MLR_my_solutions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\KMaughan\\Anaconda2\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\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 numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm;\n",
    "\n",
    "df = pd.read_csv(\"house_prices.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>Tue, 09 Jan 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:36:06</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>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>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>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:                Tue, 09 Jan 2018   Prob (F-statistic):               0.00\n",
       "Time:                        13:36:06   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",
       "bathrooms   7345.3917   1.43e+04      0.515      0.607   -2.06e+04    3.53e+04\n",
       "bedrooms   -2925.8063   1.03e+04     -0.285      0.775    -2.3e+04    1.72e+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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['intercept'] = 1\n",
    "lm = sm.OLS(df['price'], df[['intercept','bathrooms','bedrooms','area']]) # lienar model,\n",
    "# plot price against all the other quantitative values\n",
    "results = lm.fit()\n",
    "results.summary()"
   ]
  },
  {
   "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>   0.541</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.541</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7116.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 09 Jan 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:41:51</td>     <th>  Log-Likelihood:    </th> <td> -85583.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6028</td>      <th>  AIC:               </th> <td>1.712e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6026</td>      <th>  BIC:               </th> <td>1.712e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th> <td> 4.314e+04</td> <td> 9587.189</td> <td>    4.500</td> <td> 0.000</td> <td> 2.43e+04</td> <td> 6.19e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bathrooms</th> <td> 3.295e+05</td> <td> 3905.540</td> <td>   84.358</td> <td> 0.000</td> <td> 3.22e+05</td> <td> 3.37e+05</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>915.429</td> <th>  Durbin-Watson:     </th> <td>   2.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1537.531</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.010</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.428</td>  <th>  Cond. No.          </th> <td>    5.84</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.541\n",
       "Model:                            OLS   Adj. R-squared:                  0.541\n",
       "Method:                 Least Squares   F-statistic:                     7116.\n",
       "Date:                Tue, 09 Jan 2018   Prob (F-statistic):               0.00\n",
       "Time:                        13:41:51   Log-Likelihood:                -85583.\n",
       "No. Observations:                6028   AIC:                         1.712e+05\n",
       "Df Residuals:                    6026   BIC:                         1.712e+05\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept   4.314e+04   9587.189      4.500      0.000    2.43e+04    6.19e+04\n",
       "bathrooms   3.295e+05   3905.540     84.358      0.000    3.22e+05    3.37e+05\n",
       "==============================================================================\n",
       "Omnibus:                      915.429   Durbin-Watson:                   2.003\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1537.531\n",
       "Skew:                           1.010   Prob(JB):                         0.00\n",
       "Kurtosis:                       4.428   Cond. No.                         5.84\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm1 = sm.OLS(df['price'], df[['intercept','bathrooms']]) # lienar model,\n",
    "# plot price against all the other quantitative values\n",
    "results1 = lm1.fit()\n",
    "results1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>   0.553</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.553</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7446.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 09 Jan 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:42:26</td>     <th>  Log-Likelihood:    </th> <td> -85509.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6028</td>      <th>  AIC:               </th> <td>1.710e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6026</td>      <th>  BIC:               </th> <td>1.710e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th> <td>-9.485e+04</td> <td> 1.08e+04</td> <td>   -8.762</td> <td> 0.000</td> <td>-1.16e+05</td> <td>-7.36e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bedrooms</th>  <td> 2.284e+05</td> <td> 2646.744</td> <td>   86.289</td> <td> 0.000</td> <td> 2.23e+05</td> <td> 2.34e+05</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>967.118</td> <th>  Durbin-Watson:     </th> <td>   2.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1599.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.074</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.325</td>  <th>  Cond. No.          </th> <td>    10.3</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.553\n",
       "Model:                            OLS   Adj. R-squared:                  0.553\n",
       "Method:                 Least Squares   F-statistic:                     7446.\n",
       "Date:                Tue, 09 Jan 2018   Prob (F-statistic):               0.00\n",
       "Time:                        13:42:26   Log-Likelihood:                -85509.\n",
       "No. Observations:                6028   AIC:                         1.710e+05\n",
       "Df Residuals:                    6026   BIC:                         1.710e+05\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept  -9.485e+04   1.08e+04     -8.762      0.000   -1.16e+05   -7.36e+04\n",
       "bedrooms    2.284e+05   2646.744     86.289      0.000    2.23e+05    2.34e+05\n",
       "==============================================================================\n",
       "Omnibus:                      967.118   Durbin-Watson:                   2.014\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1599.431\n",
       "Skew:                           1.074   Prob(JB):                         0.00\n",
       "Kurtosis:                       4.325   Cond. No.                         10.3\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm2 = sm.OLS(df['price'], df[['intercept','bedrooms']]) # lienar model,\n",
    "# plot price against all the other quantitative values\n",
    "results2 = lm2.fit()\n",
    "results2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>1.269e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 09 Jan 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:42:45</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>  6026</td>      <th>  BIC:               </th> <td>1.691e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>intercept</th> <td> 9587.8878</td> <td> 7637.479</td> <td>    1.255</td> <td> 0.209</td> <td>-5384.303</td> <td> 2.46e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>area</th>      <td>  348.4664</td> <td>    3.093</td> <td>  112.662</td> <td> 0.000</td> <td>  342.403</td> <td>  354.530</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>368.609</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> 349.279</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.534</td>  <th>  Prob(JB):          </th> <td>1.43e-76</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.499</td>  <th>  Cond. No.          </th> <td>4.93e+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:                 1.269e+04\n",
       "Date:                Tue, 09 Jan 2018   Prob (F-statistic):               0.00\n",
       "Time:                        13:42:45   Log-Likelihood:                -84517.\n",
       "No. Observations:                6028   AIC:                         1.690e+05\n",
       "Df Residuals:                    6026   BIC:                         1.691e+05\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "intercept   9587.8878   7637.479      1.255      0.209   -5384.303    2.46e+04\n",
       "area         348.4664      3.093    112.662      0.000     342.403     354.530\n",
       "==============================================================================\n",
       "Omnibus:                      368.609   Durbin-Watson:                   2.007\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              349.279\n",
       "Skew:                           0.534   Prob(JB):                     1.43e-76\n",
       "Kurtosis:                       2.499   Cond. No.                     4.93e+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, 4.93e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm3 = sm.OLS(df['price'], df[['intercept','area']]) # lienar model,\n",
    "# plot price against all the other quantitative values\n",
    "results3 = lm3.fit()\n",
    "results3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>Tue, 09 Jan 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:46:28</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>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>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>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:                Tue, 09 Jan 2018   Prob (F-statistic):               0.00\n",
       "Time:                        13:46:28   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",
       "bathrooms   7345.3917   1.43e+04      0.515      0.607   -2.06e+04    3.53e+04\n",
       "bedrooms   -2925.8063   1.03e+04     -0.285      0.775    -2.3e+04    1.72e+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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm5 = sm.OLS(df['price'],df[['intercept','bathrooms','bedrooms','area']])\n",
    "results5 = lm5.fit()\n",
    "results5.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# transpose, inverse, transpose, dot product \n",
    "x = df[['intercept', 'bathrooms','bedrooms','area']]\n",
    "y = df['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 10072.10704672,   7345.39171369,  -2925.80632467,    345.91101884])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# chain operations together\n",
    "np.dot(np.dot(np.linalg.inv(np.dot(x.transpose(),x)),x.transpose()),y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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