Size-Price regression .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#importing the relevant libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Loading the data for our linear regression \n",
    "data=pd.read_csv(r'D:\\Stu\\Data Science\\Exercises Regression\\real_estate_price_size.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>252460.400</td>\n",
       "      <td>549.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>310522.592</td>\n",
       "      <td>1037.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>383635.568</td>\n",
       "      <td>1504.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>225145.248</td>\n",
       "      <td>648.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>274922.856</td>\n",
       "      <td>705.29</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 2 columns</p>\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\n",
       "..         ...      ...\n",
       "95  252460.400   549.80\n",
       "96  310522.592  1037.44\n",
       "97  383635.568  1504.75\n",
       "98  225145.248   648.29\n",
       "99  274922.856   705.29\n",
       "\n",
       "[100 rows x 2 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calling the data \n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        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": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Data has to be explored\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Defining our variables according to their dependency on each other\n",
    "# Following the regression equation, our dependent variable (y) is the size \n",
    "y = data ['size']\n",
    "# Similarly, our independent variable (x) is the price\n",
    "x1 = data ['price']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a scatter plot (first we put the horizontal axis, then the vertical axis)\n",
    "plt.scatter(x1,y)\n",
    "# Name the axes\n",
    "plt.xlabel('price', fontsize = 20)\n",
    "plt.ylabel('size', fontsize = 20)\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>size</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, 15 Jul 2020</td> <th>  Prob (F-statistic):</th> <td>8.13e-31</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:26:09</td>     <th>  Log-Likelihood:    </th> <td> -642.81</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   1290.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   1295.</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> -122.3349</td> <td>   59.633</td> <td>   -2.051</td> <td> 0.043</td> <td> -240.675</td> <td>   -3.994</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>price</th> <td>    0.0033</td> <td>    0.000</td> <td>   16.909</td> <td> 0.000</td> <td>    0.003</td> <td>    0.004</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.832</td> <th>  Durbin-Watson:     </th> <td>   2.143</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.660</td> <th>  Jarque-Bera (JB):  </th> <td>   0.941</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.153</td> <th>  Prob(JB):          </th> <td>   0.625</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.636</td> <th>  Cond. No.          </th> <td>1.19e+06</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.19e+06. 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:                   size   R-squared:                       0.745\n",
       "Model:                            OLS   Adj. R-squared:                  0.742\n",
       "Method:                 Least Squares   F-statistic:                     285.9\n",
       "Date:                Wed, 15 Jul 2020   Prob (F-statistic):           8.13e-31\n",
       "Time:                        10:26:09   Log-Likelihood:                -642.81\n",
       "No. Observations:                 100   AIC:                             1290.\n",
       "Df Residuals:                      98   BIC:                             1295.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const       -122.3349     59.633     -2.051      0.043    -240.675      -3.994\n",
       "price          0.0033      0.000     16.909      0.000       0.003       0.004\n",
       "==============================================================================\n",
       "Omnibus:                        0.832   Durbin-Watson:                   2.143\n",
       "Prob(Omnibus):                  0.660   Jarque-Bera (JB):                0.941\n",
       "Skew:                           0.153   Prob(JB):                        0.625\n",
       "Kurtosis:                       2.636   Cond. No.                     1.19e+06\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, 1.19e+06. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add a constant. Essentially, we are adding a new column (equal in lenght to x), which consists only of is\n",
    "x = sm.add_constant(x1)\n",
    "# Fit the model, according to the OLS (ordinary least squares) method with a dependent variable y and an idependent x\n",
    "results = sm.OLS(y,x).fit()\n",
    "# Print a nice summary of the regression. That's one of the strong points of statsmodels -> the summaries\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a scatter plot\n",
    "plt.scatter(x1,y)\n",
    "# Define the regression equation, so we can plot it later\n",
    "yhat = 0.0033*x1 - 122.3349\n",
    "# Plot the regression line against the independent variable (SAT)\n",
    "fig = plt.plot(x1,yhat, lw=4, c='orange', label ='regression line')\n",
    "# Label the axes\n",
    "plt.xlabel('price', fontsize = 20)\n",
    "plt.ylabel('size', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}