price_size_year_view Dummy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Linear Regression with Dummies "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is located in the file: 'real_estate_price_size_year_view.csv'. \n",
    "\n",
    "We are to create a multiple linear regression using the data. \n",
    "\n",
    "In this exercise, the dependent variable is 'price', while the independent variables are 'size', 'year', and 'view'.\n",
    "\n",
    "#### Regarding the 'view' variable:\n",
    "There are two options: 'Sea view' and 'No sea view'. We are expected to create a dummy variable for view and include it in the regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_data = pd.read_csv('real_estate_price_size_year_view.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>size</th>\n",
       "      <th>year</th>\n",
       "      <th>view</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>234314.144</td>\n",
       "      <td>643.09</td>\n",
       "      <td>2015</td>\n",
       "      <td>No sea view</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>228581.528</td>\n",
       "      <td>656.22</td>\n",
       "      <td>2009</td>\n",
       "      <td>No sea view</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>281626.336</td>\n",
       "      <td>487.29</td>\n",
       "      <td>2018</td>\n",
       "      <td>Sea view</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>401255.608</td>\n",
       "      <td>1504.75</td>\n",
       "      <td>2015</td>\n",
       "      <td>No sea view</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>458674.256</td>\n",
       "      <td>1275.46</td>\n",
       "      <td>2009</td>\n",
       "      <td>Sea view</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        price     size  year         view\n",
       "0  234314.144   643.09  2015  No sea view\n",
       "1  228581.528   656.22  2009  No sea view\n",
       "2  281626.336   487.29  2018     Sea view\n",
       "3  401255.608  1504.75  2015  No sea view\n",
       "4  458674.256  1275.46  2009     Sea view"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>size</th>\n",
       "      <th>year</th>\n",
       "      <th>view</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>No sea view</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>292289.470160</td>\n",
       "      <td>853.024200</td>\n",
       "      <td>2012.600000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>77051.727525</td>\n",
       "      <td>297.941951</td>\n",
       "      <td>4.729021</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>154282.128000</td>\n",
       "      <td>479.750000</td>\n",
       "      <td>2006.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>234280.148000</td>\n",
       "      <td>643.330000</td>\n",
       "      <td>2009.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>280590.716000</td>\n",
       "      <td>696.405000</td>\n",
       "      <td>2015.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>335723.696000</td>\n",
       "      <td>1029.322500</td>\n",
       "      <td>2018.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>500681.128000</td>\n",
       "      <td>1842.510000</td>\n",
       "      <td>2018.000000</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                price         size         year         view\n",
       "count      100.000000   100.000000   100.000000          100\n",
       "unique            NaN          NaN          NaN            2\n",
       "top               NaN          NaN          NaN  No sea view\n",
       "freq              NaN          NaN          NaN           51\n",
       "mean    292289.470160   853.024200  2012.600000          NaN\n",
       "std      77051.727525   297.941951     4.729021          NaN\n",
       "min     154282.128000   479.750000  2006.000000          NaN\n",
       "25%     234280.148000   643.330000  2009.000000          NaN\n",
       "50%     280590.716000   696.405000  2015.000000          NaN\n",
       "75%     335723.696000  1029.322500  2018.000000          NaN\n",
       "max     500681.128000  1842.510000  2018.000000          NaN"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data.describe(include='all')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a dummy variable for 'view'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = raw_data.copy()\n",
    "data['view'] = data['view'].map({'Sea view': 1, 'No sea view': 0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>size</th>\n",
       "      <th>year</th>\n",
       "      <th>view</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>234314.144</td>\n",
       "      <td>643.09</td>\n",
       "      <td>2015</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>228581.528</td>\n",
       "      <td>656.22</td>\n",
       "      <td>2009</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>281626.336</td>\n",
       "      <td>487.29</td>\n",
       "      <td>2018</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>401255.608</td>\n",
       "      <td>1504.75</td>\n",
       "      <td>2015</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>458674.256</td>\n",
       "      <td>1275.46</td>\n",
       "      <td>2009</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "        price     size  year  view\n",
       "0  234314.144   643.09  2015     0\n",
       "1  228581.528   656.22  2009     0\n",
       "2  281626.336   487.29  2018     1\n",
       "3  401255.608  1504.75  2015     0\n",
       "4  458674.256  1275.46  2009     1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Declare the dependent and the independent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['price']\n",
    "x1 = data[['size','year','view']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression"
   ]
  },
  {
   "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>   0.913</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.910</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   335.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 26 Jun 2018</td> <th>  Prob (F-statistic):</th> <td>1.02e-50</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:20:46</td>     <th>  Log-Likelihood:    </th> <td> -1144.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   2297.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    96</td>      <th>  BIC:               </th> <td>   2308.</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>const</th> <td>-5.398e+06</td> <td> 9.94e+05</td> <td>   -5.431</td> <td> 0.000</td> <td>-7.37e+06</td> <td>-3.43e+06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>size</th>  <td>  223.0316</td> <td>    7.838</td> <td>   28.455</td> <td> 0.000</td> <td>  207.473</td> <td>  238.590</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>year</th>  <td> 2718.9489</td> <td>  493.502</td> <td>    5.510</td> <td> 0.000</td> <td> 1739.356</td> <td> 3698.542</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>view</th>  <td> 5.673e+04</td> <td> 4627.695</td> <td>   12.258</td> <td> 0.000</td> <td> 4.75e+04</td> <td> 6.59e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>29.224</td> <th>  Durbin-Watson:     </th> <td>   1.965</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  64.957</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.088</td> <th>  Prob(JB):          </th> <td>7.85e-15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.295</td> <th>  Cond. No.          </th> <td>9.42e+05</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.913\n",
       "Model:                            OLS   Adj. R-squared:                  0.910\n",
       "Method:                 Least Squares   F-statistic:                     335.2\n",
       "Date:                Tue, 26 Jun 2018   Prob (F-statistic):           1.02e-50\n",
       "Time:                        11:20:46   Log-Likelihood:                -1144.6\n",
       "No. Observations:                 100   AIC:                             2297.\n",
       "Df Residuals:                      96   BIC:                             2308.\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const      -5.398e+06   9.94e+05     -5.431      0.000   -7.37e+06   -3.43e+06\n",
       "size         223.0316      7.838     28.455      0.000     207.473     238.590\n",
       "year        2718.9489    493.502      5.510      0.000    1739.356    3698.542\n",
       "view        5.673e+04   4627.695     12.258      0.000    4.75e+04    6.59e+04\n",
       "==============================================================================\n",
       "Omnibus:                       29.224   Durbin-Watson:                   1.965\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               64.957\n",
       "Skew:                           1.088   Prob(JB):                     7.85e-15\n",
       "Kurtosis:                       6.295   Cond. No.                     9.42e+05\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, 9.42e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x1)\n",
    "results = sm.OLS(y,x).fit()\n",
    "results.summary()"
   ]
  }
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