Simple_Linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "acce1b0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import plotly.express as px\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from scipy.stats import norm, skew\n",
    "from sklearn.preprocessing import OneHotEncoder\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.neighbors import KNeighborsClassifier  \n",
    "from sklearn.svm import SVC\n",
    "from sklearn.tree import DecisionTreeClassifier \n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from xgboost import XGBClassifier\n",
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "from sklearn import metrics\n",
    "from sklearn.metrics import confusion_matrix, accuracy_score, classification_report, precision_score, recall_score, f1_score\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from imblearn.over_sampling import SMOTE #generating synthetic samples of the minority class \n",
    "#from imblearn.under_sampling import RandomUnderSampler\n",
    "from imblearn.pipeline import Pipeline\n",
    "from collections import Counter\n",
    "import math\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "82aeb78d",
   "metadata": {},
   "outputs": [],
   "source": [
    "area_price=pd.read_csv(\"/Users/souravghoshhansda/Library/CloudStorage/OneDrive-Personal/data_exploration_ml/Area_Price.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2a628599",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Area</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2600</td>\n",
       "      <td>550000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3000</td>\n",
       "      <td>565000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3200</td>\n",
       "      <td>610000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3600</td>\n",
       "      <td>680000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4000</td>\n",
       "      <td>725000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <th>94</th>\n",
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       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>9273</td>\n",
       "      <td>740444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>6130</td>\n",
       "      <td>812544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>99 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Area   Price\n",
       "0   2600  550000\n",
       "1   3000  565000\n",
       "2   3200  610000\n",
       "3   3600  680000\n",
       "4   4000  725000\n",
       "..   ...     ...\n",
       "94  4844  617067\n",
       "95  9273  740444\n",
       "96  6130  812544\n",
       "97  9806  677646\n",
       "98  9798  742147\n",
       "\n",
       "[99 rows x 2 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "area_price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ce19cc66",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/souravghoshhansda/anaconda3/envs/notebook/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead\n",
      "  if pd.api.types.is_categorical_dtype(vector):\n",
      "/Users/souravghoshhansda/anaconda3/envs/notebook/lib/python3.10/site-packages/seaborn/_oldcore.py:1498: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead\n",
      "  if pd.api.types.is_categorical_dtype(vector):\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Area', ylabel='Price'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x='Area',y='Price',data=area_price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b3bece0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x=area_price.drop('Price',axis=1)\n",
    "y=area_price['Price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ebc7323d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(    Area\n",
       " 49  3302\n",
       " 70  8491\n",
       " 68  6588\n",
       " 15  4204\n",
       " 39  3983\n",
       " ..   ...\n",
       " 60  7025\n",
       " 71  7718\n",
       " 14  4073\n",
       " 92  4712\n",
       " 51  6876\n",
       " \n",
       " [79 rows x 1 columns],\n",
       "     Area\n",
       " 62  5876\n",
       " 40  4393\n",
       " 95  9273\n",
       " 18  8229\n",
       " 97  9806\n",
       " 84  5436\n",
       " 64  7250\n",
       " 42  8105\n",
       " 10  4900\n",
       " 0   2600\n",
       " 31  3253\n",
       " 76  8492\n",
       " 47  5272\n",
       " 26  5358\n",
       " 44  7510\n",
       " 4   4000\n",
       " 22  5090\n",
       " 12  4400\n",
       " 88  7387\n",
       " 73  2897,\n",
       " 49    976026\n",
       " 70    635957\n",
       " 68    988978\n",
       " 15    713918\n",
       " 39    582040\n",
       "        ...  \n",
       " 60    745573\n",
       " 71    784970\n",
       " 14    780196\n",
       " 92    638635\n",
       " 51    914000\n",
       " Name: Price, Length: 79, dtype: int64,\n",
       " 62    751103\n",
       " 40    757789\n",
       " 95    740444\n",
       " 18    718395\n",
       " 97    677646\n",
       " 84    932095\n",
       " 64    614333\n",
       " 42    984343\n",
       " 10    785000\n",
       " 0     550000\n",
       " 31    820140\n",
       " 76    911984\n",
       " 47    873188\n",
       " 26    814657\n",
       " 44    831526\n",
       " 4     725000\n",
       " 22    981871\n",
       " 12    805000\n",
       " 88    755020\n",
       " 73    694530\n",
       " Name: Price, dtype: int64)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#train-test split\n",
    "x_train,x_test,y_train,y_test=train_test_split(x,y,test_size=0.2,random_state=42)\n",
    "x_train,x_test,y_train,y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "84f16fc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_reg=linear_model.LinearRegression()\n",
    "linear_reg.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8925bd1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "input = np.array([3300])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b2823063",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/souravghoshhansda/anaconda3/envs/notebook/lib/python3.10/site-packages/sklearn/base.py:464: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "input_reshaped = input.reshape(-1, 1)\n",
    "prediction = linear_reg.predict(input_reshaped)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7e3a284a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([735187.38697518])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7cb1501f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11.48131018])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "adc84c3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "697299.063378724"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "034179a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "735187.386972724"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "11.48131018*3300+697299.063378724"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9f7862cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([764763.24200078, 747736.45900274, 803765.25268478, 791778.76485608,\n",
       "       809884.79101111, 759711.46552126, 780538.56218913, 790355.08239367,\n",
       "       753557.48326438, 727150.46984866, 734647.76539669, 794798.34943362,\n",
       "       757828.53065161, 758815.92332716, 783523.70283612, 743224.30410171,\n",
       "       755738.93219872, 747816.828174  , 782111.50168389, 730560.41897234])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred=linear_reg.predict(x_test)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f52745f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12552683097.803013"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#calculation of evaluation of regression metrics\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error, median_absolute_error, explained_variance_score, r2_score\n",
    "mse = mean_squared_error(y_test, y_pred)\n",
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0f5dc4fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "112038.75712360886"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse = np.sqrt(mse)\n",
    "rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9582c3ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "91018.43925742629"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mae = mean_absolute_error(y_test, y_pred)\n",
    "mae"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6dde6d88",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Absolute Error (MSAE): 8284356284.8578\n"
     ]
    }
   ],
   "source": [
    "msae = mae ** 2\n",
    "print(f\"Mean Squared Absolute Error (MSAE): {msae}\")\n",
    "# Mean Squared Absolute Error (MSAE) - There is no direct function, we can define it as MAE squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e788dd6f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median Absolute Error (MedAE): 68352.50877042825\n"
     ]
    }
   ],
   "source": [
    "medae = median_absolute_error(y_test, y_pred)\n",
    "print(f\"Median Absolute Error (MedAE): {medae}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b8a8ca3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained Variance Score: 0.01113702975494879\n"
     ]
    }
   ],
   "source": [
    "explained_variance = explained_variance_score(y_test, y_pred)\n",
    "print(f\"Explained Variance Score: {explained_variance}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1f39d53f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 Score: -0.022386426258041325\n"
     ]
    }
   ],
   "source": [
    "r2 = r2_score(y_test, y_pred)\n",
    "print(f\"R^2 Score: {r2}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e9f66014",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adjusted R^2 Score: -0.07918567216126582\n"
     ]
    }
   ],
   "source": [
    "n = len(y_test)  # Number of observations\n",
    "p = 1  # Number of predictor variables\n",
    "adjusted_r2 = 1 - (1 - r2) * (n - 1) / (n - p - 1)\n",
    "print(f\"Adjusted R^2 Score: {adjusted_r2}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "68a13a40",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3920aa77",
   "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 (uncentered):</th>      <td>   0.882</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.880</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   581.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 29 Jun 2024</td> <th>  Prob (F-statistic):</th>          <td>6.66e-38</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>22:36:07</td>     <th>  Log-Likelihood:    </th>          <td> -1099.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    79</td>      <th>  AIC:               </th>          <td>   2200.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    78</td>      <th>  BIC:               </th>          <td>   2203.</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>Area</th> <td>  115.5052</td> <td>    4.790</td> <td>   24.114</td> <td> 0.000</td> <td>  105.969</td> <td>  125.041</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.456</td> <th>  Durbin-Watson:     </th> <td>   2.302</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.796</td> <th>  Jarque-Bera (JB):  </th> <td>   0.587</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.158</td> <th>  Prob(JB):          </th> <td>   0.746</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.721</td> <th>  Cond. No.          </th> <td>    1.00</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &      Price       & \\textbf{  R-squared (uncentered):}      &     0.882   \\\\\n",
       "\\textbf{Model:}            &       OLS        & \\textbf{  Adj. R-squared (uncentered):} &     0.880   \\\\\n",
       "\\textbf{Method:}           &  Least Squares   & \\textbf{  F-statistic:       }          &     581.5   \\\\\n",
       "\\textbf{Date:}             & Sat, 29 Jun 2024 & \\textbf{  Prob (F-statistic):}          &  6.66e-38   \\\\\n",
       "\\textbf{Time:}             &     22:36:07     & \\textbf{  Log-Likelihood:    }          &   -1099.1   \\\\\n",
       "\\textbf{No. Observations:} &          79      & \\textbf{  AIC:               }          &     2200.   \\\\\n",
       "\\textbf{Df Residuals:}     &          78      & \\textbf{  BIC:               }          &     2203.   \\\\\n",
       "\\textbf{Df Model:}         &           1      & \\textbf{                     }          &             \\\\\n",
       "\\textbf{Covariance Type:}  &    nonrobust     & \\textbf{                     }          &             \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "              & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Area} &     115.5052  &        4.790     &    24.114  &         0.000        &      105.969    &      125.041     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       &  0.456 & \\textbf{  Durbin-Watson:     } &    2.302  \\\\\n",
       "\\textbf{Prob(Omnibus):} &  0.796 & \\textbf{  Jarque-Bera (JB):  } &    0.587  \\\\\n",
       "\\textbf{Skew:}          & -0.158 & \\textbf{  Prob(JB):          } &    0.746  \\\\\n",
       "\\textbf{Kurtosis:}      &  2.721 & \\textbf{  Cond. No.          } &     1.00  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] R² is computed without centering (uncentered) since the model does not contain a constant. \\newline\n",
       " [2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                  Price   R-squared (uncentered):                   0.882\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.880\n",
       "Method:                 Least Squares   F-statistic:                              581.5\n",
       "Date:                Sat, 29 Jun 2024   Prob (F-statistic):                    6.66e-38\n",
       "Time:                        22:36:07   Log-Likelihood:                         -1099.1\n",
       "No. Observations:                  79   AIC:                                      2200.\n",
       "Df Residuals:                      78   BIC:                                      2203.\n",
       "Df Model:                           1                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Area         115.5052      4.790     24.114      0.000     105.969     125.041\n",
       "==============================================================================\n",
       "Omnibus:                        0.456   Durbin-Watson:                   2.302\n",
       "Prob(Omnibus):                  0.796   Jarque-Bera (JB):                0.587\n",
       "Skew:                          -0.158   Prob(JB):                        0.746\n",
       "Kurtosis:                       2.721   Cond. No.                         1.00\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_OLS = sm.OLS(y_train, x_train)\n",
    "results = model_OLS.fit()\n",
    "results.summary()\n",
    "#OLS-ordinary least squares:It is a type of linear regression model for estimating the parameters in a linear regression model. The goal of OLS is to find the line that minimizes the sum of squared differences (of residuals) between observed values and values predicted by the model.\n",
    "#It assumes linear relationship between the dependent and independent variables of the model and expresses the dependent variable 'y' as a linear combination of one or more independent variables 'x'.\n",
    "#Objective of OLS is to estimate the coefficients Beta(i)such that the sum of squared residuals is minimized.\n",
    "#Assumptions of OLS- The relationship between dependent and independent variables is linear, the observations are independent of each other and there is constant variance of the errors. The errors are normally distributed and there is no multi-collinearity meaning that the independent variables are not highly correlated.\n",
    "#Note-OLS does not perform well generally if the assumptions are violated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2aee6644",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_OLS = results.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a6d204ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "72819053676.66666"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse_OLS = mean_squared_error(y_test, y_pred_OLS)\n",
    "mse_OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "cf65e6ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "269850.0577666543"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_OLS = np.sqrt(mse_OLS)\n",
    "rmse_OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8b1f6924",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "240286.88473731125"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mae_OLS = mean_absolute_error(y_test, y_pred_OLS)\n",
    "mae_OLS"
   ]
  }
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