td>65.30064</td><td>57.67139</td><td>58.89893</td></tr>\n",
       "\t<tr><th scope=row>76</th><td>3148</td><td>3</td><td>92.28000</td><td>10</td><td>630.000</td><td>460000.0</td><td>13.30469</td><td>3.800000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>77.37348</td><td>73.75159</td><td>73.75159</td><td>73.75159</td><td>85.57030</td></tr>\n",
       "\t<tr><th scope=row>82</th><td>3182</td><td>3</td><td>98.34000</td><td> 5</td><td>300.000</td><td>600000.0</td><td>14.16617</td><td>3.800000</td><td>3.300000</td><td>3.600000</td><td>⋯</td><td>0</td><td>250</td><td>0</td><td>0</td><td>0</td><td>82.17729</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>93.03070</td></tr>\n",
       "\t<tr><th scope=row>84</th><td>3184</td><td>3</td><td>96.77000</td><td>10</td><td>480.000</td><td>570000.0</td><td>13.12237</td><td>4.000000</td><td>3.900000</td><td>3.900000</td><td>⋯</td><td>0</td><td>200</td><td>0</td><td>1</td><td>0</td><td>79.32101</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>93.58710</td></tr>\n",
       "\t<tr><th scope=row>⋮</th><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋱</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><th scope=row>303</th><td>6283</td><td>6</td><td>87.28000</td><td>13.0</td><td>196.875</td><td> 370000</td><td>12.61154</td><td>4.000000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>92.78713</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>91.13583</td></tr>\n",
       "\t<tr><th scope=row>305</th><td>6285</td><td>6</td><td>92.61000</td><td> 6.0</td><td>240.000</td><td> 430000</td><td>12.91411</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.90717</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>91.82660</td></tr>\n",
       "\t<tr><th scope=row>307</th><td>6289</td><td>6</td><td>97.98000</td><td> 7.0</td><td>300.000</td><td> 570000</td><td>13.32122</td><td>3.900000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>1</td><td>155</td><td>0</td><td>1</td><td>0</td><td>92.27407</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>97.16614</td></tr>\n",
       "\t<tr><th scope=row>311</th><td>6303</td><td>6</td><td>75.18000</td><td> 5.0</td><td>240.000</td><td> 240000</td><td>12.98540</td><td>4.000000</td><td>4.200000</td><td>4.100000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.50074</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>65.67000</td></tr>\n",
       "\t<tr><th scope=row>313</th><td>6305</td><td>6</td><td>46.17000</td><td> 5.0</td><td>210.000</td><td> 192000</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>0</td><td>0</td><td>64.01767</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>61.57288</td></tr>\n",
       "\t<tr><th scope=row>314</th><td>6307</td><td>6</td><td>83.32000</td><td>12.0</td><td>255.000</td><td> 370000</td><td>12.76569</td><td>4.100000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.96029</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>89.76211</td></tr>\n",
       "\t<tr><th scope=row>320</th><td>6317</td><td>6</td><td>79.53000</td><td>11.0</td><td>630.000</td><td> 310000</td><td>12.54255</td><td>3.500000</td><td>3.300000</td><td>3.700000</td><td>⋯</td><td>1</td><td>301</td><td>0</td><td>1</td><td>0</td><td>83.93804</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>84.42921</td></tr>\n",
       "\t<tr><th scope=row>322</th><td>6319</td><td>6</td><td>63.05000</td><td> 6.0</td><td>360.000</td><td> 308000</td><td>12.76569</td><td>3.600000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.35820</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.28742</td></tr>\n",
       "\t<tr><th scope=row>324</th><td>6321</td><td>6</td><td>45.67000</td><td> 6.0</td><td>300.000</td><td> 240000</td><td>12.79386</td><td>3.200000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.14082</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>62.82214</td></tr>\n",
       "\t<tr><th scope=row>328</th><td>6325</td><td>6</td><td>78.05000</td><td> 5.0</td><td>480.000</td><td> 230000</td><td>13.99783</td><td>3.600000</td><td>3.300000</td><td>4.200000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>79.16464</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>66.11722</td></tr>\n",
       "\t<tr><th scope=row>330</th><td>6419</td><td>6</td><td>78.35000</td><td> 6.0</td><td>360.000</td><td> 330000</td><td>12.50618</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.71905</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>83.55063</td></tr>\n",
       "\t<tr><th scope=row>331</th><td>6444</td><td>6</td><td>44.34375</td><td> 5.0</td><td>196.875</td><td> 141000</td><td>12.79562</td><td>3.200000</td><td>3.500000</td><td>4.000000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.30986</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>49.25645</td></tr>\n",
       "\t<tr><th scope=row>337</th><td>6620</td><td>6</td><td>73.99000</td><td>13.5</td><td>196.875</td><td>1080000</td><td>13.35348</td><td>3.600000</td><td>4.200000</td><td>3.400000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>85.04649</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>72.71361</td></tr>\n",
       "\t<tr><th scope=row>339</th><td>6622</td><td>6</td><td>85.85000</td><td> 6.0</td><td>360.000</td><td> 280000</td><td>12.76569</td><td>3.500000</td><td>3.500000</td><td>3.900000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>73.16798</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>71.99251</td></tr>\n",
       "\t<tr><th scope=row>341</th><td>6628</td><td>6</td><td>56.76500</td><td> 5.0</td><td>196.875</td><td> 400000</td><td>12.56025</td><td>3.400000</td><td>3.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>0</td><td>1</td><td>75.75998</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>81.94778</td></tr>\n",
       "\t<tr><th scope=row>345</th><td>6635</td><td>6</td><td>67.11200</td><td> 9.0</td><td>420.000</td><td> 300000</td><td>12.42922</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.07599</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>78.96625</td></tr>\n",
       "\t<tr><th scope=row>347</th><td>6643</td><td>6</td><td>81.98400</td><td> 5.0</td><td>360.000</td><td> 310000</td><td>12.20608</td><td>4.200000</td><td>4.500000</td><td>4.300000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>73.32382</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.17784</td></tr>\n",
       "\t<tr><th scope=row>348</th><td>6644</td><td>6</td><td>56.76000</td><td> 7.0</td><td>300.000</td><td> 320000</td><td>12.79386</td><td>3.000000</td><td>3.800000</td><td>3.100000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.82040</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>65.14153</td></tr>\n",
       "\t<tr><th scope=row>354</th><td>6757</td><td>6</td><td>60.73000</td><td> 7.0</td><td>360.000</td><td> 310000</td><td>12.76569</td><td>3.800000</td><td>4.000000</td><td>3.700000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>74.10919</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.10538</td></tr>\n",
       "\t<tr><th scope=row>356</th><td>6759</td><td>6</td><td>68.70000</td><td> 5.0</td><td>270.000</td><td> 270000</td><td>12.61154</td><td>4.600000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>80.30998</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>63.63364</td></tr>\n",
       "\t<tr><th scope=row>358</th><td>6766</td><td>6</td><td>63.08000</td><td> 5.0</td><td>300.000</td><td> 260000</td><td>12.76569</td><td>4.700000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>0</td><td>0</td><td>76.38859</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>62.21482</td></tr>\n",
       "\t<tr><th scope=row>362</th><td>6770</td><td>6</td><td>77.03000</td><td> 5.0</td><td>300.000</td><td> 410000</td><td>12.38840</td><td>3.800000</td><td>4.100000</td><td>3.600000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.97872</td><td>70.52405</td><td>70.52405</td><td>70.52405</td><td>83.54821</td></tr>\n",
       "\t<tr><th scope=row>364</th><td>6772</td><td>6</td><td>87.28000</td><td> 6.0</td><td>510.000</td><td> 400000</td><td>12.57764</td><td>4.000000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.21836</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>86.58241</td></tr>\n",
       "\t<tr><th scope=row>365</th><td>6780</td><td>6</td><td>71.76000</td><td>11.0</td><td>420.000</td><td> 250000</td><td>12.38840</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.23241</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>75.24435</td></tr>\n",
       "\t<tr><th scope=row>371</th><td>6795</td><td>6</td><td>52.82000</td><td> 4.0</td><td>210.000</td><td> 240000</td><td>12.79562</td><td>3.000000</td><td>3.000000</td><td>3.300000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.36720</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>57.46492</td></tr>\n",
       "\t<tr><th scope=row>373</th><td>6797</td><td>6</td><td>74.20000</td><td> 5.0</td><td>240.000</td><td> 320000</td><td>12.79562</td><td>4.100000</td><td>4.400000</td><td>4.400000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.90800</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>70.35977</td></tr>\n",
       "\t<tr><th scope=row>375</th><td>6803</td><td>6</td><td>74.51000</td><td> 6.0</td><td>360.000</td><td> 240000</td><td>12.89922</td><td>4.100000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.98160</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>72.07914</td></tr>\n",
       "\t<tr><th scope=row>379</th><td>6811</td><td>6</td><td>44.34375</td><td>13.5</td><td>630.000</td><td> 620000</td><td>12.84793</td><td>4.100000</td><td>4.700000</td><td>3.900000</td><td>⋯</td><td>0</td><td>301</td><td>1</td><td>1</td><td>0</td><td>78.02752</td><td>73.75159</td><td>73.75159</td><td>73.75159</td><td>79.40319</td></tr>\n",
       "\t<tr><th scope=row>381</th><td>6822</td><td>6</td><td>96.46000</td><td> 9.0</td><td>480.000</td><td> 400000</td><td>12.50618</td><td>4.000000</td><td>3.600000</td><td>4.300000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.30797</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>82.83327</td></tr>\n",
       "\t<tr><th scope=row>382</th><td>6834</td><td>6</td><td>80.45000</td><td> 6.0</td><td>360.000</td><td> 300000</td><td>12.61154</td><td>3.000000</td><td>3.400000</td><td>3.100000</td><td>⋯</td><td>0</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.83997</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>64.00270</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 136 × 22\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & ⋯ & autonomous & rank & new\\_ban & hostel\\_BOTH & hostel\\_ONE & linear & decision & fulltree & pruned & bagging\\\\\n",
       "  & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ⋯ & <int> & <int> & <int> & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1002 & 1 & 96.44000 &  8 & 300.000 & 240000.0 & 12.87391 & 3.400000 & 3.200000 & 3.500000 & ⋯ & 1 & 301 & 0 & 1 & 0 & 95.25097 & 88.05211 & 88.05211 & 92.45139 & 87.14085\\\\\n",
       "\t5 & 1105 & 1 & 88.05000 &  8 & 480.000 & 440000.0 & 12.70685 & 3.900000 & 4.000000 & 3.900000 & ⋯ & 1 & 250 & 0 & 0 & 0 & 83.98529 & 97.36824 & 97.36824 & 92.45139 & 91.94186\\\\\n",
       "\t7 & 1108 & 1 & 44.34375 &  5 & 300.000 & 310000.0 & 12.61154 & 3.900000 & 4.000000 & 4.300000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 67.03529 & 63.77202 & 63.77202 & 67.33875 & 70.91037\\\\\n",
       "\t8 & 1114 & 1 & 81.55000 &  6 & 300.000 & 320000.0 & 12.82126 & 4.000000 & 4.400000 & 3.900000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 70.98257 & 73.49375 & 70.32917 & 67.33875 & 73.05704\\\\\n",
       "\t14 & 1122 & 1 & 44.34375 &  5 & 300.000 & 200000.0 & 12.61154 & 2.200000 & 3.000000 & 2.000000 & ⋯ & 0 & 301 & 1 & 0 & 0 & 57.34506 & 69.04323 & 69.04323 & 67.33875 & 54.54966\\\\\n",
       "\t16 & 1124 & 1 & 49.08000 &  5 & 300.000 & 490000.0 & 12.34584 & 3.600000 & 4.300000 & 3.600000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 59.01199 & 70.52405 & 70.52405 & 70.52405 & 69.83709\\\\\n",
       "\t18 & 1126 & 1 & 67.71000 &  5 & 300.000 & 170000.0 & 13.10216 & 5.000000 & 5.000000 & 5.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 74.53221 & 63.77202 & 63.77202 & 67.33875 & 57.85599\\\\\n",
       "\t22 & 1130 & 1 & 45.98000 &  6 & 480.000 & 180000.0 & 12.10072 & 2.200000 & 4.000000 & 2.000000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 36.59204 & 52.71238 & 56.88917 & 57.67139 & 56.40356\\\\\n",
       "\t24 & 1182 & 1 & 59.68000 &  4 & 630.000 & 200000.0 & 13.01701 & 4.200000 & 4.000000 & 5.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 78.07224 & 59.83230 & 56.23467 & 59.83230 & 61.11015\\\\\n",
       "\t25 & 1251 & 1 & 44.34375 &  6 & 300.000 & 284000.0 & 12.54255 & 3.400000 & 3.200000 & 3.400000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 60.02308 & 69.04323 & 69.04323 & 67.33875 & 63.24937\\\\\n",
       "\t31 & 2008 & 2 & 97.84000 & 10 & 540.000 & 190000.0 & 13.38473 & 3.900000 & 3.800000 & 3.900000 & ⋯ & 1 &  97 & 0 & 1 & 0 & 97.83733 & 97.36824 & 97.36824 & 92.45139 & 93.19946\\\\\n",
       "\t33 & 2021 & 2 & 72.61000 &  2 & 240.000 &  80000.0 & 12.70685 & 3.800000 & 3.900000 & 4.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 77.88152 & 59.83230 & 56.23467 & 59.83230 & 73.75753\\\\\n",
       "\t35 & 2111 & 2 & 65.26000 &  4 & 300.000 & 170000.0 & 12.61154 & 3.800000 & 3.700000 & 4.300000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 67.06327 & 59.83230 & 56.23467 & 59.83230 & 59.49070\\\\\n",
       "\t39 & 2116 & 2 & 54.60000 & 10 & 294.000 & 200000.0 & 12.61154 & 3.100000 & 3.000000 & 3.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 66.33838 & 52.71238 & 56.88917 & 57.67139 & 55.81445\\\\\n",
       "\t41 & 2127 & 2 & 80.37000 &  5 & 420.000 & 350000.0 & 12.79386 & 3.900000 & 4.300000 & 4.300000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 70.52523 & 88.68862 & 84.42333 & 88.68862 & 78.27550\\\\\n",
       "\t42 & 2128 & 2 & 44.34375 &  3 & 196.875 & 170000.0 & 12.61154 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 67.18494 & 59.83230 & 56.23467 & 59.83230 & 59.67666\\\\\n",
       "\t48 & 2134 & 2 & 72.88000 &  9 & 360.000 & 240000.0 & 12.67608 & 3.300000 & 3.400000 & 3.500000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 69.44201 & 69.04323 & 69.04323 & 67.33875 & 64.49678\\\\\n",
       "\t50 & 2136 & 2 & 44.34375 &  9 & 240.000 & 480000.0 & 13.30469 & 4.300000 & 5.000000 & 5.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 89.85680 & 88.68862 & 88.48143 & 88.68862 & 84.47547\\\\\n",
       "\t52 & 2138 & 2 & 64.49000 &  4 & 270.000 & 250000.0 & 12.70685 & 3.900000 & 4.500000 & 5.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 81.48739 & 59.83230 & 56.23467 & 59.83230 & 63.52538\\\\\n",
       "\t56 & 2250 & 2 & 63.71000 &  6 & 196.875 & 220000.0 & 12.79562 & 4.000000 & 4.000000 & 3.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 71.14808 & 55.15813 & 55.15813 & 67.33875 & 62.93025\\\\\n",
       "\t58 & 2254 & 2 & 59.41000 &  5 & 196.875 & 160000.0 & 12.79562 & 2.800000 & 3.000000 & 3.000000 & ⋯ & 0 & 301 & 0 & 0 & 0 & 56.74210 & 52.71238 & 49.29500 & 57.67139 & 51.01997\\\\\n",
       "\t59 & 2255 & 2 & 71.74876 &  3 & 196.875 & 220000.0 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 0 & 301 & 1 & 0 & 0 & 59.76323 & 59.83230 & 56.23467 & 59.83230 & 60.48674\\\\\n",
       "\t65 & 2641 & 2 & 71.74876 &  4 & 382.000 & 322661.9 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 0 & 301 & 1 & 0 & 0 & 61.80546 & 59.83230 & 65.52854 & 59.83230 & 66.70431\\\\\n",
       "\t67 & 3014 & 3 & 98.48000 &  6 & 300.000 & 340000.0 & 13.21768 & 4.100000 & 3.900000 & 4.200000 & ⋯ & 1 & 150 & 0 & 1 & 0 & 99.68131 & 97.36824 & 97.36824 & 92.45139 & 95.94890\\\\\n",
       "\t69 & 3035 & 3 & 89.48000 &  7 & 196.875 & 420000.0 & 12.97155 & 3.600000 & 3.100000 & 3.800000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 74.01919 & 88.68862 & 91.75308 & 88.68862 & 87.07321\\\\\n",
       "\t73 & 3139 & 3 & 96.84000 & 10 & 630.000 & 550000.0 & 12.76569 & 4.300000 & 4.700000 & 4.300000 & ⋯ & 1 & 301 & 0 & 0 & 0 & 88.69525 & 88.05211 & 88.05211 & 92.45139 & 84.10130\\\\\n",
       "\t75 & 3147 & 3 & 83.40000 &  6 & 300.000 & 264000.0 & 12.30139 & 2.200000 & 2.400000 & 2.200000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 53.97024 & 65.30064 & 65.30064 & 57.67139 & 58.89893\\\\\n",
       "\t76 & 3148 & 3 & 92.28000 & 10 & 630.000 & 460000.0 & 13.30469 & 3.800000 & 3.700000 & 3.700000 & ⋯ & 0 & 301 & 0 & 0 & 0 & 77.37348 & 73.75159 & 73.75159 & 73.75159 & 85.57030\\\\\n",
       "\t82 & 3182 & 3 & 98.34000 &  5 & 300.000 & 600000.0 & 14.16617 & 3.800000 & 3.300000 & 3.600000 & ⋯ & 0 & 250 & 0 & 0 & 0 & 82.17729 & 88.68862 & 91.75308 & 88.68862 & 93.03070\\\\\n",
       "\t84 & 3184 & 3 & 96.77000 & 10 & 480.000 & 570000.0 & 13.12237 & 4.000000 & 3.900000 & 3.900000 & ⋯ & 0 & 200 & 0 & 1 & 0 & 79.32101 & 88.68862 & 88.48143 & 88.68862 & 93.58710\\\\\n",
       "\t⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋱ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t303 & 6283 & 6 & 87.28000 & 13.0 & 196.875 &  370000 & 12.61154 & 4.000000 & 4.200000 & 4.200000 & ⋯ & 1 & 301 & 0 & 1 & 0 & 92.78713 & 88.05211 & 88.05211 & 92.45139 & 91.13583\\\\\n",
       "\t305 & 6285 & 6 & 92.61000 &  6.0 & 240.000 &  430000 & 12.91411 & 3.900000 & 3.800000 & 3.900000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 77.90717 & 88.68862 & 91.75308 & 88.68862 & 91.82660\\\\\n",
       "\t307 & 6289 & 6 & 97.98000 &  7.0 & 300.000 &  570000 & 13.32122 & 3.900000 & 3.700000 & 4.300000 & ⋯ & 1 & 155 & 0 & 1 & 0 & 92.27407 & 97.36824 & 97.36824 & 92.45139 & 97.16614\\\\\n",
       "\t311 & 6303 & 6 & 75.18000 &  5.0 & 240.000 &  240000 & 12.98540 & 4.000000 & 4.200000 & 4.100000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 74.50074 & 68.62492 & 68.62492 & 75.84690 & 65.67000\\\\\n",
       "\t313 & 6305 & 6 & 46.17000 &  5.0 & 210.000 &  192000 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 0 & 301 & 1 & 0 & 0 & 64.01767 & 68.62492 & 68.62492 & 75.84690 & 61.57288\\\\\n",
       "\t314 & 6307 & 6 & 83.32000 & 12.0 & 255.000 &  370000 & 12.76569 & 4.100000 & 4.200000 & 4.200000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 81.96029 & 88.68862 & 88.48143 & 88.68862 & 89.76211\\\\\n",
       "\t320 & 6317 & 6 & 79.53000 & 11.0 & 630.000 &  310000 & 12.54255 & 3.500000 & 3.300000 & 3.700000 & ⋯ & 1 & 301 & 0 & 1 & 0 & 83.93804 & 88.05211 & 88.05211 & 92.45139 & 84.42921\\\\\n",
       "\t322 & 6319 & 6 & 63.05000 &  6.0 & 360.000 &  308000 & 12.76569 & 3.600000 & 3.900000 & 4.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 74.35820 & 81.86522 & 81.86522 & 75.84690 & 76.28742\\\\\n",
       "\t324 & 6321 & 6 & 45.67000 &  6.0 & 300.000 &  240000 & 12.79386 & 3.200000 & 3.700000 & 3.700000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 67.14082 & 52.71238 & 56.88917 & 57.67139 & 62.82214\\\\\n",
       "\t328 & 6325 & 6 & 78.05000 &  5.0 & 480.000 &  230000 & 13.99783 & 3.600000 & 3.300000 & 4.200000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 79.16464 & 68.62492 & 68.62492 & 75.84690 & 66.11722\\\\\n",
       "\t330 & 6419 & 6 & 78.35000 &  6.0 & 360.000 &  330000 & 12.50618 & 4.200000 & 4.100000 & 4.200000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 71.71905 & 81.86522 & 81.86522 & 75.84690 & 83.55063\\\\\n",
       "\t331 & 6444 & 6 & 44.34375 &  5.0 & 196.875 &  141000 & 12.79562 & 3.200000 & 3.500000 & 4.000000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 59.30986 & 52.71238 & 49.29500 & 57.67139 & 49.25645\\\\\n",
       "\t337 & 6620 & 6 & 73.99000 & 13.5 & 196.875 & 1080000 & 13.35348 & 3.600000 & 4.200000 & 3.400000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 85.04649 & 88.68862 & 91.75308 & 88.68862 & 72.71361\\\\\n",
       "\t339 & 6622 & 6 & 85.85000 &  6.0 & 360.000 &  280000 & 12.76569 & 3.500000 & 3.500000 & 3.900000 & ⋯ & 0 & 301 & 0 & 0 & 0 & 73.16798 & 68.62492 & 68.62492 & 75.84690 & 71.99251\\\\\n",
       "\t341 & 6628 & 6 & 56.76500 &  5.0 & 196.875 &  400000 & 12.56025 & 3.400000 & 3.000000 & 4.000000 & ⋯ & 0 & 301 & 0 & 0 & 1 & 75.75998 & 88.68862 & 91.75308 & 88.68862 & 81.94778\\\\\n",
       "\t345 & 6635 & 6 & 67.11200 &  9.0 & 420.000 &  300000 & 12.42922 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 76.07599 & 81.86522 & 81.86522 & 75.84690 & 78.96625\\\\\n",
       "\t347 & 6643 & 6 & 81.98400 &  5.0 & 360.000 &  310000 & 12.20608 & 4.200000 & 4.500000 & 4.300000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 73.32382 & 81.86522 & 81.86522 & 75.84690 & 76.17784\\\\\n",
       "\t348 & 6644 & 6 & 56.76000 &  7.0 & 300.000 &  320000 & 12.79386 & 3.000000 & 3.800000 & 3.100000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 68.82040 & 52.71238 & 56.88917 & 57.67139 & 65.14153\\\\\n",
       "\t354 & 6757 & 6 & 60.73000 &  7.0 & 360.000 &  310000 & 12.76569 & 3.800000 & 4.000000 & 3.700000 & ⋯ & 0 & 301 & 0 & 0 & 0 & 74.10919 & 81.86522 & 81.86522 & 75.84690 & 76.10538\\\\\n",
       "\t356 & 6759 & 6 & 68.70000 &  5.0 & 270.000 &  270000 & 12.61154 & 4.600000 & 5.000000 & 5.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 80.30998 & 68.62492 & 68.62492 & 75.84690 & 63.63364\\\\\n",
       "\t358 & 6766 & 6 & 63.08000 &  5.0 & 300.000 &  260000 & 12.76569 & 4.700000 & 5.000000 & 5.000000 & ⋯ & 0 & 301 & 0 & 0 & 0 & 76.38859 & 68.62492 & 68.62492 & 75.84690 & 62.21482\\\\\n",
       "\t362 & 6770 & 6 & 77.03000 &  5.0 & 300.000 &  410000 & 12.38840 & 3.800000 & 4.100000 & 3.600000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 70.97872 & 70.52405 & 70.52405 & 70.52405 & 83.54821\\\\\n",
       "\t364 & 6772 & 6 & 87.28000 &  6.0 & 510.000 &  400000 & 12.57764 & 4.000000 & 4.000000 & 3.900000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 75.21836 & 88.68862 & 88.48143 & 88.68862 & 86.58241\\\\\n",
       "\t365 & 6780 & 6 & 71.76000 & 11.0 & 420.000 &  250000 & 12.38840 & 4.000000 & 4.000000 & 4.000000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 76.23241 & 68.62492 & 68.62492 & 75.84690 & 75.24435\\\\\n",
       "\t371 & 6795 & 6 & 52.82000 &  4.0 & 210.000 &  240000 & 12.79562 & 3.000000 & 3.000000 & 3.300000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 67.36720 & 52.71238 & 49.29500 & 57.67139 & 57.46492\\\\\n",
       "\t373 & 6797 & 6 & 74.20000 &  5.0 & 240.000 &  320000 & 12.79562 & 4.100000 & 4.400000 & 4.400000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 74.90800 & 81.86522 & 81.86522 & 75.84690 & 70.35977\\\\\n",
       "\t375 & 6803 & 6 & 74.51000 &  6.0 & 360.000 &  240000 & 12.89922 & 4.100000 & 4.100000 & 4.200000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 75.98160 & 68.62492 & 68.62492 & 75.84690 & 72.07914\\\\\n",
       "\t379 & 6811 & 6 & 44.34375 & 13.5 & 630.000 &  620000 & 12.84793 & 4.100000 & 4.700000 & 3.900000 & ⋯ & 0 & 301 & 1 & 1 & 0 & 78.02752 & 73.75159 & 73.75159 & 73.75159 & 79.40319\\\\\n",
       "\t381 & 6822 & 6 & 96.46000 &  9.0 & 480.000 &  400000 & 12.50618 & 4.000000 & 3.600000 & 4.300000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 75.30797 & 88.68862 & 88.48143 & 88.68862 & 82.83327\\\\\n",
       "\t382 & 6834 & 6 & 80.45000 &  6.0 & 360.000 &  300000 & 12.61154 & 3.000000 & 3.400000 & 3.100000 & ⋯ & 0 & 301 & 0 & 1 & 0 & 68.83997 & 81.86522 & 81.86522 & 75.84690 & 64.00270\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 136 × 22\n",
       "\n",
       "| <!--/--> | college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;dbl&gt; | intake &lt;dbl&gt; | fees &lt;dbl&gt; | salary &lt;dbl&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | ⋯ ⋯ | autonomous &lt;int&gt; | rank &lt;int&gt; | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_ONE &lt;int&gt; | linear &lt;dbl&gt; | decision &lt;dbl&gt; | fulltree &lt;dbl&gt; | pruned &lt;dbl&gt; | bagging &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1002 | 1 | 96.44000 |  8 | 300.000 | 240000.0 | 12.87391 | 3.400000 | 3.200000 | 3.500000 | ⋯ | 1 | 301 | 0 | 1 | 0 | 95.25097 | 88.05211 | 88.05211 | 92.45139 | 87.14085 |\n",
       "| 5 | 1105 | 1 | 88.05000 |  8 | 480.000 | 440000.0 | 12.70685 | 3.900000 | 4.000000 | 3.900000 | ⋯ | 1 | 250 | 0 | 0 | 0 | 83.98529 | 97.36824 | 97.36824 | 92.45139 | 91.94186 |\n",
       "| 7 | 1108 | 1 | 44.34375 |  5 | 300.000 | 310000.0 | 12.61154 | 3.900000 | 4.000000 | 4.300000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 67.03529 | 63.77202 | 63.77202 | 67.33875 | 70.91037 |\n",
       "| 8 | 1114 | 1 | 81.55000 |  6 | 300.000 | 320000.0 | 12.82126 | 4.000000 | 4.400000 | 3.900000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 70.98257 | 73.49375 | 70.32917 | 67.33875 | 73.05704 |\n",
       "| 14 | 1122 | 1 | 44.34375 |  5 | 300.000 | 200000.0 | 12.61154 | 2.200000 | 3.000000 | 2.000000 | ⋯ | 0 | 301 | 1 | 0 | 0 | 57.34506 | 69.04323 | 69.04323 | 67.33875 | 54.54966 |\n",
       "| 16 | 1124 | 1 | 49.08000 |  5 | 300.000 | 490000.0 | 12.34584 | 3.600000 | 4.300000 | 3.600000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 59.01199 | 70.52405 | 70.52405 | 70.52405 | 69.83709 |\n",
       "| 18 | 1126 | 1 | 67.71000 |  5 | 300.000 | 170000.0 | 13.10216 | 5.000000 | 5.000000 | 5.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 74.53221 | 63.77202 | 63.77202 | 67.33875 | 57.85599 |\n",
       "| 22 | 1130 | 1 | 45.98000 |  6 | 480.000 | 180000.0 | 12.10072 | 2.200000 | 4.000000 | 2.000000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 36.59204 | 52.71238 | 56.88917 | 57.67139 | 56.40356 |\n",
       "| 24 | 1182 | 1 | 59.68000 |  4 | 630.000 | 200000.0 | 13.01701 | 4.200000 | 4.000000 | 5.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 78.07224 | 59.83230 | 56.23467 | 59.83230 | 61.11015 |\n",
       "| 25 | 1251 | 1 | 44.34375 |  6 | 300.000 | 284000.0 | 12.54255 | 3.400000 | 3.200000 | 3.400000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 60.02308 | 69.04323 | 69.04323 | 67.33875 | 63.24937 |\n",
       "| 31 | 2008 | 2 | 97.84000 | 10 | 540.000 | 190000.0 | 13.38473 | 3.900000 | 3.800000 | 3.900000 | ⋯ | 1 |  97 | 0 | 1 | 0 | 97.83733 | 97.36824 | 97.36824 | 92.45139 | 93.19946 |\n",
       "| 33 | 2021 | 2 | 72.61000 |  2 | 240.000 |  80000.0 | 12.70685 | 3.800000 | 3.900000 | 4.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 77.88152 | 59.83230 | 56.23467 | 59.83230 | 73.75753 |\n",
       "| 35 | 2111 | 2 | 65.26000 |  4 | 300.000 | 170000.0 | 12.61154 | 3.800000 | 3.700000 | 4.300000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 67.06327 | 59.83230 | 56.23467 | 59.83230 | 59.49070 |\n",
       "| 39 | 2116 | 2 | 54.60000 | 10 | 294.000 | 200000.0 | 12.61154 | 3.100000 | 3.000000 | 3.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 66.33838 | 52.71238 | 56.88917 | 57.67139 | 55.81445 |\n",
       "| 41 | 2127 | 2 | 80.37000 |  5 | 420.000 | 350000.0 | 12.79386 | 3.900000 | 4.300000 | 4.300000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 70.52523 | 88.68862 | 84.42333 | 88.68862 | 78.27550 |\n",
       "| 42 | 2128 | 2 | 44.34375 |  3 | 196.875 | 170000.0 | 12.61154 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 67.18494 | 59.83230 | 56.23467 | 59.83230 | 59.67666 |\n",
       "| 48 | 2134 | 2 | 72.88000 |  9 | 360.000 | 240000.0 | 12.67608 | 3.300000 | 3.400000 | 3.500000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 69.44201 | 69.04323 | 69.04323 | 67.33875 | 64.49678 |\n",
       "| 50 | 2136 | 2 | 44.34375 |  9 | 240.000 | 480000.0 | 13.30469 | 4.300000 | 5.000000 | 5.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 89.85680 | 88.68862 | 88.48143 | 88.68862 | 84.47547 |\n",
       "| 52 | 2138 | 2 | 64.49000 |  4 | 270.000 | 250000.0 | 12.70685 | 3.900000 | 4.500000 | 5.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 81.48739 | 59.83230 | 56.23467 | 59.83230 | 63.52538 |\n",
       "| 56 | 2250 | 2 | 63.71000 |  6 | 196.875 | 220000.0 | 12.79562 | 4.000000 | 4.000000 | 3.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 71.14808 | 55.15813 | 55.15813 | 67.33875 | 62.93025 |\n",
       "| 58 | 2254 | 2 | 59.41000 |  5 | 196.875 | 160000.0 | 12.79562 | 2.800000 | 3.000000 | 3.000000 | ⋯ | 0 | 301 | 0 | 0 | 0 | 56.74210 | 52.71238 | 49.29500 | 57.67139 | 51.01997 |\n",
       "| 59 | 2255 | 2 | 71.74876 |  3 | 196.875 | 220000.0 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 0 | 301 | 1 | 0 | 0 | 59.76323 | 59.83230 | 56.23467 | 59.83230 | 60.48674 |\n",
       "| 65 | 2641 | 2 | 71.74876 |  4 | 382.000 | 322661.9 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 0 | 301 | 1 | 0 | 0 | 61.80546 | 59.83230 | 65.52854 | 59.83230 | 66.70431 |\n",
       "| 67 | 3014 | 3 | 98.48000 |  6 | 300.000 | 340000.0 | 13.21768 | 4.100000 | 3.900000 | 4.200000 | ⋯ | 1 | 150 | 0 | 1 | 0 | 99.68131 | 97.36824 | 97.36824 | 92.45139 | 95.94890 |\n",
       "| 69 | 3035 | 3 | 89.48000 |  7 | 196.875 | 420000.0 | 12.97155 | 3.600000 | 3.100000 | 3.800000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 74.01919 | 88.68862 | 91.75308 | 88.68862 | 87.07321 |\n",
       "| 73 | 3139 | 3 | 96.84000 | 10 | 630.000 | 550000.0 | 12.76569 | 4.300000 | 4.700000 | 4.300000 | ⋯ | 1 | 301 | 0 | 0 | 0 | 88.69525 | 88.05211 | 88.05211 | 92.45139 | 84.10130 |\n",
       "| 75 | 3147 | 3 | 83.40000 |  6 | 300.000 | 264000.0 | 12.30139 | 2.200000 | 2.400000 | 2.200000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 53.97024 | 65.30064 | 65.30064 | 57.67139 | 58.89893 |\n",
       "| 76 | 3148 | 3 | 92.28000 | 10 | 630.000 | 460000.0 | 13.30469 | 3.800000 | 3.700000 | 3.700000 | ⋯ | 0 | 301 | 0 | 0 | 0 | 77.37348 | 73.75159 | 73.75159 | 73.75159 | 85.57030 |\n",
       "| 82 | 3182 | 3 | 98.34000 |  5 | 300.000 | 600000.0 | 14.16617 | 3.800000 | 3.300000 | 3.600000 | ⋯ | 0 | 250 | 0 | 0 | 0 | 82.17729 | 88.68862 | 91.75308 | 88.68862 | 93.03070 |\n",
       "| 84 | 3184 | 3 | 96.77000 | 10 | 480.000 | 570000.0 | 13.12237 | 4.000000 | 3.900000 | 3.900000 | ⋯ | 0 | 200 | 0 | 1 | 0 | 79.32101 | 88.68862 | 88.48143 | 88.68862 | 93.58710 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 303 | 6283 | 6 | 87.28000 | 13.0 | 196.875 |  370000 | 12.61154 | 4.000000 | 4.200000 | 4.200000 | ⋯ | 1 | 301 | 0 | 1 | 0 | 92.78713 | 88.05211 | 88.05211 | 92.45139 | 91.13583 |\n",
       "| 305 | 6285 | 6 | 92.61000 |  6.0 | 240.000 |  430000 | 12.91411 | 3.900000 | 3.800000 | 3.900000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 77.90717 | 88.68862 | 91.75308 | 88.68862 | 91.82660 |\n",
       "| 307 | 6289 | 6 | 97.98000 |  7.0 | 300.000 |  570000 | 13.32122 | 3.900000 | 3.700000 | 4.300000 | ⋯ | 1 | 155 | 0 | 1 | 0 | 92.27407 | 97.36824 | 97.36824 | 92.45139 | 97.16614 |\n",
       "| 311 | 6303 | 6 | 75.18000 |  5.0 | 240.000 |  240000 | 12.98540 | 4.000000 | 4.200000 | 4.100000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 74.50074 | 68.62492 | 68.62492 | 75.84690 | 65.67000 |\n",
       "| 313 | 6305 | 6 | 46.17000 |  5.0 | 210.000 |  192000 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 0 | 301 | 1 | 0 | 0 | 64.01767 | 68.62492 | 68.62492 | 75.84690 | 61.57288 |\n",
       "| 314 | 6307 | 6 | 83.32000 | 12.0 | 255.000 |  370000 | 12.76569 | 4.100000 | 4.200000 | 4.200000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 81.96029 | 88.68862 | 88.48143 | 88.68862 | 89.76211 |\n",
       "| 320 | 6317 | 6 | 79.53000 | 11.0 | 630.000 |  310000 | 12.54255 | 3.500000 | 3.300000 | 3.700000 | ⋯ | 1 | 301 | 0 | 1 | 0 | 83.93804 | 88.05211 | 88.05211 | 92.45139 | 84.42921 |\n",
       "| 322 | 6319 | 6 | 63.05000 |  6.0 | 360.000 |  308000 | 12.76569 | 3.600000 | 3.900000 | 4.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 74.35820 | 81.86522 | 81.86522 | 75.84690 | 76.28742 |\n",
       "| 324 | 6321 | 6 | 45.67000 |  6.0 | 300.000 |  240000 | 12.79386 | 3.200000 | 3.700000 | 3.700000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 67.14082 | 52.71238 | 56.88917 | 57.67139 | 62.82214 |\n",
       "| 328 | 6325 | 6 | 78.05000 |  5.0 | 480.000 |  230000 | 13.99783 | 3.600000 | 3.300000 | 4.200000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 79.16464 | 68.62492 | 68.62492 | 75.84690 | 66.11722 |\n",
       "| 330 | 6419 | 6 | 78.35000 |  6.0 | 360.000 |  330000 | 12.50618 | 4.200000 | 4.100000 | 4.200000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 71.71905 | 81.86522 | 81.86522 | 75.84690 | 83.55063 |\n",
       "| 331 | 6444 | 6 | 44.34375 |  5.0 | 196.875 |  141000 | 12.79562 | 3.200000 | 3.500000 | 4.000000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 59.30986 | 52.71238 | 49.29500 | 57.67139 | 49.25645 |\n",
       "| 337 | 6620 | 6 | 73.99000 | 13.5 | 196.875 | 1080000 | 13.35348 | 3.600000 | 4.200000 | 3.400000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 85.04649 | 88.68862 | 91.75308 | 88.68862 | 72.71361 |\n",
       "| 339 | 6622 | 6 | 85.85000 |  6.0 | 360.000 |  280000 | 12.76569 | 3.500000 | 3.500000 | 3.900000 | ⋯ | 0 | 301 | 0 | 0 | 0 | 73.16798 | 68.62492 | 68.62492 | 75.84690 | 71.99251 |\n",
       "| 341 | 6628 | 6 | 56.76500 |  5.0 | 196.875 |  400000 | 12.56025 | 3.400000 | 3.000000 | 4.000000 | ⋯ | 0 | 301 | 0 | 0 | 1 | 75.75998 | 88.68862 | 91.75308 | 88.68862 | 81.94778 |\n",
       "| 345 | 6635 | 6 | 67.11200 |  9.0 | 420.000 |  300000 | 12.42922 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 76.07599 | 81.86522 | 81.86522 | 75.84690 | 78.96625 |\n",
       "| 347 | 6643 | 6 | 81.98400 |  5.0 | 360.000 |  310000 | 12.20608 | 4.200000 | 4.500000 | 4.300000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 73.32382 | 81.86522 | 81.86522 | 75.84690 | 76.17784 |\n",
       "| 348 | 6644 | 6 | 56.76000 |  7.0 | 300.000 |  320000 | 12.79386 | 3.000000 | 3.800000 | 3.100000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 68.82040 | 52.71238 | 56.88917 | 57.67139 | 65.14153 |\n",
       "| 354 | 6757 | 6 | 60.73000 |  7.0 | 360.000 |  310000 | 12.76569 | 3.800000 | 4.000000 | 3.700000 | ⋯ | 0 | 301 | 0 | 0 | 0 | 74.10919 | 81.86522 | 81.86522 | 75.84690 | 76.10538 |\n",
       "| 356 | 6759 | 6 | 68.70000 |  5.0 | 270.000 |  270000 | 12.61154 | 4.600000 | 5.000000 | 5.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 80.30998 | 68.62492 | 68.62492 | 75.84690 | 63.63364 |\n",
       "| 358 | 6766 | 6 | 63.08000 |  5.0 | 300.000 |  260000 | 12.76569 | 4.700000 | 5.000000 | 5.000000 | ⋯ | 0 | 301 | 0 | 0 | 0 | 76.38859 | 68.62492 | 68.62492 | 75.84690 | 62.21482 |\n",
       "| 362 | 6770 | 6 | 77.03000 |  5.0 | 300.000 |  410000 | 12.38840 | 3.800000 | 4.100000 | 3.600000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 70.97872 | 70.52405 | 70.52405 | 70.52405 | 83.54821 |\n",
       "| 364 | 6772 | 6 | 87.28000 |  6.0 | 510.000 |  400000 | 12.57764 | 4.000000 | 4.000000 | 3.900000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 75.21836 | 88.68862 | 88.48143 | 88.68862 | 86.58241 |\n",
       "| 365 | 6780 | 6 | 71.76000 | 11.0 | 420.000 |  250000 | 12.38840 | 4.000000 | 4.000000 | 4.000000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 76.23241 | 68.62492 | 68.62492 | 75.84690 | 75.24435 |\n",
       "| 371 | 6795 | 6 | 52.82000 |  4.0 | 210.000 |  240000 | 12.79562 | 3.000000 | 3.000000 | 3.300000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 67.36720 | 52.71238 | 49.29500 | 57.67139 | 57.46492 |\n",
       "| 373 | 6797 | 6 | 74.20000 |  5.0 | 240.000 |  320000 | 12.79562 | 4.100000 | 4.400000 | 4.400000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 74.90800 | 81.86522 | 81.86522 | 75.84690 | 70.35977 |\n",
       "| 375 | 6803 | 6 | 74.51000 |  6.0 | 360.000 |  240000 | 12.89922 | 4.100000 | 4.100000 | 4.200000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 75.98160 | 68.62492 | 68.62492 | 75.84690 | 72.07914 |\n",
       "| 379 | 6811 | 6 | 44.34375 | 13.5 | 630.000 |  620000 | 12.84793 | 4.100000 | 4.700000 | 3.900000 | ⋯ | 0 | 301 | 1 | 1 | 0 | 78.02752 | 73.75159 | 73.75159 | 73.75159 | 79.40319 |\n",
       "| 381 | 6822 | 6 | 96.46000 |  9.0 | 480.000 |  400000 | 12.50618 | 4.000000 | 3.600000 | 4.300000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 75.30797 | 88.68862 | 88.48143 | 88.68862 | 82.83327 |\n",
       "| 382 | 6834 | 6 | 80.45000 |  6.0 | 360.000 |  300000 | 12.61154 | 3.000000 | 3.400000 | 3.100000 | ⋯ | 0 | 301 | 0 | 1 | 0 | 68.83997 | 81.86522 | 81.86522 | 75.84690 | 64.00270 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff   courses intake  fees     salary   rating  \n",
       "1   1002         1        96.44000  8      300.000 240000.0 12.87391 3.400000\n",
       "5   1105         1        88.05000  8      480.000 440000.0 12.70685 3.900000\n",
       "7   1108         1        44.34375  5      300.000 310000.0 12.61154 3.900000\n",
       "8   1114         1        81.55000  6      300.000 320000.0 12.82126 4.000000\n",
       "14  1122         1        44.34375  5      300.000 200000.0 12.61154 2.200000\n",
       "16  1124         1        49.08000  5      300.000 490000.0 12.34584 3.600000\n",
       "18  1126         1        67.71000  5      300.000 170000.0 13.10216 5.000000\n",
       "22  1130         1        45.98000  6      480.000 180000.0 12.10072 2.200000\n",
       "24  1182         1        59.68000  4      630.000 200000.0 13.01701 4.200000\n",
       "25  1251         1        44.34375  6      300.000 284000.0 12.54255 3.400000\n",
       "31  2008         2        97.84000 10      540.000 190000.0 13.38473 3.900000\n",
       "33  2021         2        72.61000  2      240.000  80000.0 12.70685 3.800000\n",
       "35  2111         2        65.26000  4      300.000 170000.0 12.61154 3.800000\n",
       "39  2116         2        54.60000 10      294.000 200000.0 12.61154 3.100000\n",
       "41  2127         2        80.37000  5      420.000 350000.0 12.79386 3.900000\n",
       "42  2128         2        44.34375  3      196.875 170000.0 12.61154 3.800000\n",
       "48  2134         2        72.88000  9      360.000 240000.0 12.67608 3.300000\n",
       "50  2136         2        44.34375  9      240.000 480000.0 13.30469 4.300000\n",
       "52  2138         2        64.49000  4      270.000 250000.0 12.70685 3.900000\n",
       "56  2250         2        63.71000  6      196.875 220000.0 12.79562 4.000000\n",
       "58  2254         2        59.41000  5      196.875 160000.0 12.79562 2.800000\n",
       "59  2255         2        71.74876  3      196.875 220000.0 12.79562 3.666295\n",
       "65  2641         2        71.74876  4      382.000 322661.9 12.79562 3.666295\n",
       "67  3014         3        98.48000  6      300.000 340000.0 13.21768 4.100000\n",
       "69  3035         3        89.48000  7      196.875 420000.0 12.97155 3.600000\n",
       "73  3139         3        96.84000 10      630.000 550000.0 12.76569 4.300000\n",
       "75  3147         3        83.40000  6      300.000 264000.0 12.30139 2.200000\n",
       "76  3148         3        92.28000 10      630.000 460000.0 13.30469 3.800000\n",
       "82  3182         3        98.34000  5      300.000 600000.0 14.16617 3.800000\n",
       "84  3184         3        96.77000 10      480.000 570000.0 13.12237 4.000000\n",
       "⋮   ⋮            ⋮        ⋮        ⋮       ⋮       ⋮        ⋮        ⋮       \n",
       "303 6283         6        87.28000 13.0    196.875  370000  12.61154 4.000000\n",
       "305 6285         6        92.61000  6.0    240.000  430000  12.91411 3.900000\n",
       "307 6289         6        97.98000  7.0    300.000  570000  13.32122 3.900000\n",
       "311 6303         6        75.18000  5.0    240.000  240000  12.98540 4.000000\n",
       "313 6305         6        46.17000  5.0    210.000  192000  12.79562 3.666295\n",
       "314 6307         6        83.32000 12.0    255.000  370000  12.76569 4.100000\n",
       "320 6317         6        79.53000 11.0    630.000  310000  12.54255 3.500000\n",
       "322 6319         6        63.05000  6.0    360.000  308000  12.76569 3.600000\n",
       "324 6321         6        45.67000  6.0    300.000  240000  12.79386 3.200000\n",
       "328 6325         6        78.05000  5.0    480.000  230000  13.99783 3.600000\n",
       "330 6419         6        78.35000  6.0    360.000  330000  12.50618 4.200000\n",
       "331 6444         6        44.34375  5.0    196.875  141000  12.79562 3.200000\n",
       "337 6620         6        73.99000 13.5    196.875 1080000  13.35348 3.600000\n",
       "339 6622         6        85.85000  6.0    360.000  280000  12.76569 3.500000\n",
       "341 6628         6        56.76500  5.0    196.875  400000  12.56025 3.400000\n",
       "345 6635         6        67.11200  9.0    420.000  300000  12.42922 3.800000\n",
       "347 6643         6        81.98400  5.0    360.000  310000  12.20608 4.200000\n",
       "348 6644         6        56.76000  7.0    300.000  320000  12.79386 3.000000\n",
       "354 6757         6        60.73000  7.0    360.000  310000  12.76569 3.800000\n",
       "356 6759         6        68.70000  5.0    270.000  270000  12.61154 4.600000\n",
       "358 6766         6        63.08000  5.0    300.000  260000  12.76569 4.700000\n",
       "362 6770         6        77.03000  5.0    300.000  410000  12.38840 3.800000\n",
       "364 6772         6        87.28000  6.0    510.000  400000  12.57764 4.000000\n",
       "365 6780         6        71.76000 11.0    420.000  250000  12.38840 4.000000\n",
       "371 6795         6        52.82000  4.0    210.000  240000  12.79562 3.000000\n",
       "373 6797         6        74.20000  5.0    240.000  320000  12.79562 4.100000\n",
       "375 6803         6        74.51000  6.0    360.000  240000  12.89922 4.100000\n",
       "379 6811         6        44.34375 13.5    630.000  620000  12.84793 4.100000\n",
       "381 6822         6        96.46000  9.0    480.000  400000  12.50618 4.000000\n",
       "382 6834         6        80.45000  6.0    360.000  300000  12.61154 3.000000\n",
       "    infrastructure faculty  ⋯ autonomous rank new_ban hostel_BOTH hostel_ONE\n",
       "1   3.200000       3.500000 ⋯ 1          301  0       1           0         \n",
       "5   4.000000       3.900000 ⋯ 1          250  0       0           0         \n",
       "7   4.000000       4.300000 ⋯ 0          301  0       1           0         \n",
       "8   4.400000       3.900000 ⋯ 0          301  0       1           0         \n",
       "14  3.000000       2.000000 ⋯ 0          301  1       0           0         \n",
       "16  4.300000       3.600000 ⋯ 0          301  1       1           0         \n",
       "18  5.000000       5.000000 ⋯ 0          301  0       1           0         \n",
       "22  4.000000       2.000000 ⋯ 0          301  1       1           0         \n",
       "24  4.000000       5.000000 ⋯ 0          301  0       1           0         \n",
       "25  3.200000       3.400000 ⋯ 0          301  1       1           0         \n",
       "31  3.800000       3.900000 ⋯ 1           97  0       1           0         \n",
       "33  3.900000       4.000000 ⋯ 0          301  0       1           0         \n",
       "35  3.700000       4.300000 ⋯ 0          301  0       1           0         \n",
       "39  3.000000       3.000000 ⋯ 0          301  0       1           0         \n",
       "41  4.300000       4.300000 ⋯ 0          301  0       1           0         \n",
       "42  4.000000       4.000000 ⋯ 0          301  1       1           0         \n",
       "48  3.400000       3.500000 ⋯ 0          301  0       1           0         \n",
       "50  5.000000       5.000000 ⋯ 0          301  0       1           0         \n",
       "52  4.500000       5.000000 ⋯ 0          301  0       1           0         \n",
       "56  4.000000       3.000000 ⋯ 0          301  0       1           0         \n",
       "58  3.000000       3.000000 ⋯ 0          301  0       0           0         \n",
       "59  3.804457       3.822472 ⋯ 0          301  1       0           0         \n",
       "65  3.804457       3.822472 ⋯ 0          301  1       0           0         \n",
       "67  3.900000       4.200000 ⋯ 1          150  0       1           0         \n",
       "69  3.100000       3.800000 ⋯ 0          301  0       1           0         \n",
       "73  4.700000       4.300000 ⋯ 1          301  0       0           0         \n",
       "75  2.400000       2.200000 ⋯ 0          301  1       1           0         \n",
       "76  3.700000       3.700000 ⋯ 0          301  0       0           0         \n",
       "82  3.300000       3.600000 ⋯ 0          250  0       0           0         \n",
       "84  3.900000       3.900000 ⋯ 0          200  0       1           0         \n",
       "⋮   ⋮              ⋮        ⋱ ⋮          ⋮    ⋮       ⋮           ⋮         \n",
       "303 4.200000       4.200000 ⋯ 1          301  0       1           0         \n",
       "305 3.800000       3.900000 ⋯ 0          301  0       1           0         \n",
       "307 3.700000       4.300000 ⋯ 1          155  0       1           0         \n",
       "311 4.200000       4.100000 ⋯ 0          301  0       1           0         \n",
       "313 3.804457       3.822472 ⋯ 0          301  1       0           0         \n",
       "314 4.200000       4.200000 ⋯ 0          301  0       1           0         \n",
       "320 3.300000       3.700000 ⋯ 1          301  0       1           0         \n",
       "322 3.900000       4.000000 ⋯ 0          301  0       1           0         \n",
       "324 3.700000       3.700000 ⋯ 0          301  0       1           0         \n",
       "328 3.300000       4.200000 ⋯ 0          301  0       1           0         \n",
       "330 4.100000       4.200000 ⋯ 0          301  0       1           0         \n",
       "331 3.500000       4.000000 ⋯ 0          301  1       1           0         \n",
       "337 4.200000       3.400000 ⋯ 0          301  1       1           0         \n",
       "339 3.500000       3.900000 ⋯ 0          301  0       0           0         \n",
       "341 3.000000       4.000000 ⋯ 0          301  0       0           1         \n",
       "345 4.000000       4.000000 ⋯ 0          301  0       1           0         \n",
       "347 4.500000       4.300000 ⋯ 0          301  0       1           0         \n",
       "348 3.800000       3.100000 ⋯ 0          301  0       1           0         \n",
       "354 4.000000       3.700000 ⋯ 0          301  0       0           0         \n",
       "356 5.000000       5.000000 ⋯ 0          301  0       1           0         \n",
       "358 5.000000       5.000000 ⋯ 0          301  0       0           0         \n",
       "362 4.100000       3.600000 ⋯ 0          301  0       1           0         \n",
       "364 4.000000       3.900000 ⋯ 0          301  0       1           0         \n",
       "365 4.000000       4.000000 ⋯ 0          301  0       1           0         \n",
       "371 3.000000       3.300000 ⋯ 0          301  0       1           0         \n",
       "373 4.400000       4.400000 ⋯ 0          301  0       1           0         \n",
       "375 4.100000       4.200000 ⋯ 0          301  0       1           0         \n",
       "379 4.700000       3.900000 ⋯ 0          301  1       1           0         \n",
       "381 3.600000       4.300000 ⋯ 0          301  0       1           0         \n",
       "382 3.400000       3.100000 ⋯ 0          301  0       1           0         \n",
       "    linear   decision fulltree pruned   bagging \n",
       "1   95.25097 88.05211 88.05211 92.45139 87.14085\n",
       "5   83.98529 97.36824 97.36824 92.45139 91.94186\n",
       "7   67.03529 63.77202 63.77202 67.33875 70.91037\n",
       "8   70.98257 73.49375 70.32917 67.33875 73.05704\n",
       "14  57.34506 69.04323 69.04323 67.33875 54.54966\n",
       "16  59.01199 70.52405 70.52405 70.52405 69.83709\n",
       "18  74.53221 63.77202 63.77202 67.33875 57.85599\n",
       "22  36.59204 52.71238 56.88917 57.67139 56.40356\n",
       "24  78.07224 59.83230 56.23467 59.83230 61.11015\n",
       "25  60.02308 69.04323 69.04323 67.33875 63.24937\n",
       "31  97.83733 97.36824 97.36824 92.45139 93.19946\n",
       "33  77.88152 59.83230 56.23467 59.83230 73.75753\n",
       "35  67.06327 59.83230 56.23467 59.83230 59.49070\n",
       "39  66.33838 52.71238 56.88917 57.67139 55.81445\n",
       "41  70.52523 88.68862 84.42333 88.68862 78.27550\n",
       "42  67.18494 59.83230 56.23467 59.83230 59.67666\n",
       "48  69.44201 69.04323 69.04323 67.33875 64.49678\n",
       "50  89.85680 88.68862 88.48143 88.68862 84.47547\n",
       "52  81.48739 59.83230 56.23467 59.83230 63.52538\n",
       "56  71.14808 55.15813 55.15813 67.33875 62.93025\n",
       "58  56.74210 52.71238 49.29500 57.67139 51.01997\n",
       "59  59.76323 59.83230 56.23467 59.83230 60.48674\n",
       "65  61.80546 59.83230 65.52854 59.83230 66.70431\n",
       "67  99.68131 97.36824 97.36824 92.45139 95.94890\n",
       "69  74.01919 88.68862 91.75308 88.68862 87.07321\n",
       "73  88.69525 88.05211 88.05211 92.45139 84.10130\n",
       "75  53.97024 65.30064 65.30064 57.67139 58.89893\n",
       "76  77.37348 73.75159 73.75159 73.75159 85.57030\n",
       "82  82.17729 88.68862 91.75308 88.68862 93.03070\n",
       "84  79.32101 88.68862 88.48143 88.68862 93.58710\n",
       "⋮   ⋮        ⋮        ⋮        ⋮        ⋮       \n",
       "303 92.78713 88.05211 88.05211 92.45139 91.13583\n",
       "305 77.90717 88.68862 91.75308 88.68862 91.82660\n",
       "307 92.27407 97.36824 97.36824 92.45139 97.16614\n",
       "311 74.50074 68.62492 68.62492 75.84690 65.67000\n",
       "313 64.01767 68.62492 68.62492 75.84690 61.57288\n",
       "314 81.96029 88.68862 88.48143 88.68862 89.76211\n",
       "320 83.93804 88.05211 88.05211 92.45139 84.42921\n",
       "322 74.35820 81.86522 81.86522 75.84690 76.28742\n",
       "324 67.14082 52.71238 56.88917 57.67139 62.82214\n",
       "328 79.16464 68.62492 68.62492 75.84690 66.11722\n",
       "330 71.71905 81.86522 81.86522 75.84690 83.55063\n",
       "331 59.30986 52.71238 49.29500 57.67139 49.25645\n",
       "337 85.04649 88.68862 91.75308 88.68862 72.71361\n",
       "339 73.16798 68.62492 68.62492 75.84690 71.99251\n",
       "341 75.75998 88.68862 91.75308 88.68862 81.94778\n",
       "345 76.07599 81.86522 81.86522 75.84690 78.96625\n",
       "347 73.32382 81.86522 81.86522 75.84690 76.17784\n",
       "348 68.82040 52.71238 56.88917 57.67139 65.14153\n",
       "354 74.10919 81.86522 81.86522 75.84690 76.10538\n",
       "356 80.30998 68.62492 68.62492 75.84690 63.63364\n",
       "358 76.38859 68.62492 68.62492 75.84690 62.21482\n",
       "362 70.97872 70.52405 70.52405 70.52405 83.54821\n",
       "364 75.21836 88.68862 88.48143 88.68862 86.58241\n",
       "365 76.23241 68.62492 68.62492 75.84690 75.24435\n",
       "371 67.36720 52.71238 49.29500 57.67139 57.46492\n",
       "373 74.90800 81.86522 81.86522 75.84690 70.35977\n",
       "375 75.98160 68.62492 68.62492 75.84690 72.07914\n",
       "379 78.02752 73.75159 73.75159 73.75159 79.40319\n",
       "381 75.30797 88.68862 88.48143 88.68862 82.83327\n",
       "382 68.83997 81.86522 81.86522 75.84690 64.00270"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(randomForest)\n",
    "set.seed(0)\n",
    "bagging <- randomForest(cutoff~.-college_code, data=train, mtry=15)\n",
    "test$bagging <- predict(bagging, test)\n",
    "View(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "84f84775",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "159.082607141864"
      ],
      "text/latex": [
       "159.082607141864"
      ],
      "text/markdown": [
       "159.082607141864"
      ],
      "text/plain": [
       "[1] 159.0826"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSEbagging <- mean((test$bagging - test$cutoff)^2)\n",
    "MSEbagging"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c2b5c20",
   "metadata": {},
   "source": [
    "### Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "e22d24b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 136 × 23</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>⋯</th><th scope=col>rank</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_ONE</th><th scope=col>linear</th><th scope=col>decision</th><th scope=col>fulltree</th><th scope=col>pruned</th><th scope=col>bagging</th><th scope=col>randomforest</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>⋯</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1002</td><td>1</td><td>96.44000</td><td> 8</td><td>300.000</td><td>240000.0</td><td>12.87391</td><td>3.400000</td><td>3.200000</td><td>3.500000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>95.25097</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>87.14085</td><td>82.41035</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1105</td><td>1</td><td>88.05000</td><td> 8</td><td>480.000</td><td>440000.0</td><td>12.70685</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>250</td><td>0</td><td>0</td><td>0</td><td>83.98529</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>91.94186</td><td>92.13631</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1108</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>310000.0</td><td>12.61154</td><td>3.900000</td><td>4.000000</td><td>4.300000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.03529</td><td>63.77202</td><td>63.77202</td><td>67.33875</td><td>70.91037</td><td>70.83759</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>1114</td><td>1</td><td>81.55000</td><td> 6</td><td>300.000</td><td>320000.0</td><td>12.82126</td><td>4.000000</td><td>4.400000</td><td>3.900000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.98257</td><td>73.49375</td><td>70.32917</td><td>67.33875</td><td>73.05704</td><td>73.94291</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1122</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>200000.0</td><td>12.61154</td><td>2.200000</td><td>3.000000</td><td>2.000000</td><td>⋯</td><td>301</td><td>1</td><td>0</td><td>0</td><td>57.34506</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>54.54966</td><td>56.92909</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>1124</td><td>1</td><td>49.08000</td><td> 5</td><td>300.000</td><td>490000.0</td><td>12.34584</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.01199</td><td>70.52405</td><td>70.52405</td><td>70.52405</td><td>69.83709</td><td>69.92331</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>1126</td><td>1</td><td>67.71000</td><td> 5</td><td>300.000</td><td>170000.0</td><td>13.10216</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.53221</td><td>63.77202</td><td>63.77202</td><td>67.33875</td><td>57.85599</td><td>60.52810</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>1130</td><td>1</td><td>45.98000</td><td> 6</td><td>480.000</td><td>180000.0</td><td>12.10072</td><td>2.200000</td><td>4.000000</td><td>2.000000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>36.59204</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>56.40356</td><td>55.63638</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>1182</td><td>1</td><td>59.68000</td><td> 4</td><td>630.000</td><td>200000.0</td><td>13.01701</td><td>4.200000</td><td>4.000000</td><td>5.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>78.07224</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>61.11015</td><td>61.59383</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>1251</td><td>1</td><td>44.34375</td><td> 6</td><td>300.000</td><td>284000.0</td><td>12.54255</td><td>3.400000</td><td>3.200000</td><td>3.400000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>60.02308</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>63.24937</td><td>61.99935</td></tr>\n",
       "\t<tr><th scope=row>31</th><td>2008</td><td>2</td><td>97.84000</td><td>10</td><td>540.000</td><td>190000.0</td><td>13.38473</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td> 97</td><td>0</td><td>1</td><td>0</td><td>97.83733</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>93.19946</td><td>93.16599</td></tr>\n",
       "\t<tr><th scope=row>33</th><td>2021</td><td>2</td><td>72.61000</td><td> 2</td><td>240.000</td><td> 80000.0</td><td>12.70685</td><td>3.800000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.88152</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>73.75753</td><td>72.12574</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>2111</td><td>2</td><td>65.26000</td><td> 4</td><td>300.000</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.06327</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>59.49070</td><td>62.80911</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>2116</td><td>2</td><td>54.60000</td><td>10</td><td>294.000</td><td>200000.0</td><td>12.61154</td><td>3.100000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>66.33838</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>55.81445</td><td>58.13235</td></tr>\n",
       "\t<tr><th scope=row>41</th><td>2127</td><td>2</td><td>80.37000</td><td> 5</td><td>420.000</td><td>350000.0</td><td>12.79386</td><td>3.900000</td><td>4.300000</td><td>4.300000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.52523</td><td>88.68862</td><td>84.42333</td><td>88.68862</td><td>78.27550</td><td>76.29939</td></tr>\n",
       "\t<tr><th scope=row>42</th><td>2128</td><td>2</td><td>44.34375</td><td> 3</td><td>196.875</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>67.18494</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>59.67666</td><td>61.06195</td></tr>\n",
       "\t<tr><th scope=row>48</th><td>2134</td><td>2</td><td>72.88000</td><td> 9</td><td>360.000</td><td>240000.0</td><td>12.67608</td><td>3.300000</td><td>3.400000</td><td>3.500000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>69.44201</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>64.49678</td><td>65.05105</td></tr>\n",
       "\t<tr><th scope=row>50</th><td>2136</td><td>2</td><td>44.34375</td><td> 9</td><td>240.000</td><td>480000.0</td><td>13.30469</td><td>4.300000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>89.85680</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>84.47547</td><td>82.64416</td></tr>\n",
       "\t<tr><th scope=row>52</th><td>2138</td><td>2</td><td>64.49000</td><td> 4</td><td>270.000</td><td>250000.0</td><td>12.70685</td><td>3.900000</td><td>4.500000</td><td>5.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.48739</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>63.52538</td><td>62.28017</td></tr>\n",
       "\t<tr><th scope=row>56</th><td>2250</td><td>2</td><td>63.71000</td><td> 6</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>4.000000</td><td>4.000000</td><td>3.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.14808</td><td>55.15813</td><td>55.15813</td><td>67.33875</td><td>62.93025</td><td>62.64716</td></tr>\n",
       "\t<tr><th scope=row>58</th><td>2254</td><td>2</td><td>59.41000</td><td> 5</td><td>196.875</td><td>160000.0</td><td>12.79562</td><td>2.800000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>301</td><td>0</td><td>0</td><td>0</td><td>56.74210</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>51.01997</td><td>52.50172</td></tr>\n",
       "\t<tr><th scope=row>59</th><td>2255</td><td>2</td><td>71.74876</td><td> 3</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>301</td><td>1</td><td>0</td><td>0</td><td>59.76323</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>60.48674</td><td>59.80988</td></tr>\n",
       "\t<tr><th scope=row>65</th><td>2641</td><td>2</td><td>71.74876</td><td> 4</td><td>382.000</td><td>322661.9</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>301</td><td>1</td><td>0</td><td>0</td><td>61.80546</td><td>59.83230</td><td>65.52854</td><td>59.83230</td><td>66.70431</td><td>66.34055</td></tr>\n",
       "\t<tr><th scope=row>67</th><td>3014</td><td>3</td><td>98.48000</td><td> 6</td><td>300.000</td><td>340000.0</td><td>13.21768</td><td>4.100000</td><td>3.900000</td><td>4.200000</td><td>⋯</td><td>150</td><td>0</td><td>1</td><td>0</td><td>99.68131</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>95.94890</td><td>95.52757</td></tr>\n",
       "\t<tr><th scope=row>69</th><td>3035</td><td>3</td><td>89.48000</td><td> 7</td><td>196.875</td><td>420000.0</td><td>12.97155</td><td>3.600000</td><td>3.100000</td><td>3.800000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.01919</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>87.07321</td><td>82.54296</td></tr>\n",
       "\t<tr><th scope=row>73</th><td>3139</td><td>3</td><td>96.84000</td><td>10</td><td>630.000</td><td>550000.0</td><td>12.76569</td><td>4.300000</td><td>4.700000</td><td>4.300000</td><td>⋯</td><td>301</td><td>0</td><td>0</td><td>0</td><td>88.69525</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>84.10130</td><td>85.09154</td></tr>\n",
       "\t<tr><th scope=row>75</th><td>3147</td><td>3</td><td>83.40000</td><td> 6</td><td>300.000</td><td>264000.0</td><td>12.30139</td><td>2.200000</td><td>2.400000</td><td>2.200000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>53.97024</td><td>65.30064</td><td>65.30064</td><td>57.67139</td><td>58.89893</td><td>59.25145</td></tr>\n",
       "\t<tr><th scope=row>76</th><td>3148</td><td>3</td><td>92.28000</td><td>10</td><td>630.000</td><td>460000.0</td><td>13.30469</td><td>3.800000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>301</td><td>0</td><td>0</td><td>0</td><td>77.37348</td><td>73.75159</td><td>73.75159</td><td>73.75159</td><td>85.57030</td><td>85.71103</td></tr>\n",
       "\t<tr><th scope=row>82</th><td>3182</td><td>3</td><td>98.34000</td><td> 5</td><td>300.000</td><td>600000.0</td><td>14.16617</td><td>3.800000</td><td>3.300000</td><td>3.600000</td><td>⋯</td><td>250</td><td>0</td><td>0</td><td>0</td><td>82.17729</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>93.03070</td><td>92.60175</td></tr>\n",
       "\t<tr><th scope=row>84</th><td>3184</td><td>3</td><td>96.77000</td><td>10</td><td>480.000</td><td>570000.0</td><td>13.12237</td><td>4.000000</td><td>3.900000</td><td>3.900000</td><td>⋯</td><td>200</td><td>0</td><td>1</td><td>0</td><td>79.32101</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>93.58710</td><td>93.43344</td></tr>\n",
       "\t<tr><th scope=row>⋮</th><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋱</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><th scope=row>303</th><td>6283</td><td>6</td><td>87.28000</td><td>13.0</td><td>196.875</td><td> 370000</td><td>12.61154</td><td>4.000000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>92.78713</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>91.13583</td><td>90.52472</td></tr>\n",
       "\t<tr><th scope=row>305</th><td>6285</td><td>6</td><td>92.61000</td><td> 6.0</td><td>240.000</td><td> 430000</td><td>12.91411</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>77.90717</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>91.82660</td><td>86.91258</td></tr>\n",
       "\t<tr><th scope=row>307</th><td>6289</td><td>6</td><td>97.98000</td><td> 7.0</td><td>300.000</td><td> 570000</td><td>13.32122</td><td>3.900000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>155</td><td>0</td><td>1</td><td>0</td><td>92.27407</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>97.16614</td><td>96.67641</td></tr>\n",
       "\t<tr><th scope=row>311</th><td>6303</td><td>6</td><td>75.18000</td><td> 5.0</td><td>240.000</td><td> 240000</td><td>12.98540</td><td>4.000000</td><td>4.200000</td><td>4.100000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.50074</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>65.67000</td><td>65.37580</td></tr>\n",
       "\t<tr><th scope=row>313</th><td>6305</td><td>6</td><td>46.17000</td><td> 5.0</td><td>210.000</td><td> 192000</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>301</td><td>1</td><td>0</td><td>0</td><td>64.01767</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>61.57288</td><td>60.92357</td></tr>\n",
       "\t<tr><th scope=row>314</th><td>6307</td><td>6</td><td>83.32000</td><td>12.0</td><td>255.000</td><td> 370000</td><td>12.76569</td><td>4.100000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>81.96029</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>89.76211</td><td>88.88252</td></tr>\n",
       "\t<tr><th scope=row>320</th><td>6317</td><td>6</td><td>79.53000</td><td>11.0</td><td>630.000</td><td> 310000</td><td>12.54255</td><td>3.500000</td><td>3.300000</td><td>3.700000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>83.93804</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>84.42921</td><td>81.79265</td></tr>\n",
       "\t<tr><th scope=row>322</th><td>6319</td><td>6</td><td>63.05000</td><td> 6.0</td><td>360.000</td><td> 308000</td><td>12.76569</td><td>3.600000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.35820</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.28742</td><td>73.24378</td></tr>\n",
       "\t<tr><th scope=row>324</th><td>6321</td><td>6</td><td>45.67000</td><td> 6.0</td><td>300.000</td><td> 240000</td><td>12.79386</td><td>3.200000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.14082</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>62.82214</td><td>61.13303</td></tr>\n",
       "\t<tr><th scope=row>328</th><td>6325</td><td>6</td><td>78.05000</td><td> 5.0</td><td>480.000</td><td> 230000</td><td>13.99783</td><td>3.600000</td><td>3.300000</td><td>4.200000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>79.16464</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>66.11722</td><td>68.46897</td></tr>\n",
       "\t<tr><th scope=row>330</th><td>6419</td><td>6</td><td>78.35000</td><td> 6.0</td><td>360.000</td><td> 330000</td><td>12.50618</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>71.71905</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>83.55063</td><td>82.73521</td></tr>\n",
       "\t<tr><th scope=row>331</th><td>6444</td><td>6</td><td>44.34375</td><td> 5.0</td><td>196.875</td><td> 141000</td><td>12.79562</td><td>3.200000</td><td>3.500000</td><td>4.000000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>59.30986</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>49.25645</td><td>50.07344</td></tr>\n",
       "\t<tr><th scope=row>337</th><td>6620</td><td>6</td><td>73.99000</td><td>13.5</td><td>196.875</td><td>1080000</td><td>13.35348</td><td>3.600000</td><td>4.200000</td><td>3.400000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>85.04649</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>72.71361</td><td>74.79597</td></tr>\n",
       "\t<tr><th scope=row>339</th><td>6622</td><td>6</td><td>85.85000</td><td> 6.0</td><td>360.000</td><td> 280000</td><td>12.76569</td><td>3.500000</td><td>3.500000</td><td>3.900000</td><td>⋯</td><td>301</td><td>0</td><td>0</td><td>0</td><td>73.16798</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>71.99251</td><td>71.40742</td></tr>\n",
       "\t<tr><th scope=row>341</th><td>6628</td><td>6</td><td>56.76500</td><td> 5.0</td><td>196.875</td><td> 400000</td><td>12.56025</td><td>3.400000</td><td>3.000000</td><td>4.000000</td><td>⋯</td><td>301</td><td>0</td><td>0</td><td>1</td><td>75.75998</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>81.94778</td><td>76.32833</td></tr>\n",
       "\t<tr><th scope=row>345</th><td>6635</td><td>6</td><td>67.11200</td><td> 9.0</td><td>420.000</td><td> 300000</td><td>12.42922</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.07599</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>78.96625</td><td>78.25982</td></tr>\n",
       "\t<tr><th scope=row>347</th><td>6643</td><td>6</td><td>81.98400</td><td> 5.0</td><td>360.000</td><td> 310000</td><td>12.20608</td><td>4.200000</td><td>4.500000</td><td>4.300000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>73.32382</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.17784</td><td>74.75446</td></tr>\n",
       "\t<tr><th scope=row>348</th><td>6644</td><td>6</td><td>56.76000</td><td> 7.0</td><td>300.000</td><td> 320000</td><td>12.79386</td><td>3.000000</td><td>3.800000</td><td>3.100000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.82040</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>65.14153</td><td>62.40650</td></tr>\n",
       "\t<tr><th scope=row>354</th><td>6757</td><td>6</td><td>60.73000</td><td> 7.0</td><td>360.000</td><td> 310000</td><td>12.76569</td><td>3.800000</td><td>4.000000</td><td>3.700000</td><td>⋯</td><td>301</td><td>0</td><td>0</td><td>0</td><td>74.10919</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.10538</td><td>75.33128</td></tr>\n",
       "\t<tr><th scope=row>356</th><td>6759</td><td>6</td><td>68.70000</td><td> 5.0</td><td>270.000</td><td> 270000</td><td>12.61154</td><td>4.600000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>80.30998</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>63.63364</td><td>62.21199</td></tr>\n",
       "\t<tr><th scope=row>358</th><td>6766</td><td>6</td><td>63.08000</td><td> 5.0</td><td>300.000</td><td> 260000</td><td>12.76569</td><td>4.700000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>301</td><td>0</td><td>0</td><td>0</td><td>76.38859</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>62.21482</td><td>61.51063</td></tr>\n",
       "\t<tr><th scope=row>362</th><td>6770</td><td>6</td><td>77.03000</td><td> 5.0</td><td>300.000</td><td> 410000</td><td>12.38840</td><td>3.800000</td><td>4.100000</td><td>3.600000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>70.97872</td><td>70.52405</td><td>70.52405</td><td>70.52405</td><td>83.54821</td><td>83.40511</td></tr>\n",
       "\t<tr><th scope=row>364</th><td>6772</td><td>6</td><td>87.28000</td><td> 6.0</td><td>510.000</td><td> 400000</td><td>12.57764</td><td>4.000000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.21836</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>86.58241</td><td>85.71080</td></tr>\n",
       "\t<tr><th scope=row>365</th><td>6780</td><td>6</td><td>71.76000</td><td>11.0</td><td>420.000</td><td> 250000</td><td>12.38840</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>76.23241</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>75.24435</td><td>74.22877</td></tr>\n",
       "\t<tr><th scope=row>371</th><td>6795</td><td>6</td><td>52.82000</td><td> 4.0</td><td>210.000</td><td> 240000</td><td>12.79562</td><td>3.000000</td><td>3.000000</td><td>3.300000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>67.36720</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>57.46492</td><td>57.11157</td></tr>\n",
       "\t<tr><th scope=row>373</th><td>6797</td><td>6</td><td>74.20000</td><td> 5.0</td><td>240.000</td><td> 320000</td><td>12.79562</td><td>4.100000</td><td>4.400000</td><td>4.400000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>74.90800</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>70.35977</td><td>71.74794</td></tr>\n",
       "\t<tr><th scope=row>375</th><td>6803</td><td>6</td><td>74.51000</td><td> 6.0</td><td>360.000</td><td> 240000</td><td>12.89922</td><td>4.100000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.98160</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>72.07914</td><td>72.31876</td></tr>\n",
       "\t<tr><th scope=row>379</th><td>6811</td><td>6</td><td>44.34375</td><td>13.5</td><td>630.000</td><td> 620000</td><td>12.84793</td><td>4.100000</td><td>4.700000</td><td>3.900000</td><td>⋯</td><td>301</td><td>1</td><td>1</td><td>0</td><td>78.02752</td><td>73.75159</td><td>73.75159</td><td>73.75159</td><td>79.40319</td><td>79.46782</td></tr>\n",
       "\t<tr><th scope=row>381</th><td>6822</td><td>6</td><td>96.46000</td><td> 9.0</td><td>480.000</td><td> 400000</td><td>12.50618</td><td>4.000000</td><td>3.600000</td><td>4.300000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>75.30797</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>82.83327</td><td>82.79423</td></tr>\n",
       "\t<tr><th scope=row>382</th><td>6834</td><td>6</td><td>80.45000</td><td> 6.0</td><td>360.000</td><td> 300000</td><td>12.61154</td><td>3.000000</td><td>3.400000</td><td>3.100000</td><td>⋯</td><td>301</td><td>0</td><td>1</td><td>0</td><td>68.83997</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>64.00270</td><td>61.96992</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 136 × 23\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & ⋯ & rank & new\\_ban & hostel\\_BOTH & hostel\\_ONE & linear & decision & fulltree & pruned & bagging & randomforest\\\\\n",
       "  & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ⋯ & <int> & <int> & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1002 & 1 & 96.44000 &  8 & 300.000 & 240000.0 & 12.87391 & 3.400000 & 3.200000 & 3.500000 & ⋯ & 301 & 0 & 1 & 0 & 95.25097 & 88.05211 & 88.05211 & 92.45139 & 87.14085 & 82.41035\\\\\n",
       "\t5 & 1105 & 1 & 88.05000 &  8 & 480.000 & 440000.0 & 12.70685 & 3.900000 & 4.000000 & 3.900000 & ⋯ & 250 & 0 & 0 & 0 & 83.98529 & 97.36824 & 97.36824 & 92.45139 & 91.94186 & 92.13631\\\\\n",
       "\t7 & 1108 & 1 & 44.34375 &  5 & 300.000 & 310000.0 & 12.61154 & 3.900000 & 4.000000 & 4.300000 & ⋯ & 301 & 0 & 1 & 0 & 67.03529 & 63.77202 & 63.77202 & 67.33875 & 70.91037 & 70.83759\\\\\n",
       "\t8 & 1114 & 1 & 81.55000 &  6 & 300.000 & 320000.0 & 12.82126 & 4.000000 & 4.400000 & 3.900000 & ⋯ & 301 & 0 & 1 & 0 & 70.98257 & 73.49375 & 70.32917 & 67.33875 & 73.05704 & 73.94291\\\\\n",
       "\t14 & 1122 & 1 & 44.34375 &  5 & 300.000 & 200000.0 & 12.61154 & 2.200000 & 3.000000 & 2.000000 & ⋯ & 301 & 1 & 0 & 0 & 57.34506 & 69.04323 & 69.04323 & 67.33875 & 54.54966 & 56.92909\\\\\n",
       "\t16 & 1124 & 1 & 49.08000 &  5 & 300.000 & 490000.0 & 12.34584 & 3.600000 & 4.300000 & 3.600000 & ⋯ & 301 & 1 & 1 & 0 & 59.01199 & 70.52405 & 70.52405 & 70.52405 & 69.83709 & 69.92331\\\\\n",
       "\t18 & 1126 & 1 & 67.71000 &  5 & 300.000 & 170000.0 & 13.10216 & 5.000000 & 5.000000 & 5.000000 & ⋯ & 301 & 0 & 1 & 0 & 74.53221 & 63.77202 & 63.77202 & 67.33875 & 57.85599 & 60.52810\\\\\n",
       "\t22 & 1130 & 1 & 45.98000 &  6 & 480.000 & 180000.0 & 12.10072 & 2.200000 & 4.000000 & 2.000000 & ⋯ & 301 & 1 & 1 & 0 & 36.59204 & 52.71238 & 56.88917 & 57.67139 & 56.40356 & 55.63638\\\\\n",
       "\t24 & 1182 & 1 & 59.68000 &  4 & 630.000 & 200000.0 & 13.01701 & 4.200000 & 4.000000 & 5.000000 & ⋯ & 301 & 0 & 1 & 0 & 78.07224 & 59.83230 & 56.23467 & 59.83230 & 61.11015 & 61.59383\\\\\n",
       "\t25 & 1251 & 1 & 44.34375 &  6 & 300.000 & 284000.0 & 12.54255 & 3.400000 & 3.200000 & 3.400000 & ⋯ & 301 & 1 & 1 & 0 & 60.02308 & 69.04323 & 69.04323 & 67.33875 & 63.24937 & 61.99935\\\\\n",
       "\t31 & 2008 & 2 & 97.84000 & 10 & 540.000 & 190000.0 & 13.38473 & 3.900000 & 3.800000 & 3.900000 & ⋯ &  97 & 0 & 1 & 0 & 97.83733 & 97.36824 & 97.36824 & 92.45139 & 93.19946 & 93.16599\\\\\n",
       "\t33 & 2021 & 2 & 72.61000 &  2 & 240.000 &  80000.0 & 12.70685 & 3.800000 & 3.900000 & 4.000000 & ⋯ & 301 & 0 & 1 & 0 & 77.88152 & 59.83230 & 56.23467 & 59.83230 & 73.75753 & 72.12574\\\\\n",
       "\t35 & 2111 & 2 & 65.26000 &  4 & 300.000 & 170000.0 & 12.61154 & 3.800000 & 3.700000 & 4.300000 & ⋯ & 301 & 0 & 1 & 0 & 67.06327 & 59.83230 & 56.23467 & 59.83230 & 59.49070 & 62.80911\\\\\n",
       "\t39 & 2116 & 2 & 54.60000 & 10 & 294.000 & 200000.0 & 12.61154 & 3.100000 & 3.000000 & 3.000000 & ⋯ & 301 & 0 & 1 & 0 & 66.33838 & 52.71238 & 56.88917 & 57.67139 & 55.81445 & 58.13235\\\\\n",
       "\t41 & 2127 & 2 & 80.37000 &  5 & 420.000 & 350000.0 & 12.79386 & 3.900000 & 4.300000 & 4.300000 & ⋯ & 301 & 0 & 1 & 0 & 70.52523 & 88.68862 & 84.42333 & 88.68862 & 78.27550 & 76.29939\\\\\n",
       "\t42 & 2128 & 2 & 44.34375 &  3 & 196.875 & 170000.0 & 12.61154 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 301 & 1 & 1 & 0 & 67.18494 & 59.83230 & 56.23467 & 59.83230 & 59.67666 & 61.06195\\\\\n",
       "\t48 & 2134 & 2 & 72.88000 &  9 & 360.000 & 240000.0 & 12.67608 & 3.300000 & 3.400000 & 3.500000 & ⋯ & 301 & 0 & 1 & 0 & 69.44201 & 69.04323 & 69.04323 & 67.33875 & 64.49678 & 65.05105\\\\\n",
       "\t50 & 2136 & 2 & 44.34375 &  9 & 240.000 & 480000.0 & 13.30469 & 4.300000 & 5.000000 & 5.000000 & ⋯ & 301 & 0 & 1 & 0 & 89.85680 & 88.68862 & 88.48143 & 88.68862 & 84.47547 & 82.64416\\\\\n",
       "\t52 & 2138 & 2 & 64.49000 &  4 & 270.000 & 250000.0 & 12.70685 & 3.900000 & 4.500000 & 5.000000 & ⋯ & 301 & 0 & 1 & 0 & 81.48739 & 59.83230 & 56.23467 & 59.83230 & 63.52538 & 62.28017\\\\\n",
       "\t56 & 2250 & 2 & 63.71000 &  6 & 196.875 & 220000.0 & 12.79562 & 4.000000 & 4.000000 & 3.000000 & ⋯ & 301 & 0 & 1 & 0 & 71.14808 & 55.15813 & 55.15813 & 67.33875 & 62.93025 & 62.64716\\\\\n",
       "\t58 & 2254 & 2 & 59.41000 &  5 & 196.875 & 160000.0 & 12.79562 & 2.800000 & 3.000000 & 3.000000 & ⋯ & 301 & 0 & 0 & 0 & 56.74210 & 52.71238 & 49.29500 & 57.67139 & 51.01997 & 52.50172\\\\\n",
       "\t59 & 2255 & 2 & 71.74876 &  3 & 196.875 & 220000.0 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 301 & 1 & 0 & 0 & 59.76323 & 59.83230 & 56.23467 & 59.83230 & 60.48674 & 59.80988\\\\\n",
       "\t65 & 2641 & 2 & 71.74876 &  4 & 382.000 & 322661.9 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 301 & 1 & 0 & 0 & 61.80546 & 59.83230 & 65.52854 & 59.83230 & 66.70431 & 66.34055\\\\\n",
       "\t67 & 3014 & 3 & 98.48000 &  6 & 300.000 & 340000.0 & 13.21768 & 4.100000 & 3.900000 & 4.200000 & ⋯ & 150 & 0 & 1 & 0 & 99.68131 & 97.36824 & 97.36824 & 92.45139 & 95.94890 & 95.52757\\\\\n",
       "\t69 & 3035 & 3 & 89.48000 &  7 & 196.875 & 420000.0 & 12.97155 & 3.600000 & 3.100000 & 3.800000 & ⋯ & 301 & 0 & 1 & 0 & 74.01919 & 88.68862 & 91.75308 & 88.68862 & 87.07321 & 82.54296\\\\\n",
       "\t73 & 3139 & 3 & 96.84000 & 10 & 630.000 & 550000.0 & 12.76569 & 4.300000 & 4.700000 & 4.300000 & ⋯ & 301 & 0 & 0 & 0 & 88.69525 & 88.05211 & 88.05211 & 92.45139 & 84.10130 & 85.09154\\\\\n",
       "\t75 & 3147 & 3 & 83.40000 &  6 & 300.000 & 264000.0 & 12.30139 & 2.200000 & 2.400000 & 2.200000 & ⋯ & 301 & 1 & 1 & 0 & 53.97024 & 65.30064 & 65.30064 & 57.67139 & 58.89893 & 59.25145\\\\\n",
       "\t76 & 3148 & 3 & 92.28000 & 10 & 630.000 & 460000.0 & 13.30469 & 3.800000 & 3.700000 & 3.700000 & ⋯ & 301 & 0 & 0 & 0 & 77.37348 & 73.75159 & 73.75159 & 73.75159 & 85.57030 & 85.71103\\\\\n",
       "\t82 & 3182 & 3 & 98.34000 &  5 & 300.000 & 600000.0 & 14.16617 & 3.800000 & 3.300000 & 3.600000 & ⋯ & 250 & 0 & 0 & 0 & 82.17729 & 88.68862 & 91.75308 & 88.68862 & 93.03070 & 92.60175\\\\\n",
       "\t84 & 3184 & 3 & 96.77000 & 10 & 480.000 & 570000.0 & 13.12237 & 4.000000 & 3.900000 & 3.900000 & ⋯ & 200 & 0 & 1 & 0 & 79.32101 & 88.68862 & 88.48143 & 88.68862 & 93.58710 & 93.43344\\\\\n",
       "\t⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋱ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t303 & 6283 & 6 & 87.28000 & 13.0 & 196.875 &  370000 & 12.61154 & 4.000000 & 4.200000 & 4.200000 & ⋯ & 301 & 0 & 1 & 0 & 92.78713 & 88.05211 & 88.05211 & 92.45139 & 91.13583 & 90.52472\\\\\n",
       "\t305 & 6285 & 6 & 92.61000 &  6.0 & 240.000 &  430000 & 12.91411 & 3.900000 & 3.800000 & 3.900000 & ⋯ & 301 & 0 & 1 & 0 & 77.90717 & 88.68862 & 91.75308 & 88.68862 & 91.82660 & 86.91258\\\\\n",
       "\t307 & 6289 & 6 & 97.98000 &  7.0 & 300.000 &  570000 & 13.32122 & 3.900000 & 3.700000 & 4.300000 & ⋯ & 155 & 0 & 1 & 0 & 92.27407 & 97.36824 & 97.36824 & 92.45139 & 97.16614 & 96.67641\\\\\n",
       "\t311 & 6303 & 6 & 75.18000 &  5.0 & 240.000 &  240000 & 12.98540 & 4.000000 & 4.200000 & 4.100000 & ⋯ & 301 & 0 & 1 & 0 & 74.50074 & 68.62492 & 68.62492 & 75.84690 & 65.67000 & 65.37580\\\\\n",
       "\t313 & 6305 & 6 & 46.17000 &  5.0 & 210.000 &  192000 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 301 & 1 & 0 & 0 & 64.01767 & 68.62492 & 68.62492 & 75.84690 & 61.57288 & 60.92357\\\\\n",
       "\t314 & 6307 & 6 & 83.32000 & 12.0 & 255.000 &  370000 & 12.76569 & 4.100000 & 4.200000 & 4.200000 & ⋯ & 301 & 0 & 1 & 0 & 81.96029 & 88.68862 & 88.48143 & 88.68862 & 89.76211 & 88.88252\\\\\n",
       "\t320 & 6317 & 6 & 79.53000 & 11.0 & 630.000 &  310000 & 12.54255 & 3.500000 & 3.300000 & 3.700000 & ⋯ & 301 & 0 & 1 & 0 & 83.93804 & 88.05211 & 88.05211 & 92.45139 & 84.42921 & 81.79265\\\\\n",
       "\t322 & 6319 & 6 & 63.05000 &  6.0 & 360.000 &  308000 & 12.76569 & 3.600000 & 3.900000 & 4.000000 & ⋯ & 301 & 0 & 1 & 0 & 74.35820 & 81.86522 & 81.86522 & 75.84690 & 76.28742 & 73.24378\\\\\n",
       "\t324 & 6321 & 6 & 45.67000 &  6.0 & 300.000 &  240000 & 12.79386 & 3.200000 & 3.700000 & 3.700000 & ⋯ & 301 & 0 & 1 & 0 & 67.14082 & 52.71238 & 56.88917 & 57.67139 & 62.82214 & 61.13303\\\\\n",
       "\t328 & 6325 & 6 & 78.05000 &  5.0 & 480.000 &  230000 & 13.99783 & 3.600000 & 3.300000 & 4.200000 & ⋯ & 301 & 0 & 1 & 0 & 79.16464 & 68.62492 & 68.62492 & 75.84690 & 66.11722 & 68.46897\\\\\n",
       "\t330 & 6419 & 6 & 78.35000 &  6.0 & 360.000 &  330000 & 12.50618 & 4.200000 & 4.100000 & 4.200000 & ⋯ & 301 & 0 & 1 & 0 & 71.71905 & 81.86522 & 81.86522 & 75.84690 & 83.55063 & 82.73521\\\\\n",
       "\t331 & 6444 & 6 & 44.34375 &  5.0 & 196.875 &  141000 & 12.79562 & 3.200000 & 3.500000 & 4.000000 & ⋯ & 301 & 1 & 1 & 0 & 59.30986 & 52.71238 & 49.29500 & 57.67139 & 49.25645 & 50.07344\\\\\n",
       "\t337 & 6620 & 6 & 73.99000 & 13.5 & 196.875 & 1080000 & 13.35348 & 3.600000 & 4.200000 & 3.400000 & ⋯ & 301 & 1 & 1 & 0 & 85.04649 & 88.68862 & 91.75308 & 88.68862 & 72.71361 & 74.79597\\\\\n",
       "\t339 & 6622 & 6 & 85.85000 &  6.0 & 360.000 &  280000 & 12.76569 & 3.500000 & 3.500000 & 3.900000 & ⋯ & 301 & 0 & 0 & 0 & 73.16798 & 68.62492 & 68.62492 & 75.84690 & 71.99251 & 71.40742\\\\\n",
       "\t341 & 6628 & 6 & 56.76500 &  5.0 & 196.875 &  400000 & 12.56025 & 3.400000 & 3.000000 & 4.000000 & ⋯ & 301 & 0 & 0 & 1 & 75.75998 & 88.68862 & 91.75308 & 88.68862 & 81.94778 & 76.32833\\\\\n",
       "\t345 & 6635 & 6 & 67.11200 &  9.0 & 420.000 &  300000 & 12.42922 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 301 & 0 & 1 & 0 & 76.07599 & 81.86522 & 81.86522 & 75.84690 & 78.96625 & 78.25982\\\\\n",
       "\t347 & 6643 & 6 & 81.98400 &  5.0 & 360.000 &  310000 & 12.20608 & 4.200000 & 4.500000 & 4.300000 & ⋯ & 301 & 0 & 1 & 0 & 73.32382 & 81.86522 & 81.86522 & 75.84690 & 76.17784 & 74.75446\\\\\n",
       "\t348 & 6644 & 6 & 56.76000 &  7.0 & 300.000 &  320000 & 12.79386 & 3.000000 & 3.800000 & 3.100000 & ⋯ & 301 & 0 & 1 & 0 & 68.82040 & 52.71238 & 56.88917 & 57.67139 & 65.14153 & 62.40650\\\\\n",
       "\t354 & 6757 & 6 & 60.73000 &  7.0 & 360.000 &  310000 & 12.76569 & 3.800000 & 4.000000 & 3.700000 & ⋯ & 301 & 0 & 0 & 0 & 74.10919 & 81.86522 & 81.86522 & 75.84690 & 76.10538 & 75.33128\\\\\n",
       "\t356 & 6759 & 6 & 68.70000 &  5.0 & 270.000 &  270000 & 12.61154 & 4.600000 & 5.000000 & 5.000000 & ⋯ & 301 & 0 & 1 & 0 & 80.30998 & 68.62492 & 68.62492 & 75.84690 & 63.63364 & 62.21199\\\\\n",
       "\t358 & 6766 & 6 & 63.08000 &  5.0 & 300.000 &  260000 & 12.76569 & 4.700000 & 5.000000 & 5.000000 & ⋯ & 301 & 0 & 0 & 0 & 76.38859 & 68.62492 & 68.62492 & 75.84690 & 62.21482 & 61.51063\\\\\n",
       "\t362 & 6770 & 6 & 77.03000 &  5.0 & 300.000 &  410000 & 12.38840 & 3.800000 & 4.100000 & 3.600000 & ⋯ & 301 & 0 & 1 & 0 & 70.97872 & 70.52405 & 70.52405 & 70.52405 & 83.54821 & 83.40511\\\\\n",
       "\t364 & 6772 & 6 & 87.28000 &  6.0 & 510.000 &  400000 & 12.57764 & 4.000000 & 4.000000 & 3.900000 & ⋯ & 301 & 0 & 1 & 0 & 75.21836 & 88.68862 & 88.48143 & 88.68862 & 86.58241 & 85.71080\\\\\n",
       "\t365 & 6780 & 6 & 71.76000 & 11.0 & 420.000 &  250000 & 12.38840 & 4.000000 & 4.000000 & 4.000000 & ⋯ & 301 & 0 & 1 & 0 & 76.23241 & 68.62492 & 68.62492 & 75.84690 & 75.24435 & 74.22877\\\\\n",
       "\t371 & 6795 & 6 & 52.82000 &  4.0 & 210.000 &  240000 & 12.79562 & 3.000000 & 3.000000 & 3.300000 & ⋯ & 301 & 0 & 1 & 0 & 67.36720 & 52.71238 & 49.29500 & 57.67139 & 57.46492 & 57.11157\\\\\n",
       "\t373 & 6797 & 6 & 74.20000 &  5.0 & 240.000 &  320000 & 12.79562 & 4.100000 & 4.400000 & 4.400000 & ⋯ & 301 & 0 & 1 & 0 & 74.90800 & 81.86522 & 81.86522 & 75.84690 & 70.35977 & 71.74794\\\\\n",
       "\t375 & 6803 & 6 & 74.51000 &  6.0 & 360.000 &  240000 & 12.89922 & 4.100000 & 4.100000 & 4.200000 & ⋯ & 301 & 0 & 1 & 0 & 75.98160 & 68.62492 & 68.62492 & 75.84690 & 72.07914 & 72.31876\\\\\n",
       "\t379 & 6811 & 6 & 44.34375 & 13.5 & 630.000 &  620000 & 12.84793 & 4.100000 & 4.700000 & 3.900000 & ⋯ & 301 & 1 & 1 & 0 & 78.02752 & 73.75159 & 73.75159 & 73.75159 & 79.40319 & 79.46782\\\\\n",
       "\t381 & 6822 & 6 & 96.46000 &  9.0 & 480.000 &  400000 & 12.50618 & 4.000000 & 3.600000 & 4.300000 & ⋯ & 301 & 0 & 1 & 0 & 75.30797 & 88.68862 & 88.48143 & 88.68862 & 82.83327 & 82.79423\\\\\n",
       "\t382 & 6834 & 6 & 80.45000 &  6.0 & 360.000 &  300000 & 12.61154 & 3.000000 & 3.400000 & 3.100000 & ⋯ & 301 & 0 & 1 & 0 & 68.83997 & 81.86522 & 81.86522 & 75.84690 & 64.00270 & 61.96992\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 136 × 23\n",
       "\n",
       "| <!--/--> | college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;dbl&gt; | intake &lt;dbl&gt; | fees &lt;dbl&gt; | salary &lt;dbl&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | ⋯ ⋯ | rank &lt;int&gt; | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_ONE &lt;int&gt; | linear &lt;dbl&gt; | decision &lt;dbl&gt; | fulltree &lt;dbl&gt; | pruned &lt;dbl&gt; | bagging &lt;dbl&gt; | randomforest &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1002 | 1 | 96.44000 |  8 | 300.000 | 240000.0 | 12.87391 | 3.400000 | 3.200000 | 3.500000 | ⋯ | 301 | 0 | 1 | 0 | 95.25097 | 88.05211 | 88.05211 | 92.45139 | 87.14085 | 82.41035 |\n",
       "| 5 | 1105 | 1 | 88.05000 |  8 | 480.000 | 440000.0 | 12.70685 | 3.900000 | 4.000000 | 3.900000 | ⋯ | 250 | 0 | 0 | 0 | 83.98529 | 97.36824 | 97.36824 | 92.45139 | 91.94186 | 92.13631 |\n",
       "| 7 | 1108 | 1 | 44.34375 |  5 | 300.000 | 310000.0 | 12.61154 | 3.900000 | 4.000000 | 4.300000 | ⋯ | 301 | 0 | 1 | 0 | 67.03529 | 63.77202 | 63.77202 | 67.33875 | 70.91037 | 70.83759 |\n",
       "| 8 | 1114 | 1 | 81.55000 |  6 | 300.000 | 320000.0 | 12.82126 | 4.000000 | 4.400000 | 3.900000 | ⋯ | 301 | 0 | 1 | 0 | 70.98257 | 73.49375 | 70.32917 | 67.33875 | 73.05704 | 73.94291 |\n",
       "| 14 | 1122 | 1 | 44.34375 |  5 | 300.000 | 200000.0 | 12.61154 | 2.200000 | 3.000000 | 2.000000 | ⋯ | 301 | 1 | 0 | 0 | 57.34506 | 69.04323 | 69.04323 | 67.33875 | 54.54966 | 56.92909 |\n",
       "| 16 | 1124 | 1 | 49.08000 |  5 | 300.000 | 490000.0 | 12.34584 | 3.600000 | 4.300000 | 3.600000 | ⋯ | 301 | 1 | 1 | 0 | 59.01199 | 70.52405 | 70.52405 | 70.52405 | 69.83709 | 69.92331 |\n",
       "| 18 | 1126 | 1 | 67.71000 |  5 | 300.000 | 170000.0 | 13.10216 | 5.000000 | 5.000000 | 5.000000 | ⋯ | 301 | 0 | 1 | 0 | 74.53221 | 63.77202 | 63.77202 | 67.33875 | 57.85599 | 60.52810 |\n",
       "| 22 | 1130 | 1 | 45.98000 |  6 | 480.000 | 180000.0 | 12.10072 | 2.200000 | 4.000000 | 2.000000 | ⋯ | 301 | 1 | 1 | 0 | 36.59204 | 52.71238 | 56.88917 | 57.67139 | 56.40356 | 55.63638 |\n",
       "| 24 | 1182 | 1 | 59.68000 |  4 | 630.000 | 200000.0 | 13.01701 | 4.200000 | 4.000000 | 5.000000 | ⋯ | 301 | 0 | 1 | 0 | 78.07224 | 59.83230 | 56.23467 | 59.83230 | 61.11015 | 61.59383 |\n",
       "| 25 | 1251 | 1 | 44.34375 |  6 | 300.000 | 284000.0 | 12.54255 | 3.400000 | 3.200000 | 3.400000 | ⋯ | 301 | 1 | 1 | 0 | 60.02308 | 69.04323 | 69.04323 | 67.33875 | 63.24937 | 61.99935 |\n",
       "| 31 | 2008 | 2 | 97.84000 | 10 | 540.000 | 190000.0 | 13.38473 | 3.900000 | 3.800000 | 3.900000 | ⋯ |  97 | 0 | 1 | 0 | 97.83733 | 97.36824 | 97.36824 | 92.45139 | 93.19946 | 93.16599 |\n",
       "| 33 | 2021 | 2 | 72.61000 |  2 | 240.000 |  80000.0 | 12.70685 | 3.800000 | 3.900000 | 4.000000 | ⋯ | 301 | 0 | 1 | 0 | 77.88152 | 59.83230 | 56.23467 | 59.83230 | 73.75753 | 72.12574 |\n",
       "| 35 | 2111 | 2 | 65.26000 |  4 | 300.000 | 170000.0 | 12.61154 | 3.800000 | 3.700000 | 4.300000 | ⋯ | 301 | 0 | 1 | 0 | 67.06327 | 59.83230 | 56.23467 | 59.83230 | 59.49070 | 62.80911 |\n",
       "| 39 | 2116 | 2 | 54.60000 | 10 | 294.000 | 200000.0 | 12.61154 | 3.100000 | 3.000000 | 3.000000 | ⋯ | 301 | 0 | 1 | 0 | 66.33838 | 52.71238 | 56.88917 | 57.67139 | 55.81445 | 58.13235 |\n",
       "| 41 | 2127 | 2 | 80.37000 |  5 | 420.000 | 350000.0 | 12.79386 | 3.900000 | 4.300000 | 4.300000 | ⋯ | 301 | 0 | 1 | 0 | 70.52523 | 88.68862 | 84.42333 | 88.68862 | 78.27550 | 76.29939 |\n",
       "| 42 | 2128 | 2 | 44.34375 |  3 | 196.875 | 170000.0 | 12.61154 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 301 | 1 | 1 | 0 | 67.18494 | 59.83230 | 56.23467 | 59.83230 | 59.67666 | 61.06195 |\n",
       "| 48 | 2134 | 2 | 72.88000 |  9 | 360.000 | 240000.0 | 12.67608 | 3.300000 | 3.400000 | 3.500000 | ⋯ | 301 | 0 | 1 | 0 | 69.44201 | 69.04323 | 69.04323 | 67.33875 | 64.49678 | 65.05105 |\n",
       "| 50 | 2136 | 2 | 44.34375 |  9 | 240.000 | 480000.0 | 13.30469 | 4.300000 | 5.000000 | 5.000000 | ⋯ | 301 | 0 | 1 | 0 | 89.85680 | 88.68862 | 88.48143 | 88.68862 | 84.47547 | 82.64416 |\n",
       "| 52 | 2138 | 2 | 64.49000 |  4 | 270.000 | 250000.0 | 12.70685 | 3.900000 | 4.500000 | 5.000000 | ⋯ | 301 | 0 | 1 | 0 | 81.48739 | 59.83230 | 56.23467 | 59.83230 | 63.52538 | 62.28017 |\n",
       "| 56 | 2250 | 2 | 63.71000 |  6 | 196.875 | 220000.0 | 12.79562 | 4.000000 | 4.000000 | 3.000000 | ⋯ | 301 | 0 | 1 | 0 | 71.14808 | 55.15813 | 55.15813 | 67.33875 | 62.93025 | 62.64716 |\n",
       "| 58 | 2254 | 2 | 59.41000 |  5 | 196.875 | 160000.0 | 12.79562 | 2.800000 | 3.000000 | 3.000000 | ⋯ | 301 | 0 | 0 | 0 | 56.74210 | 52.71238 | 49.29500 | 57.67139 | 51.01997 | 52.50172 |\n",
       "| 59 | 2255 | 2 | 71.74876 |  3 | 196.875 | 220000.0 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 301 | 1 | 0 | 0 | 59.76323 | 59.83230 | 56.23467 | 59.83230 | 60.48674 | 59.80988 |\n",
       "| 65 | 2641 | 2 | 71.74876 |  4 | 382.000 | 322661.9 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 301 | 1 | 0 | 0 | 61.80546 | 59.83230 | 65.52854 | 59.83230 | 66.70431 | 66.34055 |\n",
       "| 67 | 3014 | 3 | 98.48000 |  6 | 300.000 | 340000.0 | 13.21768 | 4.100000 | 3.900000 | 4.200000 | ⋯ | 150 | 0 | 1 | 0 | 99.68131 | 97.36824 | 97.36824 | 92.45139 | 95.94890 | 95.52757 |\n",
       "| 69 | 3035 | 3 | 89.48000 |  7 | 196.875 | 420000.0 | 12.97155 | 3.600000 | 3.100000 | 3.800000 | ⋯ | 301 | 0 | 1 | 0 | 74.01919 | 88.68862 | 91.75308 | 88.68862 | 87.07321 | 82.54296 |\n",
       "| 73 | 3139 | 3 | 96.84000 | 10 | 630.000 | 550000.0 | 12.76569 | 4.300000 | 4.700000 | 4.300000 | ⋯ | 301 | 0 | 0 | 0 | 88.69525 | 88.05211 | 88.05211 | 92.45139 | 84.10130 | 85.09154 |\n",
       "| 75 | 3147 | 3 | 83.40000 |  6 | 300.000 | 264000.0 | 12.30139 | 2.200000 | 2.400000 | 2.200000 | ⋯ | 301 | 1 | 1 | 0 | 53.97024 | 65.30064 | 65.30064 | 57.67139 | 58.89893 | 59.25145 |\n",
       "| 76 | 3148 | 3 | 92.28000 | 10 | 630.000 | 460000.0 | 13.30469 | 3.800000 | 3.700000 | 3.700000 | ⋯ | 301 | 0 | 0 | 0 | 77.37348 | 73.75159 | 73.75159 | 73.75159 | 85.57030 | 85.71103 |\n",
       "| 82 | 3182 | 3 | 98.34000 |  5 | 300.000 | 600000.0 | 14.16617 | 3.800000 | 3.300000 | 3.600000 | ⋯ | 250 | 0 | 0 | 0 | 82.17729 | 88.68862 | 91.75308 | 88.68862 | 93.03070 | 92.60175 |\n",
       "| 84 | 3184 | 3 | 96.77000 | 10 | 480.000 | 570000.0 | 13.12237 | 4.000000 | 3.900000 | 3.900000 | ⋯ | 200 | 0 | 1 | 0 | 79.32101 | 88.68862 | 88.48143 | 88.68862 | 93.58710 | 93.43344 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 303 | 6283 | 6 | 87.28000 | 13.0 | 196.875 |  370000 | 12.61154 | 4.000000 | 4.200000 | 4.200000 | ⋯ | 301 | 0 | 1 | 0 | 92.78713 | 88.05211 | 88.05211 | 92.45139 | 91.13583 | 90.52472 |\n",
       "| 305 | 6285 | 6 | 92.61000 |  6.0 | 240.000 |  430000 | 12.91411 | 3.900000 | 3.800000 | 3.900000 | ⋯ | 301 | 0 | 1 | 0 | 77.90717 | 88.68862 | 91.75308 | 88.68862 | 91.82660 | 86.91258 |\n",
       "| 307 | 6289 | 6 | 97.98000 |  7.0 | 300.000 |  570000 | 13.32122 | 3.900000 | 3.700000 | 4.300000 | ⋯ | 155 | 0 | 1 | 0 | 92.27407 | 97.36824 | 97.36824 | 92.45139 | 97.16614 | 96.67641 |\n",
       "| 311 | 6303 | 6 | 75.18000 |  5.0 | 240.000 |  240000 | 12.98540 | 4.000000 | 4.200000 | 4.100000 | ⋯ | 301 | 0 | 1 | 0 | 74.50074 | 68.62492 | 68.62492 | 75.84690 | 65.67000 | 65.37580 |\n",
       "| 313 | 6305 | 6 | 46.17000 |  5.0 | 210.000 |  192000 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 301 | 1 | 0 | 0 | 64.01767 | 68.62492 | 68.62492 | 75.84690 | 61.57288 | 60.92357 |\n",
       "| 314 | 6307 | 6 | 83.32000 | 12.0 | 255.000 |  370000 | 12.76569 | 4.100000 | 4.200000 | 4.200000 | ⋯ | 301 | 0 | 1 | 0 | 81.96029 | 88.68862 | 88.48143 | 88.68862 | 89.76211 | 88.88252 |\n",
       "| 320 | 6317 | 6 | 79.53000 | 11.0 | 630.000 |  310000 | 12.54255 | 3.500000 | 3.300000 | 3.700000 | ⋯ | 301 | 0 | 1 | 0 | 83.93804 | 88.05211 | 88.05211 | 92.45139 | 84.42921 | 81.79265 |\n",
       "| 322 | 6319 | 6 | 63.05000 |  6.0 | 360.000 |  308000 | 12.76569 | 3.600000 | 3.900000 | 4.000000 | ⋯ | 301 | 0 | 1 | 0 | 74.35820 | 81.86522 | 81.86522 | 75.84690 | 76.28742 | 73.24378 |\n",
       "| 324 | 6321 | 6 | 45.67000 |  6.0 | 300.000 |  240000 | 12.79386 | 3.200000 | 3.700000 | 3.700000 | ⋯ | 301 | 0 | 1 | 0 | 67.14082 | 52.71238 | 56.88917 | 57.67139 | 62.82214 | 61.13303 |\n",
       "| 328 | 6325 | 6 | 78.05000 |  5.0 | 480.000 |  230000 | 13.99783 | 3.600000 | 3.300000 | 4.200000 | ⋯ | 301 | 0 | 1 | 0 | 79.16464 | 68.62492 | 68.62492 | 75.84690 | 66.11722 | 68.46897 |\n",
       "| 330 | 6419 | 6 | 78.35000 |  6.0 | 360.000 |  330000 | 12.50618 | 4.200000 | 4.100000 | 4.200000 | ⋯ | 301 | 0 | 1 | 0 | 71.71905 | 81.86522 | 81.86522 | 75.84690 | 83.55063 | 82.73521 |\n",
       "| 331 | 6444 | 6 | 44.34375 |  5.0 | 196.875 |  141000 | 12.79562 | 3.200000 | 3.500000 | 4.000000 | ⋯ | 301 | 1 | 1 | 0 | 59.30986 | 52.71238 | 49.29500 | 57.67139 | 49.25645 | 50.07344 |\n",
       "| 337 | 6620 | 6 | 73.99000 | 13.5 | 196.875 | 1080000 | 13.35348 | 3.600000 | 4.200000 | 3.400000 | ⋯ | 301 | 1 | 1 | 0 | 85.04649 | 88.68862 | 91.75308 | 88.68862 | 72.71361 | 74.79597 |\n",
       "| 339 | 6622 | 6 | 85.85000 |  6.0 | 360.000 |  280000 | 12.76569 | 3.500000 | 3.500000 | 3.900000 | ⋯ | 301 | 0 | 0 | 0 | 73.16798 | 68.62492 | 68.62492 | 75.84690 | 71.99251 | 71.40742 |\n",
       "| 341 | 6628 | 6 | 56.76500 |  5.0 | 196.875 |  400000 | 12.56025 | 3.400000 | 3.000000 | 4.000000 | ⋯ | 301 | 0 | 0 | 1 | 75.75998 | 88.68862 | 91.75308 | 88.68862 | 81.94778 | 76.32833 |\n",
       "| 345 | 6635 | 6 | 67.11200 |  9.0 | 420.000 |  300000 | 12.42922 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 301 | 0 | 1 | 0 | 76.07599 | 81.86522 | 81.86522 | 75.84690 | 78.96625 | 78.25982 |\n",
       "| 347 | 6643 | 6 | 81.98400 |  5.0 | 360.000 |  310000 | 12.20608 | 4.200000 | 4.500000 | 4.300000 | ⋯ | 301 | 0 | 1 | 0 | 73.32382 | 81.86522 | 81.86522 | 75.84690 | 76.17784 | 74.75446 |\n",
       "| 348 | 6644 | 6 | 56.76000 |  7.0 | 300.000 |  320000 | 12.79386 | 3.000000 | 3.800000 | 3.100000 | ⋯ | 301 | 0 | 1 | 0 | 68.82040 | 52.71238 | 56.88917 | 57.67139 | 65.14153 | 62.40650 |\n",
       "| 354 | 6757 | 6 | 60.73000 |  7.0 | 360.000 |  310000 | 12.76569 | 3.800000 | 4.000000 | 3.700000 | ⋯ | 301 | 0 | 0 | 0 | 74.10919 | 81.86522 | 81.86522 | 75.84690 | 76.10538 | 75.33128 |\n",
       "| 356 | 6759 | 6 | 68.70000 |  5.0 | 270.000 |  270000 | 12.61154 | 4.600000 | 5.000000 | 5.000000 | ⋯ | 301 | 0 | 1 | 0 | 80.30998 | 68.62492 | 68.62492 | 75.84690 | 63.63364 | 62.21199 |\n",
       "| 358 | 6766 | 6 | 63.08000 |  5.0 | 300.000 |  260000 | 12.76569 | 4.700000 | 5.000000 | 5.000000 | ⋯ | 301 | 0 | 0 | 0 | 76.38859 | 68.62492 | 68.62492 | 75.84690 | 62.21482 | 61.51063 |\n",
       "| 362 | 6770 | 6 | 77.03000 |  5.0 | 300.000 |  410000 | 12.38840 | 3.800000 | 4.100000 | 3.600000 | ⋯ | 301 | 0 | 1 | 0 | 70.97872 | 70.52405 | 70.52405 | 70.52405 | 83.54821 | 83.40511 |\n",
       "| 364 | 6772 | 6 | 87.28000 |  6.0 | 510.000 |  400000 | 12.57764 | 4.000000 | 4.000000 | 3.900000 | ⋯ | 301 | 0 | 1 | 0 | 75.21836 | 88.68862 | 88.48143 | 88.68862 | 86.58241 | 85.71080 |\n",
       "| 365 | 6780 | 6 | 71.76000 | 11.0 | 420.000 |  250000 | 12.38840 | 4.000000 | 4.000000 | 4.000000 | ⋯ | 301 | 0 | 1 | 0 | 76.23241 | 68.62492 | 68.62492 | 75.84690 | 75.24435 | 74.22877 |\n",
       "| 371 | 6795 | 6 | 52.82000 |  4.0 | 210.000 |  240000 | 12.79562 | 3.000000 | 3.000000 | 3.300000 | ⋯ | 301 | 0 | 1 | 0 | 67.36720 | 52.71238 | 49.29500 | 57.67139 | 57.46492 | 57.11157 |\n",
       "| 373 | 6797 | 6 | 74.20000 |  5.0 | 240.000 |  320000 | 12.79562 | 4.100000 | 4.400000 | 4.400000 | ⋯ | 301 | 0 | 1 | 0 | 74.90800 | 81.86522 | 81.86522 | 75.84690 | 70.35977 | 71.74794 |\n",
       "| 375 | 6803 | 6 | 74.51000 |  6.0 | 360.000 |  240000 | 12.89922 | 4.100000 | 4.100000 | 4.200000 | ⋯ | 301 | 0 | 1 | 0 | 75.98160 | 68.62492 | 68.62492 | 75.84690 | 72.07914 | 72.31876 |\n",
       "| 379 | 6811 | 6 | 44.34375 | 13.5 | 630.000 |  620000 | 12.84793 | 4.100000 | 4.700000 | 3.900000 | ⋯ | 301 | 1 | 1 | 0 | 78.02752 | 73.75159 | 73.75159 | 73.75159 | 79.40319 | 79.46782 |\n",
       "| 381 | 6822 | 6 | 96.46000 |  9.0 | 480.000 |  400000 | 12.50618 | 4.000000 | 3.600000 | 4.300000 | ⋯ | 301 | 0 | 1 | 0 | 75.30797 | 88.68862 | 88.48143 | 88.68862 | 82.83327 | 82.79423 |\n",
       "| 382 | 6834 | 6 | 80.45000 |  6.0 | 360.000 |  300000 | 12.61154 | 3.000000 | 3.400000 | 3.100000 | ⋯ | 301 | 0 | 1 | 0 | 68.83997 | 81.86522 | 81.86522 | 75.84690 | 64.00270 | 61.96992 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff   courses intake  fees     salary   rating  \n",
       "1   1002         1        96.44000  8      300.000 240000.0 12.87391 3.400000\n",
       "5   1105         1        88.05000  8      480.000 440000.0 12.70685 3.900000\n",
       "7   1108         1        44.34375  5      300.000 310000.0 12.61154 3.900000\n",
       "8   1114         1        81.55000  6      300.000 320000.0 12.82126 4.000000\n",
       "14  1122         1        44.34375  5      300.000 200000.0 12.61154 2.200000\n",
       "16  1124         1        49.08000  5      300.000 490000.0 12.34584 3.600000\n",
       "18  1126         1        67.71000  5      300.000 170000.0 13.10216 5.000000\n",
       "22  1130         1        45.98000  6      480.000 180000.0 12.10072 2.200000\n",
       "24  1182         1        59.68000  4      630.000 200000.0 13.01701 4.200000\n",
       "25  1251         1        44.34375  6      300.000 284000.0 12.54255 3.400000\n",
       "31  2008         2        97.84000 10      540.000 190000.0 13.38473 3.900000\n",
       "33  2021         2        72.61000  2      240.000  80000.0 12.70685 3.800000\n",
       "35  2111         2        65.26000  4      300.000 170000.0 12.61154 3.800000\n",
       "39  2116         2        54.60000 10      294.000 200000.0 12.61154 3.100000\n",
       "41  2127         2        80.37000  5      420.000 350000.0 12.79386 3.900000\n",
       "42  2128         2        44.34375  3      196.875 170000.0 12.61154 3.800000\n",
       "48  2134         2        72.88000  9      360.000 240000.0 12.67608 3.300000\n",
       "50  2136         2        44.34375  9      240.000 480000.0 13.30469 4.300000\n",
       "52  2138         2        64.49000  4      270.000 250000.0 12.70685 3.900000\n",
       "56  2250         2        63.71000  6      196.875 220000.0 12.79562 4.000000\n",
       "58  2254         2        59.41000  5      196.875 160000.0 12.79562 2.800000\n",
       "59  2255         2        71.74876  3      196.875 220000.0 12.79562 3.666295\n",
       "65  2641         2        71.74876  4      382.000 322661.9 12.79562 3.666295\n",
       "67  3014         3        98.48000  6      300.000 340000.0 13.21768 4.100000\n",
       "69  3035         3        89.48000  7      196.875 420000.0 12.97155 3.600000\n",
       "73  3139         3        96.84000 10      630.000 550000.0 12.76569 4.300000\n",
       "75  3147         3        83.40000  6      300.000 264000.0 12.30139 2.200000\n",
       "76  3148         3        92.28000 10      630.000 460000.0 13.30469 3.800000\n",
       "82  3182         3        98.34000  5      300.000 600000.0 14.16617 3.800000\n",
       "84  3184         3        96.77000 10      480.000 570000.0 13.12237 4.000000\n",
       "⋮   ⋮            ⋮        ⋮        ⋮       ⋮       ⋮        ⋮        ⋮       \n",
       "303 6283         6        87.28000 13.0    196.875  370000  12.61154 4.000000\n",
       "305 6285         6        92.61000  6.0    240.000  430000  12.91411 3.900000\n",
       "307 6289         6        97.98000  7.0    300.000  570000  13.32122 3.900000\n",
       "311 6303         6        75.18000  5.0    240.000  240000  12.98540 4.000000\n",
       "313 6305         6        46.17000  5.0    210.000  192000  12.79562 3.666295\n",
       "314 6307         6        83.32000 12.0    255.000  370000  12.76569 4.100000\n",
       "320 6317         6        79.53000 11.0    630.000  310000  12.54255 3.500000\n",
       "322 6319         6        63.05000  6.0    360.000  308000  12.76569 3.600000\n",
       "324 6321         6        45.67000  6.0    300.000  240000  12.79386 3.200000\n",
       "328 6325         6        78.05000  5.0    480.000  230000  13.99783 3.600000\n",
       "330 6419         6        78.35000  6.0    360.000  330000  12.50618 4.200000\n",
       "331 6444         6        44.34375  5.0    196.875  141000  12.79562 3.200000\n",
       "337 6620         6        73.99000 13.5    196.875 1080000  13.35348 3.600000\n",
       "339 6622         6        85.85000  6.0    360.000  280000  12.76569 3.500000\n",
       "341 6628         6        56.76500  5.0    196.875  400000  12.56025 3.400000\n",
       "345 6635         6        67.11200  9.0    420.000  300000  12.42922 3.800000\n",
       "347 6643         6        81.98400  5.0    360.000  310000  12.20608 4.200000\n",
       "348 6644         6        56.76000  7.0    300.000  320000  12.79386 3.000000\n",
       "354 6757         6        60.73000  7.0    360.000  310000  12.76569 3.800000\n",
       "356 6759         6        68.70000  5.0    270.000  270000  12.61154 4.600000\n",
       "358 6766         6        63.08000  5.0    300.000  260000  12.76569 4.700000\n",
       "362 6770         6        77.03000  5.0    300.000  410000  12.38840 3.800000\n",
       "364 6772         6        87.28000  6.0    510.000  400000  12.57764 4.000000\n",
       "365 6780         6        71.76000 11.0    420.000  250000  12.38840 4.000000\n",
       "371 6795         6        52.82000  4.0    210.000  240000  12.79562 3.000000\n",
       "373 6797         6        74.20000  5.0    240.000  320000  12.79562 4.100000\n",
       "375 6803         6        74.51000  6.0    360.000  240000  12.89922 4.100000\n",
       "379 6811         6        44.34375 13.5    630.000  620000  12.84793 4.100000\n",
       "381 6822         6        96.46000  9.0    480.000  400000  12.50618 4.000000\n",
       "382 6834         6        80.45000  6.0    360.000  300000  12.61154 3.000000\n",
       "    infrastructure faculty  ⋯ rank new_ban hostel_BOTH hostel_ONE linear  \n",
       "1   3.200000       3.500000 ⋯ 301  0       1           0          95.25097\n",
       "5   4.000000       3.900000 ⋯ 250  0       0           0          83.98529\n",
       "7   4.000000       4.300000 ⋯ 301  0       1           0          67.03529\n",
       "8   4.400000       3.900000 ⋯ 301  0       1           0          70.98257\n",
       "14  3.000000       2.000000 ⋯ 301  1       0           0          57.34506\n",
       "16  4.300000       3.600000 ⋯ 301  1       1           0          59.01199\n",
       "18  5.000000       5.000000 ⋯ 301  0       1           0          74.53221\n",
       "22  4.000000       2.000000 ⋯ 301  1       1           0          36.59204\n",
       "24  4.000000       5.000000 ⋯ 301  0       1           0          78.07224\n",
       "25  3.200000       3.400000 ⋯ 301  1       1           0          60.02308\n",
       "31  3.800000       3.900000 ⋯  97  0       1           0          97.83733\n",
       "33  3.900000       4.000000 ⋯ 301  0       1           0          77.88152\n",
       "35  3.700000       4.300000 ⋯ 301  0       1           0          67.06327\n",
       "39  3.000000       3.000000 ⋯ 301  0       1           0          66.33838\n",
       "41  4.300000       4.300000 ⋯ 301  0       1           0          70.52523\n",
       "42  4.000000       4.000000 ⋯ 301  1       1           0          67.18494\n",
       "48  3.400000       3.500000 ⋯ 301  0       1           0          69.44201\n",
       "50  5.000000       5.000000 ⋯ 301  0       1           0          89.85680\n",
       "52  4.500000       5.000000 ⋯ 301  0       1           0          81.48739\n",
       "56  4.000000       3.000000 ⋯ 301  0       1           0          71.14808\n",
       "58  3.000000       3.000000 ⋯ 301  0       0           0          56.74210\n",
       "59  3.804457       3.822472 ⋯ 301  1       0           0          59.76323\n",
       "65  3.804457       3.822472 ⋯ 301  1       0           0          61.80546\n",
       "67  3.900000       4.200000 ⋯ 150  0       1           0          99.68131\n",
       "69  3.100000       3.800000 ⋯ 301  0       1           0          74.01919\n",
       "73  4.700000       4.300000 ⋯ 301  0       0           0          88.69525\n",
       "75  2.400000       2.200000 ⋯ 301  1       1           0          53.97024\n",
       "76  3.700000       3.700000 ⋯ 301  0       0           0          77.37348\n",
       "82  3.300000       3.600000 ⋯ 250  0       0           0          82.17729\n",
       "84  3.900000       3.900000 ⋯ 200  0       1           0          79.32101\n",
       "⋮   ⋮              ⋮        ⋱ ⋮    ⋮       ⋮           ⋮          ⋮       \n",
       "303 4.200000       4.200000 ⋯ 301  0       1           0          92.78713\n",
       "305 3.800000       3.900000 ⋯ 301  0       1           0          77.90717\n",
       "307 3.700000       4.300000 ⋯ 155  0       1           0          92.27407\n",
       "311 4.200000       4.100000 ⋯ 301  0       1           0          74.50074\n",
       "313 3.804457       3.822472 ⋯ 301  1       0           0          64.01767\n",
       "314 4.200000       4.200000 ⋯ 301  0       1           0          81.96029\n",
       "320 3.300000       3.700000 ⋯ 301  0       1           0          83.93804\n",
       "322 3.900000       4.000000 ⋯ 301  0       1           0          74.35820\n",
       "324 3.700000       3.700000 ⋯ 301  0       1           0          67.14082\n",
       "328 3.300000       4.200000 ⋯ 301  0       1           0          79.16464\n",
       "330 4.100000       4.200000 ⋯ 301  0       1           0          71.71905\n",
       "331 3.500000       4.000000 ⋯ 301  1       1           0          59.30986\n",
       "337 4.200000       3.400000 ⋯ 301  1       1           0          85.04649\n",
       "339 3.500000       3.900000 ⋯ 301  0       0           0          73.16798\n",
       "341 3.000000       4.000000 ⋯ 301  0       0           1          75.75998\n",
       "345 4.000000       4.000000 ⋯ 301  0       1           0          76.07599\n",
       "347 4.500000       4.300000 ⋯ 301  0       1           0          73.32382\n",
       "348 3.800000       3.100000 ⋯ 301  0       1           0          68.82040\n",
       "354 4.000000       3.700000 ⋯ 301  0       0           0          74.10919\n",
       "356 5.000000       5.000000 ⋯ 301  0       1           0          80.30998\n",
       "358 5.000000       5.000000 ⋯ 301  0       0           0          76.38859\n",
       "362 4.100000       3.600000 ⋯ 301  0       1           0          70.97872\n",
       "364 4.000000       3.900000 ⋯ 301  0       1           0          75.21836\n",
       "365 4.000000       4.000000 ⋯ 301  0       1           0          76.23241\n",
       "371 3.000000       3.300000 ⋯ 301  0       1           0          67.36720\n",
       "373 4.400000       4.400000 ⋯ 301  0       1           0          74.90800\n",
       "375 4.100000       4.200000 ⋯ 301  0       1           0          75.98160\n",
       "379 4.700000       3.900000 ⋯ 301  1       1           0          78.02752\n",
       "381 3.600000       4.300000 ⋯ 301  0       1           0          75.30797\n",
       "382 3.400000       3.100000 ⋯ 301  0       1           0          68.83997\n",
       "    decision fulltree pruned   bagging  randomforest\n",
       "1   88.05211 88.05211 92.45139 87.14085 82.41035    \n",
       "5   97.36824 97.36824 92.45139 91.94186 92.13631    \n",
       "7   63.77202 63.77202 67.33875 70.91037 70.83759    \n",
       "8   73.49375 70.32917 67.33875 73.05704 73.94291    \n",
       "14  69.04323 69.04323 67.33875 54.54966 56.92909    \n",
       "16  70.52405 70.52405 70.52405 69.83709 69.92331    \n",
       "18  63.77202 63.77202 67.33875 57.85599 60.52810    \n",
       "22  52.71238 56.88917 57.67139 56.40356 55.63638    \n",
       "24  59.83230 56.23467 59.83230 61.11015 61.59383    \n",
       "25  69.04323 69.04323 67.33875 63.24937 61.99935    \n",
       "31  97.36824 97.36824 92.45139 93.19946 93.16599    \n",
       "33  59.83230 56.23467 59.83230 73.75753 72.12574    \n",
       "35  59.83230 56.23467 59.83230 59.49070 62.80911    \n",
       "39  52.71238 56.88917 57.67139 55.81445 58.13235    \n",
       "41  88.68862 84.42333 88.68862 78.27550 76.29939    \n",
       "42  59.83230 56.23467 59.83230 59.67666 61.06195    \n",
       "48  69.04323 69.04323 67.33875 64.49678 65.05105    \n",
       "50  88.68862 88.48143 88.68862 84.47547 82.64416    \n",
       "52  59.83230 56.23467 59.83230 63.52538 62.28017    \n",
       "56  55.15813 55.15813 67.33875 62.93025 62.64716    \n",
       "58  52.71238 49.29500 57.67139 51.01997 52.50172    \n",
       "59  59.83230 56.23467 59.83230 60.48674 59.80988    \n",
       "65  59.83230 65.52854 59.83230 66.70431 66.34055    \n",
       "67  97.36824 97.36824 92.45139 95.94890 95.52757    \n",
       "69  88.68862 91.75308 88.68862 87.07321 82.54296    \n",
       "73  88.05211 88.05211 92.45139 84.10130 85.09154    \n",
       "75  65.30064 65.30064 57.67139 58.89893 59.25145    \n",
       "76  73.75159 73.75159 73.75159 85.57030 85.71103    \n",
       "82  88.68862 91.75308 88.68862 93.03070 92.60175    \n",
       "84  88.68862 88.48143 88.68862 93.58710 93.43344    \n",
       "⋮   ⋮        ⋮        ⋮        ⋮        ⋮           \n",
       "303 88.05211 88.05211 92.45139 91.13583 90.52472    \n",
       "305 88.68862 91.75308 88.68862 91.82660 86.91258    \n",
       "307 97.36824 97.36824 92.45139 97.16614 96.67641    \n",
       "311 68.62492 68.62492 75.84690 65.67000 65.37580    \n",
       "313 68.62492 68.62492 75.84690 61.57288 60.92357    \n",
       "314 88.68862 88.48143 88.68862 89.76211 88.88252    \n",
       "320 88.05211 88.05211 92.45139 84.42921 81.79265    \n",
       "322 81.86522 81.86522 75.84690 76.28742 73.24378    \n",
       "324 52.71238 56.88917 57.67139 62.82214 61.13303    \n",
       "328 68.62492 68.62492 75.84690 66.11722 68.46897    \n",
       "330 81.86522 81.86522 75.84690 83.55063 82.73521    \n",
       "331 52.71238 49.29500 57.67139 49.25645 50.07344    \n",
       "337 88.68862 91.75308 88.68862 72.71361 74.79597    \n",
       "339 68.62492 68.62492 75.84690 71.99251 71.40742    \n",
       "341 88.68862 91.75308 88.68862 81.94778 76.32833    \n",
       "345 81.86522 81.86522 75.84690 78.96625 78.25982    \n",
       "347 81.86522 81.86522 75.84690 76.17784 74.75446    \n",
       "348 52.71238 56.88917 57.67139 65.14153 62.40650    \n",
       "354 81.86522 81.86522 75.84690 76.10538 75.33128    \n",
       "356 68.62492 68.62492 75.84690 63.63364 62.21199    \n",
       "358 68.62492 68.62492 75.84690 62.21482 61.51063    \n",
       "362 70.52405 70.52405 70.52405 83.54821 83.40511    \n",
       "364 88.68862 88.48143 88.68862 86.58241 85.71080    \n",
       "365 68.62492 68.62492 75.84690 75.24435 74.22877    \n",
       "371 52.71238 49.29500 57.67139 57.46492 57.11157    \n",
       "373 81.86522 81.86522 75.84690 70.35977 71.74794    \n",
       "375 68.62492 68.62492 75.84690 72.07914 72.31876    \n",
       "379 73.75159 73.75159 73.75159 79.40319 79.46782    \n",
       "381 88.68862 88.48143 88.68862 82.83327 82.79423    \n",
       "382 81.86522 81.86522 75.84690 64.00270 61.96992    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "randomforest <- randomForest(cutoff~.-college_code, data=train, ntree=500)\n",
    "test$randomforest <- predict(randomforest, test)\n",
    "View(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "69c9acc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "153.811092531594"
      ],
      "text/latex": [
       "153.811092531594"
      ],
      "text/markdown": [
       "153.811092531594"
      ],
      "text/plain": [
       "[1] 153.8111"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSErandomforest <- mean((test$randomforest - test$cutoff)^2)\n",
    "MSErandomforest"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc2d89dc",
   "metadata": {},
   "source": [
    "### Gradient Boost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "32c7c520",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loaded gbm 2.1.8.1\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 136 × 24</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>college_code</th><th scope=col>division</th><th scope=col>cutoff</th><th scope=col>courses</th><th scope=col>intake</th><th scope=col>fees</th><th scope=col>salary</th><th scope=col>rating</th><th scope=col>infrastructure</th><th scope=col>faculty</th><th scope=col>⋯</th><th scope=col>new_ban</th><th scope=col>hostel_BOTH</th><th scope=col>hostel_ONE</th><th scope=col>linear</th><th scope=col>decision</th><th scope=col>fulltree</th><th scope=col>pruned</th><th scope=col>bagging</th><th scope=col>randomforest</th><th scope=col>boost</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>⋯</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1002</td><td>1</td><td>96.44000</td><td> 8</td><td>300.000</td><td>240000.0</td><td>12.87391</td><td>3.400000</td><td>3.200000</td><td>3.500000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>95.25097</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>87.14085</td><td>82.41035</td><td> 78.68306</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>1105</td><td>1</td><td>88.05000</td><td> 8</td><td>480.000</td><td>440000.0</td><td>12.70685</td><td>3.900000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>83.98529</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>91.94186</td><td>92.13631</td><td> 98.92230</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>1108</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>310000.0</td><td>12.61154</td><td>3.900000</td><td>4.000000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>67.03529</td><td>63.77202</td><td>63.77202</td><td>67.33875</td><td>70.91037</td><td>70.83759</td><td> 77.19284</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>1114</td><td>1</td><td>81.55000</td><td> 6</td><td>300.000</td><td>320000.0</td><td>12.82126</td><td>4.000000</td><td>4.400000</td><td>3.900000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>70.98257</td><td>73.49375</td><td>70.32917</td><td>67.33875</td><td>73.05704</td><td>73.94291</td><td> 74.01368</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1122</td><td>1</td><td>44.34375</td><td> 5</td><td>300.000</td><td>200000.0</td><td>12.61154</td><td>2.200000</td><td>3.000000</td><td>2.000000</td><td>⋯</td><td>1</td><td>0</td><td>0</td><td>57.34506</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>54.54966</td><td>56.92909</td><td> 48.92507</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>1124</td><td>1</td><td>49.08000</td><td> 5</td><td>300.000</td><td>490000.0</td><td>12.34584</td><td>3.600000</td><td>4.300000</td><td>3.600000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>59.01199</td><td>70.52405</td><td>70.52405</td><td>70.52405</td><td>69.83709</td><td>69.92331</td><td> 64.97646</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>1126</td><td>1</td><td>67.71000</td><td> 5</td><td>300.000</td><td>170000.0</td><td>13.10216</td><td>5.000000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>74.53221</td><td>63.77202</td><td>63.77202</td><td>67.33875</td><td>57.85599</td><td>60.52810</td><td> 58.76920</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>1130</td><td>1</td><td>45.98000</td><td> 6</td><td>480.000</td><td>180000.0</td><td>12.10072</td><td>2.200000</td><td>4.000000</td><td>2.000000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>36.59204</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>56.40356</td><td>55.63638</td><td> 49.02708</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>1182</td><td>1</td><td>59.68000</td><td> 4</td><td>630.000</td><td>200000.0</td><td>13.01701</td><td>4.200000</td><td>4.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>78.07224</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>61.11015</td><td>61.59383</td><td> 62.58601</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>1251</td><td>1</td><td>44.34375</td><td> 6</td><td>300.000</td><td>284000.0</td><td>12.54255</td><td>3.400000</td><td>3.200000</td><td>3.400000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>60.02308</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>63.24937</td><td>61.99935</td><td> 51.28076</td></tr>\n",
       "\t<tr><th scope=row>31</th><td>2008</td><td>2</td><td>97.84000</td><td>10</td><td>540.000</td><td>190000.0</td><td>13.38473</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>97.83733</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>93.19946</td><td>93.16599</td><td> 89.70917</td></tr>\n",
       "\t<tr><th scope=row>33</th><td>2021</td><td>2</td><td>72.61000</td><td> 2</td><td>240.000</td><td> 80000.0</td><td>12.70685</td><td>3.800000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>77.88152</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>73.75753</td><td>72.12574</td><td> 66.32289</td></tr>\n",
       "\t<tr><th scope=row>35</th><td>2111</td><td>2</td><td>65.26000</td><td> 4</td><td>300.000</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>67.06327</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>59.49070</td><td>62.80911</td><td> 55.95299</td></tr>\n",
       "\t<tr><th scope=row>39</th><td>2116</td><td>2</td><td>54.60000</td><td>10</td><td>294.000</td><td>200000.0</td><td>12.61154</td><td>3.100000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>66.33838</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>55.81445</td><td>58.13235</td><td> 48.63402</td></tr>\n",
       "\t<tr><th scope=row>41</th><td>2127</td><td>2</td><td>80.37000</td><td> 5</td><td>420.000</td><td>350000.0</td><td>12.79386</td><td>3.900000</td><td>4.300000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>70.52523</td><td>88.68862</td><td>84.42333</td><td>88.68862</td><td>78.27550</td><td>76.29939</td><td> 73.88875</td></tr>\n",
       "\t<tr><th scope=row>42</th><td>2128</td><td>2</td><td>44.34375</td><td> 3</td><td>196.875</td><td>170000.0</td><td>12.61154</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>67.18494</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>59.67666</td><td>61.06195</td><td> 48.79167</td></tr>\n",
       "\t<tr><th scope=row>48</th><td>2134</td><td>2</td><td>72.88000</td><td> 9</td><td>360.000</td><td>240000.0</td><td>12.67608</td><td>3.300000</td><td>3.400000</td><td>3.500000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>69.44201</td><td>69.04323</td><td>69.04323</td><td>67.33875</td><td>64.49678</td><td>65.05105</td><td> 55.09393</td></tr>\n",
       "\t<tr><th scope=row>50</th><td>2136</td><td>2</td><td>44.34375</td><td> 9</td><td>240.000</td><td>480000.0</td><td>13.30469</td><td>4.300000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>89.85680</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>84.47547</td><td>82.64416</td><td> 81.57779</td></tr>\n",
       "\t<tr><th scope=row>52</th><td>2138</td><td>2</td><td>64.49000</td><td> 4</td><td>270.000</td><td>250000.0</td><td>12.70685</td><td>3.900000</td><td>4.500000</td><td>5.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>81.48739</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>63.52538</td><td>62.28017</td><td> 48.66816</td></tr>\n",
       "\t<tr><th scope=row>56</th><td>2250</td><td>2</td><td>63.71000</td><td> 6</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>4.000000</td><td>4.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>71.14808</td><td>55.15813</td><td>55.15813</td><td>67.33875</td><td>62.93025</td><td>62.64716</td><td> 53.04594</td></tr>\n",
       "\t<tr><th scope=row>58</th><td>2254</td><td>2</td><td>59.41000</td><td> 5</td><td>196.875</td><td>160000.0</td><td>12.79562</td><td>2.800000</td><td>3.000000</td><td>3.000000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>56.74210</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>51.01997</td><td>52.50172</td><td> 24.07780</td></tr>\n",
       "\t<tr><th scope=row>59</th><td>2255</td><td>2</td><td>71.74876</td><td> 3</td><td>196.875</td><td>220000.0</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>1</td><td>0</td><td>0</td><td>59.76323</td><td>59.83230</td><td>56.23467</td><td>59.83230</td><td>60.48674</td><td>59.80988</td><td> 58.51329</td></tr>\n",
       "\t<tr><th scope=row>65</th><td>2641</td><td>2</td><td>71.74876</td><td> 4</td><td>382.000</td><td>322661.9</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>1</td><td>0</td><td>0</td><td>61.80546</td><td>59.83230</td><td>65.52854</td><td>59.83230</td><td>66.70431</td><td>66.34055</td><td> 63.35222</td></tr>\n",
       "\t<tr><th scope=row>67</th><td>3014</td><td>3</td><td>98.48000</td><td> 6</td><td>300.000</td><td>340000.0</td><td>13.21768</td><td>4.100000</td><td>3.900000</td><td>4.200000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>99.68131</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>95.94890</td><td>95.52757</td><td>110.99909</td></tr>\n",
       "\t<tr><th scope=row>69</th><td>3035</td><td>3</td><td>89.48000</td><td> 7</td><td>196.875</td><td>420000.0</td><td>12.97155</td><td>3.600000</td><td>3.100000</td><td>3.800000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>74.01919</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>87.07321</td><td>82.54296</td><td> 95.17807</td></tr>\n",
       "\t<tr><th scope=row>73</th><td>3139</td><td>3</td><td>96.84000</td><td>10</td><td>630.000</td><td>550000.0</td><td>12.76569</td><td>4.300000</td><td>4.700000</td><td>4.300000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>88.69525</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>84.10130</td><td>85.09154</td><td> 87.26669</td></tr>\n",
       "\t<tr><th scope=row>75</th><td>3147</td><td>3</td><td>83.40000</td><td> 6</td><td>300.000</td><td>264000.0</td><td>12.30139</td><td>2.200000</td><td>2.400000</td><td>2.200000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>53.97024</td><td>65.30064</td><td>65.30064</td><td>57.67139</td><td>58.89893</td><td>59.25145</td><td> 59.08716</td></tr>\n",
       "\t<tr><th scope=row>76</th><td>3148</td><td>3</td><td>92.28000</td><td>10</td><td>630.000</td><td>460000.0</td><td>13.30469</td><td>3.800000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>77.37348</td><td>73.75159</td><td>73.75159</td><td>73.75159</td><td>85.57030</td><td>85.71103</td><td> 97.18984</td></tr>\n",
       "\t<tr><th scope=row>82</th><td>3182</td><td>3</td><td>98.34000</td><td> 5</td><td>300.000</td><td>600000.0</td><td>14.16617</td><td>3.800000</td><td>3.300000</td><td>3.600000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>82.17729</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>93.03070</td><td>92.60175</td><td> 99.33804</td></tr>\n",
       "\t<tr><th scope=row>84</th><td>3184</td><td>3</td><td>96.77000</td><td>10</td><td>480.000</td><td>570000.0</td><td>13.12237</td><td>4.000000</td><td>3.900000</td><td>3.900000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>79.32101</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>93.58710</td><td>93.43344</td><td> 96.42166</td></tr>\n",
       "\t<tr><th scope=row>⋮</th><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋱</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><th scope=row>303</th><td>6283</td><td>6</td><td>87.28000</td><td>13.0</td><td>196.875</td><td> 370000</td><td>12.61154</td><td>4.000000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>92.78713</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>91.13583</td><td>90.52472</td><td> 95.42930</td></tr>\n",
       "\t<tr><th scope=row>305</th><td>6285</td><td>6</td><td>92.61000</td><td> 6.0</td><td>240.000</td><td> 430000</td><td>12.91411</td><td>3.900000</td><td>3.800000</td><td>3.900000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>77.90717</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>91.82660</td><td>86.91258</td><td> 77.82207</td></tr>\n",
       "\t<tr><th scope=row>307</th><td>6289</td><td>6</td><td>97.98000</td><td> 7.0</td><td>300.000</td><td> 570000</td><td>13.32122</td><td>3.900000</td><td>3.700000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>92.27407</td><td>97.36824</td><td>97.36824</td><td>92.45139</td><td>97.16614</td><td>96.67641</td><td> 96.94700</td></tr>\n",
       "\t<tr><th scope=row>311</th><td>6303</td><td>6</td><td>75.18000</td><td> 5.0</td><td>240.000</td><td> 240000</td><td>12.98540</td><td>4.000000</td><td>4.200000</td><td>4.100000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>74.50074</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>65.67000</td><td>65.37580</td><td> 56.32315</td></tr>\n",
       "\t<tr><th scope=row>313</th><td>6305</td><td>6</td><td>46.17000</td><td> 5.0</td><td>210.000</td><td> 192000</td><td>12.79562</td><td>3.666295</td><td>3.804457</td><td>3.822472</td><td>⋯</td><td>1</td><td>0</td><td>0</td><td>64.01767</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>61.57288</td><td>60.92357</td><td> 42.62498</td></tr>\n",
       "\t<tr><th scope=row>314</th><td>6307</td><td>6</td><td>83.32000</td><td>12.0</td><td>255.000</td><td> 370000</td><td>12.76569</td><td>4.100000</td><td>4.200000</td><td>4.200000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>81.96029</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>89.76211</td><td>88.88252</td><td> 96.11581</td></tr>\n",
       "\t<tr><th scope=row>320</th><td>6317</td><td>6</td><td>79.53000</td><td>11.0</td><td>630.000</td><td> 310000</td><td>12.54255</td><td>3.500000</td><td>3.300000</td><td>3.700000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>83.93804</td><td>88.05211</td><td>88.05211</td><td>92.45139</td><td>84.42921</td><td>81.79265</td><td> 88.51835</td></tr>\n",
       "\t<tr><th scope=row>322</th><td>6319</td><td>6</td><td>63.05000</td><td> 6.0</td><td>360.000</td><td> 308000</td><td>12.76569</td><td>3.600000</td><td>3.900000</td><td>4.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>74.35820</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.28742</td><td>73.24378</td><td> 68.62145</td></tr>\n",
       "\t<tr><th scope=row>324</th><td>6321</td><td>6</td><td>45.67000</td><td> 6.0</td><td>300.000</td><td> 240000</td><td>12.79386</td><td>3.200000</td><td>3.700000</td><td>3.700000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>67.14082</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>62.82214</td><td>61.13303</td><td> 54.08510</td></tr>\n",
       "\t<tr><th scope=row>328</th><td>6325</td><td>6</td><td>78.05000</td><td> 5.0</td><td>480.000</td><td> 230000</td><td>13.99783</td><td>3.600000</td><td>3.300000</td><td>4.200000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>79.16464</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>66.11722</td><td>68.46897</td><td> 72.25199</td></tr>\n",
       "\t<tr><th scope=row>330</th><td>6419</td><td>6</td><td>78.35000</td><td> 6.0</td><td>360.000</td><td> 330000</td><td>12.50618</td><td>4.200000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>71.71905</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>83.55063</td><td>82.73521</td><td> 88.23035</td></tr>\n",
       "\t<tr><th scope=row>331</th><td>6444</td><td>6</td><td>44.34375</td><td> 5.0</td><td>196.875</td><td> 141000</td><td>12.79562</td><td>3.200000</td><td>3.500000</td><td>4.000000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>59.30986</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>49.25645</td><td>50.07344</td><td> 30.98763</td></tr>\n",
       "\t<tr><th scope=row>337</th><td>6620</td><td>6</td><td>73.99000</td><td>13.5</td><td>196.875</td><td>1080000</td><td>13.35348</td><td>3.600000</td><td>4.200000</td><td>3.400000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>85.04649</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>72.71361</td><td>74.79597</td><td> 58.54335</td></tr>\n",
       "\t<tr><th scope=row>339</th><td>6622</td><td>6</td><td>85.85000</td><td> 6.0</td><td>360.000</td><td> 280000</td><td>12.76569</td><td>3.500000</td><td>3.500000</td><td>3.900000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>73.16798</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>71.99251</td><td>71.40742</td><td> 77.59945</td></tr>\n",
       "\t<tr><th scope=row>341</th><td>6628</td><td>6</td><td>56.76500</td><td> 5.0</td><td>196.875</td><td> 400000</td><td>12.56025</td><td>3.400000</td><td>3.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>0</td><td>1</td><td>75.75998</td><td>88.68862</td><td>91.75308</td><td>88.68862</td><td>81.94778</td><td>76.32833</td><td> 76.38430</td></tr>\n",
       "\t<tr><th scope=row>345</th><td>6635</td><td>6</td><td>67.11200</td><td> 9.0</td><td>420.000</td><td> 300000</td><td>12.42922</td><td>3.800000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>76.07599</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>78.96625</td><td>78.25982</td><td>100.27036</td></tr>\n",
       "\t<tr><th scope=row>347</th><td>6643</td><td>6</td><td>81.98400</td><td> 5.0</td><td>360.000</td><td> 310000</td><td>12.20608</td><td>4.200000</td><td>4.500000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>73.32382</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.17784</td><td>74.75446</td><td> 70.20127</td></tr>\n",
       "\t<tr><th scope=row>348</th><td>6644</td><td>6</td><td>56.76000</td><td> 7.0</td><td>300.000</td><td> 320000</td><td>12.79386</td><td>3.000000</td><td>3.800000</td><td>3.100000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>68.82040</td><td>52.71238</td><td>56.88917</td><td>57.67139</td><td>65.14153</td><td>62.40650</td><td> 61.07314</td></tr>\n",
       "\t<tr><th scope=row>354</th><td>6757</td><td>6</td><td>60.73000</td><td> 7.0</td><td>360.000</td><td> 310000</td><td>12.76569</td><td>3.800000</td><td>4.000000</td><td>3.700000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>74.10919</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>76.10538</td><td>75.33128</td><td> 81.90277</td></tr>\n",
       "\t<tr><th scope=row>356</th><td>6759</td><td>6</td><td>68.70000</td><td> 5.0</td><td>270.000</td><td> 270000</td><td>12.61154</td><td>4.600000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>80.30998</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>63.63364</td><td>62.21199</td><td> 77.75982</td></tr>\n",
       "\t<tr><th scope=row>358</th><td>6766</td><td>6</td><td>63.08000</td><td> 5.0</td><td>300.000</td><td> 260000</td><td>12.76569</td><td>4.700000</td><td>5.000000</td><td>5.000000</td><td>⋯</td><td>0</td><td>0</td><td>0</td><td>76.38859</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>62.21482</td><td>61.51063</td><td> 64.81565</td></tr>\n",
       "\t<tr><th scope=row>362</th><td>6770</td><td>6</td><td>77.03000</td><td> 5.0</td><td>300.000</td><td> 410000</td><td>12.38840</td><td>3.800000</td><td>4.100000</td><td>3.600000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>70.97872</td><td>70.52405</td><td>70.52405</td><td>70.52405</td><td>83.54821</td><td>83.40511</td><td>104.08819</td></tr>\n",
       "\t<tr><th scope=row>364</th><td>6772</td><td>6</td><td>87.28000</td><td> 6.0</td><td>510.000</td><td> 400000</td><td>12.57764</td><td>4.000000</td><td>4.000000</td><td>3.900000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>75.21836</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>86.58241</td><td>85.71080</td><td> 81.62469</td></tr>\n",
       "\t<tr><th scope=row>365</th><td>6780</td><td>6</td><td>71.76000</td><td>11.0</td><td>420.000</td><td> 250000</td><td>12.38840</td><td>4.000000</td><td>4.000000</td><td>4.000000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>76.23241</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>75.24435</td><td>74.22877</td><td> 90.38688</td></tr>\n",
       "\t<tr><th scope=row>371</th><td>6795</td><td>6</td><td>52.82000</td><td> 4.0</td><td>210.000</td><td> 240000</td><td>12.79562</td><td>3.000000</td><td>3.000000</td><td>3.300000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>67.36720</td><td>52.71238</td><td>49.29500</td><td>57.67139</td><td>57.46492</td><td>57.11157</td><td> 49.19333</td></tr>\n",
       "\t<tr><th scope=row>373</th><td>6797</td><td>6</td><td>74.20000</td><td> 5.0</td><td>240.000</td><td> 320000</td><td>12.79562</td><td>4.100000</td><td>4.400000</td><td>4.400000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>74.90800</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>70.35977</td><td>71.74794</td><td> 60.08470</td></tr>\n",
       "\t<tr><th scope=row>375</th><td>6803</td><td>6</td><td>74.51000</td><td> 6.0</td><td>360.000</td><td> 240000</td><td>12.89922</td><td>4.100000</td><td>4.100000</td><td>4.200000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>75.98160</td><td>68.62492</td><td>68.62492</td><td>75.84690</td><td>72.07914</td><td>72.31876</td><td> 70.84991</td></tr>\n",
       "\t<tr><th scope=row>379</th><td>6811</td><td>6</td><td>44.34375</td><td>13.5</td><td>630.000</td><td> 620000</td><td>12.84793</td><td>4.100000</td><td>4.700000</td><td>3.900000</td><td>⋯</td><td>1</td><td>1</td><td>0</td><td>78.02752</td><td>73.75159</td><td>73.75159</td><td>73.75159</td><td>79.40319</td><td>79.46782</td><td> 72.18232</td></tr>\n",
       "\t<tr><th scope=row>381</th><td>6822</td><td>6</td><td>96.46000</td><td> 9.0</td><td>480.000</td><td> 400000</td><td>12.50618</td><td>4.000000</td><td>3.600000</td><td>4.300000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>75.30797</td><td>88.68862</td><td>88.48143</td><td>88.68862</td><td>82.83327</td><td>82.79423</td><td> 80.63574</td></tr>\n",
       "\t<tr><th scope=row>382</th><td>6834</td><td>6</td><td>80.45000</td><td> 6.0</td><td>360.000</td><td> 300000</td><td>12.61154</td><td>3.000000</td><td>3.400000</td><td>3.100000</td><td>⋯</td><td>0</td><td>1</td><td>0</td><td>68.83997</td><td>81.86522</td><td>81.86522</td><td>75.84690</td><td>64.00270</td><td>61.96992</td><td> 59.07848</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 136 × 24\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & college\\_code & division & cutoff & courses & intake & fees & salary & rating & infrastructure & faculty & ⋯ & new\\_ban & hostel\\_BOTH & hostel\\_ONE & linear & decision & fulltree & pruned & bagging & randomforest & boost\\\\\n",
       "  & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ⋯ & <int> & <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1002 & 1 & 96.44000 &  8 & 300.000 & 240000.0 & 12.87391 & 3.400000 & 3.200000 & 3.500000 & ⋯ & 0 & 1 & 0 & 95.25097 & 88.05211 & 88.05211 & 92.45139 & 87.14085 & 82.41035 &  78.68306\\\\\n",
       "\t5 & 1105 & 1 & 88.05000 &  8 & 480.000 & 440000.0 & 12.70685 & 3.900000 & 4.000000 & 3.900000 & ⋯ & 0 & 0 & 0 & 83.98529 & 97.36824 & 97.36824 & 92.45139 & 91.94186 & 92.13631 &  98.92230\\\\\n",
       "\t7 & 1108 & 1 & 44.34375 &  5 & 300.000 & 310000.0 & 12.61154 & 3.900000 & 4.000000 & 4.300000 & ⋯ & 0 & 1 & 0 & 67.03529 & 63.77202 & 63.77202 & 67.33875 & 70.91037 & 70.83759 &  77.19284\\\\\n",
       "\t8 & 1114 & 1 & 81.55000 &  6 & 300.000 & 320000.0 & 12.82126 & 4.000000 & 4.400000 & 3.900000 & ⋯ & 0 & 1 & 0 & 70.98257 & 73.49375 & 70.32917 & 67.33875 & 73.05704 & 73.94291 &  74.01368\\\\\n",
       "\t14 & 1122 & 1 & 44.34375 &  5 & 300.000 & 200000.0 & 12.61154 & 2.200000 & 3.000000 & 2.000000 & ⋯ & 1 & 0 & 0 & 57.34506 & 69.04323 & 69.04323 & 67.33875 & 54.54966 & 56.92909 &  48.92507\\\\\n",
       "\t16 & 1124 & 1 & 49.08000 &  5 & 300.000 & 490000.0 & 12.34584 & 3.600000 & 4.300000 & 3.600000 & ⋯ & 1 & 1 & 0 & 59.01199 & 70.52405 & 70.52405 & 70.52405 & 69.83709 & 69.92331 &  64.97646\\\\\n",
       "\t18 & 1126 & 1 & 67.71000 &  5 & 300.000 & 170000.0 & 13.10216 & 5.000000 & 5.000000 & 5.000000 & ⋯ & 0 & 1 & 0 & 74.53221 & 63.77202 & 63.77202 & 67.33875 & 57.85599 & 60.52810 &  58.76920\\\\\n",
       "\t22 & 1130 & 1 & 45.98000 &  6 & 480.000 & 180000.0 & 12.10072 & 2.200000 & 4.000000 & 2.000000 & ⋯ & 1 & 1 & 0 & 36.59204 & 52.71238 & 56.88917 & 57.67139 & 56.40356 & 55.63638 &  49.02708\\\\\n",
       "\t24 & 1182 & 1 & 59.68000 &  4 & 630.000 & 200000.0 & 13.01701 & 4.200000 & 4.000000 & 5.000000 & ⋯ & 0 & 1 & 0 & 78.07224 & 59.83230 & 56.23467 & 59.83230 & 61.11015 & 61.59383 &  62.58601\\\\\n",
       "\t25 & 1251 & 1 & 44.34375 &  6 & 300.000 & 284000.0 & 12.54255 & 3.400000 & 3.200000 & 3.400000 & ⋯ & 1 & 1 & 0 & 60.02308 & 69.04323 & 69.04323 & 67.33875 & 63.24937 & 61.99935 &  51.28076\\\\\n",
       "\t31 & 2008 & 2 & 97.84000 & 10 & 540.000 & 190000.0 & 13.38473 & 3.900000 & 3.800000 & 3.900000 & ⋯ & 0 & 1 & 0 & 97.83733 & 97.36824 & 97.36824 & 92.45139 & 93.19946 & 93.16599 &  89.70917\\\\\n",
       "\t33 & 2021 & 2 & 72.61000 &  2 & 240.000 &  80000.0 & 12.70685 & 3.800000 & 3.900000 & 4.000000 & ⋯ & 0 & 1 & 0 & 77.88152 & 59.83230 & 56.23467 & 59.83230 & 73.75753 & 72.12574 &  66.32289\\\\\n",
       "\t35 & 2111 & 2 & 65.26000 &  4 & 300.000 & 170000.0 & 12.61154 & 3.800000 & 3.700000 & 4.300000 & ⋯ & 0 & 1 & 0 & 67.06327 & 59.83230 & 56.23467 & 59.83230 & 59.49070 & 62.80911 &  55.95299\\\\\n",
       "\t39 & 2116 & 2 & 54.60000 & 10 & 294.000 & 200000.0 & 12.61154 & 3.100000 & 3.000000 & 3.000000 & ⋯ & 0 & 1 & 0 & 66.33838 & 52.71238 & 56.88917 & 57.67139 & 55.81445 & 58.13235 &  48.63402\\\\\n",
       "\t41 & 2127 & 2 & 80.37000 &  5 & 420.000 & 350000.0 & 12.79386 & 3.900000 & 4.300000 & 4.300000 & ⋯ & 0 & 1 & 0 & 70.52523 & 88.68862 & 84.42333 & 88.68862 & 78.27550 & 76.29939 &  73.88875\\\\\n",
       "\t42 & 2128 & 2 & 44.34375 &  3 & 196.875 & 170000.0 & 12.61154 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 1 & 1 & 0 & 67.18494 & 59.83230 & 56.23467 & 59.83230 & 59.67666 & 61.06195 &  48.79167\\\\\n",
       "\t48 & 2134 & 2 & 72.88000 &  9 & 360.000 & 240000.0 & 12.67608 & 3.300000 & 3.400000 & 3.500000 & ⋯ & 0 & 1 & 0 & 69.44201 & 69.04323 & 69.04323 & 67.33875 & 64.49678 & 65.05105 &  55.09393\\\\\n",
       "\t50 & 2136 & 2 & 44.34375 &  9 & 240.000 & 480000.0 & 13.30469 & 4.300000 & 5.000000 & 5.000000 & ⋯ & 0 & 1 & 0 & 89.85680 & 88.68862 & 88.48143 & 88.68862 & 84.47547 & 82.64416 &  81.57779\\\\\n",
       "\t52 & 2138 & 2 & 64.49000 &  4 & 270.000 & 250000.0 & 12.70685 & 3.900000 & 4.500000 & 5.000000 & ⋯ & 0 & 1 & 0 & 81.48739 & 59.83230 & 56.23467 & 59.83230 & 63.52538 & 62.28017 &  48.66816\\\\\n",
       "\t56 & 2250 & 2 & 63.71000 &  6 & 196.875 & 220000.0 & 12.79562 & 4.000000 & 4.000000 & 3.000000 & ⋯ & 0 & 1 & 0 & 71.14808 & 55.15813 & 55.15813 & 67.33875 & 62.93025 & 62.64716 &  53.04594\\\\\n",
       "\t58 & 2254 & 2 & 59.41000 &  5 & 196.875 & 160000.0 & 12.79562 & 2.800000 & 3.000000 & 3.000000 & ⋯ & 0 & 0 & 0 & 56.74210 & 52.71238 & 49.29500 & 57.67139 & 51.01997 & 52.50172 &  24.07780\\\\\n",
       "\t59 & 2255 & 2 & 71.74876 &  3 & 196.875 & 220000.0 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 1 & 0 & 0 & 59.76323 & 59.83230 & 56.23467 & 59.83230 & 60.48674 & 59.80988 &  58.51329\\\\\n",
       "\t65 & 2641 & 2 & 71.74876 &  4 & 382.000 & 322661.9 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 1 & 0 & 0 & 61.80546 & 59.83230 & 65.52854 & 59.83230 & 66.70431 & 66.34055 &  63.35222\\\\\n",
       "\t67 & 3014 & 3 & 98.48000 &  6 & 300.000 & 340000.0 & 13.21768 & 4.100000 & 3.900000 & 4.200000 & ⋯ & 0 & 1 & 0 & 99.68131 & 97.36824 & 97.36824 & 92.45139 & 95.94890 & 95.52757 & 110.99909\\\\\n",
       "\t69 & 3035 & 3 & 89.48000 &  7 & 196.875 & 420000.0 & 12.97155 & 3.600000 & 3.100000 & 3.800000 & ⋯ & 0 & 1 & 0 & 74.01919 & 88.68862 & 91.75308 & 88.68862 & 87.07321 & 82.54296 &  95.17807\\\\\n",
       "\t73 & 3139 & 3 & 96.84000 & 10 & 630.000 & 550000.0 & 12.76569 & 4.300000 & 4.700000 & 4.300000 & ⋯ & 0 & 0 & 0 & 88.69525 & 88.05211 & 88.05211 & 92.45139 & 84.10130 & 85.09154 &  87.26669\\\\\n",
       "\t75 & 3147 & 3 & 83.40000 &  6 & 300.000 & 264000.0 & 12.30139 & 2.200000 & 2.400000 & 2.200000 & ⋯ & 1 & 1 & 0 & 53.97024 & 65.30064 & 65.30064 & 57.67139 & 58.89893 & 59.25145 &  59.08716\\\\\n",
       "\t76 & 3148 & 3 & 92.28000 & 10 & 630.000 & 460000.0 & 13.30469 & 3.800000 & 3.700000 & 3.700000 & ⋯ & 0 & 0 & 0 & 77.37348 & 73.75159 & 73.75159 & 73.75159 & 85.57030 & 85.71103 &  97.18984\\\\\n",
       "\t82 & 3182 & 3 & 98.34000 &  5 & 300.000 & 600000.0 & 14.16617 & 3.800000 & 3.300000 & 3.600000 & ⋯ & 0 & 0 & 0 & 82.17729 & 88.68862 & 91.75308 & 88.68862 & 93.03070 & 92.60175 &  99.33804\\\\\n",
       "\t84 & 3184 & 3 & 96.77000 & 10 & 480.000 & 570000.0 & 13.12237 & 4.000000 & 3.900000 & 3.900000 & ⋯ & 0 & 1 & 0 & 79.32101 & 88.68862 & 88.48143 & 88.68862 & 93.58710 & 93.43344 &  96.42166\\\\\n",
       "\t⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋱ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t303 & 6283 & 6 & 87.28000 & 13.0 & 196.875 &  370000 & 12.61154 & 4.000000 & 4.200000 & 4.200000 & ⋯ & 0 & 1 & 0 & 92.78713 & 88.05211 & 88.05211 & 92.45139 & 91.13583 & 90.52472 &  95.42930\\\\\n",
       "\t305 & 6285 & 6 & 92.61000 &  6.0 & 240.000 &  430000 & 12.91411 & 3.900000 & 3.800000 & 3.900000 & ⋯ & 0 & 1 & 0 & 77.90717 & 88.68862 & 91.75308 & 88.68862 & 91.82660 & 86.91258 &  77.82207\\\\\n",
       "\t307 & 6289 & 6 & 97.98000 &  7.0 & 300.000 &  570000 & 13.32122 & 3.900000 & 3.700000 & 4.300000 & ⋯ & 0 & 1 & 0 & 92.27407 & 97.36824 & 97.36824 & 92.45139 & 97.16614 & 96.67641 &  96.94700\\\\\n",
       "\t311 & 6303 & 6 & 75.18000 &  5.0 & 240.000 &  240000 & 12.98540 & 4.000000 & 4.200000 & 4.100000 & ⋯ & 0 & 1 & 0 & 74.50074 & 68.62492 & 68.62492 & 75.84690 & 65.67000 & 65.37580 &  56.32315\\\\\n",
       "\t313 & 6305 & 6 & 46.17000 &  5.0 & 210.000 &  192000 & 12.79562 & 3.666295 & 3.804457 & 3.822472 & ⋯ & 1 & 0 & 0 & 64.01767 & 68.62492 & 68.62492 & 75.84690 & 61.57288 & 60.92357 &  42.62498\\\\\n",
       "\t314 & 6307 & 6 & 83.32000 & 12.0 & 255.000 &  370000 & 12.76569 & 4.100000 & 4.200000 & 4.200000 & ⋯ & 0 & 1 & 0 & 81.96029 & 88.68862 & 88.48143 & 88.68862 & 89.76211 & 88.88252 &  96.11581\\\\\n",
       "\t320 & 6317 & 6 & 79.53000 & 11.0 & 630.000 &  310000 & 12.54255 & 3.500000 & 3.300000 & 3.700000 & ⋯ & 0 & 1 & 0 & 83.93804 & 88.05211 & 88.05211 & 92.45139 & 84.42921 & 81.79265 &  88.51835\\\\\n",
       "\t322 & 6319 & 6 & 63.05000 &  6.0 & 360.000 &  308000 & 12.76569 & 3.600000 & 3.900000 & 4.000000 & ⋯ & 0 & 1 & 0 & 74.35820 & 81.86522 & 81.86522 & 75.84690 & 76.28742 & 73.24378 &  68.62145\\\\\n",
       "\t324 & 6321 & 6 & 45.67000 &  6.0 & 300.000 &  240000 & 12.79386 & 3.200000 & 3.700000 & 3.700000 & ⋯ & 0 & 1 & 0 & 67.14082 & 52.71238 & 56.88917 & 57.67139 & 62.82214 & 61.13303 &  54.08510\\\\\n",
       "\t328 & 6325 & 6 & 78.05000 &  5.0 & 480.000 &  230000 & 13.99783 & 3.600000 & 3.300000 & 4.200000 & ⋯ & 0 & 1 & 0 & 79.16464 & 68.62492 & 68.62492 & 75.84690 & 66.11722 & 68.46897 &  72.25199\\\\\n",
       "\t330 & 6419 & 6 & 78.35000 &  6.0 & 360.000 &  330000 & 12.50618 & 4.200000 & 4.100000 & 4.200000 & ⋯ & 0 & 1 & 0 & 71.71905 & 81.86522 & 81.86522 & 75.84690 & 83.55063 & 82.73521 &  88.23035\\\\\n",
       "\t331 & 6444 & 6 & 44.34375 &  5.0 & 196.875 &  141000 & 12.79562 & 3.200000 & 3.500000 & 4.000000 & ⋯ & 1 & 1 & 0 & 59.30986 & 52.71238 & 49.29500 & 57.67139 & 49.25645 & 50.07344 &  30.98763\\\\\n",
       "\t337 & 6620 & 6 & 73.99000 & 13.5 & 196.875 & 1080000 & 13.35348 & 3.600000 & 4.200000 & 3.400000 & ⋯ & 1 & 1 & 0 & 85.04649 & 88.68862 & 91.75308 & 88.68862 & 72.71361 & 74.79597 &  58.54335\\\\\n",
       "\t339 & 6622 & 6 & 85.85000 &  6.0 & 360.000 &  280000 & 12.76569 & 3.500000 & 3.500000 & 3.900000 & ⋯ & 0 & 0 & 0 & 73.16798 & 68.62492 & 68.62492 & 75.84690 & 71.99251 & 71.40742 &  77.59945\\\\\n",
       "\t341 & 6628 & 6 & 56.76500 &  5.0 & 196.875 &  400000 & 12.56025 & 3.400000 & 3.000000 & 4.000000 & ⋯ & 0 & 0 & 1 & 75.75998 & 88.68862 & 91.75308 & 88.68862 & 81.94778 & 76.32833 &  76.38430\\\\\n",
       "\t345 & 6635 & 6 & 67.11200 &  9.0 & 420.000 &  300000 & 12.42922 & 3.800000 & 4.000000 & 4.000000 & ⋯ & 0 & 1 & 0 & 76.07599 & 81.86522 & 81.86522 & 75.84690 & 78.96625 & 78.25982 & 100.27036\\\\\n",
       "\t347 & 6643 & 6 & 81.98400 &  5.0 & 360.000 &  310000 & 12.20608 & 4.200000 & 4.500000 & 4.300000 & ⋯ & 0 & 1 & 0 & 73.32382 & 81.86522 & 81.86522 & 75.84690 & 76.17784 & 74.75446 &  70.20127\\\\\n",
       "\t348 & 6644 & 6 & 56.76000 &  7.0 & 300.000 &  320000 & 12.79386 & 3.000000 & 3.800000 & 3.100000 & ⋯ & 0 & 1 & 0 & 68.82040 & 52.71238 & 56.88917 & 57.67139 & 65.14153 & 62.40650 &  61.07314\\\\\n",
       "\t354 & 6757 & 6 & 60.73000 &  7.0 & 360.000 &  310000 & 12.76569 & 3.800000 & 4.000000 & 3.700000 & ⋯ & 0 & 0 & 0 & 74.10919 & 81.86522 & 81.86522 & 75.84690 & 76.10538 & 75.33128 &  81.90277\\\\\n",
       "\t356 & 6759 & 6 & 68.70000 &  5.0 & 270.000 &  270000 & 12.61154 & 4.600000 & 5.000000 & 5.000000 & ⋯ & 0 & 1 & 0 & 80.30998 & 68.62492 & 68.62492 & 75.84690 & 63.63364 & 62.21199 &  77.75982\\\\\n",
       "\t358 & 6766 & 6 & 63.08000 &  5.0 & 300.000 &  260000 & 12.76569 & 4.700000 & 5.000000 & 5.000000 & ⋯ & 0 & 0 & 0 & 76.38859 & 68.62492 & 68.62492 & 75.84690 & 62.21482 & 61.51063 &  64.81565\\\\\n",
       "\t362 & 6770 & 6 & 77.03000 &  5.0 & 300.000 &  410000 & 12.38840 & 3.800000 & 4.100000 & 3.600000 & ⋯ & 0 & 1 & 0 & 70.97872 & 70.52405 & 70.52405 & 70.52405 & 83.54821 & 83.40511 & 104.08819\\\\\n",
       "\t364 & 6772 & 6 & 87.28000 &  6.0 & 510.000 &  400000 & 12.57764 & 4.000000 & 4.000000 & 3.900000 & ⋯ & 0 & 1 & 0 & 75.21836 & 88.68862 & 88.48143 & 88.68862 & 86.58241 & 85.71080 &  81.62469\\\\\n",
       "\t365 & 6780 & 6 & 71.76000 & 11.0 & 420.000 &  250000 & 12.38840 & 4.000000 & 4.000000 & 4.000000 & ⋯ & 0 & 1 & 0 & 76.23241 & 68.62492 & 68.62492 & 75.84690 & 75.24435 & 74.22877 &  90.38688\\\\\n",
       "\t371 & 6795 & 6 & 52.82000 &  4.0 & 210.000 &  240000 & 12.79562 & 3.000000 & 3.000000 & 3.300000 & ⋯ & 0 & 1 & 0 & 67.36720 & 52.71238 & 49.29500 & 57.67139 & 57.46492 & 57.11157 &  49.19333\\\\\n",
       "\t373 & 6797 & 6 & 74.20000 &  5.0 & 240.000 &  320000 & 12.79562 & 4.100000 & 4.400000 & 4.400000 & ⋯ & 0 & 1 & 0 & 74.90800 & 81.86522 & 81.86522 & 75.84690 & 70.35977 & 71.74794 &  60.08470\\\\\n",
       "\t375 & 6803 & 6 & 74.51000 &  6.0 & 360.000 &  240000 & 12.89922 & 4.100000 & 4.100000 & 4.200000 & ⋯ & 0 & 1 & 0 & 75.98160 & 68.62492 & 68.62492 & 75.84690 & 72.07914 & 72.31876 &  70.84991\\\\\n",
       "\t379 & 6811 & 6 & 44.34375 & 13.5 & 630.000 &  620000 & 12.84793 & 4.100000 & 4.700000 & 3.900000 & ⋯ & 1 & 1 & 0 & 78.02752 & 73.75159 & 73.75159 & 73.75159 & 79.40319 & 79.46782 &  72.18232\\\\\n",
       "\t381 & 6822 & 6 & 96.46000 &  9.0 & 480.000 &  400000 & 12.50618 & 4.000000 & 3.600000 & 4.300000 & ⋯ & 0 & 1 & 0 & 75.30797 & 88.68862 & 88.48143 & 88.68862 & 82.83327 & 82.79423 &  80.63574\\\\\n",
       "\t382 & 6834 & 6 & 80.45000 &  6.0 & 360.000 &  300000 & 12.61154 & 3.000000 & 3.400000 & 3.100000 & ⋯ & 0 & 1 & 0 & 68.83997 & 81.86522 & 81.86522 & 75.84690 & 64.00270 & 61.96992 &  59.07848\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 136 × 24\n",
       "\n",
       "| <!--/--> | college_code &lt;int&gt; | division &lt;int&gt; | cutoff &lt;dbl&gt; | courses &lt;dbl&gt; | intake &lt;dbl&gt; | fees &lt;dbl&gt; | salary &lt;dbl&gt; | rating &lt;dbl&gt; | infrastructure &lt;dbl&gt; | faculty &lt;dbl&gt; | ⋯ ⋯ | new_ban &lt;int&gt; | hostel_BOTH &lt;int&gt; | hostel_ONE &lt;int&gt; | linear &lt;dbl&gt; | decision &lt;dbl&gt; | fulltree &lt;dbl&gt; | pruned &lt;dbl&gt; | bagging &lt;dbl&gt; | randomforest &lt;dbl&gt; | boost &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1002 | 1 | 96.44000 |  8 | 300.000 | 240000.0 | 12.87391 | 3.400000 | 3.200000 | 3.500000 | ⋯ | 0 | 1 | 0 | 95.25097 | 88.05211 | 88.05211 | 92.45139 | 87.14085 | 82.41035 |  78.68306 |\n",
       "| 5 | 1105 | 1 | 88.05000 |  8 | 480.000 | 440000.0 | 12.70685 | 3.900000 | 4.000000 | 3.900000 | ⋯ | 0 | 0 | 0 | 83.98529 | 97.36824 | 97.36824 | 92.45139 | 91.94186 | 92.13631 |  98.92230 |\n",
       "| 7 | 1108 | 1 | 44.34375 |  5 | 300.000 | 310000.0 | 12.61154 | 3.900000 | 4.000000 | 4.300000 | ⋯ | 0 | 1 | 0 | 67.03529 | 63.77202 | 63.77202 | 67.33875 | 70.91037 | 70.83759 |  77.19284 |\n",
       "| 8 | 1114 | 1 | 81.55000 |  6 | 300.000 | 320000.0 | 12.82126 | 4.000000 | 4.400000 | 3.900000 | ⋯ | 0 | 1 | 0 | 70.98257 | 73.49375 | 70.32917 | 67.33875 | 73.05704 | 73.94291 |  74.01368 |\n",
       "| 14 | 1122 | 1 | 44.34375 |  5 | 300.000 | 200000.0 | 12.61154 | 2.200000 | 3.000000 | 2.000000 | ⋯ | 1 | 0 | 0 | 57.34506 | 69.04323 | 69.04323 | 67.33875 | 54.54966 | 56.92909 |  48.92507 |\n",
       "| 16 | 1124 | 1 | 49.08000 |  5 | 300.000 | 490000.0 | 12.34584 | 3.600000 | 4.300000 | 3.600000 | ⋯ | 1 | 1 | 0 | 59.01199 | 70.52405 | 70.52405 | 70.52405 | 69.83709 | 69.92331 |  64.97646 |\n",
       "| 18 | 1126 | 1 | 67.71000 |  5 | 300.000 | 170000.0 | 13.10216 | 5.000000 | 5.000000 | 5.000000 | ⋯ | 0 | 1 | 0 | 74.53221 | 63.77202 | 63.77202 | 67.33875 | 57.85599 | 60.52810 |  58.76920 |\n",
       "| 22 | 1130 | 1 | 45.98000 |  6 | 480.000 | 180000.0 | 12.10072 | 2.200000 | 4.000000 | 2.000000 | ⋯ | 1 | 1 | 0 | 36.59204 | 52.71238 | 56.88917 | 57.67139 | 56.40356 | 55.63638 |  49.02708 |\n",
       "| 24 | 1182 | 1 | 59.68000 |  4 | 630.000 | 200000.0 | 13.01701 | 4.200000 | 4.000000 | 5.000000 | ⋯ | 0 | 1 | 0 | 78.07224 | 59.83230 | 56.23467 | 59.83230 | 61.11015 | 61.59383 |  62.58601 |\n",
       "| 25 | 1251 | 1 | 44.34375 |  6 | 300.000 | 284000.0 | 12.54255 | 3.400000 | 3.200000 | 3.400000 | ⋯ | 1 | 1 | 0 | 60.02308 | 69.04323 | 69.04323 | 67.33875 | 63.24937 | 61.99935 |  51.28076 |\n",
       "| 31 | 2008 | 2 | 97.84000 | 10 | 540.000 | 190000.0 | 13.38473 | 3.900000 | 3.800000 | 3.900000 | ⋯ | 0 | 1 | 0 | 97.83733 | 97.36824 | 97.36824 | 92.45139 | 93.19946 | 93.16599 |  89.70917 |\n",
       "| 33 | 2021 | 2 | 72.61000 |  2 | 240.000 |  80000.0 | 12.70685 | 3.800000 | 3.900000 | 4.000000 | ⋯ | 0 | 1 | 0 | 77.88152 | 59.83230 | 56.23467 | 59.83230 | 73.75753 | 72.12574 |  66.32289 |\n",
       "| 35 | 2111 | 2 | 65.26000 |  4 | 300.000 | 170000.0 | 12.61154 | 3.800000 | 3.700000 | 4.300000 | ⋯ | 0 | 1 | 0 | 67.06327 | 59.83230 | 56.23467 | 59.83230 | 59.49070 | 62.80911 |  55.95299 |\n",
       "| 39 | 2116 | 2 | 54.60000 | 10 | 294.000 | 200000.0 | 12.61154 | 3.100000 | 3.000000 | 3.000000 | ⋯ | 0 | 1 | 0 | 66.33838 | 52.71238 | 56.88917 | 57.67139 | 55.81445 | 58.13235 |  48.63402 |\n",
       "| 41 | 2127 | 2 | 80.37000 |  5 | 420.000 | 350000.0 | 12.79386 | 3.900000 | 4.300000 | 4.300000 | ⋯ | 0 | 1 | 0 | 70.52523 | 88.68862 | 84.42333 | 88.68862 | 78.27550 | 76.29939 |  73.88875 |\n",
       "| 42 | 2128 | 2 | 44.34375 |  3 | 196.875 | 170000.0 | 12.61154 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 1 | 1 | 0 | 67.18494 | 59.83230 | 56.23467 | 59.83230 | 59.67666 | 61.06195 |  48.79167 |\n",
       "| 48 | 2134 | 2 | 72.88000 |  9 | 360.000 | 240000.0 | 12.67608 | 3.300000 | 3.400000 | 3.500000 | ⋯ | 0 | 1 | 0 | 69.44201 | 69.04323 | 69.04323 | 67.33875 | 64.49678 | 65.05105 |  55.09393 |\n",
       "| 50 | 2136 | 2 | 44.34375 |  9 | 240.000 | 480000.0 | 13.30469 | 4.300000 | 5.000000 | 5.000000 | ⋯ | 0 | 1 | 0 | 89.85680 | 88.68862 | 88.48143 | 88.68862 | 84.47547 | 82.64416 |  81.57779 |\n",
       "| 52 | 2138 | 2 | 64.49000 |  4 | 270.000 | 250000.0 | 12.70685 | 3.900000 | 4.500000 | 5.000000 | ⋯ | 0 | 1 | 0 | 81.48739 | 59.83230 | 56.23467 | 59.83230 | 63.52538 | 62.28017 |  48.66816 |\n",
       "| 56 | 2250 | 2 | 63.71000 |  6 | 196.875 | 220000.0 | 12.79562 | 4.000000 | 4.000000 | 3.000000 | ⋯ | 0 | 1 | 0 | 71.14808 | 55.15813 | 55.15813 | 67.33875 | 62.93025 | 62.64716 |  53.04594 |\n",
       "| 58 | 2254 | 2 | 59.41000 |  5 | 196.875 | 160000.0 | 12.79562 | 2.800000 | 3.000000 | 3.000000 | ⋯ | 0 | 0 | 0 | 56.74210 | 52.71238 | 49.29500 | 57.67139 | 51.01997 | 52.50172 |  24.07780 |\n",
       "| 59 | 2255 | 2 | 71.74876 |  3 | 196.875 | 220000.0 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 1 | 0 | 0 | 59.76323 | 59.83230 | 56.23467 | 59.83230 | 60.48674 | 59.80988 |  58.51329 |\n",
       "| 65 | 2641 | 2 | 71.74876 |  4 | 382.000 | 322661.9 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 1 | 0 | 0 | 61.80546 | 59.83230 | 65.52854 | 59.83230 | 66.70431 | 66.34055 |  63.35222 |\n",
       "| 67 | 3014 | 3 | 98.48000 |  6 | 300.000 | 340000.0 | 13.21768 | 4.100000 | 3.900000 | 4.200000 | ⋯ | 0 | 1 | 0 | 99.68131 | 97.36824 | 97.36824 | 92.45139 | 95.94890 | 95.52757 | 110.99909 |\n",
       "| 69 | 3035 | 3 | 89.48000 |  7 | 196.875 | 420000.0 | 12.97155 | 3.600000 | 3.100000 | 3.800000 | ⋯ | 0 | 1 | 0 | 74.01919 | 88.68862 | 91.75308 | 88.68862 | 87.07321 | 82.54296 |  95.17807 |\n",
       "| 73 | 3139 | 3 | 96.84000 | 10 | 630.000 | 550000.0 | 12.76569 | 4.300000 | 4.700000 | 4.300000 | ⋯ | 0 | 0 | 0 | 88.69525 | 88.05211 | 88.05211 | 92.45139 | 84.10130 | 85.09154 |  87.26669 |\n",
       "| 75 | 3147 | 3 | 83.40000 |  6 | 300.000 | 264000.0 | 12.30139 | 2.200000 | 2.400000 | 2.200000 | ⋯ | 1 | 1 | 0 | 53.97024 | 65.30064 | 65.30064 | 57.67139 | 58.89893 | 59.25145 |  59.08716 |\n",
       "| 76 | 3148 | 3 | 92.28000 | 10 | 630.000 | 460000.0 | 13.30469 | 3.800000 | 3.700000 | 3.700000 | ⋯ | 0 | 0 | 0 | 77.37348 | 73.75159 | 73.75159 | 73.75159 | 85.57030 | 85.71103 |  97.18984 |\n",
       "| 82 | 3182 | 3 | 98.34000 |  5 | 300.000 | 600000.0 | 14.16617 | 3.800000 | 3.300000 | 3.600000 | ⋯ | 0 | 0 | 0 | 82.17729 | 88.68862 | 91.75308 | 88.68862 | 93.03070 | 92.60175 |  99.33804 |\n",
       "| 84 | 3184 | 3 | 96.77000 | 10 | 480.000 | 570000.0 | 13.12237 | 4.000000 | 3.900000 | 3.900000 | ⋯ | 0 | 1 | 0 | 79.32101 | 88.68862 | 88.48143 | 88.68862 | 93.58710 | 93.43344 |  96.42166 |\n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n",
       "| 303 | 6283 | 6 | 87.28000 | 13.0 | 196.875 |  370000 | 12.61154 | 4.000000 | 4.200000 | 4.200000 | ⋯ | 0 | 1 | 0 | 92.78713 | 88.05211 | 88.05211 | 92.45139 | 91.13583 | 90.52472 |  95.42930 |\n",
       "| 305 | 6285 | 6 | 92.61000 |  6.0 | 240.000 |  430000 | 12.91411 | 3.900000 | 3.800000 | 3.900000 | ⋯ | 0 | 1 | 0 | 77.90717 | 88.68862 | 91.75308 | 88.68862 | 91.82660 | 86.91258 |  77.82207 |\n",
       "| 307 | 6289 | 6 | 97.98000 |  7.0 | 300.000 |  570000 | 13.32122 | 3.900000 | 3.700000 | 4.300000 | ⋯ | 0 | 1 | 0 | 92.27407 | 97.36824 | 97.36824 | 92.45139 | 97.16614 | 96.67641 |  96.94700 |\n",
       "| 311 | 6303 | 6 | 75.18000 |  5.0 | 240.000 |  240000 | 12.98540 | 4.000000 | 4.200000 | 4.100000 | ⋯ | 0 | 1 | 0 | 74.50074 | 68.62492 | 68.62492 | 75.84690 | 65.67000 | 65.37580 |  56.32315 |\n",
       "| 313 | 6305 | 6 | 46.17000 |  5.0 | 210.000 |  192000 | 12.79562 | 3.666295 | 3.804457 | 3.822472 | ⋯ | 1 | 0 | 0 | 64.01767 | 68.62492 | 68.62492 | 75.84690 | 61.57288 | 60.92357 |  42.62498 |\n",
       "| 314 | 6307 | 6 | 83.32000 | 12.0 | 255.000 |  370000 | 12.76569 | 4.100000 | 4.200000 | 4.200000 | ⋯ | 0 | 1 | 0 | 81.96029 | 88.68862 | 88.48143 | 88.68862 | 89.76211 | 88.88252 |  96.11581 |\n",
       "| 320 | 6317 | 6 | 79.53000 | 11.0 | 630.000 |  310000 | 12.54255 | 3.500000 | 3.300000 | 3.700000 | ⋯ | 0 | 1 | 0 | 83.93804 | 88.05211 | 88.05211 | 92.45139 | 84.42921 | 81.79265 |  88.51835 |\n",
       "| 322 | 6319 | 6 | 63.05000 |  6.0 | 360.000 |  308000 | 12.76569 | 3.600000 | 3.900000 | 4.000000 | ⋯ | 0 | 1 | 0 | 74.35820 | 81.86522 | 81.86522 | 75.84690 | 76.28742 | 73.24378 |  68.62145 |\n",
       "| 324 | 6321 | 6 | 45.67000 |  6.0 | 300.000 |  240000 | 12.79386 | 3.200000 | 3.700000 | 3.700000 | ⋯ | 0 | 1 | 0 | 67.14082 | 52.71238 | 56.88917 | 57.67139 | 62.82214 | 61.13303 |  54.08510 |\n",
       "| 328 | 6325 | 6 | 78.05000 |  5.0 | 480.000 |  230000 | 13.99783 | 3.600000 | 3.300000 | 4.200000 | ⋯ | 0 | 1 | 0 | 79.16464 | 68.62492 | 68.62492 | 75.84690 | 66.11722 | 68.46897 |  72.25199 |\n",
       "| 330 | 6419 | 6 | 78.35000 |  6.0 | 360.000 |  330000 | 12.50618 | 4.200000 | 4.100000 | 4.200000 | ⋯ | 0 | 1 | 0 | 71.71905 | 81.86522 | 81.86522 | 75.84690 | 83.55063 | 82.73521 |  88.23035 |\n",
       "| 331 | 6444 | 6 | 44.34375 |  5.0 | 196.875 |  141000 | 12.79562 | 3.200000 | 3.500000 | 4.000000 | ⋯ | 1 | 1 | 0 | 59.30986 | 52.71238 | 49.29500 | 57.67139 | 49.25645 | 50.07344 |  30.98763 |\n",
       "| 337 | 6620 | 6 | 73.99000 | 13.5 | 196.875 | 1080000 | 13.35348 | 3.600000 | 4.200000 | 3.400000 | ⋯ | 1 | 1 | 0 | 85.04649 | 88.68862 | 91.75308 | 88.68862 | 72.71361 | 74.79597 |  58.54335 |\n",
       "| 339 | 6622 | 6 | 85.85000 |  6.0 | 360.000 |  280000 | 12.76569 | 3.500000 | 3.500000 | 3.900000 | ⋯ | 0 | 0 | 0 | 73.16798 | 68.62492 | 68.62492 | 75.84690 | 71.99251 | 71.40742 |  77.59945 |\n",
       "| 341 | 6628 | 6 | 56.76500 |  5.0 | 196.875 |  400000 | 12.56025 | 3.400000 | 3.000000 | 4.000000 | ⋯ | 0 | 0 | 1 | 75.75998 | 88.68862 | 91.75308 | 88.68862 | 81.94778 | 76.32833 |  76.38430 |\n",
       "| 345 | 6635 | 6 | 67.11200 |  9.0 | 420.000 |  300000 | 12.42922 | 3.800000 | 4.000000 | 4.000000 | ⋯ | 0 | 1 | 0 | 76.07599 | 81.86522 | 81.86522 | 75.84690 | 78.96625 | 78.25982 | 100.27036 |\n",
       "| 347 | 6643 | 6 | 81.98400 |  5.0 | 360.000 |  310000 | 12.20608 | 4.200000 | 4.500000 | 4.300000 | ⋯ | 0 | 1 | 0 | 73.32382 | 81.86522 | 81.86522 | 75.84690 | 76.17784 | 74.75446 |  70.20127 |\n",
       "| 348 | 6644 | 6 | 56.76000 |  7.0 | 300.000 |  320000 | 12.79386 | 3.000000 | 3.800000 | 3.100000 | ⋯ | 0 | 1 | 0 | 68.82040 | 52.71238 | 56.88917 | 57.67139 | 65.14153 | 62.40650 |  61.07314 |\n",
       "| 354 | 6757 | 6 | 60.73000 |  7.0 | 360.000 |  310000 | 12.76569 | 3.800000 | 4.000000 | 3.700000 | ⋯ | 0 | 0 | 0 | 74.10919 | 81.86522 | 81.86522 | 75.84690 | 76.10538 | 75.33128 |  81.90277 |\n",
       "| 356 | 6759 | 6 | 68.70000 |  5.0 | 270.000 |  270000 | 12.61154 | 4.600000 | 5.000000 | 5.000000 | ⋯ | 0 | 1 | 0 | 80.30998 | 68.62492 | 68.62492 | 75.84690 | 63.63364 | 62.21199 |  77.75982 |\n",
       "| 358 | 6766 | 6 | 63.08000 |  5.0 | 300.000 |  260000 | 12.76569 | 4.700000 | 5.000000 | 5.000000 | ⋯ | 0 | 0 | 0 | 76.38859 | 68.62492 | 68.62492 | 75.84690 | 62.21482 | 61.51063 |  64.81565 |\n",
       "| 362 | 6770 | 6 | 77.03000 |  5.0 | 300.000 |  410000 | 12.38840 | 3.800000 | 4.100000 | 3.600000 | ⋯ | 0 | 1 | 0 | 70.97872 | 70.52405 | 70.52405 | 70.52405 | 83.54821 | 83.40511 | 104.08819 |\n",
       "| 364 | 6772 | 6 | 87.28000 |  6.0 | 510.000 |  400000 | 12.57764 | 4.000000 | 4.000000 | 3.900000 | ⋯ | 0 | 1 | 0 | 75.21836 | 88.68862 | 88.48143 | 88.68862 | 86.58241 | 85.71080 |  81.62469 |\n",
       "| 365 | 6780 | 6 | 71.76000 | 11.0 | 420.000 |  250000 | 12.38840 | 4.000000 | 4.000000 | 4.000000 | ⋯ | 0 | 1 | 0 | 76.23241 | 68.62492 | 68.62492 | 75.84690 | 75.24435 | 74.22877 |  90.38688 |\n",
       "| 371 | 6795 | 6 | 52.82000 |  4.0 | 210.000 |  240000 | 12.79562 | 3.000000 | 3.000000 | 3.300000 | ⋯ | 0 | 1 | 0 | 67.36720 | 52.71238 | 49.29500 | 57.67139 | 57.46492 | 57.11157 |  49.19333 |\n",
       "| 373 | 6797 | 6 | 74.20000 |  5.0 | 240.000 |  320000 | 12.79562 | 4.100000 | 4.400000 | 4.400000 | ⋯ | 0 | 1 | 0 | 74.90800 | 81.86522 | 81.86522 | 75.84690 | 70.35977 | 71.74794 |  60.08470 |\n",
       "| 375 | 6803 | 6 | 74.51000 |  6.0 | 360.000 |  240000 | 12.89922 | 4.100000 | 4.100000 | 4.200000 | ⋯ | 0 | 1 | 0 | 75.98160 | 68.62492 | 68.62492 | 75.84690 | 72.07914 | 72.31876 |  70.84991 |\n",
       "| 379 | 6811 | 6 | 44.34375 | 13.5 | 630.000 |  620000 | 12.84793 | 4.100000 | 4.700000 | 3.900000 | ⋯ | 1 | 1 | 0 | 78.02752 | 73.75159 | 73.75159 | 73.75159 | 79.40319 | 79.46782 |  72.18232 |\n",
       "| 381 | 6822 | 6 | 96.46000 |  9.0 | 480.000 |  400000 | 12.50618 | 4.000000 | 3.600000 | 4.300000 | ⋯ | 0 | 1 | 0 | 75.30797 | 88.68862 | 88.48143 | 88.68862 | 82.83327 | 82.79423 |  80.63574 |\n",
       "| 382 | 6834 | 6 | 80.45000 |  6.0 | 360.000 |  300000 | 12.61154 | 3.000000 | 3.400000 | 3.100000 | ⋯ | 0 | 1 | 0 | 68.83997 | 81.86522 | 81.86522 | 75.84690 | 64.00270 | 61.96992 |  59.07848 |\n",
       "\n"
      ],
      "text/plain": [
       "    college_code division cutoff   courses intake  fees     salary   rating  \n",
       "1   1002         1        96.44000  8      300.000 240000.0 12.87391 3.400000\n",
       "5   1105         1        88.05000  8      480.000 440000.0 12.70685 3.900000\n",
       "7   1108         1        44.34375  5      300.000 310000.0 12.61154 3.900000\n",
       "8   1114         1        81.55000  6      300.000 320000.0 12.82126 4.000000\n",
       "14  1122         1        44.34375  5      300.000 200000.0 12.61154 2.200000\n",
       "16  1124         1        49.08000  5      300.000 490000.0 12.34584 3.600000\n",
       "18  1126         1        67.71000  5      300.000 170000.0 13.10216 5.000000\n",
       "22  1130         1        45.98000  6      480.000 180000.0 12.10072 2.200000\n",
       "24  1182         1        59.68000  4      630.000 200000.0 13.01701 4.200000\n",
       "25  1251         1        44.34375  6      300.000 284000.0 12.54255 3.400000\n",
       "31  2008         2        97.84000 10      540.000 190000.0 13.38473 3.900000\n",
       "33  2021         2        72.61000  2      240.000  80000.0 12.70685 3.800000\n",
       "35  2111         2        65.26000  4      300.000 170000.0 12.61154 3.800000\n",
       "39  2116         2        54.60000 10      294.000 200000.0 12.61154 3.100000\n",
       "41  2127         2        80.37000  5      420.000 350000.0 12.79386 3.900000\n",
       "42  2128         2        44.34375  3      196.875 170000.0 12.61154 3.800000\n",
       "48  2134         2        72.88000  9      360.000 240000.0 12.67608 3.300000\n",
       "50  2136         2        44.34375  9      240.000 480000.0 13.30469 4.300000\n",
       "52  2138         2        64.49000  4      270.000 250000.0 12.70685 3.900000\n",
       "56  2250         2        63.71000  6      196.875 220000.0 12.79562 4.000000\n",
       "58  2254         2        59.41000  5      196.875 160000.0 12.79562 2.800000\n",
       "59  2255         2        71.74876  3      196.875 220000.0 12.79562 3.666295\n",
       "65  2641         2        71.74876  4      382.000 322661.9 12.79562 3.666295\n",
       "67  3014         3        98.48000  6      300.000 340000.0 13.21768 4.100000\n",
       "69  3035         3        89.48000  7      196.875 420000.0 12.97155 3.600000\n",
       "73  3139         3        96.84000 10      630.000 550000.0 12.76569 4.300000\n",
       "75  3147         3        83.40000  6      300.000 264000.0 12.30139 2.200000\n",
       "76  3148         3        92.28000 10      630.000 460000.0 13.30469 3.800000\n",
       "82  3182         3        98.34000  5      300.000 600000.0 14.16617 3.800000\n",
       "84  3184         3        96.77000 10      480.000 570000.0 13.12237 4.000000\n",
       "⋮   ⋮            ⋮        ⋮        ⋮       ⋮       ⋮        ⋮        ⋮       \n",
       "303 6283         6        87.28000 13.0    196.875  370000  12.61154 4.000000\n",
       "305 6285         6        92.61000  6.0    240.000  430000  12.91411 3.900000\n",
       "307 6289         6        97.98000  7.0    300.000  570000  13.32122 3.900000\n",
       "311 6303         6        75.18000  5.0    240.000  240000  12.98540 4.000000\n",
       "313 6305         6        46.17000  5.0    210.000  192000  12.79562 3.666295\n",
       "314 6307         6        83.32000 12.0    255.000  370000  12.76569 4.100000\n",
       "320 6317         6        79.53000 11.0    630.000  310000  12.54255 3.500000\n",
       "322 6319         6        63.05000  6.0    360.000  308000  12.76569 3.600000\n",
       "324 6321         6        45.67000  6.0    300.000  240000  12.79386 3.200000\n",
       "328 6325         6        78.05000  5.0    480.000  230000  13.99783 3.600000\n",
       "330 6419         6        78.35000  6.0    360.000  330000  12.50618 4.200000\n",
       "331 6444         6        44.34375  5.0    196.875  141000  12.79562 3.200000\n",
       "337 6620         6        73.99000 13.5    196.875 1080000  13.35348 3.600000\n",
       "339 6622         6        85.85000  6.0    360.000  280000  12.76569 3.500000\n",
       "341 6628         6        56.76500  5.0    196.875  400000  12.56025 3.400000\n",
       "345 6635         6        67.11200  9.0    420.000  300000  12.42922 3.800000\n",
       "347 6643         6        81.98400  5.0    360.000  310000  12.20608 4.200000\n",
       "348 6644         6        56.76000  7.0    300.000  320000  12.79386 3.000000\n",
       "354 6757         6        60.73000  7.0    360.000  310000  12.76569 3.800000\n",
       "356 6759         6        68.70000  5.0    270.000  270000  12.61154 4.600000\n",
       "358 6766         6        63.08000  5.0    300.000  260000  12.76569 4.700000\n",
       "362 6770         6        77.03000  5.0    300.000  410000  12.38840 3.800000\n",
       "364 6772         6        87.28000  6.0    510.000  400000  12.57764 4.000000\n",
       "365 6780         6        71.76000 11.0    420.000  250000  12.38840 4.000000\n",
       "371 6795         6        52.82000  4.0    210.000  240000  12.79562 3.000000\n",
       "373 6797         6        74.20000  5.0    240.000  320000  12.79562 4.100000\n",
       "375 6803         6        74.51000  6.0    360.000  240000  12.89922 4.100000\n",
       "379 6811         6        44.34375 13.5    630.000  620000  12.84793 4.100000\n",
       "381 6822         6        96.46000  9.0    480.000  400000  12.50618 4.000000\n",
       "382 6834         6        80.45000  6.0    360.000  300000  12.61154 3.000000\n",
       "    infrastructure faculty  ⋯ new_ban hostel_BOTH hostel_ONE linear   decision\n",
       "1   3.200000       3.500000 ⋯ 0       1           0          95.25097 88.05211\n",
       "5   4.000000       3.900000 ⋯ 0       0           0          83.98529 97.36824\n",
       "7   4.000000       4.300000 ⋯ 0       1           0          67.03529 63.77202\n",
       "8   4.400000       3.900000 ⋯ 0       1           0          70.98257 73.49375\n",
       "14  3.000000       2.000000 ⋯ 1       0           0          57.34506 69.04323\n",
       "16  4.300000       3.600000 ⋯ 1       1           0          59.01199 70.52405\n",
       "18  5.000000       5.000000 ⋯ 0       1           0          74.53221 63.77202\n",
       "22  4.000000       2.000000 ⋯ 1       1           0          36.59204 52.71238\n",
       "24  4.000000       5.000000 ⋯ 0       1           0          78.07224 59.83230\n",
       "25  3.200000       3.400000 ⋯ 1       1           0          60.02308 69.04323\n",
       "31  3.800000       3.900000 ⋯ 0       1           0          97.83733 97.36824\n",
       "33  3.900000       4.000000 ⋯ 0       1           0          77.88152 59.83230\n",
       "35  3.700000       4.300000 ⋯ 0       1           0          67.06327 59.83230\n",
       "39  3.000000       3.000000 ⋯ 0       1           0          66.33838 52.71238\n",
       "41  4.300000       4.300000 ⋯ 0       1           0          70.52523 88.68862\n",
       "42  4.000000       4.000000 ⋯ 1       1           0          67.18494 59.83230\n",
       "48  3.400000       3.500000 ⋯ 0       1           0          69.44201 69.04323\n",
       "50  5.000000       5.000000 ⋯ 0       1           0          89.85680 88.68862\n",
       "52  4.500000       5.000000 ⋯ 0       1           0          81.48739 59.83230\n",
       "56  4.000000       3.000000 ⋯ 0       1           0          71.14808 55.15813\n",
       "58  3.000000       3.000000 ⋯ 0       0           0          56.74210 52.71238\n",
       "59  3.804457       3.822472 ⋯ 1       0           0          59.76323 59.83230\n",
       "65  3.804457       3.822472 ⋯ 1       0           0          61.80546 59.83230\n",
       "67  3.900000       4.200000 ⋯ 0       1           0          99.68131 97.36824\n",
       "69  3.100000       3.800000 ⋯ 0       1           0          74.01919 88.68862\n",
       "73  4.700000       4.300000 ⋯ 0       0           0          88.69525 88.05211\n",
       "75  2.400000       2.200000 ⋯ 1       1           0          53.97024 65.30064\n",
       "76  3.700000       3.700000 ⋯ 0       0           0          77.37348 73.75159\n",
       "82  3.300000       3.600000 ⋯ 0       0           0          82.17729 88.68862\n",
       "84  3.900000       3.900000 ⋯ 0       1           0          79.32101 88.68862\n",
       "⋮   ⋮              ⋮        ⋱ ⋮       ⋮           ⋮          ⋮        ⋮       \n",
       "303 4.200000       4.200000 ⋯ 0       1           0          92.78713 88.05211\n",
       "305 3.800000       3.900000 ⋯ 0       1           0          77.90717 88.68862\n",
       "307 3.700000       4.300000 ⋯ 0       1           0          92.27407 97.36824\n",
       "311 4.200000       4.100000 ⋯ 0       1           0          74.50074 68.62492\n",
       "313 3.804457       3.822472 ⋯ 1       0           0          64.01767 68.62492\n",
       "314 4.200000       4.200000 ⋯ 0       1           0          81.96029 88.68862\n",
       "320 3.300000       3.700000 ⋯ 0       1           0          83.93804 88.05211\n",
       "322 3.900000       4.000000 ⋯ 0       1           0          74.35820 81.86522\n",
       "324 3.700000       3.700000 ⋯ 0       1           0          67.14082 52.71238\n",
       "328 3.300000       4.200000 ⋯ 0       1           0          79.16464 68.62492\n",
       "330 4.100000       4.200000 ⋯ 0       1           0          71.71905 81.86522\n",
       "331 3.500000       4.000000 ⋯ 1       1           0          59.30986 52.71238\n",
       "337 4.200000       3.400000 ⋯ 1       1           0          85.04649 88.68862\n",
       "339 3.500000       3.900000 ⋯ 0       0           0          73.16798 68.62492\n",
       "341 3.000000       4.000000 ⋯ 0       0           1          75.75998 88.68862\n",
       "345 4.000000       4.000000 ⋯ 0       1           0          76.07599 81.86522\n",
       "347 4.500000       4.300000 ⋯ 0       1           0          73.32382 81.86522\n",
       "348 3.800000       3.100000 ⋯ 0       1           0          68.82040 52.71238\n",
       "354 4.000000       3.700000 ⋯ 0       0           0          74.10919 81.86522\n",
       "356 5.000000       5.000000 ⋯ 0       1           0          80.30998 68.62492\n",
       "358 5.000000       5.000000 ⋯ 0       0           0          76.38859 68.62492\n",
       "362 4.100000       3.600000 ⋯ 0       1           0          70.97872 70.52405\n",
       "364 4.000000       3.900000 ⋯ 0       1           0          75.21836 88.68862\n",
       "365 4.000000       4.000000 ⋯ 0       1           0          76.23241 68.62492\n",
       "371 3.000000       3.300000 ⋯ 0       1           0          67.36720 52.71238\n",
       "373 4.400000       4.400000 ⋯ 0       1           0          74.90800 81.86522\n",
       "375 4.100000       4.200000 ⋯ 0       1           0          75.98160 68.62492\n",
       "379 4.700000       3.900000 ⋯ 1       1           0          78.02752 73.75159\n",
       "381 3.600000       4.300000 ⋯ 0       1           0          75.30797 88.68862\n",
       "382 3.400000       3.100000 ⋯ 0       1           0          68.83997 81.86522\n",
       "    fulltree pruned   bagging  randomforest boost    \n",
       "1   88.05211 92.45139 87.14085 82.41035      78.68306\n",
       "5   97.36824 92.45139 91.94186 92.13631      98.92230\n",
       "7   63.77202 67.33875 70.91037 70.83759      77.19284\n",
       "8   70.32917 67.33875 73.05704 73.94291      74.01368\n",
       "14  69.04323 67.33875 54.54966 56.92909      48.92507\n",
       "16  70.52405 70.52405 69.83709 69.92331      64.97646\n",
       "18  63.77202 67.33875 57.85599 60.52810      58.76920\n",
       "22  56.88917 57.67139 56.40356 55.63638      49.02708\n",
       "24  56.23467 59.83230 61.11015 61.59383      62.58601\n",
       "25  69.04323 67.33875 63.24937 61.99935      51.28076\n",
       "31  97.36824 92.45139 93.19946 93.16599      89.70917\n",
       "33  56.23467 59.83230 73.75753 72.12574      66.32289\n",
       "35  56.23467 59.83230 59.49070 62.80911      55.95299\n",
       "39  56.88917 57.67139 55.81445 58.13235      48.63402\n",
       "41  84.42333 88.68862 78.27550 76.29939      73.88875\n",
       "42  56.23467 59.83230 59.67666 61.06195      48.79167\n",
       "48  69.04323 67.33875 64.49678 65.05105      55.09393\n",
       "50  88.48143 88.68862 84.47547 82.64416      81.57779\n",
       "52  56.23467 59.83230 63.52538 62.28017      48.66816\n",
       "56  55.15813 67.33875 62.93025 62.64716      53.04594\n",
       "58  49.29500 57.67139 51.01997 52.50172      24.07780\n",
       "59  56.23467 59.83230 60.48674 59.80988      58.51329\n",
       "65  65.52854 59.83230 66.70431 66.34055      63.35222\n",
       "67  97.36824 92.45139 95.94890 95.52757     110.99909\n",
       "69  91.75308 88.68862 87.07321 82.54296      95.17807\n",
       "73  88.05211 92.45139 84.10130 85.09154      87.26669\n",
       "75  65.30064 57.67139 58.89893 59.25145      59.08716\n",
       "76  73.75159 73.75159 85.57030 85.71103      97.18984\n",
       "82  91.75308 88.68862 93.03070 92.60175      99.33804\n",
       "84  88.48143 88.68862 93.58710 93.43344      96.42166\n",
       "⋮   ⋮        ⋮        ⋮        ⋮            ⋮        \n",
       "303 88.05211 92.45139 91.13583 90.52472      95.42930\n",
       "305 91.75308 88.68862 91.82660 86.91258      77.82207\n",
       "307 97.36824 92.45139 97.16614 96.67641      96.94700\n",
       "311 68.62492 75.84690 65.67000 65.37580      56.32315\n",
       "313 68.62492 75.84690 61.57288 60.92357      42.62498\n",
       "314 88.48143 88.68862 89.76211 88.88252      96.11581\n",
       "320 88.05211 92.45139 84.42921 81.79265      88.51835\n",
       "322 81.86522 75.84690 76.28742 73.24378      68.62145\n",
       "324 56.88917 57.67139 62.82214 61.13303      54.08510\n",
       "328 68.62492 75.84690 66.11722 68.46897      72.25199\n",
       "330 81.86522 75.84690 83.55063 82.73521      88.23035\n",
       "331 49.29500 57.67139 49.25645 50.07344      30.98763\n",
       "337 91.75308 88.68862 72.71361 74.79597      58.54335\n",
       "339 68.62492 75.84690 71.99251 71.40742      77.59945\n",
       "341 91.75308 88.68862 81.94778 76.32833      76.38430\n",
       "345 81.86522 75.84690 78.96625 78.25982     100.27036\n",
       "347 81.86522 75.84690 76.17784 74.75446      70.20127\n",
       "348 56.88917 57.67139 65.14153 62.40650      61.07314\n",
       "354 81.86522 75.84690 76.10538 75.33128      81.90277\n",
       "356 68.62492 75.84690 63.63364 62.21199      77.75982\n",
       "358 68.62492 75.84690 62.21482 61.51063      64.81565\n",
       "362 70.52405 70.52405 83.54821 83.40511     104.08819\n",
       "364 88.48143 88.68862 86.58241 85.71080      81.62469\n",
       "365 68.62492 75.84690 75.24435 74.22877      90.38688\n",
       "371 49.29500 57.67139 57.46492 57.11157      49.19333\n",
       "373 81.86522 75.84690 70.35977 71.74794      60.08470\n",
       "375 68.62492 75.84690 72.07914 72.31876      70.84991\n",
       "379 73.75159 73.75159 79.40319 79.46782      72.18232\n",
       "381 88.48143 88.68862 82.83327 82.79423      80.63574\n",
       "382 81.86522 75.84690 64.00270 61.96992      59.07848"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(gbm)\n",
    "set.seed(0)\n",
    "boosting <- gbm(cutoff~.-college_code, data=train, distribution=\"gaussian\", n.trees=5000, interaction.depth=4, shrinkage=0.2, verbose = F)\n",
    "test$boost <- predict(boosting, test, n.trees=5000)\n",
    "View(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "dc29fcfa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "223.119709991501"
      ],
      "text/latex": [
       "223.119709991501"
      ],
      "text/markdown": [
       "223.119709991501"
      ],
      "text/plain": [
       "[1] 223.1197"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSEboost <- mean((test$boost-test$cutoff)^2)\n",
    "MSEboost"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af7b33a5",
   "metadata": {},
   "source": [
    "### Support Vector Machines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "072bc18a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "svm(formula = cutoff ~ . - college_code, data = train, kernel = \"linear\", \n",
       "    cost = 0.1, scale = TRUE)\n",
       "\n",
       "\n",
       "Parameters:\n",
       "   SVM-Type:  eps-regression \n",
       " SVM-Kernel:  linear \n",
       "       cost:  0.1 \n",
       "      gamma:  0.06666667 \n",
       "    epsilon:  0.1 \n",
       "\n",
       "\n",
       "Number of Support Vectors:  226\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library (e1071)\n",
    "svmfit <- svm(cutoff~.-college_code, data=train , kernel = \"linear\", cost =0.1, scale = TRUE )\n",
    "summary (svmfit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "f3810c89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "193.058784705845"
      ],
      "text/latex": [
       "193.058784705845"
      ],
      "text/markdown": [
       "193.058784705845"
      ],
      "text/plain": [
       "[1] 193.0588"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Predicting on test set\n",
    "test$svm <- predict (svmfit,test)\n",
    "MSEsvm <- mean((test$svm-test$cutoff)^2)\n",
    "MSEsvm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "1627f712",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AECBAkQIEiAAEECBAgSIECQAAGnQQIyM2Av1wfHSpK7ShGKjLJ9Qlk8nxQptAhB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\nQOA/nXmMCK13eA4AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(test$svm,test$cutoff)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20eb1e2b",
   "metadata": {},
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "480ad82e",
   "metadata": {},
   "source": [
    "The Random Forest Model provides the least error rate of 217.78 on the test set and its predicted values are best suited for predicting the cutoffs"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.3.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}