2 statsmodels - Catagorical data into Continous with prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dummy variables or how to deal with categorical predictors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "# We can override the default matplotlib styles with those of Seaborn\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the data from a .csv in the same folder. Since we will do some preprocessing, the variable is not called 'data' just yet!\n",
    "raw_data = pd.read_csv('1.03. Dummies.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "      <th>Attendance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT   GPA Attendance\n",
       "0  1714  2.40         No\n",
       "1  1664  2.52         No\n",
       "2  1760  2.54         No\n",
       "3  1685  2.74         No\n",
       "4  1693  2.83         No"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's check what's inside this data frame\n",
    "raw_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Map the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "      <th>Attendance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1670</td>\n",
       "      <td>2.91</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1764</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1764</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1792</td>\n",
       "      <td>3.01</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1850</td>\n",
       "      <td>3.01</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1735</td>\n",
       "      <td>3.02</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1775</td>\n",
       "      <td>3.07</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1735</td>\n",
       "      <td>3.08</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1712</td>\n",
       "      <td>3.08</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1773</td>\n",
       "      <td>3.12</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1872</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1755</td>\n",
       "      <td>3.17</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1674</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1842</td>\n",
       "      <td>3.17</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1786</td>\n",
       "      <td>3.19</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1761</td>\n",
       "      <td>3.19</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1722</td>\n",
       "      <td>3.19</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1663</td>\n",
       "      <td>3.20</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1687</td>\n",
       "      <td>3.21</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1974</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>1826</td>\n",
       "      <td>3.28</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>1787</td>\n",
       "      <td>3.28</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>1821</td>\n",
       "      <td>3.28</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2020</td>\n",
       "      <td>3.28</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>1794</td>\n",
       "      <td>3.28</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>1879</td>\n",
       "      <td>3.44</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>1887</td>\n",
       "      <td>3.47</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>1730</td>\n",
       "      <td>3.47</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>1953</td>\n",
       "      <td>3.47</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>1781</td>\n",
       "      <td>3.47</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>1891</td>\n",
       "      <td>3.48</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>1964</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>1808</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>1893</td>\n",
       "      <td>3.50</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>2041</td>\n",
       "      <td>3.51</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>1893</td>\n",
       "      <td>3.51</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>1832</td>\n",
       "      <td>3.52</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>1850</td>\n",
       "      <td>3.52</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>1934</td>\n",
       "      <td>3.54</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>1861</td>\n",
       "      <td>3.58</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>1931</td>\n",
       "      <td>3.58</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>1933</td>\n",
       "      <td>3.59</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>1778</td>\n",
       "      <td>3.59</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>1975</td>\n",
       "      <td>3.60</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>1934</td>\n",
       "      <td>3.60</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>2021</td>\n",
       "      <td>3.61</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>2015</td>\n",
       "      <td>3.62</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>1997</td>\n",
       "      <td>3.64</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>2020</td>\n",
       "      <td>3.65</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>1843</td>\n",
       "      <td>3.71</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>1936</td>\n",
       "      <td>3.71</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>1810</td>\n",
       "      <td>3.71</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>1987</td>\n",
       "      <td>3.73</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>1962</td>\n",
       "      <td>3.76</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>2050</td>\n",
       "      <td>3.81</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>84 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT   GPA  Attendance\n",
       "0   1714  2.40           0\n",
       "1   1664  2.52           0\n",
       "2   1760  2.54           0\n",
       "3   1685  2.74           0\n",
       "4   1693  2.83           0\n",
       "5   1670  2.91           0\n",
       "6   1764  3.00           0\n",
       "7   1764  3.00           0\n",
       "8   1792  3.01           0\n",
       "9   1850  3.01           0\n",
       "10  1735  3.02           0\n",
       "11  1775  3.07           0\n",
       "12  1735  3.08           0\n",
       "13  1712  3.08           0\n",
       "14  1773  3.12           0\n",
       "15  1872  3.17           1\n",
       "16  1755  3.17           0\n",
       "17  1674  3.17           1\n",
       "18  1842  3.17           0\n",
       "19  1786  3.19           1\n",
       "20  1761  3.19           0\n",
       "21  1722  3.19           0\n",
       "22  1663  3.20           0\n",
       "23  1687  3.21           0\n",
       "24  1974  3.24           0\n",
       "25  1826  3.28           0\n",
       "26  1787  3.28           0\n",
       "27  1821  3.28           0\n",
       "28  2020  3.28           0\n",
       "29  1794  3.28           0\n",
       "..   ...   ...         ...\n",
       "54  1879  3.44           1\n",
       "55  1887  3.47           1\n",
       "56  1730  3.47           1\n",
       "57  1953  3.47           0\n",
       "58  1781  3.47           1\n",
       "59  1891  3.48           1\n",
       "60  1964  3.49           0\n",
       "61  1808  3.49           0\n",
       "62  1893  3.50           1\n",
       "63  2041  3.51           0\n",
       "64  1893  3.51           1\n",
       "65  1832  3.52           1\n",
       "66  1850  3.52           1\n",
       "67  1934  3.54           1\n",
       "68  1861  3.58           1\n",
       "69  1931  3.58           1\n",
       "70  1933  3.59           1\n",
       "71  1778  3.59           1\n",
       "72  1975  3.60           1\n",
       "73  1934  3.60           1\n",
       "74  2021  3.61           1\n",
       "75  2015  3.62           1\n",
       "76  1997  3.64           1\n",
       "77  2020  3.65           0\n",
       "78  1843  3.71           1\n",
       "79  1936  3.71           1\n",
       "80  1810  3.71           1\n",
       "81  1987  3.73           0\n",
       "82  1962  3.76           1\n",
       "83  2050  3.81           1\n",
       "\n",
       "[84 rows x 3 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Map all 'No' entries with 0, and all 'Yes' entries with 1. Put that in a new variable called 'data'\n",
    "# Note data is a copy of raw_data, because of how pointers in Python work\n",
    "data = raw_data.copy()\n",
    "data['Attendance'] = data['Attendance'].map({'Yes': 1, 'No': 0})\n",
    "\n",
    "# Let's see what's inside\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# This method gives us very nice descriptive statistics.\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Following the regression equation, our dependent variable (y) is the GPA\n",
    "y = data ['GPA']\n",
    "# Similarly, our independent variable (x) is the SAT score\n",
    "x1 = data [['SAT','Attendance']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\abc\\Anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    },
    {
     "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>   0.565</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.555</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   52.70</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 10 Apr 2020</td> <th>  Prob (F-statistic):</th> <td>2.19e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>04:54:26</td>     <th>  Log-Likelihood:    </th> <td>  25.798</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    84</td>      <th>  AIC:               </th> <td>  -45.60</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    81</td>      <th>  BIC:               </th> <td>  -38.30</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</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>    0.6439</td> <td>    0.358</td> <td>    1.797</td> <td> 0.076</td> <td>   -0.069</td> <td>    1.357</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SAT</th>        <td>    0.0014</td> <td>    0.000</td> <td>    7.141</td> <td> 0.000</td> <td>    0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Attendance</th> <td>    0.2226</td> <td>    0.041</td> <td>    5.451</td> <td> 0.000</td> <td>    0.141</td> <td>    0.304</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>19.560</td> <th>  Durbin-Watson:     </th> <td>   1.009</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  27.189</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.028</td> <th>  Prob(JB):          </th> <td>1.25e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.881</td> <th>  Cond. No.          </th> <td>3.35e+04</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 condition number is large, 3.35e+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:                       0.565\n",
       "Model:                            OLS   Adj. R-squared:                  0.555\n",
       "Method:                 Least Squares   F-statistic:                     52.70\n",
       "Date:                Fri, 10 Apr 2020   Prob (F-statistic):           2.19e-15\n",
       "Time:                        04:54:26   Log-Likelihood:                 25.798\n",
       "No. Observations:                  84   AIC:                            -45.60\n",
       "Df Residuals:                      81   BIC:                            -38.30\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.6439      0.358      1.797      0.076      -0.069       1.357\n",
       "SAT            0.0014      0.000      7.141      0.000       0.001       0.002\n",
       "Attendance     0.2226      0.041      5.451      0.000       0.141       0.304\n",
       "==============================================================================\n",
       "Omnibus:                       19.560   Durbin-Watson:                   1.009\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               27.189\n",
       "Skew:                          -1.028   Prob(JB):                     1.25e-06\n",
       "Kurtosis:                       4.881   Cond. No.                     3.35e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.35e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a constant. Esentially, we are adding a new column (equal in lenght to x), which consists only of 1s\n",
    "x = sm.add_constant(x1)\n",
    "# Fit the model, according to the OLS (ordinary least squares) method with a dependent variable y and an idependent x\n",
    "results = sm.OLS(y,x).fit()\n",
    "# Print a nice summary of the regression.\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the regression line(s) on the scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "# Create a scatter plot of SAT and GPA\n",
    "plt.scatter(data['SAT'],y)\n",
    "# Define the two regression equations, depending on whether they attended (yes), or didn't (no)\n",
    "yhat_no = 0.6439 + 0.0014*data['SAT']\n",
    "yhat_yes = 0.8665 + 0.0014*data['SAT']\n",
    "# Plot the two regression lines\n",
    "fig = plt.plot(data['SAT'],yhat_no, lw=2, c='#006837')\n",
    "fig = plt.plot(data['SAT'],yhat_yes, lw=2, c='#a50026')\n",
    "# Name your axes :)\n",
    "plt.xlabel('SAT', fontsize = 20)\n",
    "plt.ylabel('GPA', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the regression line(s) on the scatter plot and color the data points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "# In this code I want to colour the points depending on attendance\n",
    "# Note: This code would have been very easy in Seaborn\n",
    "\n",
    "# Create one scatter plot which contains all observations\n",
    "# Use the series 'Attendance' as color, and choose a colour map of your choice\n",
    "# The colour map we've chosen is completely arbitrary\n",
    "plt.scatter(data['SAT'],data['GPA'], c=data['Attendance'],cmap='RdYlGn_r')\n",
    "\n",
    "# Define the two regression equations (one with a dummy = 1, the other with dummy = 0)\n",
    "# We have those above already, but for the sake of consistency, we will also include them here\n",
    "yhat_no = 0.6439 + 0.0014*data['SAT']\n",
    "yhat_yes = 0.8665 + 0.0014*data['SAT']\n",
    "\n",
    "# Plot the two regression lines\n",
    "fig = plt.plot(data['SAT'],yhat_no, lw=2, c='#006837')\n",
    "fig = plt.plot(data['SAT'],yhat_yes, lw=2, c='#a50026')\n",
    "plt.xlabel('SAT', fontsize = 20)\n",
    "plt.ylabel('GPA', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Add the original regression line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "# Same as above, this time we are including the regression line WITHOUT the dummies.\n",
    "\n",
    "# In this code I want to color the points depending on attendance\n",
    "# Note: This code would have been very easy in Seaborn\n",
    "\n",
    "# Create one scatter plot which contains all observations\n",
    "# Use the series 'Attendance' as color, and choose a colour map of your choice\n",
    "# The colour map we've chosen is completely arbitrary\n",
    "plt.scatter(data['SAT'],data['GPA'], c=data['Attendance'],cmap='RdYlGn_r')\n",
    "\n",
    "# Define the two regression equations (one with a dummy = 1, the other with dummy = 0)\n",
    "# We have those above already, but for the sake of consistency, we will also include them here\n",
    "yhat_no = 0.6439 + 0.0014*data['SAT']\n",
    "yhat_yes = 0.8665 + 0.0014*data['SAT']\n",
    "# Original regression line\n",
    "yhat = 0.0017*data['SAT'] + 0.275\n",
    "\n",
    "# Plot the two regression lines\n",
    "fig = plt.plot(data['SAT'],yhat_no, lw=2, c='#006837', label ='regression line1')\n",
    "fig = plt.plot(data['SAT'],yhat_yes, lw=2, c='#a50026', label ='regression line2')\n",
    "# Plot the original regression line\n",
    "fig = plt.plot(data['SAT'],yhat, lw=3, c='#4C72B0', label ='regression line')\n",
    "\n",
    "plt.xlabel('SAT', fontsize = 20)\n",
    "plt.ylabel('GPA', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to make predictions based on the regressions we create"
   ]
  },
  {
   "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>const</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Attendance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1714</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1664</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1760</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1685</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   const   SAT  Attendance\n",
       "0    1.0  1714           0\n",
       "1    1.0  1664           0\n",
       "2    1.0  1760           0\n",
       "3    1.0  1685           0\n",
       "4    1.0  1693           0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see what's inside the independent variable. \n",
    "# The first column comes from the 'add_constant' method. It's only 1s, told ya! \n",
    "x.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>const</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Attendance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1700</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1670</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   const   SAT  Attendance\n",
       "0      1  1700           0\n",
       "1      1  1670           1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a new data frame, identical in organization to X.\n",
    "# The constant is always 1, while each of the lines corresponds to an observation (student)\n",
    "new_data = pd.DataFrame({'const': 1,'SAT': [1700, 1670], 'Attendance': [0, 1]})\n",
    "# By default, when you create a df (not load, but create), the columns are sorted alphabetically\n",
    "# So if we don't reorder them, they would be 'Attendance', 'const', 'SAT'\n",
    "# If you feed them in the wrong order, you will get wrong results!\n",
    "new_data = new_data[['const','SAT','Attendance']]\n",
    "new_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>const</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Attendance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bob</th>\n",
       "      <td>1</td>\n",
       "      <td>1700</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alice</th>\n",
       "      <td>1</td>\n",
       "      <td>1670</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       const   SAT  Attendance\n",
       "Bob        1  1700           0\n",
       "Alice      1  1670           1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I am renaming the indices for the purposes of this example.\n",
    "# That's by not really a good practice => I won't overwrite the variable.\n",
    "# If I want to use NumPy, sklearn, etc. methods on a df with renamed indices, they will simply be lost\n",
    "# and returned to 0,1,2,3, etc.\n",
    "new_data.rename(index={0: 'Bob',1:'Alice'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.023513\n",
       "1    3.204163\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the predict method on the regression with the new data as a single argument\n",
    "predictions = results.predict(new_data)\n",
    "# The result\n",
    "predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>const</th>\n",
       "      <th>SAT</th>\n",
       "      <th>Attendance</th>\n",
       "      <th>Predictions</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Bob</th>\n",
       "      <td>1</td>\n",
       "      <td>1700</td>\n",
       "      <td>0</td>\n",
       "      <td>3.023513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alice</th>\n",
       "      <td>1</td>\n",
       "      <td>1670</td>\n",
       "      <td>1</td>\n",
       "      <td>3.204163</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       const   SAT  Attendance  Predictions\n",
       "Bob        1  1700           0     3.023513\n",
       "Alice      1  1670           1     3.204163"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# If we want we can create a data frame, including everything\n",
    "predictionsdf = pd.DataFrame({'Predictions':predictions})\n",
    "# Join the two data frames\n",
    "joined = new_data.join(predictionsdf)\n",
    "# Rename the indices as before (not a good practice in general) \n",
    "joined.rename(index={0: 'Bob',1:'Alice'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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(data['SAT'],data['GPA'], c=data['Attendance'],cmap='RdYlGn_r')\n",
    "plt.scatter(joined['SAT'],joined['Predictions'])\n",
    "fig = plt.plot(data['SAT'],yhat, lw=3, c='#4C72B0', label ='regression line')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}