wkshop_1_min-REG_P1_Mario.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2q0LzcwlP9aj"
   },
   "source": [
    "# Regression - Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vwfq9iLzP9au"
   },
   "source": [
    "## Exercise 1: housing regression\n",
    "\n",
    "### 1.1\n",
    "\n",
    "Using the *housing.csv* file, make a regression model to predict house prices. Don't forget to add a constant (intercept) term. Note that statsmodels can take a `pd.DataFrame` as an input for `X`.\n",
    "\n",
    "Report the $R^2$ and coefficients on each feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "# exercise 1.1\n",
    "\n",
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "import statsmodels.formula.api as smf\n",
    "import pandas as pd\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn import linear_model\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>PRICE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>9.67</td>\n",
       "      <td>22.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>9.08</td>\n",
       "      <td>20.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>5.64</td>\n",
       "      <td>23.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6.48</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7.88</td>\n",
       "      <td>11.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        CRIM   ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "501  0.06263  0.0  11.93   0.0  0.573  6.593  69.1  2.4786  1.0  273.0   \n",
       "502  0.04527  0.0  11.93   0.0  0.573  6.120  76.7  2.2875  1.0  273.0   \n",
       "503  0.06076  0.0  11.93   0.0  0.573  6.976  91.0  2.1675  1.0  273.0   \n",
       "504  0.10959  0.0  11.93   0.0  0.573  6.794  89.3  2.3889  1.0  273.0   \n",
       "505  0.04741  0.0  11.93   0.0  0.573  6.030  80.8  2.5050  1.0  273.0   \n",
       "\n",
       "     PTRATIO  LSTAT  PRICE  \n",
       "501     21.0   9.67   22.4  \n",
       "502     21.0   9.08   20.6  \n",
       "503     21.0   5.64   23.9  \n",
       "504     21.0   6.48   22.0  \n",
       "505     21.0   7.88   11.9  "
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('../data/housing.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "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>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>1.266e+28</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 14 Feb 2023</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:11:58</td>     <th>  Log-Likelihood:    </th>  <td>  13612.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>-2.720e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   492</td>      <th>  BIC:               </th> <td>-2.714e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    13</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>  -95.7721</td> <td> 8.41e-13</td> <td>-1.14e+14</td> <td> 0.000</td> <td>  -95.772</td> <td>  -95.772</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM</th>     <td>-1.905e-15</td> <td> 3.55e-15</td> <td>   -0.536</td> <td> 0.592</td> <td>-8.88e-15</td> <td> 5.07e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZN</th>       <td>-7.286e-16</td> <td> 1.49e-15</td> <td>   -0.489</td> <td> 0.625</td> <td>-3.66e-15</td> <td>  2.2e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>INDUS</th>    <td>-1.679e-15</td> <td>  6.6e-15</td> <td>   -0.254</td> <td> 0.799</td> <td>-1.46e-14</td> <td> 1.13e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CHAS</th>     <td> 1.332e-15</td> <td> 9.34e-14</td> <td>    0.014</td> <td> 0.989</td> <td>-1.82e-13</td> <td> 1.85e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NOX</th>      <td>-5.149e-13</td> <td> 4.19e-13</td> <td>   -1.230</td> <td> 0.219</td> <td>-1.34e-12</td> <td> 3.08e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>       <td>    6.2748</td> <td>  3.5e-14</td> <td>  1.8e+14</td> <td> 0.000</td> <td>    6.275</td> <td>    6.275</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AGE</th>      <td> 8.639e-16</td> <td> 1.42e-15</td> <td>    0.610</td> <td> 0.542</td> <td>-1.92e-15</td> <td> 3.65e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>      <td>-3.442e-15</td> <td> 2.26e-14</td> <td>   -0.153</td> <td> 0.879</td> <td>-4.78e-14</td> <td> 4.09e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RAD</th>      <td>-3.789e-15</td> <td> 7.24e-15</td> <td>   -0.523</td> <td> 0.601</td> <td> -1.8e-14</td> <td> 1.04e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TAX</th>      <td>-7.125e-16</td> <td> 4.08e-16</td> <td>   -1.746</td> <td> 0.081</td> <td>-1.51e-15</td> <td> 8.94e-17</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PTRATIO</th>  <td> -9.09e-15</td> <td> 1.47e-14</td> <td>   -0.617</td> <td> 0.538</td> <td> -3.8e-14</td> <td> 1.99e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>    <td>-2.096e-15</td> <td> 5.99e-15</td> <td>   -0.350</td> <td> 0.727</td> <td>-1.39e-14</td> <td> 9.68e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>response</th> <td>   12.5496</td> <td> 5.62e-14</td> <td> 2.23e+14</td> <td> 0.000</td> <td>   12.550</td> <td>   12.550</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>error</th>    <td>    6.2748</td> <td> 3.88e-14</td> <td> 1.62e+14</td> <td> 0.000</td> <td>    6.275</td> <td>    6.275</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>147.149</td> <th>  Durbin-Watson:     </th> <td>   0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>  72.957</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.782</td>  <th>  Prob(JB):          </th> <td>1.44e-16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 1.993</td>  <th>  Cond. No.          </th> <td>4.84e+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 4.34e-28. 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:                       1.000\n",
       "Model:                            OLS   Adj. R-squared:                  1.000\n",
       "Method:                 Least Squares   F-statistic:                 1.266e+28\n",
       "Date:                Tue, 14 Feb 2023   Prob (F-statistic):               0.00\n",
       "Time:                        13:11:58   Log-Likelihood:                 13612.\n",
       "No. Observations:                 506   AIC:                        -2.720e+04\n",
       "Df Residuals:                     492   BIC:                        -2.714e+04\n",
       "Df Model:                          13                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -95.7721   8.41e-13  -1.14e+14      0.000     -95.772     -95.772\n",
       "CRIM       -1.905e-15   3.55e-15     -0.536      0.592   -8.88e-15    5.07e-15\n",
       "ZN         -7.286e-16   1.49e-15     -0.489      0.625   -3.66e-15     2.2e-15\n",
       "INDUS      -1.679e-15    6.6e-15     -0.254      0.799   -1.46e-14    1.13e-14\n",
       "CHAS        1.332e-15   9.34e-14      0.014      0.989   -1.82e-13    1.85e-13\n",
       "NOX        -5.149e-13   4.19e-13     -1.230      0.219   -1.34e-12    3.08e-13\n",
       "RM             6.2748    3.5e-14    1.8e+14      0.000       6.275       6.275\n",
       "AGE         8.639e-16   1.42e-15      0.610      0.542   -1.92e-15    3.65e-15\n",
       "DIS        -3.442e-15   2.26e-14     -0.153      0.879   -4.78e-14    4.09e-14\n",
       "RAD        -3.789e-15   7.24e-15     -0.523      0.601    -1.8e-14    1.04e-14\n",
       "TAX        -7.125e-16   4.08e-16     -1.746      0.081   -1.51e-15    8.94e-17\n",
       "PTRATIO     -9.09e-15   1.47e-14     -0.617      0.538    -3.8e-14    1.99e-14\n",
       "LSTAT      -2.096e-15   5.99e-15     -0.350      0.727   -1.39e-14    9.68e-15\n",
       "response      12.5496   5.62e-14   2.23e+14      0.000      12.550      12.550\n",
       "error          6.2748   3.88e-14   1.62e+14      0.000       6.275       6.275\n",
       "==============================================================================\n",
       "Omnibus:                      147.149   Durbin-Watson:                   0.008\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               72.957\n",
       "Skew:                           0.782   Prob(JB):                     1.44e-16\n",
       "Kurtosis:                       1.993   Cond. No.                     4.84e+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 4.34e-28. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#adding constant and showing in summary\n",
    "X = df.drop(['PRICE'], axis=1)\n",
    "y = df.PRICE\n",
    "\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "est = sm.OLS(y, X).fit()\n",
    "est.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = smf.ols('RM~PRICE',df).fit() #dependent and indepent variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept:  5.087638671836051\n",
      "coefficient:  0.05312235406004047\n"
     ]
    }
   ],
   "source": [
    "b0 = model.params[0] #intercept\n",
    "b1 = model.params[1] #coefficient\n",
    "print('intercept: ', b0)\n",
    "print('coefficient: ',b1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "501    6.277579\n",
       "502    6.181959\n",
       "503    6.357263\n",
       "504    6.256330\n",
       "505    5.719795\n",
       "dtype: float64"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = model.predict(df)  #regression \n",
    "#prediction.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>PRICE</th>\n",
       "      <th>response</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>9.67</td>\n",
       "      <td>22.4</td>\n",
       "      <td>6.277579</td>\n",
       "      <td>-0.315421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>9.08</td>\n",
       "      <td>20.6</td>\n",
       "      <td>6.181959</td>\n",
       "      <td>0.061959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>5.64</td>\n",
       "      <td>23.9</td>\n",
       "      <td>6.357263</td>\n",
       "      <td>-0.618737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6.48</td>\n",
       "      <td>22.0</td>\n",
       "      <td>6.256330</td>\n",
       "      <td>-0.537670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>7.88</td>\n",
       "      <td>11.9</td>\n",
       "      <td>5.719795</td>\n",
       "      <td>-0.310205</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     const     CRIM   ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "501    1.0  0.06263  0.0  11.93   0.0  0.573  6.593  69.1  2.4786  1.0  273.0   \n",
       "502    1.0  0.04527  0.0  11.93   0.0  0.573  6.120  76.7  2.2875  1.0  273.0   \n",
       "503    1.0  0.06076  0.0  11.93   0.0  0.573  6.976  91.0  2.1675  1.0  273.0   \n",
       "504    1.0  0.10959  0.0  11.93   0.0  0.573  6.794  89.3  2.3889  1.0  273.0   \n",
       "505    1.0  0.04741  0.0  11.93   0.0  0.573  6.030  80.8  2.5050  1.0  273.0   \n",
       "\n",
       "     PTRATIO  LSTAT  PRICE  response     error  \n",
       "501     21.0   9.67   22.4  6.277579 -0.315421  \n",
       "502     21.0   9.08   20.6  6.181959  0.061959  \n",
       "503     21.0   5.64   23.9  6.357263 -0.618737  \n",
       "504     21.0   6.48   22.0  6.256330 -0.537670  \n",
       "505     21.0   7.88   11.9  5.719795 -0.310205  "
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['response'] = model.predict(df)  #creating an response column\n",
    "df['error'] = df['response'] - df['RM']  #creating an error column\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#LINEAR REGRESSION GRAPH\n",
    "rm = df['RM']\n",
    "price = df['PRICE']\n",
    "response= df['response']\n",
    "\n",
    "plt.scatter(price,rm)\n",
    "plt.plot(price,response,color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "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>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>1.266e+28</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 14 Feb 2023</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:13:57</td>     <th>  Log-Likelihood:    </th>  <td>  13612.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>-2.720e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   492</td>      <th>  BIC:               </th> <td>-2.714e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    13</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>  -95.7721</td> <td> 8.41e-13</td> <td>-1.14e+14</td> <td> 0.000</td> <td>  -95.772</td> <td>  -95.772</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CRIM</th>     <td>-1.905e-15</td> <td> 3.55e-15</td> <td>   -0.536</td> <td> 0.592</td> <td>-8.88e-15</td> <td> 5.07e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ZN</th>       <td>-7.286e-16</td> <td> 1.49e-15</td> <td>   -0.489</td> <td> 0.625</td> <td>-3.66e-15</td> <td>  2.2e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>INDUS</th>    <td>-1.679e-15</td> <td>  6.6e-15</td> <td>   -0.254</td> <td> 0.799</td> <td>-1.46e-14</td> <td> 1.13e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CHAS</th>     <td> 1.332e-15</td> <td> 9.34e-14</td> <td>    0.014</td> <td> 0.989</td> <td>-1.82e-13</td> <td> 1.85e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>NOX</th>      <td>-5.149e-13</td> <td> 4.19e-13</td> <td>   -1.230</td> <td> 0.219</td> <td>-1.34e-12</td> <td> 3.08e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RM</th>       <td>    6.2748</td> <td>  3.5e-14</td> <td>  1.8e+14</td> <td> 0.000</td> <td>    6.275</td> <td>    6.275</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>AGE</th>      <td> 8.639e-16</td> <td> 1.42e-15</td> <td>    0.610</td> <td> 0.542</td> <td>-1.92e-15</td> <td> 3.65e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>      <td>-3.442e-15</td> <td> 2.26e-14</td> <td>   -0.153</td> <td> 0.879</td> <td>-4.78e-14</td> <td> 4.09e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RAD</th>      <td>-3.789e-15</td> <td> 7.24e-15</td> <td>   -0.523</td> <td> 0.601</td> <td> -1.8e-14</td> <td> 1.04e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TAX</th>      <td>-7.125e-16</td> <td> 4.08e-16</td> <td>   -1.746</td> <td> 0.081</td> <td>-1.51e-15</td> <td> 8.94e-17</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PTRATIO</th>  <td> -9.09e-15</td> <td> 1.47e-14</td> <td>   -0.617</td> <td> 0.538</td> <td> -3.8e-14</td> <td> 1.99e-14</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th>    <td>-2.096e-15</td> <td> 5.99e-15</td> <td>   -0.350</td> <td> 0.727</td> <td>-1.39e-14</td> <td> 9.68e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>response</th> <td>   12.5496</td> <td> 5.62e-14</td> <td> 2.23e+14</td> <td> 0.000</td> <td>   12.550</td> <td>   12.550</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>error</th>    <td>    6.2748</td> <td> 3.88e-14</td> <td> 1.62e+14</td> <td> 0.000</td> <td>    6.275</td> <td>    6.275</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>147.149</td> <th>  Durbin-Watson:     </th> <td>   0.008</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>  72.957</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.782</td>  <th>  Prob(JB):          </th> <td>1.44e-16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 1.993</td>  <th>  Cond. No.          </th> <td>4.84e+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 4.34e-28. 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:                       1.000\n",
       "Model:                            OLS   Adj. R-squared:                  1.000\n",
       "Method:                 Least Squares   F-statistic:                 1.266e+28\n",
       "Date:                Tue, 14 Feb 2023   Prob (F-statistic):               0.00\n",
       "Time:                        13:13:57   Log-Likelihood:                 13612.\n",
       "No. Observations:                 506   AIC:                        -2.720e+04\n",
       "Df Residuals:                     492   BIC:                        -2.714e+04\n",
       "Df Model:                          13                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -95.7721   8.41e-13  -1.14e+14      0.000     -95.772     -95.772\n",
       "CRIM       -1.905e-15   3.55e-15     -0.536      0.592   -8.88e-15    5.07e-15\n",
       "ZN         -7.286e-16   1.49e-15     -0.489      0.625   -3.66e-15     2.2e-15\n",
       "INDUS      -1.679e-15    6.6e-15     -0.254      0.799   -1.46e-14    1.13e-14\n",
       "CHAS        1.332e-15   9.34e-14      0.014      0.989   -1.82e-13    1.85e-13\n",
       "NOX        -5.149e-13   4.19e-13     -1.230      0.219   -1.34e-12    3.08e-13\n",
       "RM             6.2748    3.5e-14    1.8e+14      0.000       6.275       6.275\n",
       "AGE         8.639e-16   1.42e-15      0.610      0.542   -1.92e-15    3.65e-15\n",
       "DIS        -3.442e-15   2.26e-14     -0.153      0.879   -4.78e-14    4.09e-14\n",
       "RAD        -3.789e-15   7.24e-15     -0.523      0.601    -1.8e-14    1.04e-14\n",
       "TAX        -7.125e-16   4.08e-16     -1.746      0.081   -1.51e-15    8.94e-17\n",
       "PTRATIO     -9.09e-15   1.47e-14     -0.617      0.538    -3.8e-14    1.99e-14\n",
       "LSTAT      -2.096e-15   5.99e-15     -0.350      0.727   -1.39e-14    9.68e-15\n",
       "response      12.5496   5.62e-14   2.23e+14      0.000      12.550      12.550\n",
       "error          6.2748   3.88e-14   1.62e+14      0.000       6.275       6.275\n",
       "==============================================================================\n",
       "Omnibus:                      147.149   Durbin-Watson:                   0.008\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               72.957\n",
       "Skew:                           0.782   Prob(JB):                     1.44e-16\n",
       "Kurtosis:                       1.993   Cond. No.                     4.84e+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 4.34e-28. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "est.summary()\n",
    "#r.squared is = 1.000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nvBYIqQaP9av"
   },
   "source": [
    "### Exercise 1.2: Polynomial features\n",
    "\n",
    "Use polynomial features to improve your regression model in `exercise 1.1`. You can use squared and cubic features. Try to find a model that minimizes the `AIC` or `BIC` of your output table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "1IPl0fSAP9aw"
   },
   "outputs": [],
   "source": [
    "df2 = pd.DataFrame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>RM</td>        <th>  R-squared:         </th> <td>   0.484</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.483</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   471.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 14 Feb 2023</td> <th>  Prob (F-statistic):</th> <td>2.49e-74</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:56:13</td>     <th>  Log-Likelihood:    </th> <td> -371.73</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   747.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   755.9</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>Intercept</th> <td>    5.0876</td> <td>    0.060</td> <td>   85.492</td> <td> 0.000</td> <td>    4.971</td> <td>    5.205</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PRICE</th>     <td>    0.0531</td> <td>    0.002</td> <td>   21.722</td> <td> 0.000</td> <td>    0.048</td> <td>    0.058</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>123.606</td> <th>  Durbin-Watson:     </th> <td>   1.160</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 931.463</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.840</td>  <th>  Prob(JB):          </th> <td>5.44e-203</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.431</td>  <th>  Cond. No.          </th> <td>    64.5</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                     RM   R-squared:                       0.484\n",
       "Model:                            OLS   Adj. R-squared:                  0.483\n",
       "Method:                 Least Squares   F-statistic:                     471.8\n",
       "Date:                Tue, 14 Feb 2023   Prob (F-statistic):           2.49e-74\n",
       "Time:                        12:56:13   Log-Likelihood:                -371.73\n",
       "No. Observations:                 506   AIC:                             747.5\n",
       "Df Residuals:                     504   BIC:                             755.9\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      5.0876      0.060     85.492      0.000       4.971       5.205\n",
       "PRICE          0.0531      0.002     21.722      0.000       0.048       0.058\n",
       "==============================================================================\n",
       "Omnibus:                      123.606   Durbin-Watson:                   1.160\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              931.463\n",
       "Skew:                          -0.840   Prob(JB):                    5.44e-203\n",
       "Kurtosis:                       9.431   Cond. No.                         64.5\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols('RM~PRICE',df).fit() #dependent and indepent variable\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "df2 = pd.DataFrame()\n",
    "df2['LSTAT'], df2['PRICE'] = df['LSTAT'],df['PRICE']\n",
    "\n",
    "X = df2.drop(['PRICE'], axis=1)\n",
    "y = df2.PRICE\n",
    "\n",
    "X = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "df2 = sm.add_constant(df2)\n",
    "\n",
    "lstat = df2['LSTAT']\n",
    "price = df2['PRICE']\n",
    "\n",
    "#splitting\n",
    "X_train, X_test, y_train, y_test = train_test_split(price,lstat, test_size=.20, random_state=0)\n",
    "X_train_df, X_test_df = pd.DataFrame(X_train), pd.DataFrame(X_test)\n",
    "\n",
    "#two degree polynomial\n",
    "poly = PolynomialFeatures(degree=2)\n",
    "X_train_poly = poly.fit_transform(X_train_df)\n",
    "#X_train_poly\n",
    "\n",
    "model = linear_model.LinearRegression()\n",
    "model = model.fit(X_train_poly, y_train) #power of 1, power of 2 -parameter order\n",
    "coefficient = model.coef_\n",
    "intercept = model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "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>   0.544</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.543</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   601.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 14 Feb 2023</td> <th>  Prob (F-statistic):</th> <td>5.08e-88</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:30:42</td>     <th>  Log-Likelihood:    </th> <td> -1641.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3287.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3295.</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>   34.5538</td> <td>    0.563</td> <td>   61.415</td> <td> 0.000</td> <td>   33.448</td> <td>   35.659</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>LSTAT</th> <td>   -0.9500</td> <td>    0.039</td> <td>  -24.528</td> <td> 0.000</td> <td>   -1.026</td> <td>   -0.874</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>137.043</td> <th>  Durbin-Watson:     </th> <td>   0.892</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 291.373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.453</td>  <th>  Prob(JB):          </th> <td>5.36e-64</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.319</td>  <th>  Cond. No.          </th> <td>    29.7</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  PRICE   R-squared:                       0.544\n",
       "Model:                            OLS   Adj. R-squared:                  0.543\n",
       "Method:                 Least Squares   F-statistic:                     601.6\n",
       "Date:                Tue, 14 Feb 2023   Prob (F-statistic):           5.08e-88\n",
       "Time:                        19:30:42   Log-Likelihood:                -1641.5\n",
       "No. Observations:                 506   AIC:                             3287.\n",
       "Df Residuals:                     504   BIC:                             3295.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         34.5538      0.563     61.415      0.000      33.448      35.659\n",
       "LSTAT         -0.9500      0.039    -24.528      0.000      -1.026      -0.874\n",
       "==============================================================================\n",
       "Omnibus:                      137.043   Durbin-Watson:                   0.892\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              291.373\n",
       "Skew:                           1.453   Prob(JB):                     5.36e-64\n",
       "Kurtosis:                       5.319   Cond. No.                         29.7\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "est = sm.OLS(y, X).fit()\n",
    "est.summary()\n",
    "\n",
    "#R-Squares is 0.544 compared to 1.00 as seen on exercise #1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4IL43ZEFP9aw"
   },
   "source": [
    "### Exercise 1.3: Feature plotting\n",
    "\n",
    "Now that you have a better model, make a regression figure plot for the important feature. The regression plot should be like the ones made at the end of part 3 of this lecture (scatterplot + regression line). It should have the following:\n",
    "\n",
    "- Have the `x` axis be the values from one of your important features. The values should range from the `[min, max]` of the observed values in the dataset.\n",
    "- The y axis on each chart is the target value (house price)\n",
    "- You should have a scatter plot of the datapoints for the feature + the regression line of predicted values on each\n",
    "- If you used non-linearities (squared and/or cube input) the regression curve should be nonlinear as well\n",
    "- When plotting values for a single variable, you can set all the other values to their `mean` or `median` when you put them in your model's prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "id": "7VVl_dc6P9aw"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# exercise 1.3\n",
    "x_axis = np.arange(5,50,0.1)\n",
    "response2 = intercept + coefficient[1] * x_axis + coefficient[2] * x_axis**2\n",
    "\n",
    "plt.scatter(price,lstat,color='b')\n",
    "plt.plot(x_axis,response2,color='r')\n",
    "plt.xlabel(\"LSTAT\")\n",
    "plt.ylabel(\"House Prices\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IU8dZcUsP9ax"
   },
   "source": [
    "## Exercise 2: Multi-feature plotting\n",
    "\n",
    "Make a single matplotlib `figure` object with the same chart as in **1.3**, but with 4 charts instead for your 4 most important features. \n",
    "\n",
    "Do not copy-paste code for each feature you visualize in the plot. Extract your code into a function so you can just have something like\n",
    "\n",
    "```python\n",
    "fix, ax1, ax2, ax3, ax4 = plt.subplots((2,2))\n",
    "reg_plot_on_ax(feature_1, ax1)\n",
    "reg_plot_on_ax(feature_2, ax2)\n",
    "reg_plot_on_ax(feature_3, ax3)\n",
    "reg_plot_on_ax(feature_4, ax4)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "id": "Yp39pSg4P9ax"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\anacondafolder\\lib\\site-packages\\sklearn\\base.py:443: UserWarning: X has feature names, but LinearRegression was fitted without feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "X has 2 features, but LinearRegression is expecting 3 features as input.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp\\ipykernel_492\\4059650032.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0max2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0max3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0max4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0my2_predictions\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdf2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mreg_plot_on_ax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfeature_1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\anacondafolder\\lib\\site-packages\\sklearn\\linear_model\\_base.py\u001b[0m in \u001b[0;36mpredict\u001b[1;34m(self, X)\u001b[0m\n\u001b[0;32m    360\u001b[0m             \u001b[0mReturns\u001b[0m \u001b[0mpredicted\u001b[0m \u001b[0mvalues\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    361\u001b[0m         \"\"\"\n\u001b[1;32m--> 362\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_decision_function\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    363\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    364\u001b[0m     \u001b[0m_preprocess_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mstaticmethod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_preprocess_data\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\anacondafolder\\lib\\site-packages\\sklearn\\linear_model\\_base.py\u001b[0m in \u001b[0;36m_decision_function\u001b[1;34m(self, X)\u001b[0m\n\u001b[0;32m    343\u001b[0m         \u001b[0mcheck_is_fitted\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    344\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 345\u001b[1;33m         \u001b[0mX\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_validate_data\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maccept_sparse\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"csr\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"csc\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"coo\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreset\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    346\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0msafe_sparse_dot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcoef_\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdense_output\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mintercept_\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    347\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\anacondafolder\\lib\\site-packages\\sklearn\\base.py\u001b[0m in \u001b[0;36m_validate_data\u001b[1;34m(self, X, y, reset, validate_separately, **check_params)\u001b[0m\n\u001b[0;32m    583\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    584\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mno_val_X\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mcheck_params\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"ensure_2d\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 585\u001b[1;33m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_check_n_features\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreset\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mreset\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    586\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    587\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\anacondafolder\\lib\\site-packages\\sklearn\\base.py\u001b[0m in \u001b[0;36m_check_n_features\u001b[1;34m(self, X, reset)\u001b[0m\n\u001b[0;32m    398\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    399\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mn_features\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mn_features_in_\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 400\u001b[1;33m             raise ValueError(\n\u001b[0m\u001b[0;32m    401\u001b[0m                 \u001b[1;34mf\"X has {n_features} features, but {self.__class__.__name__} \"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    402\u001b[0m                 \u001b[1;34mf\"is expecting {self.n_features_in_} features as input.\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: X has 2 features, but LinearRegression is expecting 3 features as input."
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# exercise 2\n",
    "\n",
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2,2)\n",
    "y2_predictions = model.predict(df2)\n",
    "\n",
    "def reg_plot_on_ax(feature_1, ax):\n",
    "    min_ft = df[feature_1].min()\n",
    "    max_ft = df[feature_1].max()\n",
    "\n",
    "    x = np.linspace(min_ft,max_ft,506)\n",
    "    sns.scatterplot(x=str(feature_1), y='PRICE', data=df, ax=ax)\n",
    "    sns.lineplot(x=x, y=y2_predictions, color='r', ax=ax)\n",
    "    ax.set_title(feature_1)\n",
    "    ax.set_xlabel(feature_1, labelpad=10)\n",
    "    ax.set_ylabel('Price', labelpad=10)\n",
    "\n",
    "list_ft = ['AGE', 'NOX', 'DIS', 'TAX']\n",
    "axes = [ax1, ax2, ax3, ax4]\n",
    "\n",
    "for ft, ax in zip(list_ft,axes):\n",
    "    reg_plot_on_ax(ft, ax)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "workshop.ipynb",
   "provenance": []
  },
  "file_extension": ".py",
  "interpreter": {
   "hash": "f5c9dfabb21bd2a91b63810df81acbdc6b5e617e45414f0ef050ca96090c868f"
  },
  "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": "3.9.13"
  },
  "mimetype": "text/x-python",
  "name": "python",
  "npconvert_exporter": "python",
  "pygments_lexer": "ipython3",
  "version": 3
 },
 "nbformat": 4,
 "nbformat_minor": 4
}