Python Making a basic scatter plot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "21392464",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b752242b",
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT   GPA\n",
       "0  1714  2.40\n",
       "1  1664  2.52\n",
       "2  1760  2.54\n",
       "3  1685  2.74\n",
       "4  1693  2.83"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('1.01. Simple linear regression.csv') \n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c5a4dc5f",
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>84.000000</td>\n",
       "      <td>84.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1845.273810</td>\n",
       "      <td>3.330238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>104.530661</td>\n",
       "      <td>0.271617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1634.000000</td>\n",
       "      <td>2.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1772.000000</td>\n",
       "      <td>3.190000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1846.000000</td>\n",
       "      <td>3.380000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1934.000000</td>\n",
       "      <td>3.502500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2050.000000</td>\n",
       "      <td>3.810000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SAT        GPA\n",
       "count    84.000000  84.000000\n",
       "mean   1845.273810   3.330238\n",
       "std     104.530661   0.271617\n",
       "min    1634.000000   2.400000\n",
       "25%    1772.000000   3.190000\n",
       "50%    1846.000000   3.380000\n",
       "75%    1934.000000   3.502500\n",
       "max    2050.000000   3.810000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "01ac5652",
   "metadata": {},
   "outputs": [],
   "source": [
    "y= data ['GPA']\n",
    "x1= data['SAT']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "49b63f24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "plt.xlabel('SAT',fontsize=20)\n",
    "plt.ylabel('GPA',fontsize=20)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "14dba40b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>GPA</td>       <th>  R-squared:         </th> <td>   0.406</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   56.05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 23 Dec 2022</td> <th>  Prob (F-statistic):</th> <td>7.20e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>00:16:50</td>     <th>  Log-Likelihood:    </th> <td>  12.672</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    84</td>      <th>  AIC:               </th> <td>  -21.34</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    82</td>      <th>  BIC:               </th> <td>  -16.48</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>    0.2750</td> <td>    0.409</td> <td>    0.673</td> <td> 0.503</td> <td>   -0.538</td> <td>    1.088</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SAT</th>   <td>    0.0017</td> <td>    0.000</td> <td>    7.487</td> <td> 0.000</td> <td>    0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>12.839</td> <th>  Durbin-Watson:     </th> <td>   0.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.002</td> <th>  Jarque-Bera (JB):  </th> <td>  16.155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.722</td> <th>  Prob(JB):          </th> <td>0.000310</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.590</td> <th>  Cond. No.          </th> <td>3.29e+04</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, 3.29e+04. 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:                    GPA   R-squared:                       0.406\n",
       "Model:                            OLS   Adj. R-squared:                  0.399\n",
       "Method:                 Least Squares   F-statistic:                     56.05\n",
       "Date:                Fri, 23 Dec 2022   Prob (F-statistic):           7.20e-11\n",
       "Time:                        00:16:50   Log-Likelihood:                 12.672\n",
       "No. Observations:                  84   AIC:                            -21.34\n",
       "Df Residuals:                      82   BIC:                            -16.48\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.2750      0.409      0.673      0.503      -0.538       1.088\n",
       "SAT            0.0017      0.000      7.487      0.000       0.001       0.002\n",
       "==============================================================================\n",
       "Omnibus:                       12.839   Durbin-Watson:                   0.950\n",
       "Prob(Omnibus):                  0.002   Jarque-Bera (JB):               16.155\n",
       "Skew:                          -0.722   Prob(JB):                     0.000310\n",
       "Kurtosis:                       4.590   Cond. No.                     3.29e+04\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, 3.29e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x1)\n",
    "results = sm.OLS(y,x).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d46e9732",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "yhat = 0.0017*x1+0.275\n",
    "fig=plt.plot(x1,yhat,lw=4,c='orange',label='regression line')\n",
    "plt.xlabel('SAT',fontsize = 20)\n",
    "plt.ylabel('GPA',fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "372ea0b6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}