Making predictions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sqlalchemy import create_engine\n",
    "import statsmodels.api as sm\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "from statsmodels.tools.eval_measures import mse, rmse\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "postgres_user = 'dsbc_student'\n",
    "postgres_pw = '7*.8G9QH21'\n",
    "postgres_host = '142.93.121.174'\n",
    "postgres_port = '5432'\n",
    "postgres_db = 'houseprices'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "engine = create_engine('postgresql://{}:{}@{}:{}/{}'.format(\n",
    "    postgres_user, postgres_pw, postgres_host, postgres_port, postgres_db))\n",
    "house_prices_df = pd.read_sql_query('select * from houseprices',con=engine)\n",
    "\n",
    "# no need for an open connection, as we're only doing a single query\n",
    "engine.dispose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "house_prices_df = pd.concat([house_prices_df,pd.get_dummies(house_prices_df.mszoning, prefix=\"mszoning\", drop_first=True)], axis=1)\n",
    "house_prices_df = pd.concat([house_prices_df,pd.get_dummies(house_prices_df.street, prefix=\"street\", drop_first=True)], axis=1)\n",
    "dummy_column_names = list(pd.get_dummies(house_prices_df.mszoning, prefix=\"mszoning\", drop_first=True).columns)\n",
    "dummy_column_names = dummy_column_names + list(pd.get_dummies(house_prices_df.street, prefix=\"street\", drop_first=True).columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of observations in the training set is 1168\n",
      "The number of observations in the test set is 292\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              saleprice   R-squared:                       0.768\n",
      "Model:                            OLS   Adj. R-squared:                  0.766\n",
      "Method:                 Least Squares   F-statistic:                     383.1\n",
      "Date:                Fri, 24 Jan 2020   Prob (F-statistic):               0.00\n",
      "Time:                        12:38:07   Log-Likelihood:                -13972.\n",
      "No. Observations:                1168   AIC:                         2.797e+04\n",
      "Df Residuals:                    1157   BIC:                         2.802e+04\n",
      "Df Model:                          10                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "const       -1.039e+05   2.06e+04     -5.037      0.000   -1.44e+05   -6.34e+04\n",
      "overallqual  2.433e+04   1244.706     19.548      0.000    2.19e+04    2.68e+04\n",
      "grlivarea      43.3745      2.745     15.800      0.000      37.988      48.760\n",
      "garagecars   1.407e+04   3409.600      4.126      0.000    7379.047    2.08e+04\n",
      "garagearea     17.5210     11.560      1.516      0.130      -5.161      40.203\n",
      "totalbsmtsf    23.4504      3.183      7.368      0.000      17.206      29.695\n",
      "mszoning_FV  1.933e+04    1.5e+04      1.289      0.198   -1.01e+04    4.88e+04\n",
      "mszoning_RH  7305.5078   1.72e+04      0.426      0.670   -2.63e+04     4.1e+04\n",
      "mszoning_RL  2.429e+04   1.39e+04      1.747      0.081   -2983.478    5.16e+04\n",
      "mszoning_RM  2864.3070   1.41e+04      0.203      0.839   -2.48e+04    3.05e+04\n",
      "street_Pave -8177.6681   1.74e+04     -0.470      0.639   -4.23e+04     2.6e+04\n",
      "==============================================================================\n",
      "Omnibus:                      355.774   Durbin-Watson:                   1.863\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            30190.746\n",
      "Skew:                          -0.383   Prob(JB):                         0.00\n",
      "Kurtosis:                      27.895   Cond. No.                     5.62e+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, 5.62e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "Y = house_prices_df[\"saleprice\"]\n",
    "\n",
    "X = house_prices_df[[\"overallqual\", \"grlivarea\", \"garagecars\", \"garagearea\", \"totalbsmtsf\"] + dummy_column_names]\n",
    "\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size = 0.2, random_state = 465)\n",
    "\n",
    "print(\"The number of observations in the training set is {}\".format(X_train.shape[0]))\n",
    "print(\"The number of observations in the test set is {}\".format(X_test.shape[0]))\n",
    "\n",
    "X_train = sm.add_constant(X_train)\n",
    "\n",
    "results = sm.OLS(y_train, X_train).fit()\n",
    "\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The R-squared and the adjusted R-squared of the model are 0.768 and 0.766. It means around around 23 % of the variable are unexplained by the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error of the prediction is: 25546.80382858886\n",
      "Mean squared error of the prediction is:1559083821.9730694\n",
      "Root mean squared error of the prediction is: 39485.2354934483\n",
      "Mean absolute percentage error of the prediction is: 15.551420347537784\n"
     ]
    }
   ],
   "source": [
    "X_test = sm.add_constant(X_test)\n",
    "\n",
    "y_preds = results.predict(X_test)\n",
    "\n",
    "plt.scatter(y_test, y_preds)\n",
    "plt.plot(y_test, y_test, color=\"red\")\n",
    "plt.xlabel(\"true values\")\n",
    "plt.ylabel(\"predicted values\")\n",
    "plt.title(\"Charges: true and predicted values\")\n",
    "plt.show()\n",
    "\n",
    "print(\"Mean absolute error of the prediction is: {}\".format(mean_absolute_error(y_test, y_preds)))\n",
    "print(\"Mean squared error of the prediction is:{}\".format(mse(y_test, y_preds)))\n",
    "print(\"Root mean squared error of the prediction is: {}\".format(rmse(y_test, y_preds)))\n",
    "print(\"Mean absolute percentage error of the prediction is: {}\".format(np.mean(np.abs((y_test - y_preds)/y_test))*100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>saleprice</td>    <th>  R-squared:         </th> <td>   0.832</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.831</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   520.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 24 Jan 2020</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:54:40</td>     <th>  Log-Likelihood:    </th> <td>  463.99</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1168</td>      <th>  AIC:               </th> <td>  -904.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1156</td>      <th>  BIC:               </th> <td>  -843.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    11</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>    9.9162</td> <td>    0.102</td> <td>   97.518</td> <td> 0.000</td> <td>    9.717</td> <td>   10.116</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>overallqual</th> <td>    0.1893</td> <td>    0.009</td> <td>   20.123</td> <td> 0.000</td> <td>    0.171</td> <td>    0.208</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>grlivarea</th>   <td>  9.58e-05</td> <td> 1.89e-05</td> <td>    5.074</td> <td> 0.000</td> <td> 5.88e-05</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>garagecars</th>  <td>    0.0779</td> <td>    0.015</td> <td>    5.244</td> <td> 0.000</td> <td>    0.049</td> <td>    0.107</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>garagearea</th>  <td>    0.0001</td> <td> 5.04e-05</td> <td>    2.132</td> <td> 0.033</td> <td> 8.57e-06</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>totalsf</th>     <td>    0.0003</td> <td> 2.58e-05</td> <td>   11.139</td> <td> 0.000</td> <td>    0.000</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>int_over_sf</th> <td>-2.572e-05</td> <td> 3.02e-06</td> <td>   -8.526</td> <td> 0.000</td> <td>-3.16e-05</td> <td>-1.98e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mszoning_FV</th> <td>    0.3911</td> <td>    0.065</td> <td>    6.055</td> <td> 0.000</td> <td>    0.264</td> <td>    0.518</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mszoning_RH</th> <td>    0.2650</td> <td>    0.074</td> <td>    3.593</td> <td> 0.000</td> <td>    0.120</td> <td>    0.410</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mszoning_RL</th> <td>    0.3879</td> <td>    0.060</td> <td>    6.481</td> <td> 0.000</td> <td>    0.270</td> <td>    0.505</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>mszoning_RM</th> <td>    0.2155</td> <td>    0.061</td> <td>    3.556</td> <td> 0.000</td> <td>    0.097</td> <td>    0.334</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>street_Pave</th> <td>   -0.0556</td> <td>    0.075</td> <td>   -0.744</td> <td> 0.457</td> <td>   -0.202</td> <td>    0.091</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>350.711</td> <th>  Durbin-Watson:     </th> <td>   1.876</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>2714.386</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.167</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td>10.094</td>  <th>  Cond. No.          </th> <td>5.33e+05</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, 5.33e+05. 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:              saleprice   R-squared:                       0.832\n",
       "Model:                            OLS   Adj. R-squared:                  0.831\n",
       "Method:                 Least Squares   F-statistic:                     520.9\n",
       "Date:                Fri, 24 Jan 2020   Prob (F-statistic):               0.00\n",
       "Time:                        12:54:40   Log-Likelihood:                 463.99\n",
       "No. Observations:                1168   AIC:                            -904.0\n",
       "Df Residuals:                    1156   BIC:                            -843.2\n",
       "Df Model:                          11                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "const           9.9162      0.102     97.518      0.000       9.717      10.116\n",
       "overallqual     0.1893      0.009     20.123      0.000       0.171       0.208\n",
       "grlivarea     9.58e-05   1.89e-05      5.074      0.000    5.88e-05       0.000\n",
       "garagecars      0.0779      0.015      5.244      0.000       0.049       0.107\n",
       "garagearea      0.0001   5.04e-05      2.132      0.033    8.57e-06       0.000\n",
       "totalsf         0.0003   2.58e-05     11.139      0.000       0.000       0.000\n",
       "int_over_sf -2.572e-05   3.02e-06     -8.526      0.000   -3.16e-05   -1.98e-05\n",
       "mszoning_FV     0.3911      0.065      6.055      0.000       0.264       0.518\n",
       "mszoning_RH     0.2650      0.074      3.593      0.000       0.120       0.410\n",
       "mszoning_RL     0.3879      0.060      6.481      0.000       0.270       0.505\n",
       "mszoning_RM     0.2155      0.061      3.556      0.000       0.097       0.334\n",
       "street_Pave    -0.0556      0.075     -0.744      0.457      -0.202       0.091\n",
       "==============================================================================\n",
       "Omnibus:                      350.711   Durbin-Watson:                   1.876\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2714.386\n",
       "Skew:                          -1.167   Prob(JB):                         0.00\n",
       "Kurtosis:                      10.094   Cond. No.                     5.33e+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, 5.33e+05. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "house_prices_df[\"totalsf\"] = house_prices_df[\"totalbsmtsf\"] + house_prices_df[\"firstflrsf\"] + house_prices_df[\"secondflrsf\"]\n",
    "\n",
    "house_prices_df[\"int_over_sf\"] = house_prices_df[\"totalsf\"] * house_prices_df[\"overallqual\"]\n",
    "\n",
    "Y = np.log1p(house_prices_df[\"saleprice\"])\n",
    "\n",
    "X = house_prices_df[[\"overallqual\", \"grlivarea\", \"garagecars\", \"garagearea\", \"totalsf\", \"int_over_sf\"] + dummy_column_names]\n",
    "\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size = 0.2, random_state=465)\n",
    "\n",
    "X_train = sm.add_constant(X_train)\n",
    "\n",
    "results = sm.OLS(y_train, X_train).fit()\n",
    "\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean absolute error of the prediction is: 0.12570372872846994\n",
      "Mean squared error of the prediction is: 0.029192121871241587\n",
      "Root mean squared error of the prediction is: 0.17085702172062342\n",
      "Mean absolute percentage error of the prediction is: 1.0503577667814545\n"
     ]
    }
   ],
   "source": [
    "y_preds = results.predict(X_test)\n",
    "\n",
    "plt.scatter(y_test, y_preds)\n",
    "plt.plot(y_test, y_test, color=\"red\")\n",
    "plt.xlabel(\"true values\")\n",
    "plt.ylabel(\"predicted values\")\n",
    "plt.title(\"Charges: true and predicted values\")\n",
    "plt.show()\n",
    "\n",
    "print(\"Mean absolute error of the prediction is: {}\".format(mean_absolute_error(y_test, y_preds)))\n",
    "print(\"Mean squared error of the prediction is: {}\".format(mse(y_test, y_preds)))\n",
    "print(\"Root mean squared error of the prediction is: {}\".format(rmse(y_test, y_preds)))\n",
    "print(\"Mean absolute percentage error of the prediction is: {}\".format(np.mean(np.abs((y_test - y_preds)/ y_test))*100))"
   ]
  },
  {
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}