Simple Linear Regression Exercise Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple linear regression - Exercise Solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You are given a real estate dataset. \n",
    "\n",
    "Real estate is one of those examples that every regression course goes through as it is extremely easy to understand and there is a (almost always) certain causal relationship to be found.\n",
    "\n",
    "The data is located in the file: 'real_estate_price_size.csv'. \n",
    "\n",
    "You are expected to create a simple linear regression (similar to the one in the lecture), using the new data.\n",
    "\n",
    "In this exercise, the dependent variable is 'price', while the independent variable is 'size'.\n",
    "\n",
    "Good luck!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import 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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('real_estate_price_size.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        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>price</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>234314.144</td>\n",
       "      <td>643.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>228581.528</td>\n",
       "      <td>656.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>281626.336</td>\n",
       "      <td>487.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>401255.608</td>\n",
       "      <td>1504.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>458674.256</td>\n",
       "      <td>1275.46</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        price     size\n",
       "0  234314.144   643.09\n",
       "1  228581.528   656.22\n",
       "2  281626.336   487.29\n",
       "3  401255.608  1504.75\n",
       "4  458674.256  1275.46"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>price</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>292289.470160</td>\n",
       "      <td>853.024200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>77051.727525</td>\n",
       "      <td>297.941951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>154282.128000</td>\n",
       "      <td>479.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>234280.148000</td>\n",
       "      <td>643.330000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>280590.716000</td>\n",
       "      <td>696.405000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>335723.696000</td>\n",
       "      <td>1029.322500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>500681.128000</td>\n",
       "      <td>1842.510000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               price         size\n",
       "count     100.000000   100.000000\n",
       "mean   292289.470160   853.024200\n",
       "std     77051.727525   297.941951\n",
       "min    154282.128000   479.750000\n",
       "25%    234280.148000   643.330000\n",
       "50%    280590.716000   696.405000\n",
       "75%    335723.696000  1029.322500\n",
       "max    500681.128000  1842.510000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "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": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['price']\n",
    "x1 = data['size']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explore the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "plt.xlabel('Size',fontsize=20)\n",
    "plt.ylabel('Price',fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\anaconda3\\lib\\site-packages\\statsmodels\\tsa\\tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
      "  x = pd.concat(x[::order], 1)\n"
     ]
    },
    {
     "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>   0.745</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.742</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   285.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 18 May 2022</td> <th>  Prob (F-statistic):</th> <td>8.13e-31</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:37:09</td>     <th>  Log-Likelihood:    </th> <td> -1198.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   2401.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   2406.</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> 1.019e+05</td> <td> 1.19e+04</td> <td>    8.550</td> <td> 0.000</td> <td> 7.83e+04</td> <td> 1.26e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>size</th>  <td>  223.1787</td> <td>   13.199</td> <td>   16.909</td> <td> 0.000</td> <td>  196.986</td> <td>  249.371</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 6.262</td> <th>  Durbin-Watson:     </th> <td>   2.267</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.044</td> <th>  Jarque-Bera (JB):  </th> <td>   2.938</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.117</td> <th>  Prob(JB):          </th> <td>   0.230</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.194</td> <th>  Cond. No.          </th> <td>2.75e+03</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 condition number is large, 2.75e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.745\n",
       "Model:                            OLS   Adj. R-squared:                  0.742\n",
       "Method:                 Least Squares   F-statistic:                     285.9\n",
       "Date:                Wed, 18 May 2022   Prob (F-statistic):           8.13e-31\n",
       "Time:                        10:37:09   Log-Likelihood:                -1198.3\n",
       "No. Observations:                 100   AIC:                             2401.\n",
       "Df Residuals:                      98   BIC:                             2406.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       1.019e+05   1.19e+04      8.550      0.000    7.83e+04    1.26e+05\n",
       "size         223.1787     13.199     16.909      0.000     196.986     249.371\n",
       "==============================================================================\n",
       "Omnibus:                        6.262   Durbin-Watson:                   2.267\n",
       "Prob(Omnibus):                  0.044   Jarque-Bera (JB):                2.938\n",
       "Skew:                           0.117   Prob(JB):                        0.230\n",
       "Kurtosis:                       2.194   Cond. No.                     2.75e+03\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.75e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x1)\n",
    "results = sm.OLS(y,x).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "yhat = x1*223.1787+101900\n",
    "fig = plt.plot(x1,yhat, lw=4, c='orange', label ='regression line')\n",
    "plt.xlabel('Size', fontsize = 20)\n",
    "plt.ylabel('Price', fontsize = 20)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}