{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c8e6a45e-ec06-46bf-b672-9cc0d8c0f16d",
   "metadata": {},
   "source": [
    "### Toyota Car Prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ab356672-aea9-4fc5-86a7-ea2e9088f3f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, Lasso, Ridge, LassoCV, BayesianRidge\n",
    "from sklearn import metrics\n",
    "from itertools import combinations\n",
    "import statsmodels.formula.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "67fe6d71-ba69-4a83-971e-98e1af9e351f",
   "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>Id</th>\n",
       "      <th>Model</th>\n",
       "      <th>Price</th>\n",
       "      <th>Age_08_04</th>\n",
       "      <th>Mfg_Month</th>\n",
       "      <th>Mfg_Year</th>\n",
       "      <th>KM</th>\n",
       "      <th>Fuel_Type</th>\n",
       "      <th>HP</th>\n",
       "      <th>Met_Color</th>\n",
       "      <th>...</th>\n",
       "      <th>Powered_Windows</th>\n",
       "      <th>Power_Steering</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Mistlamps</th>\n",
       "      <th>Sport_Model</th>\n",
       "      <th>Backseat_Divider</th>\n",
       "      <th>Metallic_Rim</th>\n",
       "      <th>Radio_cassette</th>\n",
       "      <th>Parking_Assistant</th>\n",
       "      <th>Tow_Bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors</td>\n",
       "      <td>13500</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>2002</td>\n",
       "      <td>46986</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>90</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors</td>\n",
       "      <td>13750</td>\n",
       "      <td>23</td>\n",
       "      <td>10</td>\n",
       "      <td>2002</td>\n",
       "      <td>72937</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>90</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors</td>\n",
       "      <td>13950</td>\n",
       "      <td>24</td>\n",
       "      <td>9</td>\n",
       "      <td>2002</td>\n",
       "      <td>41711</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>90</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors</td>\n",
       "      <td>14950</td>\n",
       "      <td>26</td>\n",
       "      <td>7</td>\n",
       "      <td>2002</td>\n",
       "      <td>48000</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>TOYOTA Corolla 2.0 D4D HATCHB SOL 2/3-Doors</td>\n",
       "      <td>13750</td>\n",
       "      <td>30</td>\n",
       "      <td>3</td>\n",
       "      <td>2002</td>\n",
       "      <td>38500</td>\n",
       "      <td>Diesel</td>\n",
       "      <td>90</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 39 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Id                                          Model  Price  Age_08_04  \\\n",
       "0   1  TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors  13500         23   \n",
       "1   2  TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors  13750         23   \n",
       "2   3  TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors  13950         24   \n",
       "3   4  TOYOTA Corolla 2.0 D4D HATCHB TERRA 2/3-Doors  14950         26   \n",
       "4   5    TOYOTA Corolla 2.0 D4D HATCHB SOL 2/3-Doors  13750         30   \n",
       "\n",
       "   Mfg_Month  Mfg_Year     KM Fuel_Type  HP  Met_Color  ... Powered_Windows  \\\n",
       "0         10      2002  46986    Diesel  90          1  ...               1   \n",
       "1         10      2002  72937    Diesel  90          1  ...               0   \n",
       "2          9      2002  41711    Diesel  90          1  ...               0   \n",
       "3          7      2002  48000    Diesel  90          0  ...               0   \n",
       "4          3      2002  38500    Diesel  90          0  ...               1   \n",
       "\n",
       "   Power_Steering  Radio  Mistlamps  Sport_Model  Backseat_Divider  \\\n",
       "0               1      0          0            0                 1   \n",
       "1               1      0          0            0                 1   \n",
       "2               1      0          0            0                 1   \n",
       "3               1      0          0            0                 1   \n",
       "4               1      0          1            0                 1   \n",
       "\n",
       "   Metallic_Rim  Radio_cassette  Parking_Assistant  Tow_Bar  \n",
       "0             0               0                  0        0  \n",
       "1             0               0                  0        0  \n",
       "2             0               0                  0        0  \n",
       "3             0               0                  0        0  \n",
       "4             0               0                  0        0  \n",
       "\n",
       "[5 rows x 39 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(r'/Users/patriciaxufre/Documents/SBE - Disciplinas/2957 | ABA/2024-25/Datasets Examples/ToyotaCorolla.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0b2a104a-27d8-451f-bfe7-f8c48d2db922",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Id', 'Model', 'Price', 'Age_08_04', 'Mfg_Month', 'Mfg_Year', 'KM',\n",
       "       'Fuel_Type', 'HP', 'Met_Color', 'Color', 'Automatic', 'CC', 'Doors',\n",
       "       'Cylinders', 'Gears', 'Quarterly_Tax', 'Weight', 'Mfr_Guarantee',\n",
       "       'BOVAG_Guarantee', 'Guarantee_Period', 'ABS', 'Airbag_1', 'Airbag_2',\n",
       "       'Airco', 'Automatic_airco', 'Boardcomputer', 'CD_Player',\n",
       "       'Central_Lock', 'Powered_Windows', 'Power_Steering', 'Radio',\n",
       "       'Mistlamps', 'Sport_Model', 'Backseat_Divider', 'Metallic_Rim',\n",
       "       'Radio_cassette', 'Parking_Assistant', 'Tow_Bar'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72795da5-086a-4986-b5ef-c4e108648605",
   "metadata": {},
   "source": [
    "#### 1st Linear Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0aceb23c-2f41-44f4-b8cd-b140007879bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a list of predictor variables by removing the output variable and text columns\n",
    "exclude = ('Price', 'Id', 'Model', 'Fuel_Type', 'Color')\n",
    "predictors = [s for s in df.columns if s not in exclude]\n",
    "outcome = 'Price'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "31cb914e-6a01-42df-a80c-b8e1519763ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "# partition data\n",
    "X = df[predictors]\n",
    "y = df[outcome]\n",
    "train_X, test_X, train_y, test_y = train_test_split(X, y, test_size = 0.4, random_state = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2b8a8dfa-655a-4872-ac98-d1c59a4acb52",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Linear Regression Model (only in the train set)\n",
    "reg = LinearRegression()\n",
    "reg.fit(train_X, train_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "65bceac3-9142-404c-b2b8-335fe934e0b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_error_train = pd.DataFrame({\n",
    "    'residual': train_y - reg.predict(train_X),\n",
    "    'data set': 'training'\n",
    "})\n",
    "pred_error_test = pd.DataFrame({\n",
    "    'residual': test_y - reg.predict(test_X),\n",
    "    'data set': 'test'\n",
    "})\n",
    "boxdata_df = pd.concat([pred_error_train, pred_error_test], ignore_index = True)\n",
    "order = ['training', 'test']\n",
    "boxdata_df['data set']= pd.Categorical(boxdata_df['data set'], categories = order, ordered = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2c3b5589-9e9f-4c70-ad22-5900d46e93e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows = 1, ncols = 3)\n",
    "fig.set_size_inches(9,4)\n",
    "common = {'bins': 100, 'range': [-6500,6500]}\n",
    "pred_error_train.hist(ax = axes[0], **common)\n",
    "pred_error_test.hist(ax = axes[1], **common)\n",
    "boxdata_df.boxplot(ax=axes[2], by = 'data set')\n",
    "axes[0].set_title(\"Training\")\n",
    "axes[1].set_title(\"Test\")\n",
    "axes[0].set_ylabel(\"\")\n",
    "axes[1].set_ylabel(\"\")\n",
    "axes[2].set_title(\"\")\n",
    "fig.suptitle(\"\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d51a14fc-7991-4734-8a41-1c55b52bb52b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance Measures - Training Set\n",
      "Mean Absolute Error: 811.68\n",
      "Mean Absolute Percentage Error: 8.01%\n",
      "Root Mean Squared Error: 1121.06\n",
      "\n",
      "Performance Measures - Test Set\n",
      "Mean Absolute Error: 880.14\n",
      "Mean Absolute Percentage Error: 8.87%\n",
      "Root Mean Squared Error: 1382.04\n"
     ]
    }
   ],
   "source": [
    "# Evaluating Performance\n",
    "# Training Set\n",
    "mae = metrics.mean_absolute_error(train_y, reg.predict(train_X))\n",
    "mape = metrics.mean_absolute_percentage_error(train_y, reg.predict(train_X))\n",
    "mse = metrics.mean_squared_error(train_y, reg.predict(train_X))\n",
    "rmse = np.sqrt(mse)\n",
    "print('Performance Measures - Training Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')\n",
    "# Test Set\n",
    "mae = metrics.mean_absolute_error(test_y,reg.predict(test_X))\n",
    "mape = metrics.mean_absolute_percentage_error(test_y, reg.predict(test_X))\n",
    "mse = metrics.mean_squared_error(test_y, reg.predict(test_X))\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures - Test Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b6aa2ce-7240-4484-bed9-2e6d60c014ad",
   "metadata": {},
   "source": [
    "#### 2nd Linear Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "183b91af-e593-440e-94b4-c049858a24d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "predictors = ['Age_08_04', 'KM', 'Fuel_Type', 'HP', 'Met_Color', 'Automatic', 'CC', 'Doors', 'Quarterly_Tax', 'Weight']\n",
    "outcome = 'Price'\n",
    "# partition data\n",
    "X = pd.get_dummies(df[predictors], drop_first = True)\n",
    "y = df[outcome]\n",
    "train_X, test_X, train_y, test_y = train_test_split(X, y, test_size = 0.4, random_state = 123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5c4108c8-a202-4227-9983-fc762b160b04",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Predictor  coefficient\n",
      "0          Age_08_04  -113.244942\n",
      "1                 KM    -0.015739\n",
      "2                 HP     2.325408\n",
      "3          Met_Color   -72.350023\n",
      "4          Automatic  -149.178152\n",
      "5                 CC    -0.038289\n",
      "6              Doors  -251.428537\n",
      "7      Quarterly_Tax    14.975890\n",
      "8             Weight    32.255569\n",
      "9   Fuel_Type_Diesel -1307.813608\n",
      "10  Fuel_Type_Petrol  2785.721080\n"
     ]
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm.fit(train_X, train_y)\n",
    "\n",
    "# coefficients:\n",
    "print(pd.DataFrame({'Predictor': X.columns, 'coefficient': lm.coef_}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f2bbbfc3-e42c-40f0-af7a-55694bcedef3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Performance Measures - Training Set\n",
      "Mean Absolute Error: 922.12\n",
      "Mean Absolute Percentage Error: 9.31%\n",
      "Root Mean Squared Error: 1190.13\n",
      "\n",
      "Performance Measures - Test Set\n",
      "Mean Absolute Error: 1018.69\n",
      "Mean Absolute Percentage Error: 9.86%\n",
      "Root Mean Squared Error: 1605.91\n"
     ]
    }
   ],
   "source": [
    "# Evaluating Performance\n",
    "# Training Set\n",
    "mae = metrics.mean_absolute_error(train_y,lm.predict(train_X))\n",
    "mape = metrics.mean_absolute_percentage_error(train_y, lm.predict(train_X))\n",
    "mse = metrics.mean_squared_error(train_y, lm.predict(train_X))\n",
    "rmse = np.sqrt(mse)\n",
    "print('Performance Measures - Training Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')\n",
    "# Test Set\n",
    "mae = metrics.mean_absolute_error(test_y,lm.predict(test_X))\n",
    "mape = metrics.mean_absolute_percentage_error(test_y, lm.predict(test_X))\n",
    "mse = metrics.mean_squared_error(test_y, lm.predict(test_X))\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures - Test Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "24fa6746-d6f2-4d9f-a56d-bd8f203349a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Residuals\n",
    "pred_error_train = pd.DataFrame({\n",
    "    'residual': train_y - lm.predict(train_X),\n",
    "    'data set': 'training'\n",
    "})\n",
    "pred_error_test = pd.DataFrame({\n",
    "    'residual': test_y - lm.predict(test_X),\n",
    "    'data set': 'test'\n",
    "})\n",
    "fig, axes = plt.subplots(nrows = 1, ncols = 2)\n",
    "fig.set_size_inches(9,4)\n",
    "common = {'bins': 100, 'range': [-6500,6500]}\n",
    "pred_error_train.hist(ax = axes[0], **common)\n",
    "pred_error_test.hist(ax = axes[1], **common)\n",
    "axes[0].set_title(\"Training\")\n",
    "axes[1].set_title(\"Test\")\n",
    "axes[0].set_ylabel(\"\")\n",
    "axes[1].set_ylabel(\"\")\n",
    "fig.suptitle(\"\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fb27e5a6-9f98-414a-a11f-23a7d25a3268",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Performance Measures\n",
    "# Function to compute Adjusted R²\n",
    "def adjusted_r2_score(y_true, y_pred, model):\n",
    "    r2 = metrics.r2_score(y_true, y_pred)\n",
    "    n = len(y_true) # number of observations\n",
    "    p = len(model.coef_) # number of predictors\n",
    "    return 1 - ((1 - r2) * (n-1) / (n-p-1)) # adj R2 formula\n",
    "    \n",
    "# Function to compute AIC (Akaike Information Criterion)\n",
    "def AIC_score(y_true, y_pred, model):\n",
    "    n = len(y_true)\n",
    "    rss = np.sum((y_true - y_pred)**2) # SSE - Residual sum of Squares\n",
    "    p = len(model.coef_)\n",
    "    return n*np.log(rss/n) + 2*(p+1) # AIC formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79418881-c7f0-4839-ac40-33a59f483906",
   "metadata": {},
   "source": [
    "#### Exhaustive Feature Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5469cf22-f89e-4319-ab7d-1e188508a088",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Exhaustive Search Function\n",
    "def exhaustive_search(variables, train_fn, score_fn):\n",
    "    best_results = []\n",
    "    for k in range(1,len(variables)+1):\n",
    "        for subset in combinations(variables, k):\n",
    "            model = train_fn(subset)\n",
    "            score = score_fn(model, subset)\n",
    "            best_results.append({'n': k, 'score': score, 'model': model, 'variables': subset})\n",
    "    return sorted(best_results, key = lambda x: x['score'], reverse = True)\n",
    "                \n",
    "# Function to train a model with selected variables\n",
    "def train_model(variables):\n",
    "    model = LinearRegression()\n",
    "    model.fit(train_X[list(variables)], train_y)\n",
    "    return model\n",
    "\n",
    "# Function to score the model using Adjusted R²\n",
    "def score_model(model, variables):\n",
    "    pred_y = model.predict(train_X[list(variables)])\n",
    "    return -adjusted_r2_score(train_y, pred_y, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "de9b3396-57c4-445b-8583-ac32bcdadb04",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define predictors\n",
    "allVariables = train_X.columns\n",
    "\n",
    "# Perform exhaustive feature search\n",
    "results = exhaustive_search(allVariables, train_model, score_model)\n",
    "\n",
    "# Store results in a DataFrame\n",
    "data = []\n",
    "for result in results:\n",
    "    model = result['model']\n",
    "    variables = list(result['variables'])\n",
    "    AIC = AIC_score(train_y, model.predict(train_X[variables]), model)\n",
    "    d = {'n': result['n'], 'r2adj': -result['score'], 'AIC': AIC}\n",
    "    d.update({var: var in result['variables'] for var in allVariables})\n",
    "    data.append(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7db67835-428d-49e7-9fa6-914d8f7b662a",
   "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>n</th>\n",
       "      <th>r2adj</th>\n",
       "      <th>AIC</th>\n",
       "      <th>Age_08_04</th>\n",
       "      <th>Automatic</th>\n",
       "      <th>CC</th>\n",
       "      <th>Doors</th>\n",
       "      <th>Fuel_Type_Diesel</th>\n",
       "      <th>Fuel_Type_Petrol</th>\n",
       "      <th>HP</th>\n",
       "      <th>KM</th>\n",
       "      <th>Met_Color</th>\n",
       "      <th>Quarterly_Tax</th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1024</th>\n",
       "      <td>1</td>\n",
       "      <td>0.765863</td>\n",
       "      <td>12807.545515</td>\n",
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       "      <td>0.800835</td>\n",
       "      <td>12669.255092</td>\n",
       "      <td>True</td>\n",
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       "      <th>1671</th>\n",
       "      <td>3</td>\n",
       "      <td>0.855124</td>\n",
       "      <td>12396.234593</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1878</th>\n",
       "      <td>4</td>\n",
       "      <td>0.871117</td>\n",
       "      <td>12296.514559</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
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       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990</th>\n",
       "      <td>5</td>\n",
       "      <td>0.878224</td>\n",
       "      <td>12248.669683</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022</th>\n",
       "      <td>6</td>\n",
       "      <td>0.881719</td>\n",
       "      <td>12224.591431</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2046</th>\n",
       "      <td>7</td>\n",
       "      <td>0.883439</td>\n",
       "      <td>12212.969194</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2045</th>\n",
       "      <td>8</td>\n",
       "      <td>0.883431</td>\n",
       "      <td>12214.014649</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2044</th>\n",
       "      <td>9</td>\n",
       "      <td>0.883388</td>\n",
       "      <td>12215.322797</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2037</th>\n",
       "      <td>10</td>\n",
       "      <td>0.883281</td>\n",
       "      <td>12217.098365</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2031</th>\n",
       "      <td>11</td>\n",
       "      <td>0.883173</td>\n",
       "      <td>12218.884757</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       n     r2adj           AIC  Age_08_04  Automatic     CC  Doors  \\\n",
       "1024   1  0.765863  12807.545515       True      False  False  False   \n",
       "1208   2  0.800835  12669.255092       True      False  False  False   \n",
       "1671   3  0.855124  12396.234593       True      False  False  False   \n",
       "1878   4  0.871117  12296.514559       True      False  False  False   \n",
       "1990   5  0.878224  12248.669683       True      False  False  False   \n",
       "2022   6  0.881719  12224.591431       True      False  False   True   \n",
       "2046   7  0.883439  12212.969194       True      False  False   True   \n",
       "2045   8  0.883431  12214.014649       True       True  False   True   \n",
       "2044   9  0.883388  12215.322797       True       True  False   True   \n",
       "2037  10  0.883281  12217.098365       True       True  False   True   \n",
       "2031  11  0.883173  12218.884757       True       True   True   True   \n",
       "\n",
       "      Fuel_Type_Diesel  Fuel_Type_Petrol     HP     KM  Met_Color  \\\n",
       "1024             False             False  False  False      False   \n",
       "1208             False             False   True  False      False   \n",
       "1671             False              True  False  False      False   \n",
       "1878             False              True  False   True      False   \n",
       "1990             False              True  False   True      False   \n",
       "2022             False              True  False   True      False   \n",
       "2046              True              True  False   True      False   \n",
       "2045              True              True  False   True      False   \n",
       "2044              True              True  False   True       True   \n",
       "2037              True              True   True   True       True   \n",
       "2031              True              True   True   True       True   \n",
       "\n",
       "      Quarterly_Tax  Weight  \n",
       "1024          False   False  \n",
       "1208          False   False  \n",
       "1671          False    True  \n",
       "1878          False    True  \n",
       "1990           True    True  \n",
       "2022           True    True  \n",
       "2046           True    True  \n",
       "2045           True    True  \n",
       "2044           True    True  \n",
       "2037           True    True  \n",
       "2031           True    True  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create DataFrame with results\n",
    "results_df = pd.DataFrame(data, columns=['n', 'r2adj', 'AIC'] + sorted(allVariables))\n",
    "\n",
    "best_models = results_df.loc[results_df.groupby('n')['r2adj'].idxmax()]  # Get the best model for each subset size\n",
    "\n",
    "# Sort by number of features\n",
    "best_models.sort_values(by='n')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb55159c-0fa1-48d5-887c-f717e75fc17f",
   "metadata": {},
   "source": [
    "#### Iterative Features Selection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd11aa92-b061-4c6b-84de-2d19c11ea6db",
   "metadata": {},
   "source": [
    "#### Forward Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "36a898ec-59fa-4ad2-b0d9-5bf1032d2f61",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Added Feature: Age_08_04, Adjusted R²: 0.7659\n",
      "Added Feature: HP, Adjusted R²: 0.8008\n",
      "Added Feature: Weight, Adjusted R²: 0.8327\n",
      "Added Feature: KM, Adjusted R²: 0.8641\n",
      "Added Feature: Fuel_Type_Petrol, Adjusted R²: 0.8724\n",
      "Added Feature: Quarterly_Tax, Adjusted R²: 0.8794\n",
      "Added Feature: Doors, Adjusted R²: 0.8823\n",
      "Added Feature: Fuel_Type_Diesel, Adjusted R²: 0.8834\n",
      "\n",
      "Selected Features: ['Age_08_04', 'HP', 'Weight', 'KM', 'Fuel_Type_Petrol', 'Quarterly_Tax', 'Doors', 'Fuel_Type_Diesel']\n",
      "\n",
      "Final Model Performance:\n",
      "Adjusted R² (Training Set): 0.8834\n",
      "Adjusted R² (Test Set): 0.8217\n"
     ]
    }
   ],
   "source": [
    "def forward_feature_selection(X, y):\n",
    "    selected_features = []\n",
    "    remaining_features = list(X.columns)\n",
    "    best_score = -np.inf  # Start with a very low Adjusted R²\n",
    "    best_features = None\n",
    "    \n",
    "    while remaining_features:\n",
    "        scores = []\n",
    "        \n",
    "        for feature in remaining_features:\n",
    "            temp_features = selected_features + [feature]\n",
    "            model = LinearRegression()\n",
    "            model.fit(X[temp_features], y)\n",
    "            y_pred = model.predict(X[temp_features])\n",
    "            adj_r2 = adjusted_r2_score(y, y_pred, model)  # Compute Adjusted R²\n",
    "            scores.append((feature, adj_r2))\n",
    "        \n",
    "        # Select the feature that maximizes Adjusted R²\n",
    "        scores.sort(key=lambda x: x[1], reverse=True)\n",
    "        best_new_feature, best_new_score = scores[0]\n",
    "        \n",
    "        # Stop if Adjusted R² does not improve significantly\n",
    "        if best_new_score <= best_score:\n",
    "            break\n",
    "        \n",
    "        selected_features.append(best_new_feature)\n",
    "        remaining_features.remove(best_new_feature)\n",
    "        best_score = best_new_score\n",
    "        best_features = selected_features.copy()\n",
    "        \n",
    "        print(f\"Added Feature: {best_new_feature}, Adjusted R²: {best_score:.4f}\")\n",
    "    \n",
    "    return best_features\n",
    "\n",
    "# Run forward feature selection\n",
    "best_selected_features = forward_feature_selection(train_X, train_y)\n",
    "\n",
    "print(\"\\nSelected Features:\", best_selected_features)\n",
    "\n",
    "# Fit final model with selected features\n",
    "final_model = LinearRegression()\n",
    "final_model.fit(train_X[best_selected_features], train_y)\n",
    "\n",
    "# Predict on train and test sets\n",
    "train_pred = final_model.predict(train_X[best_selected_features])\n",
    "test_pred = final_model.predict(test_X[best_selected_features])\n",
    "\n",
    "# Compute performance metrics\n",
    "train_adj_r2 = adjusted_r2_score(train_y, train_pred, final_model)\n",
    "test_adj_r2 = adjusted_r2_score(test_y, test_pred, final_model)\n",
    "\n",
    "print(f\"\\nFinal Model Performance:\")\n",
    "print(f\"Adjusted R² (Training Set): {train_adj_r2:.4f}\")\n",
    "print(f\"Adjusted R² (Test Set): {test_adj_r2:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b8eb5230-2a5e-49da-b066-4a0d186b9cb3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Performance Measures - Test Set\n",
      "Mean Absolute Error: 1016.99\n",
      "Mean Absolute Percentage Error: 9.83%\n",
      "Root Mean Squared Error: 1592.14\n"
     ]
    }
   ],
   "source": [
    "# Evaluating Performance\n",
    "# Test Set\n",
    "mae = metrics.mean_absolute_error(test_y,test_pred)\n",
    "mape = metrics.mean_absolute_percentage_error(test_y, test_pred)\n",
    "mse = metrics.mean_squared_error(test_y, test_pred)\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures - Test Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71be37ef-5039-4c56-a163-c9ec792b56e8",
   "metadata": {},
   "source": [
    "#### Backward Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8c9ae645-cb54-4014-9a3a-48d4318ed91a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Removed Feature: CC, Adjusted R²: 0.8833\n",
      "Removed Feature: HP, Adjusted R²: 0.8834\n",
      "Removed Feature: Met_Color, Adjusted R²: 0.8834\n",
      "Removed Feature: Automatic, Adjusted R²: 0.8834\n",
      "\n",
      "Selected Features: ['Age_08_04', 'KM', 'Doors', 'Quarterly_Tax', 'Weight', 'Fuel_Type_Diesel', 'Fuel_Type_Petrol']\n",
      "\n",
      "Final Model Performance:\n",
      "Adjusted R² (Training Set): 0.8834\n",
      "Adjusted R² (Test Set): 0.8188\n"
     ]
    }
   ],
   "source": [
    "def backward_feature_selection(X, y):\n",
    "    selected_features = list(X.columns)  # Start with all features\n",
    "    best_score = adjusted_r2_score(y, LinearRegression().fit(X, y).predict(X), LinearRegression().fit(X, y))  # Initial Adjusted R²\n",
    "    best_features = selected_features.copy()\n",
    "\n",
    "    while len(selected_features) > 1:\n",
    "        scores = []\n",
    "        \n",
    "        for feature in selected_features:\n",
    "            temp_features = [f for f in selected_features if f != feature]  # Remove one feature at a time\n",
    "            model = LinearRegression()\n",
    "            model.fit(X[temp_features], y)\n",
    "            y_pred = model.predict(X[temp_features])\n",
    "            adj_r2 = adjusted_r2_score(y, y_pred, model)  # Compute Adjusted R²\n",
    "            scores.append((feature, adj_r2))\n",
    "        \n",
    "        # Find the worst-performing feature (one whose removal improves Adjusted R²)\n",
    "        scores.sort(key=lambda x: x[1], reverse=True)\n",
    "        worst_feature, best_new_score = scores[0]  # The last item has the lowest impact\n",
    "        \n",
    "        # Stop if Adjusted R² does not improve\n",
    "       \n",
    "        if best_new_score > best_score:\n",
    "            selected_features.remove(worst_feature)\n",
    "            best_score = best_new_score\n",
    "            best_features = selected_features.copy()\n",
    "            print(f\"Removed Feature: {worst_feature}, Adjusted R²: {best_score:.4f}\")\n",
    "        else:\n",
    "            break         \n",
    " \n",
    "    return best_features\n",
    "\n",
    "# Run backward feature selection\n",
    "best_selected_features = backward_feature_selection(train_X, train_y)\n",
    "\n",
    "print(\"\\nSelected Features:\", best_selected_features)\n",
    "\n",
    "# Fit final model with selected features\n",
    "final_model = LinearRegression()\n",
    "final_model.fit(train_X[best_selected_features], train_y)\n",
    "\n",
    "# Predict on train and test sets\n",
    "train_pred = final_model.predict(train_X[best_selected_features])\n",
    "test_pred = final_model.predict(test_X[best_selected_features])\n",
    "\n",
    "# Compute performance metrics\n",
    "train_adj_r2 = adjusted_r2_score(train_y, train_pred, final_model)\n",
    "test_adj_r2 = adjusted_r2_score(test_y, test_pred, final_model)\n",
    "\n",
    "print(f\"\\nFinal Model Performance:\")\n",
    "print(f\"Adjusted R² (Training Set): {train_adj_r2:.4f}\")\n",
    "print(f\"Adjusted R² (Test Set): {test_adj_r2:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe089eca-55c5-42d7-9ade-f4eddac792eb",
   "metadata": {},
   "source": [
    "#### Stepwise Regression Function (Forward + Backward Selection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e616bae3-0ff3-4a1c-9a2e-001c14724526",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Added Feature: Age_08_04, Adjusted R²: 0.7659\n",
      "Added Feature: HP, Adjusted R²: 0.8008\n",
      "Added Feature: Weight, Adjusted R²: 0.8327\n",
      "Added Feature: KM, Adjusted R²: 0.8641\n",
      "Added Feature: Fuel_Type_Petrol, Adjusted R²: 0.8724\n",
      "Added Feature: Quarterly_Tax, Adjusted R²: 0.8794\n",
      "Added Feature: Doors, Adjusted R²: 0.8823\n",
      "Added Feature: Fuel_Type_Diesel, Adjusted R²: 0.8834\n",
      "\n",
      "Selected Features: ['Age_08_04', 'HP', 'Weight', 'KM', 'Fuel_Type_Petrol', 'Quarterly_Tax', 'Doors', 'Fuel_Type_Diesel']\n",
      "\n",
      "Final Model Performance:\n",
      "Adjusted R² (Training Set): 0.8834\n",
      "Adjusted R² (Test Set): 0.8217\n"
     ]
    }
   ],
   "source": [
    "def stepwise_regression(X, y):\n",
    "    selected_features = []  # Start with an empty set of features\n",
    "    remaining_features = list(X.columns)\n",
    "    best_score = -np.inf\n",
    "    best_features = None\n",
    "    improved = True  # Flag to track if improvement happens\n",
    "\n",
    "    while improved:\n",
    "        improved = False  # Reset improvement flag\n",
    "        \n",
    "        # FORWARD STEP: Try adding a new feature\n",
    "        forward_scores = []\n",
    "        for feature in remaining_features:\n",
    "            temp_features = selected_features + [feature]\n",
    "            model = LinearRegression()\n",
    "            model.fit(X[temp_features], y)\n",
    "            y_pred = model.predict(X[temp_features])\n",
    "            adj_r2 = adjusted_r2_score(y, y_pred, model)\n",
    "            forward_scores.append((feature, adj_r2))\n",
    "        \n",
    "        # Pick the feature that gives the best improvement\n",
    "        if forward_scores:\n",
    "            forward_scores.sort(key=lambda x: x[1], reverse=True)\n",
    "            best_new_feature, best_new_score = forward_scores[0]\n",
    "            \n",
    "            if best_new_score > best_score:  # Add feature if Adjusted R² improves\n",
    "                selected_features.append(best_new_feature)\n",
    "                remaining_features.remove(best_new_feature)\n",
    "                best_score = best_new_score\n",
    "                improved = True\n",
    "                print(f\"Added Feature: {best_new_feature}, Adjusted R²: {best_score:.4f}\")\n",
    "\n",
    "        # BACKWARD STEP: Try removing a feature\n",
    "        backward_scores = []\n",
    "        for feature in selected_features:\n",
    "            temp_features = [f for f in selected_features if f != feature]\n",
    "            if not temp_features:  # Ensure at least one feature is selected\n",
    "                continue\n",
    "            model = LinearRegression()\n",
    "            model.fit(X[temp_features], y)\n",
    "            y_pred = model.predict(X[temp_features])\n",
    "            adj_r2 = adjusted_r2_score(y, y_pred, model)\n",
    "            backward_scores.append((feature, adj_r2))\n",
    "        \n",
    "        # Remove the worst-performing feature if it improves Adjusted R²\n",
    "        if backward_scores:\n",
    "            backward_scores.sort(key=lambda x: x[1], reverse=True)\n",
    "            worst_feature, best_new_score = backward_scores[-1]  # The last item has the lowest impact\n",
    "            \n",
    "            if best_new_score > best_score:  # Remove feature if Adjusted R² improves\n",
    "                selected_features.remove(worst_feature)\n",
    "                remaining_features.append(worst_feature)\n",
    "                best_score = best_new_score\n",
    "                improved = True\n",
    "                print(f\"Removed Feature: {worst_feature}, Adjusted R²: {best_score:.4f}\")\n",
    "\n",
    "    return selected_features\n",
    "\n",
    "# Run stepwise regression\n",
    "best_selected_features = stepwise_regression(train_X, train_y)\n",
    "\n",
    "print(\"\\nSelected Features:\", best_selected_features)\n",
    "\n",
    "# Fit final model with selected features\n",
    "final_model = LinearRegression()\n",
    "final_model.fit(train_X[best_selected_features], train_y)\n",
    "\n",
    "# Predict on train and test sets\n",
    "train_pred = final_model.predict(train_X[best_selected_features])\n",
    "test_pred = final_model.predict(test_X[best_selected_features])\n",
    "\n",
    "# Compute performance metrics\n",
    "train_adj_r2 = adjusted_r2_score(train_y, train_pred, final_model)\n",
    "test_adj_r2 = adjusted_r2_score(test_y, test_pred, final_model)\n",
    "\n",
    "print(f\"\\nFinal Model Performance:\")\n",
    "print(f\"Adjusted R² (Training Set): {train_adj_r2:.4f}\")\n",
    "print(f\"Adjusted R² (Test Set): {test_adj_r2:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b52b955-5636-4a68-a3d9-28dc6d582acd",
   "metadata": {},
   "source": [
    "#### REGULARIZATION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "28cb0ca7-a200-45df-a90c-6a0bf5f442ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardize features (since regularization methods are sensitive to feature scaling)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01163fbc-5066-46ed-bf9e-cac402f896d3",
   "metadata": {},
   "source": [
    "#### Lasso Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "01f016c7-ca0c-4ccf-a33e-a89ae5d35c31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Performance Measures - Test Set\n",
      "Mean Absolute Error: 1017.99\n",
      "Mean Absolute Percentage Error: 9.85%\n",
      "Root Mean Squared Error: 1602.96\n"
     ]
    }
   ],
   "source": [
    "# Fit Lasso model: given alpha\n",
    "\n",
    "\n",
    "# Test Set\n",
    "mae = metrics.mean_absolute_error(test_y,lasso.predict(test_X_scaled))\n",
    "mape = metrics.mean_absolute_percentage_error(test_y, lasso.predict(test_X_scaled))\n",
    "mse = metrics.mean_squared_error(test_y, lasso.predict(test_X_scaled))\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures - Test Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "fc2937a5-5b72-4c0a-9a5e-f0195bc5c25b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Performance Measures - Test Set\n",
      "Mean Absolute Error: 1004.52\n",
      "Mean Absolute Percentage Error: 9.71%\n",
      "Root Mean Squared Error: 1527.54\n",
      "Lasso-CV chosen regularization: 32.8906\n"
     ]
    },
    {
     "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>Feature</th>\n",
       "      <th>Lasso_Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Age_08_04</td>\n",
       "      <td>-2064.078027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>KM</td>\n",
       "      <td>-605.185323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HP</td>\n",
       "      <td>122.425179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Met_Color</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Automatic</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>CC</td>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Doors</td>\n",
       "      <td>-151.531573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Quarterly_Tax</td>\n",
       "      <td>408.213102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Weight</td>\n",
       "      <td>1346.496654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Fuel_Type_Diesel</td>\n",
       "      <td>-246.661435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Fuel_Type_Petrol</td>\n",
       "      <td>716.945506</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Feature  Lasso_Coefficient\n",
       "0          Age_08_04       -2064.078027\n",
       "1                 KM        -605.185323\n",
       "2                 HP         122.425179\n",
       "3          Met_Color          -0.000000\n",
       "4          Automatic          -0.000000\n",
       "5                 CC          -0.000000\n",
       "6              Doors        -151.531573\n",
       "7      Quarterly_Tax         408.213102\n",
       "8             Weight        1346.496654\n",
       "9   Fuel_Type_Diesel        -246.661435\n",
       "10  Fuel_Type_Petrol         716.945506"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit Lasso model: use cross-validation to determine alpha\n",
    "\n",
    "lassoCV.fit(train_X_scaled, train_y)\n",
    "\n",
    "# Test Set\n",
    "mae = metrics.mean_absolute_error(test_y,lassoCV.predict(test_X_scaled))\n",
    "mape = metrics.mean_absolute_percentage_error(test_y, lassoCV.predict(test_X_scaled))\n",
    "mse = metrics.mean_squared_error(test_y, lassoCV.predict(test_X_scaled))\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures - Test Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')\n",
    "print(f'Lasso-CV chosen regularization: {lassoCV.alpha_:.4f}')\n",
    "\n",
    "lasso_coef_df = pd.DataFrame({\n",
    "    \"Feature\": train_X.columns,\n",
    "    \"Lasso_Coefficient\": lassoCV.coef_\n",
    "})\n",
    "lasso_coef_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1760bbc0-5fb0-4575-8f69-06145d6432bb",
   "metadata": {},
   "source": [
    "#### Ridge Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "cccd8ecf-a9cf-41ad-8f9b-94d0b7632e34",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Performance Measures - Test Set\n",
      "Mean Absolute Error: 1018.24\n",
      "Mean Absolute Percentage Error: 9.85%\n",
      "Root Mean Squared Error: 1602.86\n"
     ]
    }
   ],
   "source": [
    "# Fit Ridge model: given alpha\n",
    "\n",
    "\n",
    "# Test Set\n",
    "mae = metrics.mean_absolute_error(test_y,ridge.predict(test_X_scaled))\n",
    "mape = metrics.mean_absolute_percentage_error(test_y, ridge.predict(test_X_scaled))\n",
    "mse = metrics.mean_squared_error(test_y, ridge.predict(test_X_scaled))\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures - Test Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "39119203-7877-4998-a7b9-cfcda9a581c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Performance Measures - Test Set\n",
      "Mean Absolute Error: 1017.84\n",
      "Mean Absolute Percentage Error: 9.85%\n",
      "Root Mean Squared Error: 1600.13\n",
      "Bayesian Ridge chosen regularization: 1.9180\n"
     ]
    },
    {
     "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>Feature</th>\n",
       "      <th>Bayesian_Ridge_Coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Age_08_04</td>\n",
       "      <td>-2043.218002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>KM</td>\n",
       "      <td>-595.632852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HP</td>\n",
       "      <td>44.540875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Met_Color</td>\n",
       "      <td>-33.249048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Automatic</td>\n",
       "      <td>-33.543001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>CC</td>\n",
       "      <td>-19.911395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Doors</td>\n",
       "      <td>-233.314366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Quarterly_Tax</td>\n",
       "      <td>592.973300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Weight</td>\n",
       "      <td>1504.044958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Fuel_Type_Diesel</td>\n",
       "      <td>-400.972781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Fuel_Type_Petrol</td>\n",
       "      <td>892.664894</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Feature  Bayesian_Ridge_Coefficient\n",
       "0          Age_08_04                -2043.218002\n",
       "1                 KM                 -595.632852\n",
       "2                 HP                   44.540875\n",
       "3          Met_Color                  -33.249048\n",
       "4          Automatic                  -33.543001\n",
       "5                 CC                  -19.911395\n",
       "6              Doors                 -233.314366\n",
       "7      Quarterly_Tax                  592.973300\n",
       "8             Weight                 1504.044958\n",
       "9   Fuel_Type_Diesel                 -400.972781\n",
       "10  Fuel_Type_Petrol                  892.664894"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit Ridge model: use Bayesian method to determine alpha\n",
    "\n",
    "ridgeB.fit(train_X_scaled, train_y)\n",
    "\n",
    "# Test Set\n",
    "mae = metrics.mean_absolute_error(test_y,ridgeB.predict(test_X_scaled))\n",
    "mape = metrics.mean_absolute_percentage_error(test_y, ridgeB.predict(test_X_scaled))\n",
    "mse = metrics.mean_squared_error(test_y, ridgeB.predict(test_X_scaled))\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures - Test Set')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')\n",
    "regularization_strength = ridgeB.lambda_ / ridgeB.alpha_\n",
    "print(f'Bayesian Ridge chosen regularization: {regularization_strength:.4f}')\n",
    "\n",
    "ridge_coef_df = pd.DataFrame({\n",
    "    \"Feature\": train_X.columns,\n",
    "    \"Bayesian_Ridge_Coefficient\": ridgeB.coef_\n",
    "})\n",
    "ridge_coef_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d3a79f6-3b19-4114-b9c5-3f817136f3e3",
   "metadata": {},
   "source": [
    "### OLS REGRESSION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "2bd73a22-a02d-4df0-b52b-94ce8866ce91",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "8d1c84d2-a782-4569-9ef1-7de66a96c9c4",
   "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>   0.869</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.868</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   859.6</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 17 Mar 2025</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:50:19</td>     <th>  Log-Likelihood:    </th> <td> -12347.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1436</td>      <th>  AIC:               </th> <td>2.472e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1424</td>      <th>  BIC:               </th> <td>2.478e+04</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>Intercept</th>                <td>-7325.9928</td> <td> 1231.633</td> <td>   -5.948</td> <td> 0.000</td> <td>-9742.002</td> <td>-4909.984</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Fuel_Type_Diesel[T.True]</th> <td>  627.9746</td> <td>  375.764</td> <td>    1.671</td> <td> 0.095</td> <td> -109.136</td> <td> 1365.085</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Fuel_Type_Petrol[T.True]</th> <td> 2420.3110</td> <td>  368.314</td> <td>    6.571</td> <td> 0.000</td> <td> 1697.815</td> <td> 3142.807</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age_08_04</th>                <td> -123.1200</td> <td>    2.596</td> <td>  -47.421</td> <td> 0.000</td> <td> -128.213</td> <td> -118.027</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>KM</th>                       <td>   -0.0169</td> <td>    0.001</td> <td>  -12.901</td> <td> 0.000</td> <td>   -0.019</td> <td>   -0.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HP</th>                       <td>   23.8514</td> <td>    3.466</td> <td>    6.881</td> <td> 0.000</td> <td>   17.052</td> <td>   30.651</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Met_Color</th>                <td>   36.2887</td> <td>   74.966</td> <td>    0.484</td> <td> 0.628</td> <td> -110.767</td> <td>  183.344</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Automatic</th>                <td>  258.8277</td> <td>  157.775</td> <td>    1.640</td> <td> 0.101</td> <td>  -50.669</td> <td>  568.324</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>CC</th>                       <td>   -0.0627</td> <td>    0.091</td> <td>   -0.692</td> <td> 0.489</td> <td>   -0.241</td> <td>    0.115</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Doors</th>                    <td>  -71.6120</td> <td>   39.658</td> <td>   -1.806</td> <td> 0.071</td> <td> -149.407</td> <td>    6.183</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Quarterly_Tax</th>            <td>   12.3125</td> <td>    1.650</td> <td>    7.463</td> <td> 0.000</td> <td>    9.076</td> <td>   15.549</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Weight</th>                   <td>   19.3566</td> <td>    1.218</td> <td>   15.894</td> <td> 0.000</td> <td>   16.968</td> <td>   21.746</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>203.998</td> <th>  Durbin-Watson:     </th> <td>   1.594</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>2183.722</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.248</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.021</td>  <th>  Cond. No.          </th> <td>2.79e+06</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, 2.79e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}             &      Price       & \\textbf{  R-squared:         } &     0.869   \\\\\n",
       "\\textbf{Model:}                     &       OLS        & \\textbf{  Adj. R-squared:    } &     0.868   \\\\\n",
       "\\textbf{Method:}                    &  Least Squares   & \\textbf{  F-statistic:       } &     859.6   \\\\\n",
       "\\textbf{Date:}                      & Mon, 17 Mar 2025 & \\textbf{  Prob (F-statistic):} &     0.00    \\\\\n",
       "\\textbf{Time:}                      &     18:50:19     & \\textbf{  Log-Likelihood:    } &   -12347.   \\\\\n",
       "\\textbf{No. Observations:}          &        1436      & \\textbf{  AIC:               } & 2.472e+04   \\\\\n",
       "\\textbf{Df Residuals:}              &        1424      & \\textbf{  BIC:               } & 2.478e+04   \\\\\n",
       "\\textbf{Df Model:}                  &          11      & \\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{Intercept}                  &   -7325.9928  &     1231.633     &    -5.948  &         0.000        &    -9742.002    &    -4909.984     \\\\\n",
       "\\textbf{Fuel\\_Type\\_Diesel[T.True]} &     627.9746  &      375.764     &     1.671  &         0.095        &     -109.136    &     1365.085     \\\\\n",
       "\\textbf{Fuel\\_Type\\_Petrol[T.True]} &    2420.3110  &      368.314     &     6.571  &         0.000        &     1697.815    &     3142.807     \\\\\n",
       "\\textbf{Age\\_08\\_04}                &    -123.1200  &        2.596     &   -47.421  &         0.000        &     -128.213    &     -118.027     \\\\\n",
       "\\textbf{KM}                         &      -0.0169  &        0.001     &   -12.901  &         0.000        &       -0.019    &       -0.014     \\\\\n",
       "\\textbf{HP}                         &      23.8514  &        3.466     &     6.881  &         0.000        &       17.052    &       30.651     \\\\\n",
       "\\textbf{Met\\_Color}                 &      36.2887  &       74.966     &     0.484  &         0.628        &     -110.767    &      183.344     \\\\\n",
       "\\textbf{Automatic}                  &     258.8277  &      157.775     &     1.640  &         0.101        &      -50.669    &      568.324     \\\\\n",
       "\\textbf{CC}                         &      -0.0627  &        0.091     &    -0.692  &         0.489        &       -0.241    &        0.115     \\\\\n",
       "\\textbf{Doors}                      &     -71.6120  &       39.658     &    -1.806  &         0.071        &     -149.407    &        6.183     \\\\\n",
       "\\textbf{Quarterly\\_Tax}             &      12.3125  &        1.650     &     7.463  &         0.000        &        9.076    &       15.549     \\\\\n",
       "\\textbf{Weight}                     &      19.3566  &        1.218     &    15.894  &         0.000        &       16.968    &       21.746     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 203.998 & \\textbf{  Durbin-Watson:     } &    1.594  \\\\\n",
       "\\textbf{Prob(Omnibus):} &   0.000 & \\textbf{  Jarque-Bera (JB):  } & 2183.722  \\\\\n",
       "\\textbf{Skew:}          &  -0.248 & \\textbf{  Prob(JB):          } &     0.00  \\\\\n",
       "\\textbf{Kurtosis:}      &   9.021 & \\textbf{  Cond. No.          } & 2.79e+06  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n",
       " [2] The condition number is large, 2.79e+06. This might indicate that there are \\newline\n",
       " 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:                       0.869\n",
       "Model:                            OLS   Adj. R-squared:                  0.868\n",
       "Method:                 Least Squares   F-statistic:                     859.6\n",
       "Date:                Mon, 17 Mar 2025   Prob (F-statistic):               0.00\n",
       "Time:                        18:50:19   Log-Likelihood:                -12347.\n",
       "No. Observations:                1436   AIC:                         2.472e+04\n",
       "Df Residuals:                    1424   BIC:                         2.478e+04\n",
       "Df Model:                          11                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "============================================================================================\n",
       "                               coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------------\n",
       "Intercept                -7325.9928   1231.633     -5.948      0.000   -9742.002   -4909.984\n",
       "Fuel_Type_Diesel[T.True]   627.9746    375.764      1.671      0.095    -109.136    1365.085\n",
       "Fuel_Type_Petrol[T.True]  2420.3110    368.314      6.571      0.000    1697.815    3142.807\n",
       "Age_08_04                 -123.1200      2.596    -47.421      0.000    -128.213    -118.027\n",
       "KM                          -0.0169      0.001    -12.901      0.000      -0.019      -0.014\n",
       "HP                          23.8514      3.466      6.881      0.000      17.052      30.651\n",
       "Met_Color                   36.2887     74.966      0.484      0.628    -110.767     183.344\n",
       "Automatic                  258.8277    157.775      1.640      0.101     -50.669     568.324\n",
       "CC                          -0.0627      0.091     -0.692      0.489      -0.241       0.115\n",
       "Doors                      -71.6120     39.658     -1.806      0.071    -149.407       6.183\n",
       "Quarterly_Tax               12.3125      1.650      7.463      0.000       9.076      15.549\n",
       "Weight                      19.3566      1.218     15.894      0.000      16.968      21.746\n",
       "==============================================================================\n",
       "Omnibus:                      203.998   Durbin-Watson:                   1.594\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2183.722\n",
       "Skew:                          -0.248   Prob(JB):                         0.00\n",
       "Kurtosis:                       9.021   Cond. No.                     2.79e+06\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, 2.79e+06. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "0362501b-bfeb-4927-a873-81543963923e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age_08_04</th>\n",
       "      <th>KM</th>\n",
       "      <th>HP</th>\n",
       "      <th>Quarterly_Tax</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Fuel_Type_Petrol</th>\n",
       "      <th>Price</th>\n",
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       "      <td>23</td>\n",
       "      <td>46986</td>\n",
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       "      <td>1165</td>\n",
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       "      <td>26</td>\n",
       "      <td>48000</td>\n",
       "      <td>90</td>\n",
       "      <td>210</td>\n",
       "      <td>1165</td>\n",
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       "      <td>1170</td>\n",
       "      <td>False</td>\n",
       "      <td>13750</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age_08_04     KM  HP  Quarterly_Tax  Weight  Fuel_Type_Petrol  Price\n",
       "0         23  46986  90            210    1165             False  13500\n",
       "1         23  72937  90            210    1165             False  13750\n",
       "2         24  41711  90            210    1165             False  13950\n",
       "3         26  48000  90            210    1165             False  14950\n",
       "4         30  38500  90            210    1170             False  13750"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "formula = 'Price ~' + '+'.join(predictors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "c832c55b-e417-4063-9a58-d13eb774bd7f",
   "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>   0.868</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.868</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1569.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 17 Mar 2025</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:01:35</td>     <th>  Log-Likelihood:    </th> <td> -12352.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1436</td>      <th>  AIC:               </th> <td>2.472e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1429</td>      <th>  BIC:               </th> <td>2.475e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</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>Intercept</th>                <td>-7162.2958</td> <td> 1186.423</td> <td>   -6.037</td> <td> 0.000</td> <td>-9489.613</td> <td>-4834.979</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Fuel_Type_Petrol[T.True]</th> <td> 1940.6025</td> <td>  250.039</td> <td>    7.761</td> <td> 0.000</td> <td> 1450.119</td> <td> 2431.086</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age_08_04</th>                <td> -122.4599</td> <td>    2.571</td> <td>  -47.626</td> <td> 0.000</td> <td> -127.504</td> <td> -117.416</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>KM</th>                       <td>   -0.0172</td> <td>    0.001</td> <td>  -13.208</td> <td> 0.000</td> <td>   -0.020</td> <td>   -0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HP</th>                       <td>   21.2704</td> <td>    3.095</td> <td>    6.872</td> <td> 0.000</td> <td>   15.199</td> <td>   27.342</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Quarterly_Tax</th>            <td>   12.1300</td> <td>    1.650</td> <td>    7.351</td> <td> 0.000</td> <td>    8.893</td> <td>   15.367</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Weight</th>                   <td>   19.5809</td> <td>    1.074</td> <td>   18.240</td> <td> 0.000</td> <td>   17.475</td> <td>   21.687</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>209.991</td> <th>  Durbin-Watson:     </th> <td>   1.588</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>2292.692</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.271</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 9.166</td>  <th>  Cond. No.          </th> <td>2.68e+06</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, 2.68e+06. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}             &      Price       & \\textbf{  R-squared:         } &     0.868   \\\\\n",
       "\\textbf{Model:}                     &       OLS        & \\textbf{  Adj. R-squared:    } &     0.868   \\\\\n",
       "\\textbf{Method:}                    &  Least Squares   & \\textbf{  F-statistic:       } &     1569.   \\\\\n",
       "\\textbf{Date:}                      & Mon, 17 Mar 2025 & \\textbf{  Prob (F-statistic):} &     0.00    \\\\\n",
       "\\textbf{Time:}                      &     19:01:35     & \\textbf{  Log-Likelihood:    } &   -12352.   \\\\\n",
       "\\textbf{No. Observations:}          &        1436      & \\textbf{  AIC:               } & 2.472e+04   \\\\\n",
       "\\textbf{Df Residuals:}              &        1429      & \\textbf{  BIC:               } & 2.475e+04   \\\\\n",
       "\\textbf{Df Model:}                  &           6      & \\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{Intercept}                  &   -7162.2958  &     1186.423     &    -6.037  &         0.000        &    -9489.613    &    -4834.979     \\\\\n",
       "\\textbf{Fuel\\_Type\\_Petrol[T.True]} &    1940.6025  &      250.039     &     7.761  &         0.000        &     1450.119    &     2431.086     \\\\\n",
       "\\textbf{Age\\_08\\_04}                &    -122.4599  &        2.571     &   -47.626  &         0.000        &     -127.504    &     -117.416     \\\\\n",
       "\\textbf{KM}                         &      -0.0172  &        0.001     &   -13.208  &         0.000        &       -0.020    &       -0.015     \\\\\n",
       "\\textbf{HP}                         &      21.2704  &        3.095     &     6.872  &         0.000        &       15.199    &       27.342     \\\\\n",
       "\\textbf{Quarterly\\_Tax}             &      12.1300  &        1.650     &     7.351  &         0.000        &        8.893    &       15.367     \\\\\n",
       "\\textbf{Weight}                     &      19.5809  &        1.074     &    18.240  &         0.000        &       17.475    &       21.687     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lclc}\n",
       "\\textbf{Omnibus:}       & 209.991 & \\textbf{  Durbin-Watson:     } &    1.588  \\\\\n",
       "\\textbf{Prob(Omnibus):} &   0.000 & \\textbf{  Jarque-Bera (JB):  } & 2292.692  \\\\\n",
       "\\textbf{Skew:}          &  -0.271 & \\textbf{  Prob(JB):          } &     0.00  \\\\\n",
       "\\textbf{Kurtosis:}      &   9.166 & \\textbf{  Cond. No.          } & 2.68e+06  \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. \\newline\n",
       " [2] The condition number is large, 2.68e+06. This might indicate that there are \\newline\n",
       " 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:                       0.868\n",
       "Model:                            OLS   Adj. R-squared:                  0.868\n",
       "Method:                 Least Squares   F-statistic:                     1569.\n",
       "Date:                Mon, 17 Mar 2025   Prob (F-statistic):               0.00\n",
       "Time:                        19:01:35   Log-Likelihood:                -12352.\n",
       "No. Observations:                1436   AIC:                         2.472e+04\n",
       "Df Residuals:                    1429   BIC:                         2.475e+04\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "============================================================================================\n",
       "                               coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------------\n",
       "Intercept                -7162.2958   1186.423     -6.037      0.000   -9489.613   -4834.979\n",
       "Fuel_Type_Petrol[T.True]  1940.6025    250.039      7.761      0.000    1450.119    2431.086\n",
       "Age_08_04                 -122.4599      2.571    -47.626      0.000    -127.504    -117.416\n",
       "KM                          -0.0172      0.001    -13.208      0.000      -0.020      -0.015\n",
       "HP                          21.2704      3.095      6.872      0.000      15.199      27.342\n",
       "Quarterly_Tax               12.1300      1.650      7.351      0.000       8.893      15.367\n",
       "Weight                      19.5809      1.074     18.240      0.000      17.475      21.687\n",
       "==============================================================================\n",
       "Omnibus:                      209.991   Durbin-Watson:                   1.588\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2292.692\n",
       "Skew:                          -0.271   Prob(JB):                         0.00\n",
       "Kurtosis:                       9.166   Cond. No.                     2.68e+06\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, 2.68e+06. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "OLS_model = sm.ols(formula = formula, data = df1).fit()\n",
    "OLS_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "ca4faf6a-629f-4d71-8276-9b24a9c2dd8a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Performance Measures\n",
      "Mean Absolute Error: 975.97\n",
      "Mean Absolute Percentage Error: 9.64%\n",
      "Root Mean Squared Error: 1316.14\n"
     ]
    }
   ],
   "source": [
    "mae = metrics.mean_absolute_error(y,OLS_model.predict(X))\n",
    "mape = metrics.mean_absolute_percentage_error(y, OLS_model.predict(X))\n",
    "mse = metrics.mean_squared_error(y, OLS_model.predict(X))\n",
    "rmse = np.sqrt(mse)\n",
    "print('\\nPerformance Measures')\n",
    "print(f'Mean Absolute Error: {mae:.2f}')\n",
    "print(f'Mean Absolute Percentage Error: {mape*100:.2f}%')\n",
    "print(f'Root Mean Squared Error: {rmse:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7fa74bcf-3fbe-4a93-b7a7-5be1bd326ffe",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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