Linear_Regression_Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning -  Linear Regression in Python\n",
    "<a id=\"top\"></a>\n",
    "\n",
    "Notes on implementing Linear Regression in python.\n",
    "\n",
    "### 1. [Data Analysis](#0)\n",
    "\n",
    "### 2. [Simple Linear Regression](#0)\n",
    "* [`Gradient Descent` Python Implementation](#1)\n",
    "* [`Scipy` Implementation](#2)\n",
    "* [`Scikit-Learn` Implementation](#3)\n",
    "* [`Statsmodel` Implementation](#4)\n",
    "* [Multi-step visual of Gradient Descent](#5)\n",
    "* [Animating the Gradient Descent](#6)  \n",
    "\n",
    "### 3. [Multi Linear Regression](#7)\n",
    "* [`Gradient Descent` Python Implementation](#8)\n",
    "* [`Scikit-Learn` Implementation](#9)\n",
    "* [Solving with `Normal Equation`](#10)\n",
    "* [`Scipy` Implementation](#11)\n",
    "* [`Statsmodel` Implementation](#12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importing needed libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading our housing dataset \n",
    "We will load our data on house sales in King County to predict house prices using simple (one input) linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = pd.read_csv('datasets/kc_house_data.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We want to be able to predict `Y` which is our price variable.__ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = dataset[['price']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = dataset.drop(['price', 'id', 'date'],  axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id = '0'></a>\n",
    "# 1. Data Analysis\n",
    "[Top](#top)\n",
    "\n",
    "## Basic data discovery and analysis with `info`, `describe` and `head`\n",
    "\n",
    "using pandas `.info()` we see we have 18 columns and 21613 records. Pretty much all the features given are already in numeric format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 21613 entries, 0 to 21612\n",
      "Data columns (total 18 columns):\n",
      " #   Column         Non-Null Count  Dtype  \n",
      "---  ------         --------------  -----  \n",
      " 0   bedrooms       21613 non-null  int64  \n",
      " 1   bathrooms      21613 non-null  float64\n",
      " 2   sqft_living    21613 non-null  int64  \n",
      " 3   sqft_lot       21613 non-null  int64  \n",
      " 4   floors         21613 non-null  float64\n",
      " 5   waterfront     21613 non-null  int64  \n",
      " 6   view           21613 non-null  int64  \n",
      " 7   condition      21613 non-null  int64  \n",
      " 8   grade          21613 non-null  int64  \n",
      " 9   sqft_above     21613 non-null  int64  \n",
      " 10  sqft_basement  21613 non-null  int64  \n",
      " 11  yr_built       21613 non-null  int64  \n",
      " 12  yr_renovated   21613 non-null  int64  \n",
      " 13  zipcode        21613 non-null  int64  \n",
      " 14  lat            21613 non-null  float64\n",
      " 15  long           21613 non-null  float64\n",
      " 16  sqft_living15  21613 non-null  int64  \n",
      " 17  sqft_lot15     21613 non-null  int64  \n",
      "dtypes: float64(4), int64(14)\n",
      "memory usage: 3.0 MB\n"
     ]
    }
   ],
   "source": [
    "X.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors',\n",
       "       'waterfront', 'view', 'condition', 'grade', 'sqft_above',\n",
       "       'sqft_basement', 'yr_built', 'yr_renovated', 'zipcode', 'lat', 'long',\n",
       "       'sqft_living15', 'sqft_lot15'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#list our columns \n",
    "columns = X.columns\n",
    "columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1180</td>\n",
       "      <td>5650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
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       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1180</td>\n",
       "      <td>0</td>\n",
       "      <td>1955</td>\n",
       "      <td>0</td>\n",
       "      <td>98178</td>\n",
       "      <td>47.5112</td>\n",
       "      <td>-122.257</td>\n",
       "      <td>1340</td>\n",
       "      <td>5650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2570</td>\n",
       "      <td>7242</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>2170</td>\n",
       "      <td>400</td>\n",
       "      <td>1951</td>\n",
       "      <td>1991</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.7210</td>\n",
       "      <td>-122.319</td>\n",
       "      <td>1690</td>\n",
       "      <td>7639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>770</td>\n",
       "      <td>0</td>\n",
       "      <td>1933</td>\n",
       "      <td>0</td>\n",
       "      <td>98028</td>\n",
       "      <td>47.7379</td>\n",
       "      <td>-122.233</td>\n",
       "      <td>2720</td>\n",
       "      <td>8062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1960</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1050</td>\n",
       "      <td>910</td>\n",
       "      <td>1965</td>\n",
       "      <td>0</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.5208</td>\n",
       "      <td>-122.393</td>\n",
       "      <td>1360</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1680</td>\n",
       "      <td>8080</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1680</td>\n",
       "      <td>0</td>\n",
       "      <td>1987</td>\n",
       "      <td>0</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.6168</td>\n",
       "      <td>-122.045</td>\n",
       "      <td>1800</td>\n",
       "      <td>7503</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bedrooms  bathrooms  sqft_living  sqft_lot  floors  waterfront  view  \\\n",
       "0         3       1.00         1180      5650     1.0           0     0   \n",
       "1         3       2.25         2570      7242     2.0           0     0   \n",
       "2         2       1.00          770     10000     1.0           0     0   \n",
       "3         4       3.00         1960      5000     1.0           0     0   \n",
       "4         3       2.00         1680      8080     1.0           0     0   \n",
       "\n",
       "   condition  grade  sqft_above  sqft_basement  yr_built  yr_renovated  \\\n",
       "0          3      7        1180              0      1955             0   \n",
       "1          3      7        2170            400      1951          1991   \n",
       "2          3      6         770              0      1933             0   \n",
       "3          5      7        1050            910      1965             0   \n",
       "4          3      8        1680              0      1987             0   \n",
       "\n",
       "   zipcode      lat     long  sqft_living15  sqft_lot15  \n",
       "0    98178  47.5112 -122.257           1340        5650  \n",
       "1    98125  47.7210 -122.319           1690        7639  \n",
       "2    98028  47.7379 -122.233           2720        8062  \n",
       "3    98136  47.5208 -122.393           1360        5000  \n",
       "4    98074  47.6168 -122.045           1800        7503  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#show first 5 records\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Generates descriptive statistics that summarize the central tendency, dispersion and shape of a dataset's distribution, excluding `NaN` values__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>2.161300e+04</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "      <td>21613.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.370842</td>\n",
       "      <td>2.114757</td>\n",
       "      <td>2079.899736</td>\n",
       "      <td>1.510697e+04</td>\n",
       "      <td>1.494309</td>\n",
       "      <td>0.007542</td>\n",
       "      <td>0.234303</td>\n",
       "      <td>3.409430</td>\n",
       "      <td>7.656873</td>\n",
       "      <td>1788.390691</td>\n",
       "      <td>291.509045</td>\n",
       "      <td>1971.005136</td>\n",
       "      <td>84.402258</td>\n",
       "      <td>98077.939805</td>\n",
       "      <td>47.560053</td>\n",
       "      <td>-122.213896</td>\n",
       "      <td>1986.552492</td>\n",
       "      <td>12768.455652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.930062</td>\n",
       "      <td>0.770163</td>\n",
       "      <td>918.440897</td>\n",
       "      <td>4.142051e+04</td>\n",
       "      <td>0.539989</td>\n",
       "      <td>0.086517</td>\n",
       "      <td>0.766318</td>\n",
       "      <td>0.650743</td>\n",
       "      <td>1.175459</td>\n",
       "      <td>828.090978</td>\n",
       "      <td>442.575043</td>\n",
       "      <td>29.373411</td>\n",
       "      <td>401.679240</td>\n",
       "      <td>53.505026</td>\n",
       "      <td>0.138564</td>\n",
       "      <td>0.140828</td>\n",
       "      <td>685.391304</td>\n",
       "      <td>27304.179631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>290.000000</td>\n",
       "      <td>5.200000e+02</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>290.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1900.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98001.000000</td>\n",
       "      <td>47.155900</td>\n",
       "      <td>-122.519000</td>\n",
       "      <td>399.000000</td>\n",
       "      <td>651.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.750000</td>\n",
       "      <td>1427.000000</td>\n",
       "      <td>5.040000e+03</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1190.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1951.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98033.000000</td>\n",
       "      <td>47.471000</td>\n",
       "      <td>-122.328000</td>\n",
       "      <td>1490.000000</td>\n",
       "      <td>5100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.250000</td>\n",
       "      <td>1910.000000</td>\n",
       "      <td>7.618000e+03</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>1560.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1975.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98065.000000</td>\n",
       "      <td>47.571800</td>\n",
       "      <td>-122.230000</td>\n",
       "      <td>1840.000000</td>\n",
       "      <td>7620.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>2.500000</td>\n",
       "      <td>2550.000000</td>\n",
       "      <td>1.068800e+04</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>2210.000000</td>\n",
       "      <td>560.000000</td>\n",
       "      <td>1997.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>98118.000000</td>\n",
       "      <td>47.678000</td>\n",
       "      <td>-122.125000</td>\n",
       "      <td>2360.000000</td>\n",
       "      <td>10083.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>33.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>13540.000000</td>\n",
       "      <td>1.651359e+06</td>\n",
       "      <td>3.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>9410.000000</td>\n",
       "      <td>4820.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>98199.000000</td>\n",
       "      <td>47.777600</td>\n",
       "      <td>-121.315000</td>\n",
       "      <td>6210.000000</td>\n",
       "      <td>871200.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           bedrooms     bathrooms   sqft_living      sqft_lot        floors  \\\n",
       "count  21613.000000  21613.000000  21613.000000  2.161300e+04  21613.000000   \n",
       "mean       3.370842      2.114757   2079.899736  1.510697e+04      1.494309   \n",
       "std        0.930062      0.770163    918.440897  4.142051e+04      0.539989   \n",
       "min        0.000000      0.000000    290.000000  5.200000e+02      1.000000   \n",
       "25%        3.000000      1.750000   1427.000000  5.040000e+03      1.000000   \n",
       "50%        3.000000      2.250000   1910.000000  7.618000e+03      1.500000   \n",
       "75%        4.000000      2.500000   2550.000000  1.068800e+04      2.000000   \n",
       "max       33.000000      8.000000  13540.000000  1.651359e+06      3.500000   \n",
       "\n",
       "         waterfront          view     condition         grade    sqft_above  \\\n",
       "count  21613.000000  21613.000000  21613.000000  21613.000000  21613.000000   \n",
       "mean       0.007542      0.234303      3.409430      7.656873   1788.390691   \n",
       "std        0.086517      0.766318      0.650743      1.175459    828.090978   \n",
       "min        0.000000      0.000000      1.000000      1.000000    290.000000   \n",
       "25%        0.000000      0.000000      3.000000      7.000000   1190.000000   \n",
       "50%        0.000000      0.000000      3.000000      7.000000   1560.000000   \n",
       "75%        0.000000      0.000000      4.000000      8.000000   2210.000000   \n",
       "max        1.000000      4.000000      5.000000     13.000000   9410.000000   \n",
       "\n",
       "       sqft_basement      yr_built  yr_renovated       zipcode           lat  \\\n",
       "count   21613.000000  21613.000000  21613.000000  21613.000000  21613.000000   \n",
       "mean      291.509045   1971.005136     84.402258  98077.939805     47.560053   \n",
       "std       442.575043     29.373411    401.679240     53.505026      0.138564   \n",
       "min         0.000000   1900.000000      0.000000  98001.000000     47.155900   \n",
       "25%         0.000000   1951.000000      0.000000  98033.000000     47.471000   \n",
       "50%         0.000000   1975.000000      0.000000  98065.000000     47.571800   \n",
       "75%       560.000000   1997.000000      0.000000  98118.000000     47.678000   \n",
       "max      4820.000000   2015.000000   2015.000000  98199.000000     47.777600   \n",
       "\n",
       "               long  sqft_living15     sqft_lot15  \n",
       "count  21613.000000   21613.000000   21613.000000  \n",
       "mean    -122.213896    1986.552492   12768.455652  \n",
       "std        0.140828     685.391304   27304.179631  \n",
       "min     -122.519000     399.000000     651.000000  \n",
       "25%     -122.328000    1490.000000    5100.000000  \n",
       "50%     -122.230000    1840.000000    7620.000000  \n",
       "75%     -122.125000    2360.000000   10083.000000  \n",
       "max     -121.315000    6210.000000  871200.000000  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Compute correlation between variables and our predictor variable__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = dataset.drop(['id', 'date'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: top;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.308350</td>\n",
       "      <td>0.525138</td>\n",
       "      <td>0.702035</td>\n",
       "      <td>0.089661</td>\n",
       "      <td>0.256794</td>\n",
       "      <td>0.266369</td>\n",
       "      <td>0.397293</td>\n",
       "      <td>0.036362</td>\n",
       "      <td>0.667434</td>\n",
       "      <td>0.605567</td>\n",
       "      <td>0.323816</td>\n",
       "      <td>0.054012</td>\n",
       "      <td>0.126434</td>\n",
       "      <td>-0.053203</td>\n",
       "      <td>0.307003</td>\n",
       "      <td>0.021626</td>\n",
       "      <td>0.585379</td>\n",
       "      <td>0.082447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bedrooms</th>\n",
       "      <td>0.308350</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.515884</td>\n",
       "      <td>0.576671</td>\n",
       "      <td>0.031703</td>\n",
       "      <td>0.175429</td>\n",
       "      <td>-0.006582</td>\n",
       "      <td>0.079532</td>\n",
       "      <td>0.028472</td>\n",
       "      <td>0.356967</td>\n",
       "      <td>0.477600</td>\n",
       "      <td>0.303093</td>\n",
       "      <td>0.154178</td>\n",
       "      <td>0.018841</td>\n",
       "      <td>-0.152668</td>\n",
       "      <td>-0.008931</td>\n",
       "      <td>0.129473</td>\n",
       "      <td>0.391638</td>\n",
       "      <td>0.029244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bathrooms</th>\n",
       "      <td>0.525138</td>\n",
       "      <td>0.515884</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.754665</td>\n",
       "      <td>0.087740</td>\n",
       "      <td>0.500653</td>\n",
       "      <td>0.063744</td>\n",
       "      <td>0.187737</td>\n",
       "      <td>-0.124982</td>\n",
       "      <td>0.664983</td>\n",
       "      <td>0.685342</td>\n",
       "      <td>0.283770</td>\n",
       "      <td>0.506019</td>\n",
       "      <td>0.050739</td>\n",
       "      <td>-0.203866</td>\n",
       "      <td>0.024573</td>\n",
       "      <td>0.223042</td>\n",
       "      <td>0.568634</td>\n",
       "      <td>0.087175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sqft_living</th>\n",
       "      <td>0.702035</td>\n",
       "      <td>0.576671</td>\n",
       "      <td>0.754665</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.172826</td>\n",
       "      <td>0.353949</td>\n",
       "      <td>0.103818</td>\n",
       "      <td>0.284611</td>\n",
       "      <td>-0.058753</td>\n",
       "      <td>0.762704</td>\n",
       "      <td>0.876597</td>\n",
       "      <td>0.435043</td>\n",
       "      <td>0.318049</td>\n",
       "      <td>0.055363</td>\n",
       "      <td>-0.199430</td>\n",
       "      <td>0.052529</td>\n",
       "      <td>0.240223</td>\n",
       "      <td>0.756420</td>\n",
       "      <td>0.183286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sqft_lot</th>\n",
       "      <td>0.089661</td>\n",
       "      <td>0.031703</td>\n",
       "      <td>0.087740</td>\n",
       "      <td>0.172826</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.005201</td>\n",
       "      <td>0.021604</td>\n",
       "      <td>0.074710</td>\n",
       "      <td>-0.008958</td>\n",
       "      <td>0.113621</td>\n",
       "      <td>0.183512</td>\n",
       "      <td>0.015286</td>\n",
       "      <td>0.053080</td>\n",
       "      <td>0.007644</td>\n",
       "      <td>-0.129574</td>\n",
       "      <td>-0.085683</td>\n",
       "      <td>0.229521</td>\n",
       "      <td>0.144608</td>\n",
       "      <td>0.718557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>floors</th>\n",
       "      <td>0.256794</td>\n",
       "      <td>0.175429</td>\n",
       "      <td>0.500653</td>\n",
       "      <td>0.353949</td>\n",
       "      <td>-0.005201</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.023698</td>\n",
       "      <td>0.029444</td>\n",
       "      <td>-0.263768</td>\n",
       "      <td>0.458183</td>\n",
       "      <td>0.523885</td>\n",
       "      <td>-0.245705</td>\n",
       "      <td>0.489319</td>\n",
       "      <td>0.006338</td>\n",
       "      <td>-0.059121</td>\n",
       "      <td>0.049614</td>\n",
       "      <td>0.125419</td>\n",
       "      <td>0.279885</td>\n",
       "      <td>-0.011269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>waterfront</th>\n",
       "      <td>0.266369</td>\n",
       "      <td>-0.006582</td>\n",
       "      <td>0.063744</td>\n",
       "      <td>0.103818</td>\n",
       "      <td>0.021604</td>\n",
       "      <td>0.023698</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.401857</td>\n",
       "      <td>0.016653</td>\n",
       "      <td>0.082775</td>\n",
       "      <td>0.072075</td>\n",
       "      <td>0.080588</td>\n",
       "      <td>-0.026161</td>\n",
       "      <td>0.092885</td>\n",
       "      <td>0.030285</td>\n",
       "      <td>-0.014274</td>\n",
       "      <td>-0.041910</td>\n",
       "      <td>0.086463</td>\n",
       "      <td>0.030703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>view</th>\n",
       "      <td>0.397293</td>\n",
       "      <td>0.079532</td>\n",
       "      <td>0.187737</td>\n",
       "      <td>0.284611</td>\n",
       "      <td>0.074710</td>\n",
       "      <td>0.029444</td>\n",
       "      <td>0.401857</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.045990</td>\n",
       "      <td>0.251321</td>\n",
       "      <td>0.167649</td>\n",
       "      <td>0.276947</td>\n",
       "      <td>-0.053440</td>\n",
       "      <td>0.103917</td>\n",
       "      <td>0.084827</td>\n",
       "      <td>0.006157</td>\n",
       "      <td>-0.078400</td>\n",
       "      <td>0.280439</td>\n",
       "      <td>0.072575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>condition</th>\n",
       "      <td>0.036362</td>\n",
       "      <td>0.028472</td>\n",
       "      <td>-0.124982</td>\n",
       "      <td>-0.058753</td>\n",
       "      <td>-0.008958</td>\n",
       "      <td>-0.263768</td>\n",
       "      <td>0.016653</td>\n",
       "      <td>0.045990</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.144674</td>\n",
       "      <td>-0.158214</td>\n",
       "      <td>0.174105</td>\n",
       "      <td>-0.361417</td>\n",
       "      <td>-0.060618</td>\n",
       "      <td>0.003026</td>\n",
       "      <td>-0.014941</td>\n",
       "      <td>-0.106500</td>\n",
       "      <td>-0.092824</td>\n",
       "      <td>-0.003406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>grade</th>\n",
       "      <td>0.667434</td>\n",
       "      <td>0.356967</td>\n",
       "      <td>0.664983</td>\n",
       "      <td>0.762704</td>\n",
       "      <td>0.113621</td>\n",
       "      <td>0.458183</td>\n",
       "      <td>0.082775</td>\n",
       "      <td>0.251321</td>\n",
       "      <td>-0.144674</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.755923</td>\n",
       "      <td>0.168392</td>\n",
       "      <td>0.446963</td>\n",
       "      <td>0.014414</td>\n",
       "      <td>-0.184862</td>\n",
       "      <td>0.114084</td>\n",
       "      <td>0.198372</td>\n",
       "      <td>0.713202</td>\n",
       "      <td>0.119248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sqft_above</th>\n",
       "      <td>0.605567</td>\n",
       "      <td>0.477600</td>\n",
       "      <td>0.685342</td>\n",
       "      <td>0.876597</td>\n",
       "      <td>0.183512</td>\n",
       "      <td>0.523885</td>\n",
       "      <td>0.072075</td>\n",
       "      <td>0.167649</td>\n",
       "      <td>-0.158214</td>\n",
       "      <td>0.755923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.051943</td>\n",
       "      <td>0.423898</td>\n",
       "      <td>0.023285</td>\n",
       "      <td>-0.261190</td>\n",
       "      <td>-0.000816</td>\n",
       "      <td>0.343803</td>\n",
       "      <td>0.731870</td>\n",
       "      <td>0.194050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sqft_basement</th>\n",
       "      <td>0.323816</td>\n",
       "      <td>0.303093</td>\n",
       "      <td>0.283770</td>\n",
       "      <td>0.435043</td>\n",
       "      <td>0.015286</td>\n",
       "      <td>-0.245705</td>\n",
       "      <td>0.080588</td>\n",
       "      <td>0.276947</td>\n",
       "      <td>0.174105</td>\n",
       "      <td>0.168392</td>\n",
       "      <td>-0.051943</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.133124</td>\n",
       "      <td>0.071323</td>\n",
       "      <td>0.074845</td>\n",
       "      <td>0.110538</td>\n",
       "      <td>-0.144765</td>\n",
       "      <td>0.200355</td>\n",
       "      <td>0.017276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yr_built</th>\n",
       "      <td>0.054012</td>\n",
       "      <td>0.154178</td>\n",
       "      <td>0.506019</td>\n",
       "      <td>0.318049</td>\n",
       "      <td>0.053080</td>\n",
       "      <td>0.489319</td>\n",
       "      <td>-0.026161</td>\n",
       "      <td>-0.053440</td>\n",
       "      <td>-0.361417</td>\n",
       "      <td>0.446963</td>\n",
       "      <td>0.423898</td>\n",
       "      <td>-0.133124</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.224874</td>\n",
       "      <td>-0.346869</td>\n",
       "      <td>-0.148122</td>\n",
       "      <td>0.409356</td>\n",
       "      <td>0.326229</td>\n",
       "      <td>0.070958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yr_renovated</th>\n",
       "      <td>0.126434</td>\n",
       "      <td>0.018841</td>\n",
       "      <td>0.050739</td>\n",
       "      <td>0.055363</td>\n",
       "      <td>0.007644</td>\n",
       "      <td>0.006338</td>\n",
       "      <td>0.092885</td>\n",
       "      <td>0.103917</td>\n",
       "      <td>-0.060618</td>\n",
       "      <td>0.014414</td>\n",
       "      <td>0.023285</td>\n",
       "      <td>0.071323</td>\n",
       "      <td>-0.224874</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.064357</td>\n",
       "      <td>0.029398</td>\n",
       "      <td>-0.068372</td>\n",
       "      <td>-0.002673</td>\n",
       "      <td>0.007854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>zipcode</th>\n",
       "      <td>-0.053203</td>\n",
       "      <td>-0.152668</td>\n",
       "      <td>-0.203866</td>\n",
       "      <td>-0.199430</td>\n",
       "      <td>-0.129574</td>\n",
       "      <td>-0.059121</td>\n",
       "      <td>0.030285</td>\n",
       "      <td>0.084827</td>\n",
       "      <td>0.003026</td>\n",
       "      <td>-0.184862</td>\n",
       "      <td>-0.261190</td>\n",
       "      <td>0.074845</td>\n",
       "      <td>-0.346869</td>\n",
       "      <td>0.064357</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.267048</td>\n",
       "      <td>-0.564072</td>\n",
       "      <td>-0.279033</td>\n",
       "      <td>-0.147221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lat</th>\n",
       "      <td>0.307003</td>\n",
       "      <td>-0.008931</td>\n",
       "      <td>0.024573</td>\n",
       "      <td>0.052529</td>\n",
       "      <td>-0.085683</td>\n",
       "      <td>0.049614</td>\n",
       "      <td>-0.014274</td>\n",
       "      <td>0.006157</td>\n",
       "      <td>-0.014941</td>\n",
       "      <td>0.114084</td>\n",
       "      <td>-0.000816</td>\n",
       "      <td>0.110538</td>\n",
       "      <td>-0.148122</td>\n",
       "      <td>0.029398</td>\n",
       "      <td>0.267048</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.135512</td>\n",
       "      <td>0.048858</td>\n",
       "      <td>-0.086419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>long</th>\n",
       "      <td>0.021626</td>\n",
       "      <td>0.129473</td>\n",
       "      <td>0.223042</td>\n",
       "      <td>0.240223</td>\n",
       "      <td>0.229521</td>\n",
       "      <td>0.125419</td>\n",
       "      <td>-0.041910</td>\n",
       "      <td>-0.078400</td>\n",
       "      <td>-0.106500</td>\n",
       "      <td>0.198372</td>\n",
       "      <td>0.343803</td>\n",
       "      <td>-0.144765</td>\n",
       "      <td>0.409356</td>\n",
       "      <td>-0.068372</td>\n",
       "      <td>-0.564072</td>\n",
       "      <td>-0.135512</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.334605</td>\n",
       "      <td>0.254451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sqft_living15</th>\n",
       "      <td>0.585379</td>\n",
       "      <td>0.391638</td>\n",
       "      <td>0.568634</td>\n",
       "      <td>0.756420</td>\n",
       "      <td>0.144608</td>\n",
       "      <td>0.279885</td>\n",
       "      <td>0.086463</td>\n",
       "      <td>0.280439</td>\n",
       "      <td>-0.092824</td>\n",
       "      <td>0.713202</td>\n",
       "      <td>0.731870</td>\n",
       "      <td>0.200355</td>\n",
       "      <td>0.326229</td>\n",
       "      <td>-0.002673</td>\n",
       "      <td>-0.279033</td>\n",
       "      <td>0.048858</td>\n",
       "      <td>0.334605</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.183192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sqft_lot15</th>\n",
       "      <td>0.082447</td>\n",
       "      <td>0.029244</td>\n",
       "      <td>0.087175</td>\n",
       "      <td>0.183286</td>\n",
       "      <td>0.718557</td>\n",
       "      <td>-0.011269</td>\n",
       "      <td>0.030703</td>\n",
       "      <td>0.072575</td>\n",
       "      <td>-0.003406</td>\n",
       "      <td>0.119248</td>\n",
       "      <td>0.194050</td>\n",
       "      <td>0.017276</td>\n",
       "      <td>0.070958</td>\n",
       "      <td>0.007854</td>\n",
       "      <td>-0.147221</td>\n",
       "      <td>-0.086419</td>\n",
       "      <td>0.254451</td>\n",
       "      <td>0.183192</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  price  bedrooms  bathrooms  sqft_living  sqft_lot    floors  \\\n",
       "price          1.000000  0.308350   0.525138     0.702035  0.089661  0.256794   \n",
       "bedrooms       0.308350  1.000000   0.515884     0.576671  0.031703  0.175429   \n",
       "bathrooms      0.525138  0.515884   1.000000     0.754665  0.087740  0.500653   \n",
       "sqft_living    0.702035  0.576671   0.754665     1.000000  0.172826  0.353949   \n",
       "sqft_lot       0.089661  0.031703   0.087740     0.172826  1.000000 -0.005201   \n",
       "floors         0.256794  0.175429   0.500653     0.353949 -0.005201  1.000000   \n",
       "waterfront     0.266369 -0.006582   0.063744     0.103818  0.021604  0.023698   \n",
       "view           0.397293  0.079532   0.187737     0.284611  0.074710  0.029444   \n",
       "condition      0.036362  0.028472  -0.124982    -0.058753 -0.008958 -0.263768   \n",
       "grade          0.667434  0.356967   0.664983     0.762704  0.113621  0.458183   \n",
       "sqft_above     0.605567  0.477600   0.685342     0.876597  0.183512  0.523885   \n",
       "sqft_basement  0.323816  0.303093   0.283770     0.435043  0.015286 -0.245705   \n",
       "yr_built       0.054012  0.154178   0.506019     0.318049  0.053080  0.489319   \n",
       "yr_renovated   0.126434  0.018841   0.050739     0.055363  0.007644  0.006338   \n",
       "zipcode       -0.053203 -0.152668  -0.203866    -0.199430 -0.129574 -0.059121   \n",
       "lat            0.307003 -0.008931   0.024573     0.052529 -0.085683  0.049614   \n",
       "long           0.021626  0.129473   0.223042     0.240223  0.229521  0.125419   \n",
       "sqft_living15  0.585379  0.391638   0.568634     0.756420  0.144608  0.279885   \n",
       "sqft_lot15     0.082447  0.029244   0.087175     0.183286  0.718557 -0.011269   \n",
       "\n",
       "               waterfront      view  condition     grade  sqft_above  \\\n",
       "price            0.266369  0.397293   0.036362  0.667434    0.605567   \n",
       "bedrooms        -0.006582  0.079532   0.028472  0.356967    0.477600   \n",
       "bathrooms        0.063744  0.187737  -0.124982  0.664983    0.685342   \n",
       "sqft_living      0.103818  0.284611  -0.058753  0.762704    0.876597   \n",
       "sqft_lot         0.021604  0.074710  -0.008958  0.113621    0.183512   \n",
       "floors           0.023698  0.029444  -0.263768  0.458183    0.523885   \n",
       "waterfront       1.000000  0.401857   0.016653  0.082775    0.072075   \n",
       "view             0.401857  1.000000   0.045990  0.251321    0.167649   \n",
       "condition        0.016653  0.045990   1.000000 -0.144674   -0.158214   \n",
       "grade            0.082775  0.251321  -0.144674  1.000000    0.755923   \n",
       "sqft_above       0.072075  0.167649  -0.158214  0.755923    1.000000   \n",
       "sqft_basement    0.080588  0.276947   0.174105  0.168392   -0.051943   \n",
       "yr_built        -0.026161 -0.053440  -0.361417  0.446963    0.423898   \n",
       "yr_renovated     0.092885  0.103917  -0.060618  0.014414    0.023285   \n",
       "zipcode          0.030285  0.084827   0.003026 -0.184862   -0.261190   \n",
       "lat             -0.014274  0.006157  -0.014941  0.114084   -0.000816   \n",
       "long            -0.041910 -0.078400  -0.106500  0.198372    0.343803   \n",
       "sqft_living15    0.086463  0.280439  -0.092824  0.713202    0.731870   \n",
       "sqft_lot15       0.030703  0.072575  -0.003406  0.119248    0.194050   \n",
       "\n",
       "               sqft_basement  yr_built  yr_renovated   zipcode       lat  \\\n",
       "price               0.323816  0.054012      0.126434 -0.053203  0.307003   \n",
       "bedrooms            0.303093  0.154178      0.018841 -0.152668 -0.008931   \n",
       "bathrooms           0.283770  0.506019      0.050739 -0.203866  0.024573   \n",
       "sqft_living         0.435043  0.318049      0.055363 -0.199430  0.052529   \n",
       "sqft_lot            0.015286  0.053080      0.007644 -0.129574 -0.085683   \n",
       "floors             -0.245705  0.489319      0.006338 -0.059121  0.049614   \n",
       "waterfront          0.080588 -0.026161      0.092885  0.030285 -0.014274   \n",
       "view                0.276947 -0.053440      0.103917  0.084827  0.006157   \n",
       "condition           0.174105 -0.361417     -0.060618  0.003026 -0.014941   \n",
       "grade               0.168392  0.446963      0.014414 -0.184862  0.114084   \n",
       "sqft_above         -0.051943  0.423898      0.023285 -0.261190 -0.000816   \n",
       "sqft_basement       1.000000 -0.133124      0.071323  0.074845  0.110538   \n",
       "yr_built           -0.133124  1.000000     -0.224874 -0.346869 -0.148122   \n",
       "yr_renovated        0.071323 -0.224874      1.000000  0.064357  0.029398   \n",
       "zipcode             0.074845 -0.346869      0.064357  1.000000  0.267048   \n",
       "lat                 0.110538 -0.148122      0.029398  0.267048  1.000000   \n",
       "long               -0.144765  0.409356     -0.068372 -0.564072 -0.135512   \n",
       "sqft_living15       0.200355  0.326229     -0.002673 -0.279033  0.048858   \n",
       "sqft_lot15          0.017276  0.070958      0.007854 -0.147221 -0.086419   \n",
       "\n",
       "                   long  sqft_living15  sqft_lot15  \n",
       "price          0.021626       0.585379    0.082447  \n",
       "bedrooms       0.129473       0.391638    0.029244  \n",
       "bathrooms      0.223042       0.568634    0.087175  \n",
       "sqft_living    0.240223       0.756420    0.183286  \n",
       "sqft_lot       0.229521       0.144608    0.718557  \n",
       "floors         0.125419       0.279885   -0.011269  \n",
       "waterfront    -0.041910       0.086463    0.030703  \n",
       "view          -0.078400       0.280439    0.072575  \n",
       "condition     -0.106500      -0.092824   -0.003406  \n",
       "grade          0.198372       0.713202    0.119248  \n",
       "sqft_above     0.343803       0.731870    0.194050  \n",
       "sqft_basement -0.144765       0.200355    0.017276  \n",
       "yr_built       0.409356       0.326229    0.070958  \n",
       "yr_renovated  -0.068372      -0.002673    0.007854  \n",
       "zipcode       -0.564072      -0.279033   -0.147221  \n",
       "lat           -0.135512       0.048858   -0.086419  \n",
       "long           1.000000       0.334605    0.254451  \n",
       "sqft_living15  0.334605       1.000000    0.183192  \n",
       "sqft_lot15     0.254451       0.183192    1.000000  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.corr(method='pearson')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We can even visualize the table above__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplots(figsize=(10,8))\n",
    "sns.heatmap(dataset.corr())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `statsmodel` package can also give us some great insight and summary statistics including `p-value` \n",
    "The statsmodel can actually perform the regression modeling for us , but here I am mainly using it to help determine which variable I should focus on for my `Simple Linear Regression` (one independent variable) and get a feel of which values are statistically significant. There are techniques when dealing with `Multiple Linear Regression` (many variable) to narrow down to the most significant features/variables usiung __Step Wise Regression__ which include techniques such as __Forward Selection__ and __Backward Elimination__.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>condition</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1180</td>\n",
       "      <td>5650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1180</td>\n",
       "      <td>0</td>\n",
       "      <td>1955</td>\n",
       "      <td>0</td>\n",
       "      <td>98178</td>\n",
       "      <td>47.5112</td>\n",
       "      <td>-122.257</td>\n",
       "      <td>1340</td>\n",
       "      <td>5650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2570</td>\n",
       "      <td>7242</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>2170</td>\n",
       "      <td>400</td>\n",
       "      <td>1951</td>\n",
       "      <td>1991</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.7210</td>\n",
       "      <td>-122.319</td>\n",
       "      <td>1690</td>\n",
       "      <td>7639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>770</td>\n",
       "      <td>0</td>\n",
       "      <td>1933</td>\n",
       "      <td>0</td>\n",
       "      <td>98028</td>\n",
       "      <td>47.7379</td>\n",
       "      <td>-122.233</td>\n",
       "      <td>2720</td>\n",
       "      <td>8062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1960</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>1050</td>\n",
       "      <td>910</td>\n",
       "      <td>1965</td>\n",
       "      <td>0</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.5208</td>\n",
       "      <td>-122.393</td>\n",
       "      <td>1360</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1680</td>\n",
       "      <td>8080</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1680</td>\n",
       "      <td>0</td>\n",
       "      <td>1987</td>\n",
       "      <td>0</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.6168</td>\n",
       "      <td>-122.045</td>\n",
       "      <td>1800</td>\n",
       "      <td>7503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21608</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>1530</td>\n",
       "      <td>1131</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1530</td>\n",
       "      <td>0</td>\n",
       "      <td>2009</td>\n",
       "      <td>0</td>\n",
       "      <td>98103</td>\n",
       "      <td>47.6993</td>\n",
       "      <td>-122.346</td>\n",
       "      <td>1530</td>\n",
       "      <td>1509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21609</th>\n",
       "      <td>4</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2310</td>\n",
       "      <td>5813</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>2310</td>\n",
       "      <td>0</td>\n",
       "      <td>2014</td>\n",
       "      <td>0</td>\n",
       "      <td>98146</td>\n",
       "      <td>47.5107</td>\n",
       "      <td>-122.362</td>\n",
       "      <td>1830</td>\n",
       "      <td>7200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21610</th>\n",
       "      <td>2</td>\n",
       "      <td>0.75</td>\n",
       "      <td>1020</td>\n",
       "      <td>1350</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1020</td>\n",
       "      <td>0</td>\n",
       "      <td>2009</td>\n",
       "      <td>0</td>\n",
       "      <td>98144</td>\n",
       "      <td>47.5944</td>\n",
       "      <td>-122.299</td>\n",
       "      <td>1020</td>\n",
       "      <td>2007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21611</th>\n",
       "      <td>3</td>\n",
       "      <td>2.50</td>\n",
       "      <td>1600</td>\n",
       "      <td>2388</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>1600</td>\n",
       "      <td>0</td>\n",
       "      <td>2004</td>\n",
       "      <td>0</td>\n",
       "      <td>98027</td>\n",
       "      <td>47.5345</td>\n",
       "      <td>-122.069</td>\n",
       "      <td>1410</td>\n",
       "      <td>1287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21612</th>\n",
       "      <td>2</td>\n",
       "      <td>0.75</td>\n",
       "      <td>1020</td>\n",
       "      <td>1076</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1020</td>\n",
       "      <td>0</td>\n",
       "      <td>2008</td>\n",
       "      <td>0</td>\n",
       "      <td>98144</td>\n",
       "      <td>47.5941</td>\n",
       "      <td>-122.299</td>\n",
       "      <td>1020</td>\n",
       "      <td>1357</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>21613 rows × 18 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       bedrooms  bathrooms  sqft_living  sqft_lot  floors  waterfront  view  \\\n",
       "0             3       1.00         1180      5650     1.0           0     0   \n",
       "1             3       2.25         2570      7242     2.0           0     0   \n",
       "2             2       1.00          770     10000     1.0           0     0   \n",
       "3             4       3.00         1960      5000     1.0           0     0   \n",
       "4             3       2.00         1680      8080     1.0           0     0   \n",
       "...         ...        ...          ...       ...     ...         ...   ...   \n",
       "21608         3       2.50         1530      1131     3.0           0     0   \n",
       "21609         4       2.50         2310      5813     2.0           0     0   \n",
       "21610         2       0.75         1020      1350     2.0           0     0   \n",
       "21611         3       2.50         1600      2388     2.0           0     0   \n",
       "21612         2       0.75         1020      1076     2.0           0     0   \n",
       "\n",
       "       condition  grade  sqft_above  sqft_basement  yr_built  yr_renovated  \\\n",
       "0              3      7        1180              0      1955             0   \n",
       "1              3      7        2170            400      1951          1991   \n",
       "2              3      6         770              0      1933             0   \n",
       "3              5      7        1050            910      1965             0   \n",
       "4              3      8        1680              0      1987             0   \n",
       "...          ...    ...         ...            ...       ...           ...   \n",
       "21608          3      8        1530              0      2009             0   \n",
       "21609          3      8        2310              0      2014             0   \n",
       "21610          3      7        1020              0      2009             0   \n",
       "21611          3      8        1600              0      2004             0   \n",
       "21612          3      7        1020              0      2008             0   \n",
       "\n",
       "       zipcode      lat     long  sqft_living15  sqft_lot15  \n",
       "0        98178  47.5112 -122.257           1340        5650  \n",
       "1        98125  47.7210 -122.319           1690        7639  \n",
       "2        98028  47.7379 -122.233           2720        8062  \n",
       "3        98136  47.5208 -122.393           1360        5000  \n",
       "4        98074  47.6168 -122.045           1800        7503  \n",
       "...        ...      ...      ...            ...         ...  \n",
       "21608    98103  47.6993 -122.346           1530        1509  \n",
       "21609    98146  47.5107 -122.362           1830        7200  \n",
       "21610    98144  47.5944 -122.299           1020        2007  \n",
       "21611    98027  47.5345 -122.069           1410        1287  \n",
       "21612    98144  47.5941 -122.299           1020        1357  \n",
       "\n",
       "[21613 rows x 18 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>price</td>      <th>  R-squared:         </th>  <td>   0.700</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.700</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>   2960.</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 10 Jan 2021</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:51:59</td>     <th>  Log-Likelihood:    </th> <td>-2.9460e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 21613</td>      <th>  AIC:               </th>  <td>5.892e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 21595</td>      <th>  BIC:               </th>  <td>5.894e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    17</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>         <td>  6.69e+06</td> <td> 2.93e+06</td> <td>    2.282</td> <td> 0.022</td> <td> 9.44e+05</td> <td> 1.24e+07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>      <td>-3.577e+04</td> <td> 1891.843</td> <td>  -18.906</td> <td> 0.000</td> <td>-3.95e+04</td> <td>-3.21e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th>     <td> 4.114e+04</td> <td> 3253.678</td> <td>   12.645</td> <td> 0.000</td> <td> 3.48e+04</td> <td> 4.75e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_living</th>   <td>  110.4422</td> <td>    2.270</td> <td>   48.661</td> <td> 0.000</td> <td>  105.994</td> <td>  114.891</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_lot</th>      <td>    0.1286</td> <td>    0.048</td> <td>    2.683</td> <td> 0.007</td> <td>    0.035</td> <td>    0.223</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>floors</th>        <td> 6689.5501</td> <td> 3595.859</td> <td>    1.860</td> <td> 0.063</td> <td> -358.599</td> <td> 1.37e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waterfront</th>    <td>  5.83e+05</td> <td> 1.74e+04</td> <td>   33.580</td> <td> 0.000</td> <td> 5.49e+05</td> <td> 6.17e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>view</th>          <td> 5.287e+04</td> <td> 2140.055</td> <td>   24.705</td> <td> 0.000</td> <td> 4.87e+04</td> <td> 5.71e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>condition</th>     <td> 2.639e+04</td> <td> 2351.461</td> <td>   11.221</td> <td> 0.000</td> <td> 2.18e+04</td> <td>  3.1e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grade</th>         <td> 9.589e+04</td> <td> 2152.789</td> <td>   44.542</td> <td> 0.000</td> <td> 9.17e+04</td> <td>    1e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_above</th>    <td>   70.7859</td> <td>    2.253</td> <td>   31.413</td> <td> 0.000</td> <td>   66.369</td> <td>   75.203</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_basement</th> <td>   39.6583</td> <td>    2.646</td> <td>   14.985</td> <td> 0.000</td> <td>   34.471</td> <td>   44.846</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>yr_built</th>      <td>-2620.2232</td> <td>   72.659</td> <td>  -36.062</td> <td> 0.000</td> <td>-2762.640</td> <td>-2477.806</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>yr_renovated</th>  <td>   19.8126</td> <td>    3.656</td> <td>    5.420</td> <td> 0.000</td> <td>   12.647</td> <td>   26.978</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>zipcode</th>       <td> -582.4199</td> <td>   32.986</td> <td>  -17.657</td> <td> 0.000</td> <td> -647.074</td> <td> -517.765</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>lat</th>           <td> 6.027e+05</td> <td> 1.07e+04</td> <td>   56.149</td> <td> 0.000</td> <td> 5.82e+05</td> <td> 6.24e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>long</th>          <td>-2.147e+05</td> <td> 1.31e+04</td> <td>  -16.349</td> <td> 0.000</td> <td> -2.4e+05</td> <td>-1.89e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_living15</th> <td>   21.6814</td> <td>    3.448</td> <td>    6.289</td> <td> 0.000</td> <td>   14.924</td> <td>   28.439</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sqft_lot15</th>    <td>   -0.3826</td> <td>    0.073</td> <td>   -5.222</td> <td> 0.000</td> <td>   -0.526</td> <td>   -0.239</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>18384.201</td> <th>  Durbin-Watson:     </th>  <td>   1.990</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>1868224.491</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 3.566</td>   <th>  Prob(JB):          </th>  <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>47.985</td>   <th>  Cond. No.          </th>  <td>4.77e+17</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 9.63e-22. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.700\n",
       "Model:                            OLS   Adj. R-squared:                  0.700\n",
       "Method:                 Least Squares   F-statistic:                     2960.\n",
       "Date:                Sun, 10 Jan 2021   Prob (F-statistic):               0.00\n",
       "Time:                        11:51:59   Log-Likelihood:            -2.9460e+05\n",
       "No. Observations:               21613   AIC:                         5.892e+05\n",
       "Df Residuals:                   21595   BIC:                         5.894e+05\n",
       "Df Model:                          17                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=================================================================================\n",
       "                    coef    std err          t      P>|t|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------\n",
       "const           6.69e+06   2.93e+06      2.282      0.022    9.44e+05    1.24e+07\n",
       "bedrooms      -3.577e+04   1891.843    -18.906      0.000   -3.95e+04   -3.21e+04\n",
       "bathrooms      4.114e+04   3253.678     12.645      0.000    3.48e+04    4.75e+04\n",
       "sqft_living     110.4422      2.270     48.661      0.000     105.994     114.891\n",
       "sqft_lot          0.1286      0.048      2.683      0.007       0.035       0.223\n",
       "floors         6689.5501   3595.859      1.860      0.063    -358.599    1.37e+04\n",
       "waterfront      5.83e+05   1.74e+04     33.580      0.000    5.49e+05    6.17e+05\n",
       "view           5.287e+04   2140.055     24.705      0.000    4.87e+04    5.71e+04\n",
       "condition      2.639e+04   2351.461     11.221      0.000    2.18e+04     3.1e+04\n",
       "grade          9.589e+04   2152.789     44.542      0.000    9.17e+04       1e+05\n",
       "sqft_above       70.7859      2.253     31.413      0.000      66.369      75.203\n",
       "sqft_basement    39.6583      2.646     14.985      0.000      34.471      44.846\n",
       "yr_built      -2620.2232     72.659    -36.062      0.000   -2762.640   -2477.806\n",
       "yr_renovated     19.8126      3.656      5.420      0.000      12.647      26.978\n",
       "zipcode        -582.4199     32.986    -17.657      0.000    -647.074    -517.765\n",
       "lat            6.027e+05   1.07e+04     56.149      0.000    5.82e+05    6.24e+05\n",
       "long          -2.147e+05   1.31e+04    -16.349      0.000    -2.4e+05   -1.89e+05\n",
       "sqft_living15    21.6814      3.448      6.289      0.000      14.924      28.439\n",
       "sqft_lot15       -0.3826      0.073     -5.222      0.000      -0.526      -0.239\n",
       "==============================================================================\n",
       "Omnibus:                    18384.201   Durbin-Watson:                   1.990\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1868224.491\n",
       "Skew:                           3.566   Prob(JB):                         0.00\n",
       "Kurtosis:                      47.985   Cond. No.                     4.77e+17\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 9.63e-22. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sml\n",
    "from statsmodels import tools\n",
    "\n",
    "X_new = tools.add_constant(X)\n",
    "\n",
    "regressor_OLS = sml.OLS(endog = Y,exog =  X_new).fit()\n",
    "\n",
    "regressor_OLS.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"0\"></a>\n",
    "# <font color=\"red\">Simple </font>Linear Regression\n",
    "\n",
    "We will start with __Simple Linear Regression__ since it is easier to understand and visualize before moving to __Multiple Linear Regression__. Though, the conecpts overall are similar and the libraries we will be using are actually designed to handle both wihtout distinction. Simple Linear Regression is easier to plot and visualize so we will start with that.\n",
    "\n",
    "It is __Simple Linear Regression__ when we have one dependent variable (feature) and one independent variable. Here we will pick `sqft_living` as our independent variable `x`.\n",
    "\n",
    "Our goal is to estimate $\\hat{y} = x {\\theta_1} + \\theta_0$, where $\\theta_1$ is our coefficient and $\\theta_0$ is our `Y` intercept. To estimate $\\hat{y}$ we need to find a function such as $\\hat{y} = h(x) = x {\\theta_1} + \\theta_0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__We first start by creating our `x` and `y` variables. Then plotting to gain an intuition on how the data looks like.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = X[['sqft_living']]\n",
    "y = Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9ecab3d430>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.xlabel('House Sqft')\n",
    "plt.ylabel('House Price')\n",
    "plt.title('Price by Sqft_Living')\n",
    "plt.scatter(x,y, marker='o', color='g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Linear Regression Implementations:\n",
    "\n",
    "## 1. Using `seaborn.regplot()` and `scipy.stats`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f9ecdfc81c0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "sns.set(color_codes=True)\n",
    "\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(dataset['sqft_living'],dataset['price'])\n",
    "\n",
    "f = plt.figure(figsize=(10,6))\n",
    "data = dataset[['price','sqft_living']]\n",
    "ax = sns.regplot(x='sqft_living', y='price', data=data, \n",
    "                 scatter_kws={\"color\": \"g\"}, \n",
    "                line_kws={'color': 'r', 'label':\"y={0:.1f}x+{1:.1f}\".format(slope,intercept)})\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "280.6235678974483 -43580.74309447408\n"
     ]
    }
   ],
   "source": [
    "print(slope, intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9363985519989133\n"
     ]
    }
   ],
   "source": [
    "print(std_err)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='1'></a>\n",
    "## 2. Manual Method : Gradient Descent Implementation\n",
    "\n",
    "[Top](#top)\n",
    "\n",
    "## Equations \n",
    "Objective of Linear Regression is to minimize the cost function: \n",
    "<br>\n",
    "$\\Large J(\\theta) = \\frac{1}{2m} \\sum\\limits_{i=1}^{m} (h_\\theta(x^{(i)})-y^{(i)})^2$\n",
    "<br>\n",
    "<br>\n",
    "where the hypothesis $h_\\theta(x)$ is given by the lienar model:  \n",
    "\n",
    "$\\Large h_\\theta(x) = \\theta^T X = \\theta_1 X_1 + \\theta_0 $  \n",
    "<br>\n",
    "In batch gradient descent, each iteration performs the update:  \n",
    "$\\Large \\theta_j := \\theta_j - \\alpha \\frac{1}{m} \\sum\\limits_{i=1}^{m}(h_\\theta (x^{(i)}) - y^{(i)})x_j^{(i)}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = X[['sqft_living']]\n",
    "y = Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "xg = x.values.reshape(-1,1)\n",
    "yg = y.values.reshape(-1,1)\n",
    "xg = np.concatenate((np.ones(len(x)).reshape(-1,1), x), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implementing the Cost Function $J(\\theta)$ in python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeCost(x, y, theta):\n",
    "    m = len(y)\n",
    "    h_x = x.dot(theta)\n",
    "    j = np.sum(np.square(h_x - y))*(1/(2*m))\n",
    "    return j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(x, y, theta, alpha, iteration):\n",
    "    print('Running Gradient Descent...')\n",
    "    j_hist = []\n",
    "    m = len(y)\n",
    "    for i in range(iteration):\n",
    "        j_hist.append(computeCost(x, y, theta))\n",
    "        h_x = x.dot(theta)\n",
    "        theta = theta - ((alpha/m) *((np.dot(x.T, (h_x-y) ))))\n",
    "        #theta[0] = theta[0] - ((alpha/m) *(np.sum((h_x-y))))\n",
    "    return theta, j_hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running Gradient Descent...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-170-4c6aec17be90>:4: RuntimeWarning: overflow encountered in square\n",
      "  j = np.sum(np.square(h_x - y))*(1/(2*m))\n",
      "<ipython-input-171-e81683f4f12d>:8: RuntimeWarning: invalid value encountered in subtract\n",
      "  theta = theta - ((alpha/m) *((np.dot(x.T, (h_x-y) ))))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta found by Gradient Descent: slope = [nan] and intercept [nan]\n"
     ]
    }
   ],
   "source": [
    "theta = np.zeros((2,1))\n",
    "iteration = 2000\n",
    "alpha = 0.001\n",
    "\n",
    "theta, cost = gradientDescent(xg, yg, theta, alpha, iteration)\n",
    "print('Theta found by Gradient Descent: slope = {} and intercept {}'.format(theta[1], theta[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plotting the linear fit**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1)"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title('$\\\\theta_0$ = {} , $\\\\theta_1$ = {}'.format(theta[0], theta[1]))\n",
    "plt.scatter(x,y, marker='o', color='g')\n",
    "plt.plot(x,np.dot(x.values, theta.T))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cost')"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(cost)\n",
    "plt.xlabel('No. of iterations')\n",
    "plt.ylabel('Cost')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Manual Method: Compute Slope and Intercept using a Formula (Gradient = 0)\n",
    "\n",
    "## Slope  $a = \\frac{\\sum (x_i-\\bar{x})(y_i-\\bar{Y})}{\\sum (x_i-\\bar{x})^2}$\n",
    "\n",
    "## Intercept $b = \\bar{y}-a\\bar{x}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "def slr(X, Y):\n",
    "    mean_x = X.mean()\n",
    "    mean_y = Y.mean()\n",
    "\n",
    "    delta_x = X - mean_x\n",
    "    delta_y = Y - mean_y\n",
    "\n",
    "    slope = (delta_x * delta_y).sum()/(delta_x**2).sum()\n",
    "    intercept = mean_y - slope*mean_x\n",
    "    \n",
    "    return (slope, intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope = 280.6235678974483 and Intercept = -43580.74309447408\n",
      "y = x(280.6235678974483) + -43580.74309447408\n"
     ]
    }
   ],
   "source": [
    "xf = x.values.reshape(-1,1)\n",
    "yf = y.values.reshape(-1,1)\n",
    "\n",
    "slope, intercept = slr(xf, yf)\n",
    "print('Slope = {} and Intercept = {}'.format(slope, intercept))\n",
    "print('y = x({}) + {}'.format(slope, intercept))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='2'></a>\n",
    "## 4. Implement with using Scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "\n",
    "xs = x.iloc[:,0]\n",
    "ys = y.iloc[:,0]\n",
    "#xs = np.concatenate((np.ones(len(x)).reshape(-1,1), x), axis=1)\n",
    "\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope = 280.6235678974483 and Intercept = -43580.74309447408\n",
      "y = x(280.6235678974483) + -43580.74309447408\n"
     ]
    }
   ],
   "source": [
    "print('Slope = {} and Intercept = {}'.format(slope, intercept))\n",
    "print('y = x({}) + {}'.format(slope, intercept))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the linear fit using the slop and intercept values from scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9eb6b8af10>]"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title('$\\\\theta_0$ = {} , $\\\\theta_1$ = {}'.format(intercept, slope))\n",
    "plt.scatter(xs,y, marker='o', color='green')\n",
    "plt.plot(xs, np.dot(x, slope), 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='3'></a>\n",
    "## 5. Implement using Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta[0] =  [-43580.74309447]\n",
      "theta[1] =  [[280.6235679]]\n"
     ]
    }
   ],
   "source": [
    "xsl = x.values.reshape(-1,1)\n",
    "ysl = y.values.reshape(-1,1)\n",
    "xsl = np.concatenate((np.ones(len(xsl)).reshape(-1,1), xsl), axis=1)\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "slr = LinearRegression()\n",
    "slr.fit(xsl[:,1].reshape(-1,1), ysl.reshape(-1,1))\n",
    "y_hat = slr.predict(xsl[:,1].reshape(-1,1))\n",
    "\n",
    "print('theta[0] = ', slr.intercept_)\n",
    "print('theta[1] = ', slr.coef_)\n",
    "\n",
    "thetas = np.array((slr.intercept_, slr.coef_)).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9eb7479340>]"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.title('$\\\\theta_0$ = {} , $\\\\theta_1$ = {}'.format(thetas[0], thetas[1]))\n",
    "plt.scatter(xsl[:,1],y, marker='x', color='g')\n",
    "plt.plot(xsl[:,1], np.dot(xsl, thetas), 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='4'></a>\n",
    "## Implement using Statsmodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th>  <td>   0.493</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.493</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>2.100e+04</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 10 Jan 2021</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:36:24</td>     <th>  Log-Likelihood:    </th> <td>-3.0027e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 21613</td>      <th>  AIC:               </th>  <td>6.005e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 21611</td>      <th>  BIC:               </th>  <td>6.006e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>-4.358e+04</td> <td> 4402.690</td> <td>   -9.899</td> <td> 0.000</td> <td>-5.22e+04</td> <td> -3.5e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>  280.6236</td> <td>    1.936</td> <td>  144.920</td> <td> 0.000</td> <td>  276.828</td> <td>  284.419</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>14832.490</td> <th>  Durbin-Watson:     </th>  <td>   1.983</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>546444.713</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 2.824</td>   <th>  Prob(JB):          </th>  <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>26.977</td>   <th>  Cond. No.          </th>  <td>5.63e+03</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 5.63e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.493\n",
       "Model:                            OLS   Adj. R-squared:                  0.493\n",
       "Method:                 Least Squares   F-statistic:                 2.100e+04\n",
       "Date:                Sun, 10 Jan 2021   Prob (F-statistic):               0.00\n",
       "Time:                        12:36:24   Log-Likelihood:            -3.0027e+05\n",
       "No. Observations:               21613   AIC:                         6.005e+05\n",
       "Df Residuals:                   21611   BIC:                         6.006e+05\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const      -4.358e+04   4402.690     -9.899      0.000   -5.22e+04    -3.5e+04\n",
       "x1           280.6236      1.936    144.920      0.000     276.828     284.419\n",
       "==============================================================================\n",
       "Omnibus:                    14832.490   Durbin-Watson:                   1.983\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           546444.713\n",
       "Skew:                           2.824   Prob(JB):                         0.00\n",
       "Kurtosis:                      26.977   Cond. No.                     5.63e+03\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 5.63e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xsm = x.values.reshape(-1,1)\n",
    "ysm = y.values.reshape(-1,1)\n",
    "xsm = np.concatenate((np.ones(len(x)).reshape(-1,1), xsm), axis=1)\n",
    "\n",
    "import statsmodels.api as sm\n",
    "\n",
    "results = sm.OLS(ysm, xsm).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9eb1214790>]"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = results.params\n",
    "\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.title('$\\\\theta_0$ = {} , $\\\\theta_1$ = {}'.format(thetas[0], thetas[1]))\n",
    "plt.scatter(xsm[:,1],ysm, marker='x', color='g')\n",
    "plt.plot(xsm[:,1], np.dot(xsm, thetas), 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='7'></a>\n",
    "# <font color=\"Red\">Multiple</font> Linear Regression\n",
    "[Top](#top)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "dataset = pd.read_csv('datasets/kc_house_data.csv')\n",
    "Y = dataset[['price']]\n",
    "X = dataset.drop(['price', 'id', 'date'],  axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>date</th>\n",
       "      <th>price</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>sqft_living</th>\n",
       "      <th>sqft_lot</th>\n",
       "      <th>floors</th>\n",
       "      <th>waterfront</th>\n",
       "      <th>view</th>\n",
       "      <th>...</th>\n",
       "      <th>grade</th>\n",
       "      <th>sqft_above</th>\n",
       "      <th>sqft_basement</th>\n",
       "      <th>yr_built</th>\n",
       "      <th>yr_renovated</th>\n",
       "      <th>zipcode</th>\n",
       "      <th>lat</th>\n",
       "      <th>long</th>\n",
       "      <th>sqft_living15</th>\n",
       "      <th>sqft_lot15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7129300520</td>\n",
       "      <td>20141013T000000</td>\n",
       "      <td>221900.0</td>\n",
       "      <td>3</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1180</td>\n",
       "      <td>5650</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1180</td>\n",
       "      <td>0</td>\n",
       "      <td>1955</td>\n",
       "      <td>0</td>\n",
       "      <td>98178</td>\n",
       "      <td>47.5112</td>\n",
       "      <td>-122.257</td>\n",
       "      <td>1340</td>\n",
       "      <td>5650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6414100192</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>538000.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2570</td>\n",
       "      <td>7242</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>2170</td>\n",
       "      <td>400</td>\n",
       "      <td>1951</td>\n",
       "      <td>1991</td>\n",
       "      <td>98125</td>\n",
       "      <td>47.7210</td>\n",
       "      <td>-122.319</td>\n",
       "      <td>1690</td>\n",
       "      <td>7639</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5631500400</td>\n",
       "      <td>20150225T000000</td>\n",
       "      <td>180000.0</td>\n",
       "      <td>2</td>\n",
       "      <td>1.00</td>\n",
       "      <td>770</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>6</td>\n",
       "      <td>770</td>\n",
       "      <td>0</td>\n",
       "      <td>1933</td>\n",
       "      <td>0</td>\n",
       "      <td>98028</td>\n",
       "      <td>47.7379</td>\n",
       "      <td>-122.233</td>\n",
       "      <td>2720</td>\n",
       "      <td>8062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2487200875</td>\n",
       "      <td>20141209T000000</td>\n",
       "      <td>604000.0</td>\n",
       "      <td>4</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1960</td>\n",
       "      <td>5000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1050</td>\n",
       "      <td>910</td>\n",
       "      <td>1965</td>\n",
       "      <td>0</td>\n",
       "      <td>98136</td>\n",
       "      <td>47.5208</td>\n",
       "      <td>-122.393</td>\n",
       "      <td>1360</td>\n",
       "      <td>5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1954400510</td>\n",
       "      <td>20150218T000000</td>\n",
       "      <td>510000.0</td>\n",
       "      <td>3</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1680</td>\n",
       "      <td>8080</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>1680</td>\n",
       "      <td>0</td>\n",
       "      <td>1987</td>\n",
       "      <td>0</td>\n",
       "      <td>98074</td>\n",
       "      <td>47.6168</td>\n",
       "      <td>-122.045</td>\n",
       "      <td>1800</td>\n",
       "      <td>7503</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           id             date     price  bedrooms  bathrooms  sqft_living  \\\n",
       "0  7129300520  20141013T000000  221900.0         3       1.00         1180   \n",
       "1  6414100192  20141209T000000  538000.0         3       2.25         2570   \n",
       "2  5631500400  20150225T000000  180000.0         2       1.00          770   \n",
       "3  2487200875  20141209T000000  604000.0         4       3.00         1960   \n",
       "4  1954400510  20150218T000000  510000.0         3       2.00         1680   \n",
       "\n",
       "   sqft_lot  floors  waterfront  view  ...  grade  sqft_above  sqft_basement  \\\n",
       "0      5650     1.0           0     0  ...      7        1180              0   \n",
       "1      7242     2.0           0     0  ...      7        2170            400   \n",
       "2     10000     1.0           0     0  ...      6         770              0   \n",
       "3      5000     1.0           0     0  ...      7        1050            910   \n",
       "4      8080     1.0           0     0  ...      8        1680              0   \n",
       "\n",
       "   yr_built  yr_renovated  zipcode      lat     long  sqft_living15  \\\n",
       "0      1955             0    98178  47.5112 -122.257           1340   \n",
       "1      1951          1991    98125  47.7210 -122.319           1690   \n",
       "2      1933             0    98028  47.7379 -122.233           2720   \n",
       "3      1965             0    98136  47.5208 -122.393           1360   \n",
       "4      1987             0    98074  47.6168 -122.045           1800   \n",
       "\n",
       "   sqft_lot15  \n",
       "0        5650  \n",
       "1        7639  \n",
       "2        8062  \n",
       "3        5000  \n",
       "4        7503  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Feature Normalization**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = X.values\n",
    "y = Y.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "def featureNormalize(x_m):\n",
    "    mu = np.zeros((1,x_m.shape[1]))\n",
    "    sigma = np.zeros((1,x_m.shape[1]))\n",
    "    x_norm = x_m.astype(float)\n",
    "    \n",
    "    for i in range(0,len(mu)+1):\n",
    "        mu[:,i] = x_m[:,i].mean()\n",
    "        sigma[:,i] = x_m[:,i].std()\n",
    "        x_norm[:,i] = (x_m[:,i] - mu[:,i])/sigma[:,i]\n",
    "    return (x_norm, mu, sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Normalized**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_norm, mu, sigma = featureNormalize(x)\n",
    "x_norm = np.concatenate((np.ones(len(x_norm)).reshape(-1,1), x_norm), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeCost_m(x, y, theta):\n",
    "    m = len(y)\n",
    "    h_x = np.dot(x, theta)\n",
    "    j = np.sum(np.square(h_x - y))/(2*m)\n",
    "    return j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "price    2.132357e+11\n",
       "dtype: float64"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_init = np.zeros((19, 1))\n",
    "computeCost_m(x_norm, Y, theta_init)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='8'></a>\n",
    "## Manual - Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescentMulti(X, Y, theta, alpha, num_iters):\n",
    "    m = len(Y)\n",
    "    p = np.copy(X)\n",
    "    t = np.copy(theta)\n",
    "    j = []\n",
    "    print('Running Gradient Descent')\n",
    "    for i in range(0,num_iters+1):\n",
    "        cost = computeCost_m(p, Y, t)\n",
    "        j.append(cost)\n",
    "        h_x = np.dot(p, t)\n",
    "        err = h_x - Y\n",
    "        for f in range(theta.size):\n",
    "            t[f] = t[f] - alpha/m *(np.sum((np.dot(p[:,f].T, err))))\n",
    "    return j, t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running Gradient Descent\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-190-a9b84bc00e96>:4: RuntimeWarning: overflow encountered in square\n",
      "  j = np.sum(np.square(h_x - y))/(2*m)\n"
     ]
    },
    {
     "data": {
      "image/png": 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2ktRbdh2YyYGx2xbfbp2B0M+GfeT6gOEJLB/T0NDKCX+g77fHbK47/0heWPUyfX3w/KpXJvT6XrXzLjNZ8eyqbpfRUc65GZo25+nb9LP/3N1Yvvz5Cb+2v79v1C/SdQbCk8Db2p7vDiwdsXyPUZbXZs/BWSwvWTRnh2078ZZdNzg4mx2mNaudn3NuhibOuS51/tnp3cCRETEYETsA7wW+1VqYmU8AL0XEYWXoZOCuGuuRJI2itkDIzKeATwILgUXAgsx8OCLujIj5ZbWTgCsj4jFgFnBVXfVIkkZX63UImbkAWDBi7Ni2x4vZ8ESzJKlLvFJZkgQYCJKkwkCQJAE1n0Oo0TSo/qZ2sl7La3uVc24G59wMk5lz22umbWp539q1PXml7uHAfd0uQpJ61NuA+0cO9mogbAccTNXuohnNiCTptZtGdUHw94GXRy7s1UCQJG1hnlSWJAEGgiSpMBAkSYCBIEkqDARJEmAgSJIKA0GSBPRu64pJi4gTgQuB6cDnMvOaLpf0mkTEHOAB4LjMfDwijgKuAGYA/yMzLyzrzQNuAOYA3wXOysw1EbEPcAuwG5DASZm5svMzGZ+IuAj4zfL0jsw8rwFzvhR4H9UtZ7+YmVdM9Tm3RMSfArtm5ilTfc4RsZCq1tVl6ExgNh2cc6P2ECLidcBlVK0v5gFnRMQvdrWo1yAiDqW6/HxueT4DuBF4N/DvgIMj4piy+i3AOZk5l+r+1aeX8c8Dn8/MNwI/AD7VuRlMTPlAeCdwINW/30ER8dtM7Tn/R+AI4M3AfODDEXEAU3jOLRFxJPCfy+Op/rvdR/Xf8QGZOS8z5wFL6PCcGxUIwFHAvZn5bGauAm6l+ubVq04Hzmb9vagPAX6SmT/LzDVUvzS/ERH7AjMy86Gy3s1lfDrwH6h+DuvGO1T7ZCwDPp6Zr2TmauAfqP4jmrJzzsz/DbyjzG03qr36nZjCcwaIiF2ovrx9pgxN9d/tKP//7YhYHBHn0IU5Ny0Q9qT6UGlZBuzVpVpes8w8LTPbm/xtbn6bG98VeK78srWPb5Uy88et/wgiYj+qQ0fDTOE5A2Tm6oi4BHgUuIcp/u9cXEd1C94V5flUn/POVP+27wGOBM4C9qHDc25aIPRTHYdt6aP6QJkqNje/8Y5DD/w8ImJ/4DvAJ4Cf0oA5Z+ZFwCCwN9Ve0ZSdc0ScBvxLZt7TNjylf7cz88HMfH9m/mtm/hz4InApHZ5z0wLhSapOfy27s/5wy1SwufltbvwZYMeIaPVG34Ot/OcREYdRfZM6PzO/xBSfc0S8sZxAJDNfAG4H3s4UnjPwW8A7I2IR1Yfi8cBpTOE5R8Th5ZxJSx/wOB2ec9MC4W7gyIgYjIgdgPcC3+pyTVvS94CIiF8ovxQnAndl5hPAS+XDFODkMr6a6r4Sv1XG3w/c1emixysi9ga+AZyYmV8tw1N6zsAbgOsjYruI2JbqBON1TOE5Z+bRmfmmcmL1D4D/BRzDFJ4z1Xmhz0bE9hExm+pk+gV0eM6NCoTMfIrquORCYBGwIDMf7mpRW1BmvgScAtxGdbz5MdafYDoJuDIiHgNmAVeV8Q9R/bXVo1Q3zbiwkzVP0LnA9sAVEbGofIM8hSk858y8E7gDeAT4e+CBEoanMEXnvClT/Xc7M/+aDf+db8zMB+nwnL0fgiQJaNgegiRp8wwESRJgIEiSCgNBkgQYCJKkwkBQz4iI10fE2oj44IjxcyPi5prec++I+FH5M9e3jlh2cURcXR4fHBHXbuH3Pi0iPlQenxUR52/J7UsjNa79tXreMHB5RNyfmdmB93sH8HRmHjXGevuz5XvlHA78CCAzt2jYSJtiIKjXvAhcDiyIiLdm5ivtCyNiR+AaqvbYa6mu1LygreHXJkXEGcBHgFeB/wucA7wO+EOqdgALM/Mdm3nt3lQtFnaMiJsy89SI+FWqi4K2BV4Azs3MByPiYuCtVA3KFgMfp7ry+N9QtSB4gqpp32FULRuOjogXqfoY7ZqZ55ReTlcDA2WOl2fmlyPi7VQdQn8KvInqnh9nZubfRcThVH31p5XX/FFm3jbaz0TN4yEj9aLLgJWsb43c7ipgCPglqvsHHEB1hfNmRcQRwHlUbaYPABZQtcj4W6rWCfdtLgwAMvNf2tY7tXRi/QxwbGYeCJwB3B4RM8tL9gUOzMzfAU4AHszMt1K1qXgBODkzv07VsuHK9ps4RcQ2ZfzPM/PNVC0dPtN2OOtQqoA4ELip7Wd0CXBFZh4EfIDqHgvSBgwE9ZzMHAZ+Bzg1Io4esfgY4OrMXJuZLwPXlrHRvIvqblTLy/Zvpto7eP0kSzyaqrHYPaW9xl9SHer6hbL8odYeS2b+GfBARPwe1c1N3kTVimBz5gLbZ+bt5fVLqVobvKssfyIzF5XHPwR2KY+/BlwTEX8JHETVJ0fagIGgnlS+lZ8JfImqD3zLyBbA/VSHTkbTOozSrm8crxtte/e07nxVmrT9e8r5AKq9GwAi4r9RHW5aDvwF8O3y3hOptX2OL7aNr21tKzOvo9pr+g7wK8CSiNh+wjPTlGYgqGdl5q1U5wg+1jb8N8A5EdEXEdtRHa75zhib+hZwQkQMAkTEqVSHnf5pAuWsYf2H8j1U7ZvfWLZ3LNXtEGds4nW/QnVv769QtS8+mupDf+Q2Wx4DVkfEr5dt70nVtXfUOUbEA1SHqW6m+pnsRHXOQlrHQFCv+wjVidj257sB/6f8L6nOORARl0Z1w/oNZOZ3gCuBeyPix1Sth48rh6bG6yHgDRFxe2Y+SvWh+9WIWAx8Gjh+Mzc7vxT404hYQnVu4H7WH1q6CzgrIn6/rdbVwK8BHy2vuRu4NDMXjlHfecClEfEI1bmRSzLz8QnMTw1gt1NJEuAegiSpMBAkSYCBIEkqDARJEmAgSJIKA0GSBBgIkqTCQJAkAfD/Ae9Lpg0hrn3VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# theta_init = np.zeros((3, 1))\n",
    "alpha = 0.01\n",
    "num_iters = 5000\n",
    "theta_init = np.zeros((19, 1))\n",
    "cost, theta_final = gradientDescentMulti(x_norm, Y, theta_init, alpha, num_iters)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(cost)\n",
    "plt.xlabel('No. of Iterations')\n",
    "plt.ylabel('Cost')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan],\n",
       "       [nan]])"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [0.]])"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_init"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='9'></a>\n",
    "## Multi-variable Regression with Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "mlr = LinearRegression()\n",
    "sc_x = StandardScaler()\n",
    "X_new = sc_x.fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [],
   "source": [
    "mlr.fit(X_new, Y)\n",
    "y_hat = mlr.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6997471890109157"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr.score(X_new, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([540088.14176653])"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-33264.32545782,  31687.07437464,  81812.50710964,\n",
       "          5326.46629074,   3612.19920732,  50434.93843527,\n",
       "         40514.99473763,  17169.88047514, 112712.65585307,\n",
       "         76305.51997634,  27005.67955588, -76963.1122356 ,\n",
       "          7958.11945582, -31161.66927787,  83517.09842808,\n",
       "        -30239.34618464,  14859.89955603, -10447.48009171]])"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='10'></a>\n",
    "## Solving with Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_neq = np.concatenate((np.ones(len(x)).reshape(-1,1), x), axis=1)\n",
    "a = np.linalg.inv(np.dot(x_neq.T, x_neq))\n",
    "b = np.dot(x_neq.T, y)\n",
    "theta_neq = np.dot(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-8.87182378e+06],\n",
       "       [ 5.04750191e+06],\n",
       "       [-7.81287005e+05],\n",
       "       [ 9.94709813e+03],\n",
       "       [-1.80933539e-01],\n",
       "       [ 4.03583721e+05],\n",
       "       [-2.74465540e+06],\n",
       "       [ 3.26413834e+05],\n",
       "       [ 3.92312640e+04],\n",
       "       [-3.64827988e+04],\n",
       "       [-9.86376221e+03],\n",
       "       [-9.66659353e+03],\n",
       "       [-2.62022321e+03],\n",
       "       [ 1.98125837e+01],\n",
       "       [-5.82419866e+02],\n",
       "       [ 6.02748227e+05],\n",
       "       [-2.14729829e+05],\n",
       "       [ 2.16814005e+01],\n",
       "       [-3.82641849e-01]])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_neq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='11'></a>\n",
    "### Scipy implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(X.values.reshape(-1,1), \n",
    "                                                               Y.values)\n",
    "\n",
    "print('theta[0] = ', intercept)\n",
    "print('theta[1] = ', slope)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='12'></a>\n",
    "### Statsmodel implementation\n",
    "#### Statsmodel WITHOUT Feature Scaling/Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 558,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>price</td>      <th>  R-squared:         </th>  <td>   0.700</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.700</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>   2960.</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 22 Aug 2018</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:31:12</td>     <th>  Log-Likelihood:    </th> <td>-2.9460e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 21613</td>      <th>  AIC:               </th>  <td>5.892e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 21595</td>      <th>  BIC:               </th>  <td>5.894e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    17</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>  6.69e+06</td> <td> 2.93e+06</td> <td>    2.282</td> <td> 0.022</td> <td> 9.44e+05</td> <td> 1.24e+07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>-3.577e+04</td> <td> 1891.843</td> <td>  -18.906</td> <td> 0.000</td> <td>-3.95e+04</td> <td>-3.21e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td> 4.114e+04</td> <td> 3253.678</td> <td>   12.645</td> <td> 0.000</td> <td> 3.48e+04</td> <td> 4.75e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td>  110.4380</td> <td>    2.270</td> <td>   48.661</td> <td> 0.000</td> <td>  105.990</td> <td>  114.886</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td>    0.1286</td> <td>    0.048</td> <td>    2.683</td> <td> 0.007</td> <td>    0.035</td> <td>    0.223</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td> 6689.5501</td> <td> 3595.859</td> <td>    1.860</td> <td> 0.063</td> <td> -358.599</td> <td> 1.37e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td>  5.83e+05</td> <td> 1.74e+04</td> <td>   33.580</td> <td> 0.000</td> <td> 5.49e+05</td> <td> 6.17e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td> 5.287e+04</td> <td> 2140.055</td> <td>   24.705</td> <td> 0.000</td> <td> 4.87e+04</td> <td> 5.71e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td> 2.639e+04</td> <td> 2351.461</td> <td>   11.221</td> <td> 0.000</td> <td> 2.18e+04</td> <td>  3.1e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td> 9.589e+04</td> <td> 2152.789</td> <td>   44.542</td> <td> 0.000</td> <td> 9.17e+04</td> <td>    1e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td>   70.7901</td> <td>    2.253</td> <td>   31.418</td> <td> 0.000</td> <td>   66.374</td> <td>   75.207</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td>   39.6625</td> <td>    2.647</td> <td>   14.985</td> <td> 0.000</td> <td>   34.475</td> <td>   44.850</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>-2620.2232</td> <td>   72.659</td> <td>  -36.062</td> <td> 0.000</td> <td>-2762.640</td> <td>-2477.806</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td>   19.8126</td> <td>    3.656</td> <td>    5.420</td> <td> 0.000</td> <td>   12.647</td> <td>   26.978</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th>   <td> -582.4199</td> <td>   32.986</td> <td>  -17.657</td> <td> 0.000</td> <td> -647.074</td> <td> -517.765</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x15</th>   <td> 6.027e+05</td> <td> 1.07e+04</td> <td>   56.149</td> <td> 0.000</td> <td> 5.82e+05</td> <td> 6.24e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x16</th>   <td>-2.147e+05</td> <td> 1.31e+04</td> <td>  -16.349</td> <td> 0.000</td> <td> -2.4e+05</td> <td>-1.89e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x17</th>   <td>   21.6814</td> <td>    3.448</td> <td>    6.289</td> <td> 0.000</td> <td>   14.924</td> <td>   28.439</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x18</th>   <td>   -0.3826</td> <td>    0.073</td> <td>   -5.222</td> <td> 0.000</td> <td>   -0.526</td> <td>   -0.239</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>18384.201</td> <th>  Durbin-Watson:     </th>  <td>   1.990</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>1868224.491</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 3.566</td>   <th>  Prob(JB):          </th>  <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>47.985</td>   <th>  Cond. No.          </th>  <td>2.52e+17</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 3.45e-21. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.700\n",
       "Model:                            OLS   Adj. R-squared:                  0.700\n",
       "Method:                 Least Squares   F-statistic:                     2960.\n",
       "Date:                Wed, 22 Aug 2018   Prob (F-statistic):               0.00\n",
       "Time:                        23:31:12   Log-Likelihood:            -2.9460e+05\n",
       "No. Observations:               21613   AIC:                         5.892e+05\n",
       "Df Residuals:                   21595   BIC:                         5.894e+05\n",
       "Df Model:                          17                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        6.69e+06   2.93e+06      2.282      0.022    9.44e+05    1.24e+07\n",
       "x1         -3.577e+04   1891.843    -18.906      0.000   -3.95e+04   -3.21e+04\n",
       "x2          4.114e+04   3253.678     12.645      0.000    3.48e+04    4.75e+04\n",
       "x3           110.4380      2.270     48.661      0.000     105.990     114.886\n",
       "x4             0.1286      0.048      2.683      0.007       0.035       0.223\n",
       "x5          6689.5501   3595.859      1.860      0.063    -358.599    1.37e+04\n",
       "x6           5.83e+05   1.74e+04     33.580      0.000    5.49e+05    6.17e+05\n",
       "x7          5.287e+04   2140.055     24.705      0.000    4.87e+04    5.71e+04\n",
       "x8          2.639e+04   2351.461     11.221      0.000    2.18e+04     3.1e+04\n",
       "x9          9.589e+04   2152.789     44.542      0.000    9.17e+04       1e+05\n",
       "x10           70.7901      2.253     31.418      0.000      66.374      75.207\n",
       "x11           39.6625      2.647     14.985      0.000      34.475      44.850\n",
       "x12        -2620.2232     72.659    -36.062      0.000   -2762.640   -2477.806\n",
       "x13           19.8126      3.656      5.420      0.000      12.647      26.978\n",
       "x14         -582.4199     32.986    -17.657      0.000    -647.074    -517.765\n",
       "x15         6.027e+05   1.07e+04     56.149      0.000    5.82e+05    6.24e+05\n",
       "x16        -2.147e+05   1.31e+04    -16.349      0.000    -2.4e+05   -1.89e+05\n",
       "x17           21.6814      3.448      6.289      0.000      14.924      28.439\n",
       "x18           -0.3826      0.073     -5.222      0.000      -0.526      -0.239\n",
       "==============================================================================\n",
       "Omnibus:                    18384.201   Durbin-Watson:                   1.990\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1868224.491\n",
       "Skew:                           3.566   Prob(JB):                         0.00\n",
       "Kurtosis:                      47.985   Cond. No.                     2.52e+17\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 3.45e-21. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 558,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "#without feature scaling\n",
    "results = sm.OLS(Y, x_neq).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 559,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-52201035.94329346"
      ]
     },
     "execution_count": 559,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tt = results.params\n",
    "\n",
    "#predict house for 1650 and 3 bedroom\n",
    "tt[0] + (tt[1] * 1650) + (tt[2] * 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Statsmodel using Feature Scaling/Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 560,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>price</td>      <th>  R-squared:         </th>  <td>   0.700</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.700</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>   2960.</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 22 Aug 2018</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:31:33</td>     <th>  Log-Likelihood:    </th> <td>-2.9460e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 21613</td>      <th>  AIC:               </th>  <td>5.892e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 21595</td>      <th>  BIC:               </th>  <td>5.894e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    17</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td> 5.401e+05</td> <td> 1368.905</td> <td>  394.540</td> <td> 0.000</td> <td> 5.37e+05</td> <td> 5.43e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>-3.326e+04</td> <td> 1759.490</td> <td>  -18.906</td> <td> 0.000</td> <td>-3.67e+04</td> <td>-2.98e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>    <td> 3.169e+04</td> <td> 2505.805</td> <td>   12.645</td> <td> 0.000</td> <td> 2.68e+04</td> <td> 3.66e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>    <td> 8.181e+04</td> <td> 1588.340</td> <td>   51.508</td> <td> 0.000</td> <td> 7.87e+04</td> <td> 8.49e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>    <td> 5326.4663</td> <td> 1984.923</td> <td>    2.683</td> <td> 0.007</td> <td> 1435.870</td> <td> 9217.062</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>    <td> 3612.1992</td> <td> 1941.679</td> <td>    1.860</td> <td> 0.063</td> <td> -193.635</td> <td> 7418.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>    <td> 5.043e+04</td> <td> 1501.912</td> <td>   33.580</td> <td> 0.000</td> <td> 4.75e+04</td> <td> 5.34e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>    <td> 4.051e+04</td> <td> 1639.923</td> <td>   24.705</td> <td> 0.000</td> <td> 3.73e+04</td> <td> 4.37e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>    <td> 1.717e+04</td> <td> 1530.162</td> <td>   11.221</td> <td> 0.000</td> <td> 1.42e+04</td> <td> 2.02e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>    <td> 1.127e+05</td> <td> 2530.456</td> <td>   44.542</td> <td> 0.000</td> <td> 1.08e+05</td> <td> 1.18e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th>   <td> 7.631e+04</td> <td> 1696.376</td> <td>   44.981</td> <td> 0.000</td> <td>  7.3e+04</td> <td> 7.96e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th>   <td> 2.701e+04</td> <td> 1559.700</td> <td>   17.315</td> <td> 0.000</td> <td> 2.39e+04</td> <td> 3.01e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th>   <td>-7.696e+04</td> <td> 2134.197</td> <td>  -36.062</td> <td> 0.000</td> <td>-8.11e+04</td> <td>-7.28e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th>   <td> 7958.1195</td> <td> 1468.341</td> <td>    5.420</td> <td> 0.000</td> <td> 5080.062</td> <td> 1.08e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th>   <td>-3.116e+04</td> <td> 1764.866</td> <td>  -17.657</td> <td> 0.000</td> <td>-3.46e+04</td> <td>-2.77e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x15</th>   <td> 8.352e+04</td> <td> 1487.409</td> <td>   56.149</td> <td> 0.000</td> <td> 8.06e+04</td> <td> 8.64e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x16</th>   <td>-3.024e+04</td> <td> 1849.583</td> <td>  -16.349</td> <td> 0.000</td> <td>-3.39e+04</td> <td>-2.66e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x17</th>   <td> 1.486e+04</td> <td> 2362.983</td> <td>    6.289</td> <td> 0.000</td> <td> 1.02e+04</td> <td> 1.95e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x18</th>   <td>-1.045e+04</td> <td> 2000.508</td> <td>   -5.222</td> <td> 0.000</td> <td>-1.44e+04</td> <td>-6526.336</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>18384.201</td> <th>  Durbin-Watson:     </th>  <td>   1.990</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>1868224.491</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 3.566</td>   <th>  Prob(JB):          </th>  <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>47.985</td>   <th>  Cond. No.          </th>  <td>8.31e+15</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 1.63e-27. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.700\n",
       "Model:                            OLS   Adj. R-squared:                  0.700\n",
       "Method:                 Least Squares   F-statistic:                     2960.\n",
       "Date:                Wed, 22 Aug 2018   Prob (F-statistic):               0.00\n",
       "Time:                        23:31:33   Log-Likelihood:            -2.9460e+05\n",
       "No. Observations:               21613   AIC:                         5.892e+05\n",
       "Df Residuals:                   21595   BIC:                         5.894e+05\n",
       "Df Model:                          17                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       5.401e+05   1368.905    394.540      0.000    5.37e+05    5.43e+05\n",
       "x1         -3.326e+04   1759.490    -18.906      0.000   -3.67e+04   -2.98e+04\n",
       "x2          3.169e+04   2505.805     12.645      0.000    2.68e+04    3.66e+04\n",
       "x3          8.181e+04   1588.340     51.508      0.000    7.87e+04    8.49e+04\n",
       "x4          5326.4663   1984.923      2.683      0.007    1435.870    9217.062\n",
       "x5          3612.1992   1941.679      1.860      0.063    -193.635    7418.034\n",
       "x6          5.043e+04   1501.912     33.580      0.000    4.75e+04    5.34e+04\n",
       "x7          4.051e+04   1639.923     24.705      0.000    3.73e+04    4.37e+04\n",
       "x8          1.717e+04   1530.162     11.221      0.000    1.42e+04    2.02e+04\n",
       "x9          1.127e+05   2530.456     44.542      0.000    1.08e+05    1.18e+05\n",
       "x10         7.631e+04   1696.376     44.981      0.000     7.3e+04    7.96e+04\n",
       "x11         2.701e+04   1559.700     17.315      0.000    2.39e+04    3.01e+04\n",
       "x12        -7.696e+04   2134.197    -36.062      0.000   -8.11e+04   -7.28e+04\n",
       "x13         7958.1195   1468.341      5.420      0.000    5080.062    1.08e+04\n",
       "x14        -3.116e+04   1764.866    -17.657      0.000   -3.46e+04   -2.77e+04\n",
       "x15         8.352e+04   1487.409     56.149      0.000    8.06e+04    8.64e+04\n",
       "x16        -3.024e+04   1849.583    -16.349      0.000   -3.39e+04   -2.66e+04\n",
       "x17         1.486e+04   2362.983      6.289      0.000    1.02e+04    1.95e+04\n",
       "x18        -1.045e+04   2000.508     -5.222      0.000   -1.44e+04   -6526.336\n",
       "==============================================================================\n",
       "Omnibus:                    18384.201   Durbin-Watson:                   1.990\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1868224.491\n",
       "Skew:                           3.566   Prob(JB):                         0.00\n",
       "Kurtosis:                      47.985   Cond. No.                     8.31e+15\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 1.63e-27. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 560,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "#with feature scaling\n",
    "d = sm.add_constant(X_new)\n",
    "results = sm.OLS(Y, d).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# tt_fs = results.params\n",
    "\n",
    "# #predict house for 1650 and 3 bedroom\n",
    "# house = sc_x.transform(np.array([1650,3]).reshape(1,-1))\n",
    "# tt_fs[0] + (tt_fs[1] * house[0][0]) + (tt_fs[2] * house[0][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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