Multicollinearity & VIFs - Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multicollinearity & VIFs\n",
    "\n",
    "Using the notebook here, answer the quiz questioons below regarding multicollinearity.\n",
    "\n",
    "To get started let's read in the necessary libraries and the data that will be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>house_id</th>\n",
       "      <th>neighborhood</th>\n",
       "      <th>area</th>\n",
       "      <th>bedrooms</th>\n",
       "      <th>bathrooms</th>\n",
       "      <th>style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1112</td>\n",
       "      <td>B</td>\n",
       "      <td>1188</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>ranch</td>\n",
       "      <td>598291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>491</td>\n",
       "      <td>B</td>\n",
       "      <td>3512</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>victorian</td>\n",
       "      <td>1744259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5952</td>\n",
       "      <td>B</td>\n",
       "      <td>1134</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>ranch</td>\n",
       "      <td>571669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3525</td>\n",
       "      <td>A</td>\n",
       "      <td>1940</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>ranch</td>\n",
       "      <td>493675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5108</td>\n",
       "      <td>B</td>\n",
       "      <td>2208</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>victorian</td>\n",
       "      <td>1101539</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   house_id neighborhood  area  bedrooms  bathrooms      style    price\n",
       "0      1112            B  1188         3          2      ranch   598291\n",
       "1       491            B  3512         5          3  victorian  1744259\n",
       "2      5952            B  1134         3          2      ranch   571669\n",
       "3      3525            A  1940         4          2      ranch   493675\n",
       "4      5108            B  2208         6          4  victorian  1101539"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from patsy import dmatrices\n",
    "import statsmodels.api as sms\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "%matplotlib inline\n",
    "\n",
    "df = pd.read_csv('./house_prices.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`1.`Use [seaborn](https://seaborn.pydata.org/examples/scatterplot_matrix.html) to look at pairwise relationships for all of the quantitative, explanatory variables in the dataset by running the cell below.  You might also investigate how to add color (**hue**) for the house style or neighborhood.  Use the plot to answer the first quiz questions below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f286dd1bba8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(df[['bedrooms', 'bathrooms', 'area']]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`2.` Earlier, you fit linear models between each individual predictor variable and price, as well as using all of the variables and the price in a multiple linear regression model. Each of the individual models showed a positive relationship - that is, when bathrooms, bedrooms, or area increase, we predict the price of a home to increase. \n",
    "\n",
    "Fit a linear model to predict a home **price** using **bedrooms**, **bathrooms**, and **area**. Use the summary to answer the second quiz question below. **Don't forget an intercept.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>   0.678</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.678</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   4230.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 14 Jan 2019</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>03:46:53</td>     <th>  Log-Likelihood:    </th> <td> -84517.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6028</td>      <th>  AIC:               </th> <td>1.690e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6024</td>      <th>  BIC:               </th> <td>1.691e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</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> 1.007e+04</td> <td> 1.04e+04</td> <td>    0.972</td> <td> 0.331</td> <td>-1.02e+04</td> <td> 3.04e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>  <td>-2925.8063</td> <td> 1.03e+04</td> <td>   -0.285</td> <td> 0.775</td> <td> -2.3e+04</td> <td> 1.72e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th> <td> 7345.3917</td> <td> 1.43e+04</td> <td>    0.515</td> <td> 0.607</td> <td>-2.06e+04</td> <td> 3.53e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>area</th>      <td>  345.9110</td> <td>    7.227</td> <td>   47.863</td> <td> 0.000</td> <td>  331.743</td> <td>  360.079</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>367.658</td> <th>  Durbin-Watson:     </th> <td>   2.007</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 350.116</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.536</td>  <th>  Prob(JB):          </th> <td>9.40e-77</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.503</td>  <th>  Cond. No.          </th> <td>1.16e+04</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.678\n",
       "Model:                            OLS   Adj. R-squared:                  0.678\n",
       "Method:                 Least Squares   F-statistic:                     4230.\n",
       "Date:                Mon, 14 Jan 2019   Prob (F-statistic):               0.00\n",
       "Time:                        03:46:53   Log-Likelihood:                -84517.\n",
       "No. Observations:                6028   AIC:                         1.690e+05\n",
       "Df Residuals:                    6024   BIC:                         1.691e+05\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept   1.007e+04   1.04e+04      0.972      0.331   -1.02e+04    3.04e+04\n",
       "bedrooms   -2925.8063   1.03e+04     -0.285      0.775    -2.3e+04    1.72e+04\n",
       "bathrooms   7345.3917   1.43e+04      0.515      0.607   -2.06e+04    3.53e+04\n",
       "area         345.9110      7.227     47.863      0.000     331.743     360.079\n",
       "==============================================================================\n",
       "Omnibus:                      367.658   Durbin-Watson:                   2.007\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              350.116\n",
       "Skew:                           0.536   Prob(JB):                     9.40e-77\n",
       "Kurtosis:                       2.503   Cond. No.                     1.16e+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, 1.16e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['intercept'] = 1\n",
    "lm = sm.OLS(df['price'], df[['intercept', 'bedrooms', 'bathrooms', 'area']])\n",
    "results = lm.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`3.` Calculate the VIFs for each variable in your model.  Use quiz 3 below to provide insights about the results of your VIFs.  [Here](https://etav.github.io/python/vif_factor_python.html) is the helpful post again, in case you need it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y, X = dmatrices('price ~ area + bedrooms + bathrooms', df, return_type = 'dataframe')\n",
    "\n",
    "vif = pd.DataFrame()\n",
    "vif[\"VIF Factor\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
    "vif[\"features\"] = X.columns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "        text-align: right;\n",
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       "    }\n",
       "\n",
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       "        vertical-align: top;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VIF Factor</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.327102</td>\n",
       "      <td>Intercept</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.458190</td>\n",
       "      <td>area</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20.854484</td>\n",
       "      <td>bedrooms</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.006851</td>\n",
       "      <td>bathrooms</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   VIF Factor   features\n",
       "0    7.327102  Intercept\n",
       "1    5.458190       area\n",
       "2   20.854484   bedrooms\n",
       "3   19.006851  bathrooms"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "`4.` Remove bathrooms from your above model.  Refit the multiple linear regression model and re-compute the VIFs.  Use the final quiz below to provide insights about your results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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>   0.678</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.678</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   6345.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 14 Jan 2019</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>04:05:59</td>     <th>  Log-Likelihood:    </th> <td> -84517.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6028</td>      <th>  AIC:               </th> <td>1.690e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6025</td>      <th>  BIC:               </th> <td>1.691e+05</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>intercept</th> <td> 7857.4509</td> <td> 9425.288</td> <td>    0.834</td> <td> 0.405</td> <td>-1.06e+04</td> <td> 2.63e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>  <td> 1626.8306</td> <td> 5191.702</td> <td>    0.313</td> <td> 0.754</td> <td>-8550.763</td> <td> 1.18e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>area</th>      <td>  346.4458</td> <td>    7.152</td> <td>   48.443</td> <td> 0.000</td> <td>  332.426</td> <td>  360.466</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>368.146</td> <th>  Durbin-Watson:     </th> <td>   2.007</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 350.224</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.535</td>  <th>  Prob(JB):          </th> <td>8.91e-77</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.502</td>  <th>  Cond. No.          </th> <td>6.45e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.678\n",
       "Model:                            OLS   Adj. R-squared:                  0.678\n",
       "Method:                 Least Squares   F-statistic:                     6345.\n",
       "Date:                Mon, 14 Jan 2019   Prob (F-statistic):               0.00\n",
       "Time:                        04:05:59   Log-Likelihood:                -84517.\n",
       "No. Observations:                6028   AIC:                         1.690e+05\n",
       "Df Residuals:                    6025   BIC:                         1.691e+05\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept   7857.4509   9425.288      0.834      0.405   -1.06e+04    2.63e+04\n",
       "bedrooms    1626.8306   5191.702      0.313      0.754   -8550.763    1.18e+04\n",
       "area         346.4458      7.152     48.443      0.000     332.426     360.466\n",
       "==============================================================================\n",
       "Omnibus:                      368.146   Durbin-Watson:                   2.007\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              350.224\n",
       "Skew:                           0.535   Prob(JB):                     8.91e-77\n",
       "Kurtosis:                       2.502   Cond. No.                     6.45e+03\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, 6.45e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = sm.OLS(df['price'], df[['intercept', 'bedrooms', 'area']])\n",
    "results = lm.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "y, X = dmatrices('price ~ area + bedrooms', df, return_type = 'dataframe')\n",
    "\n",
    "vif = pd.DataFrame()\n",
    "vif[\"VIF Factor\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
    "vif[\"features\"] = X.columns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "    .dataframe thead th {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>VIF Factor</th>\n",
       "      <th>features</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.063895</td>\n",
       "      <td>Intercept</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.345400</td>\n",
       "      <td>area</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.345400</td>\n",
       "      <td>bedrooms</td>\n",
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      ],
      "text/plain": [
       "   VIF Factor   features\n",
       "0    6.063895  Intercept\n",
       "1    5.345400       area\n",
       "2    5.345400   bedrooms"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": []
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