MPG - Regularization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ref - https://www.kaggle.com/loveall/appliances-energy-prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# hide warnings\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the in-built **MPG** dataset in Seaborn library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model_year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165.0</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>usa</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration  \\\n",
       "0  18.0          8         307.0       130.0    3504          12.0   \n",
       "1  15.0          8         350.0       165.0    3693          11.5   \n",
       "2  18.0          8         318.0       150.0    3436          11.0   \n",
       "3  16.0          8         304.0       150.0    3433          12.0   \n",
       "4  17.0          8         302.0       140.0    3449          10.5   \n",
       "\n",
       "   model_year origin                       name  \n",
       "0          70    usa  chevrolet chevelle malibu  \n",
       "1          70    usa          buick skylark 320  \n",
       "2          70    usa         plymouth satellite  \n",
       "3          70    usa              amc rebel sst  \n",
       "4          70    usa                ford torino  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import data\n",
    "df = sns.load_dataset('mpg')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# EDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(398, 9)\n"
     ]
    }
   ],
   "source": [
    "# drop duplicates, if any\n",
    "df.drop_duplicates(inplace=True)\n",
    "print(df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model_year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>398.000000</td>\n",
       "      <td>398.000000</td>\n",
       "      <td>398.000000</td>\n",
       "      <td>392.000000</td>\n",
       "      <td>398.000000</td>\n",
       "      <td>398.000000</td>\n",
       "      <td>398.000000</td>\n",
       "      <td>398</td>\n",
       "      <td>398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>usa</td>\n",
       "      <td>ford pinto</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>249</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>23.514573</td>\n",
       "      <td>5.454774</td>\n",
       "      <td>193.425879</td>\n",
       "      <td>104.469388</td>\n",
       "      <td>2970.424623</td>\n",
       "      <td>15.568090</td>\n",
       "      <td>76.010050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7.815984</td>\n",
       "      <td>1.701004</td>\n",
       "      <td>104.269838</td>\n",
       "      <td>38.491160</td>\n",
       "      <td>846.841774</td>\n",
       "      <td>2.757689</td>\n",
       "      <td>3.697627</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>9.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>46.000000</td>\n",
       "      <td>1613.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>17.500000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>104.250000</td>\n",
       "      <td>75.000000</td>\n",
       "      <td>2223.750000</td>\n",
       "      <td>13.825000</td>\n",
       "      <td>73.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>23.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>148.500000</td>\n",
       "      <td>93.500000</td>\n",
       "      <td>2803.500000</td>\n",
       "      <td>15.500000</td>\n",
       "      <td>76.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>29.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>262.000000</td>\n",
       "      <td>126.000000</td>\n",
       "      <td>3608.000000</td>\n",
       "      <td>17.175000</td>\n",
       "      <td>79.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>46.600000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>455.000000</td>\n",
       "      <td>230.000000</td>\n",
       "      <td>5140.000000</td>\n",
       "      <td>24.800000</td>\n",
       "      <td>82.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               mpg   cylinders  displacement  horsepower       weight  \\\n",
       "count   398.000000  398.000000    398.000000  392.000000   398.000000   \n",
       "unique         NaN         NaN           NaN         NaN          NaN   \n",
       "top            NaN         NaN           NaN         NaN          NaN   \n",
       "freq           NaN         NaN           NaN         NaN          NaN   \n",
       "mean     23.514573    5.454774    193.425879  104.469388  2970.424623   \n",
       "std       7.815984    1.701004    104.269838   38.491160   846.841774   \n",
       "min       9.000000    3.000000     68.000000   46.000000  1613.000000   \n",
       "25%      17.500000    4.000000    104.250000   75.000000  2223.750000   \n",
       "50%      23.000000    4.000000    148.500000   93.500000  2803.500000   \n",
       "75%      29.000000    8.000000    262.000000  126.000000  3608.000000   \n",
       "max      46.600000    8.000000    455.000000  230.000000  5140.000000   \n",
       "\n",
       "        acceleration  model_year origin        name  \n",
       "count     398.000000  398.000000    398         398  \n",
       "unique           NaN         NaN      3         305  \n",
       "top              NaN         NaN    usa  ford pinto  \n",
       "freq             NaN         NaN    249           6  \n",
       "mean       15.568090   76.010050    NaN         NaN  \n",
       "std         2.757689    3.697627    NaN         NaN  \n",
       "min         8.000000   70.000000    NaN         NaN  \n",
       "25%        13.825000   73.000000    NaN         NaN  \n",
       "50%        15.500000   76.000000    NaN         NaN  \n",
       "75%        17.175000   79.000000    NaN         NaN  \n",
       "max        24.800000   82.000000    NaN         NaN  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# summary statistics\n",
    "df.describe(include='all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg             0\n",
       "cylinders       0\n",
       "displacement    0\n",
       "horsepower      6\n",
       "weight          0\n",
       "acceleration    0\n",
       "model_year      0\n",
       "origin          0\n",
       "name            0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check for NULLs\n",
    "df.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model_year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>25.0</td>\n",
       "      <td>4</td>\n",
       "      <td>98.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2046</td>\n",
       "      <td>19.0</td>\n",
       "      <td>71</td>\n",
       "      <td>usa</td>\n",
       "      <td>ford pinto</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>126</th>\n",
       "      <td>21.0</td>\n",
       "      <td>6</td>\n",
       "      <td>200.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2875</td>\n",
       "      <td>17.0</td>\n",
       "      <td>74</td>\n",
       "      <td>usa</td>\n",
       "      <td>ford maverick</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>330</th>\n",
       "      <td>40.9</td>\n",
       "      <td>4</td>\n",
       "      <td>85.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1835</td>\n",
       "      <td>17.3</td>\n",
       "      <td>80</td>\n",
       "      <td>europe</td>\n",
       "      <td>renault lecar deluxe</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>336</th>\n",
       "      <td>23.6</td>\n",
       "      <td>4</td>\n",
       "      <td>140.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2905</td>\n",
       "      <td>14.3</td>\n",
       "      <td>80</td>\n",
       "      <td>usa</td>\n",
       "      <td>ford mustang cobra</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>354</th>\n",
       "      <td>34.5</td>\n",
       "      <td>4</td>\n",
       "      <td>100.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2320</td>\n",
       "      <td>15.8</td>\n",
       "      <td>81</td>\n",
       "      <td>europe</td>\n",
       "      <td>renault 18i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>374</th>\n",
       "      <td>23.0</td>\n",
       "      <td>4</td>\n",
       "      <td>151.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3035</td>\n",
       "      <td>20.5</td>\n",
       "      <td>82</td>\n",
       "      <td>usa</td>\n",
       "      <td>amc concord dl</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mpg  cylinders  displacement  horsepower  weight  acceleration  \\\n",
       "32   25.0          4          98.0         NaN    2046          19.0   \n",
       "126  21.0          6         200.0         NaN    2875          17.0   \n",
       "330  40.9          4          85.0         NaN    1835          17.3   \n",
       "336  23.6          4         140.0         NaN    2905          14.3   \n",
       "354  34.5          4         100.0         NaN    2320          15.8   \n",
       "374  23.0          4         151.0         NaN    3035          20.5   \n",
       "\n",
       "     model_year  origin                  name  \n",
       "32           71     usa            ford pinto  \n",
       "126          74     usa         ford maverick  \n",
       "330          80  europe  renault lecar deluxe  \n",
       "336          80     usa    ford mustang cobra  \n",
       "354          81  europe           renault 18i  \n",
       "374          82     usa        amc concord dl  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df.horsepower.isnull()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32               ford pinto\n",
       "126           ford maverick\n",
       "330    renault lecar deluxe\n",
       "336      ford mustang cobra\n",
       "354             renault 18i\n",
       "374          amc concord dl\n",
       "Name: name, dtype: object"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[df.horsepower.isnull()].name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "# getting horsepower of cars where NA as it can be easily googled\n",
    "df.horsepower[(df.name == 'ford pinto') & df.horsepower.isnull()] = 75\n",
    "df.horsepower[(df.name == 'ford maverick') & df.horsepower.isnull()] = 75\n",
    "df.horsepower[(df.name == 'ford mustang cobra') & df.horsepower.isnull()] = 88\n",
    "df.horsepower[(df.name == 'renault 18i') & df.horsepower.isnull()] = 60\n",
    "df.horsepower[(df.name == 'amc concord dl') & df.horsepower.isnull()] = 82\n",
    "df.horsepower[(df.name == 'renault lecar deluxe') & df.horsepower.isnull()] = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg             0\n",
       "cylinders       0\n",
       "displacement    0\n",
       "horsepower      0\n",
       "weight          0\n",
       "acceleration    0\n",
       "model_year      0\n",
       "origin          0\n",
       "name            0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# RE-check for NULLs\n",
    "df.isna().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# drop name\n",
    "df.drop('name', axis = 1, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- All but 2 variables are numeric and there are no NULL values, so we can move ahead. \n",
    "- We will not do any feature transformation here either just to demonstrate how regularization makes better generalized predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg             float64\n",
       "cylinders         int64\n",
       "displacement    float64\n",
       "horsepower      float64\n",
       "weight            int64\n",
       "acceleration    float64\n",
       "model_year       object\n",
       "origin           object\n",
       "dtype: object"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# converting categorical vars into object\n",
    "df['model_year'] = df['model_year'].astype('object')\n",
    "df.dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check for correlation and outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we will simply check the presence of outliers and correlation since we will see how much of those factors is overcome by regularization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of outliers - \n",
      "====================\n",
      "mpg - 1\n",
      "cylinders - 0\n",
      "displacement - 0\n",
      "horsepower - 10\n",
      "weight - 0\n",
      "acceleration - 9\n"
     ]
    }
   ],
   "source": [
    "# function to get number of outliers \n",
    "def outliers(x):\n",
    "    import numpy as np\n",
    "    import pandas as pd\n",
    "    \n",
    "    # we will use values > 1.5(IQR) as outliers and equate them to the 90th/10th percentile values \n",
    "    \n",
    "    iqr = np.subtract(*np.percentile(x, [75, 25]))\n",
    "    iqr_upper_bound = 1.5*iqr + np.percentile(x, 75)\n",
    "    iqr_lower_bound = np.percentile(x, 25) - 1.5*iqr\n",
    "    \n",
    "    return iqr_upper_bound, iqr_lower_bound\n",
    "\n",
    "print(\"Number of outliers - \")\n",
    "print(\"=\"*20)\n",
    "\n",
    "for e in df.columns[:-2]:\n",
    "    print(e, \"-\", df[e][df[e] > outliers(df[e])[0]].count() + df[e][df[e] < outliers(df[e])[1]].count())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# correlation plot\n",
    "plt.figure(figsize=(8,6))\n",
    "sns.set_context('paper', font_scale=1.5)\n",
    "\n",
    "df_corr = df.corr()\n",
    "\n",
    "sns.heatmap(df_corr, annot=True, cmap = 'coolwarm', vmin = -1, vmax = 1, fmt = '.2f')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Building"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train Test Splits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train = (318, 21)\n",
      "X_test = (80, 21)\n",
      "y_train = (318,)\n",
      "y_test = (80,)\n"
     ]
    }
   ],
   "source": [
    "# train test split\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# get dummies for categorical variables\n",
    "df = pd.get_dummies(df, drop_first=False)\n",
    "\n",
    "# df.drop(['model_year', 'origin'], axis = 1, inplace=True)\n",
    "\n",
    "X = df.drop('mpg', axis = 1)\n",
    "y = df['mpg']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "\n",
    "# # add constants to X_train, X_test\n",
    "# import statsmodels.api as sm\n",
    "\n",
    "# X_train, X_test = sm.add_constant(X_train), sm.add_constant(X_test)\n",
    "\n",
    "print('X_train =', X_train.shape)\n",
    "print('X_test =', X_test.shape)\n",
    "print('y_train =', y_train.shape)\n",
    "print('y_test =', y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['mpg', 'cylinders', 'displacement', 'horsepower', 'weight',\n",
       "       'acceleration', 'model_year_70', 'model_year_71', 'model_year_72',\n",
       "       'model_year_73', 'model_year_74', 'model_year_75', 'model_year_76',\n",
       "       'model_year_77', 'model_year_78', 'model_year_79', 'model_year_80',\n",
       "       'model_year_81', 'model_year_82', 'origin_europe', 'origin_japan',\n",
       "       'origin_usa'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'fit_time': array([0.00599504, 0.00599623, 0.00299692, 0.00600386, 0.00401258]),\n",
       " 'score_time': array([0.00299788, 0.00199866, 0.0019989 , 0.00399113, 0.00198317]),\n",
       " 'test_neg_mean_squared_error': array([ -9.55243402,  -8.46179781, -11.95026333, -10.64035714,\n",
       "        -11.02142178]),\n",
       " 'train_neg_mean_squared_error': array([-9.09028382, -9.28713504, -8.62586302, -8.80629074, -8.99095648]),\n",
       " 'test_r2': array([0.85060745, 0.83550606, 0.83067871, 0.84073125, 0.80646625]),\n",
       " 'train_r2': array([0.8530289 , 0.8576228 , 0.85782757, 0.85657496, 0.85971978])}"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_validate\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "linear_regressor = LinearRegression()\n",
    "linear_regressor.fit(X_train, y_train)\n",
    "linear_regressor_cv = cross_validate(estimator = linear_regressor, X = X_train, y = y_train,\n",
    "                                     scoring=['neg_mean_squared_error', 'r2'], cv=5,\n",
    "                                     return_train_score = True)\n",
    "# mean_mse=np.mean(mse)\n",
    "# print(mean_mse)\n",
    "linear_regressor_cv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "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>fit_time</th>\n",
       "      <th>score_time</th>\n",
       "      <th>test_neg_mean_squared_error</th>\n",
       "      <th>train_neg_mean_squared_error</th>\n",
       "      <th>test_r2</th>\n",
       "      <th>train_r2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.005995</td>\n",
       "      <td>0.002998</td>\n",
       "      <td>-9.552434</td>\n",
       "      <td>-9.090284</td>\n",
       "      <td>0.850607</td>\n",
       "      <td>0.853029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.005996</td>\n",
       "      <td>0.001999</td>\n",
       "      <td>-8.461798</td>\n",
       "      <td>-9.287135</td>\n",
       "      <td>0.835506</td>\n",
       "      <td>0.857623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.002997</td>\n",
       "      <td>0.001999</td>\n",
       "      <td>-11.950263</td>\n",
       "      <td>-8.625863</td>\n",
       "      <td>0.830679</td>\n",
       "      <td>0.857828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.006004</td>\n",
       "      <td>0.003991</td>\n",
       "      <td>-10.640357</td>\n",
       "      <td>-8.806291</td>\n",
       "      <td>0.840731</td>\n",
       "      <td>0.856575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.004013</td>\n",
       "      <td>0.001983</td>\n",
       "      <td>-11.021422</td>\n",
       "      <td>-8.990956</td>\n",
       "      <td>0.806466</td>\n",
       "      <td>0.859720</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fit_time  score_time  test_neg_mean_squared_error  \\\n",
       "0  0.005995    0.002998                    -9.552434   \n",
       "1  0.005996    0.001999                    -8.461798   \n",
       "2  0.002997    0.001999                   -11.950263   \n",
       "3  0.006004    0.003991                   -10.640357   \n",
       "4  0.004013    0.001983                   -11.021422   \n",
       "\n",
       "   train_neg_mean_squared_error   test_r2  train_r2  \n",
       "0                     -9.090284  0.850607  0.853029  \n",
       "1                     -9.287135  0.835506  0.857623  \n",
       "2                     -8.625863  0.830679  0.857828  \n",
       "3                     -8.806291  0.840731  0.856575  \n",
       "4                     -8.990956  0.806466  0.859720  "
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_regressor_cv_results = pd.DataFrame(linear_regressor_cv)\n",
    "# linear_regressor_cv_results = linear_regressor_cv_results.loc[:, ['params', 'mean_test_neg_mean_squared_error', 'std_test_neg_mean_squared_error', 'mean_test_r2', 'std_test_r2']]\n",
    "# linear_regressor_cv_results.iloc[linear_regressor.best_index_, :]\n",
    "linear_regressor_cv_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-10.325254817907972"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# score\n",
    "linear_regressor_cv_results.test_neg_mean_squared_error.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# metrics\n",
    "y_pred = linear_regressor.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8409414534323778"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# explained variance\n",
    "from sklearn.metrics import explained_variance_score\n",
    "explained_variance_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8406429223064463"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# r2_score\n",
    "from sklearn.metrics import r2_score\n",
    "r2_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8.568063353974836, 2.927125442131723]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# MSE, RMSE\n",
    "from sklearn.metrics import mean_squared_error\n",
    "[mean_squared_error(y_test, y_pred), np.sqrt(mean_squared_error(y_test, y_pred))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularization Techniques"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In all of the regularization techniques, we will make use of `GridSearchCV` function from the `sklearn.model_selection` module to chose the best value of ***Alpha*** for regularization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Lasso Regression - L1 Regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=5, estimator=Lasso(),\n",
       "             param_grid={'alpha': [1e-15, 1e-10, 1e-08, 0.001, 0.01, 1, 5, 10,\n",
       "                                   20, 30, 35, 40, 45, 50, 55, 100]},\n",
       "             refit='neg_mean_squared_error', return_train_score='True',\n",
       "             scoring=['neg_mean_squared_error', 'r2'])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "lasso = Lasso()\n",
    "cv_parameters = {'alpha':[1e-15,1e-10,1e-8,1e-3,1e-2,1,5,10,20,30,35,40,45,50,55,100]}\n",
    "lasso_regressor = GridSearchCV(estimator = lasso,\n",
    "                               param_grid=cv_parameters,\n",
    "                               cv = 5,\n",
    "                               scoring = ['neg_mean_squared_error', 'r2'],\n",
    "                               refit = 'neg_mean_squared_error',\n",
    "                               return_train_score = 'True')\n",
    "lasso_regressor.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-10.298817647511822"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_regressor.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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>params</th>\n",
       "      <th>mean_test_neg_mean_squared_error</th>\n",
       "      <th>std_test_neg_mean_squared_error</th>\n",
       "      <th>mean_train_neg_mean_squared_error</th>\n",
       "      <th>std_train_neg_mean_squared_error</th>\n",
       "      <th>mean_test_r2</th>\n",
       "      <th>std_test_r2</th>\n",
       "      <th>mean_train_r2</th>\n",
       "      <th>std_train_r2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>{'alpha': 0.01}</td>\n",
       "      <td>-10.298818</td>\n",
       "      <td>1.203727</td>\n",
       "      <td>-8.983044</td>\n",
       "      <td>0.227944</td>\n",
       "      <td>0.833353</td>\n",
       "      <td>0.013232</td>\n",
       "      <td>0.856588</td>\n",
       "      <td>0.002215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>{'alpha': 0.001}</td>\n",
       "      <td>-10.320733</td>\n",
       "      <td>1.206826</td>\n",
       "      <td>-8.960338</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832884</td>\n",
       "      <td>0.014577</td>\n",
       "      <td>0.856951</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>{'alpha': 1e-08}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>{'alpha': 1e-10}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>{'alpha': 1e-15}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>{'alpha': 1}</td>\n",
       "      <td>-19.249548</td>\n",
       "      <td>2.133160</td>\n",
       "      <td>-18.660886</td>\n",
       "      <td>0.550501</td>\n",
       "      <td>0.689039</td>\n",
       "      <td>0.010507</td>\n",
       "      <td>0.702141</td>\n",
       "      <td>0.002640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>{'alpha': 5}</td>\n",
       "      <td>-19.355822</td>\n",
       "      <td>1.943487</td>\n",
       "      <td>-18.721203</td>\n",
       "      <td>0.552665</td>\n",
       "      <td>0.686850</td>\n",
       "      <td>0.013478</td>\n",
       "      <td>0.701178</td>\n",
       "      <td>0.002623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>{'alpha': 10}</td>\n",
       "      <td>-19.611907</td>\n",
       "      <td>1.742994</td>\n",
       "      <td>-18.910003</td>\n",
       "      <td>0.559434</td>\n",
       "      <td>0.682045</td>\n",
       "      <td>0.019438</td>\n",
       "      <td>0.698166</td>\n",
       "      <td>0.002573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>{'alpha': 20}</td>\n",
       "      <td>-20.016648</td>\n",
       "      <td>1.611141</td>\n",
       "      <td>-19.421622</td>\n",
       "      <td>0.473604</td>\n",
       "      <td>0.674741</td>\n",
       "      <td>0.026917</td>\n",
       "      <td>0.689933</td>\n",
       "      <td>0.004718</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>{'alpha': 45}</td>\n",
       "      <td>-20.058467</td>\n",
       "      <td>1.430870</td>\n",
       "      <td>-19.754898</td>\n",
       "      <td>0.351037</td>\n",
       "      <td>0.673913</td>\n",
       "      <td>0.026134</td>\n",
       "      <td>0.684540</td>\n",
       "      <td>0.006338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>{'alpha': 50}</td>\n",
       "      <td>-20.058661</td>\n",
       "      <td>1.433412</td>\n",
       "      <td>-19.755574</td>\n",
       "      <td>0.351034</td>\n",
       "      <td>0.673915</td>\n",
       "      <td>0.026117</td>\n",
       "      <td>0.684529</td>\n",
       "      <td>0.006338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>{'alpha': 55}</td>\n",
       "      <td>-20.058928</td>\n",
       "      <td>1.435962</td>\n",
       "      <td>-19.756321</td>\n",
       "      <td>0.351030</td>\n",
       "      <td>0.673915</td>\n",
       "      <td>0.026099</td>\n",
       "      <td>0.684517</td>\n",
       "      <td>0.006339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>{'alpha': 40}</td>\n",
       "      <td>-20.062027</td>\n",
       "      <td>1.432486</td>\n",
       "      <td>-19.745005</td>\n",
       "      <td>0.361678</td>\n",
       "      <td>0.673855</td>\n",
       "      <td>0.026149</td>\n",
       "      <td>0.684701</td>\n",
       "      <td>0.006346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>{'alpha': 100}</td>\n",
       "      <td>-20.064619</td>\n",
       "      <td>1.459230</td>\n",
       "      <td>-19.766250</td>\n",
       "      <td>0.350986</td>\n",
       "      <td>0.673867</td>\n",
       "      <td>0.025943</td>\n",
       "      <td>0.684359</td>\n",
       "      <td>0.006347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>{'alpha': 35}</td>\n",
       "      <td>-20.080430</td>\n",
       "      <td>1.451185</td>\n",
       "      <td>-19.706274</td>\n",
       "      <td>0.411399</td>\n",
       "      <td>0.673575</td>\n",
       "      <td>0.026156</td>\n",
       "      <td>0.685332</td>\n",
       "      <td>0.006531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>{'alpha': 30}</td>\n",
       "      <td>-20.092614</td>\n",
       "      <td>1.481796</td>\n",
       "      <td>-19.644492</td>\n",
       "      <td>0.444974</td>\n",
       "      <td>0.673395</td>\n",
       "      <td>0.026345</td>\n",
       "      <td>0.686334</td>\n",
       "      <td>0.006321</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              params  mean_test_neg_mean_squared_error  \\\n",
       "4    {'alpha': 0.01}                        -10.298818   \n",
       "3   {'alpha': 0.001}                        -10.320733   \n",
       "2   {'alpha': 1e-08}                        -10.325255   \n",
       "1   {'alpha': 1e-10}                        -10.325255   \n",
       "0   {'alpha': 1e-15}                        -10.325255   \n",
       "5       {'alpha': 1}                        -19.249548   \n",
       "6       {'alpha': 5}                        -19.355822   \n",
       "7      {'alpha': 10}                        -19.611907   \n",
       "8      {'alpha': 20}                        -20.016648   \n",
       "12     {'alpha': 45}                        -20.058467   \n",
       "13     {'alpha': 50}                        -20.058661   \n",
       "14     {'alpha': 55}                        -20.058928   \n",
       "11     {'alpha': 40}                        -20.062027   \n",
       "15    {'alpha': 100}                        -20.064619   \n",
       "10     {'alpha': 35}                        -20.080430   \n",
       "9      {'alpha': 30}                        -20.092614   \n",
       "\n",
       "    std_test_neg_mean_squared_error  mean_train_neg_mean_squared_error  \\\n",
       "4                          1.203727                          -8.983044   \n",
       "3                          1.206826                          -8.960338   \n",
       "2                          1.207834                          -8.960106   \n",
       "1                          1.207834                          -8.960106   \n",
       "0                          1.207834                          -8.960106   \n",
       "5                          2.133160                         -18.660886   \n",
       "6                          1.943487                         -18.721203   \n",
       "7                          1.742994                         -18.910003   \n",
       "8                          1.611141                         -19.421622   \n",
       "12                         1.430870                         -19.754898   \n",
       "13                         1.433412                         -19.755574   \n",
       "14                         1.435962                         -19.756321   \n",
       "11                         1.432486                         -19.745005   \n",
       "15                         1.459230                         -19.766250   \n",
       "10                         1.451185                         -19.706274   \n",
       "9                          1.481796                         -19.644492   \n",
       "\n",
       "    std_train_neg_mean_squared_error  mean_test_r2  std_test_r2  \\\n",
       "4                           0.227944      0.833353     0.013232   \n",
       "3                           0.228133      0.832884     0.014577   \n",
       "2                           0.228133      0.832798     0.014733   \n",
       "1                           0.228133      0.832798     0.014733   \n",
       "0                           0.228133      0.832798     0.014733   \n",
       "5                           0.550501      0.689039     0.010507   \n",
       "6                           0.552665      0.686850     0.013478   \n",
       "7                           0.559434      0.682045     0.019438   \n",
       "8                           0.473604      0.674741     0.026917   \n",
       "12                          0.351037      0.673913     0.026134   \n",
       "13                          0.351034      0.673915     0.026117   \n",
       "14                          0.351030      0.673915     0.026099   \n",
       "11                          0.361678      0.673855     0.026149   \n",
       "15                          0.350986      0.673867     0.025943   \n",
       "10                          0.411399      0.673575     0.026156   \n",
       "9                           0.444974      0.673395     0.026345   \n",
       "\n",
       "    mean_train_r2  std_train_r2  \n",
       "4        0.856588      0.002215  \n",
       "3        0.856951      0.002210  \n",
       "2        0.856955      0.002210  \n",
       "1        0.856955      0.002210  \n",
       "0        0.856955      0.002210  \n",
       "5        0.702141      0.002640  \n",
       "6        0.701178      0.002623  \n",
       "7        0.698166      0.002573  \n",
       "8        0.689933      0.004718  \n",
       "12       0.684540      0.006338  \n",
       "13       0.684529      0.006338  \n",
       "14       0.684517      0.006339  \n",
       "11       0.684701      0.006346  \n",
       "15       0.684359      0.006347  \n",
       "10       0.685332      0.006531  \n",
       "9        0.686334      0.006321  "
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso_cv_results = pd.DataFrame(lasso_regressor.cv_results_)\n",
    "lasso_cv_results = lasso_cv_results.iloc[:, [5, 11, 12, 19, 20, 26, 27, 34, 35]]\n",
    "# lasso_cv_results.iloc[lasso_regressor.best_index_, :]  # for best index\n",
    "# list(enumerate(lasso_cv_results.columns))\n",
    "lasso_cv_results.sort_values(by = 'mean_test_neg_mean_squared_error', ascending = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Ridge Regression - L2 Regularization "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=5, estimator=Ridge(),\n",
       "             param_grid={'alpha': [1e-15, 1e-10, 1e-08, 0.001, 0.01, 1, 5, 10,\n",
       "                                   20, 30, 35, 40, 45, 50, 55, 100]},\n",
       "             refit='neg_mean_squared_error', return_train_score='True',\n",
       "             scoring=['neg_mean_squared_error', 'r2'])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "ridge = Ridge()\n",
    "cv_parameters = {'alpha':[1e-15,1e-10,1e-8,1e-3,1e-2,1,5,10,20,30,35,40,45,50,55,100]}\n",
    "ridge_regressor = GridSearchCV(estimator = ridge,\n",
    "                               param_grid=cv_parameters,\n",
    "                               cv = 5,\n",
    "                               scoring = ['neg_mean_squared_error', 'r2'],\n",
    "                               refit = 'neg_mean_squared_error',\n",
    "                               return_train_score = 'True')\n",
    "ridge_regressor.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-10.311579222158336"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_regressor.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "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>params</th>\n",
       "      <th>mean_test_neg_mean_squared_error</th>\n",
       "      <th>std_test_neg_mean_squared_error</th>\n",
       "      <th>mean_train_neg_mean_squared_error</th>\n",
       "      <th>std_train_neg_mean_squared_error</th>\n",
       "      <th>mean_test_r2</th>\n",
       "      <th>std_test_r2</th>\n",
       "      <th>mean_train_r2</th>\n",
       "      <th>std_train_r2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>{'alpha': 1}</td>\n",
       "      <td>-10.311579</td>\n",
       "      <td>1.188781</td>\n",
       "      <td>-8.997841</td>\n",
       "      <td>0.227491</td>\n",
       "      <td>0.833080</td>\n",
       "      <td>0.013757</td>\n",
       "      <td>0.856352</td>\n",
       "      <td>0.002217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>{'alpha': 0.01}</td>\n",
       "      <td>-10.324647</td>\n",
       "      <td>1.207556</td>\n",
       "      <td>-8.960110</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832808</td>\n",
       "      <td>0.014722</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>{'alpha': 0.001}</td>\n",
       "      <td>-10.325194</td>\n",
       "      <td>1.207806</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832799</td>\n",
       "      <td>0.014732</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>{'alpha': 1e-08}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>{'alpha': 1e-10}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>{'alpha': 1e-15}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>{'alpha': 5}</td>\n",
       "      <td>-10.748886</td>\n",
       "      <td>1.219759</td>\n",
       "      <td>-9.534904</td>\n",
       "      <td>0.222334</td>\n",
       "      <td>0.826193</td>\n",
       "      <td>0.011669</td>\n",
       "      <td>0.847772</td>\n",
       "      <td>0.002255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>{'alpha': 10}</td>\n",
       "      <td>-11.562892</td>\n",
       "      <td>1.326397</td>\n",
       "      <td>-10.395192</td>\n",
       "      <td>0.225373</td>\n",
       "      <td>0.813162</td>\n",
       "      <td>0.010949</td>\n",
       "      <td>0.834032</td>\n",
       "      <td>0.002323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>{'alpha': 20}</td>\n",
       "      <td>-12.975287</td>\n",
       "      <td>1.505755</td>\n",
       "      <td>-11.853305</td>\n",
       "      <td>0.256120</td>\n",
       "      <td>0.790437</td>\n",
       "      <td>0.010691</td>\n",
       "      <td>0.810753</td>\n",
       "      <td>0.002617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>{'alpha': 30}</td>\n",
       "      <td>-13.992610</td>\n",
       "      <td>1.624592</td>\n",
       "      <td>-12.905215</td>\n",
       "      <td>0.290738</td>\n",
       "      <td>0.774032</td>\n",
       "      <td>0.010622</td>\n",
       "      <td>0.793961</td>\n",
       "      <td>0.002892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>{'alpha': 35}</td>\n",
       "      <td>-14.391300</td>\n",
       "      <td>1.669341</td>\n",
       "      <td>-13.319704</td>\n",
       "      <td>0.305883</td>\n",
       "      <td>0.767597</td>\n",
       "      <td>0.010602</td>\n",
       "      <td>0.787346</td>\n",
       "      <td>0.002994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>{'alpha': 40}</td>\n",
       "      <td>-14.735030</td>\n",
       "      <td>1.707275</td>\n",
       "      <td>-13.678410</td>\n",
       "      <td>0.319423</td>\n",
       "      <td>0.762048</td>\n",
       "      <td>0.010590</td>\n",
       "      <td>0.781621</td>\n",
       "      <td>0.003075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>{'alpha': 45}</td>\n",
       "      <td>-15.034035</td>\n",
       "      <td>1.739857</td>\n",
       "      <td>-13.991603</td>\n",
       "      <td>0.331501</td>\n",
       "      <td>0.757220</td>\n",
       "      <td>0.010583</td>\n",
       "      <td>0.776623</td>\n",
       "      <td>0.003137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>{'alpha': 50}</td>\n",
       "      <td>-15.296310</td>\n",
       "      <td>1.768157</td>\n",
       "      <td>-14.267306</td>\n",
       "      <td>0.342300</td>\n",
       "      <td>0.752984</td>\n",
       "      <td>0.010580</td>\n",
       "      <td>0.772223</td>\n",
       "      <td>0.003185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>{'alpha': 55}</td>\n",
       "      <td>-15.528123</td>\n",
       "      <td>1.792977</td>\n",
       "      <td>-14.511818</td>\n",
       "      <td>0.351995</td>\n",
       "      <td>0.749239</td>\n",
       "      <td>0.010580</td>\n",
       "      <td>0.768321</td>\n",
       "      <td>0.003221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>{'alpha': 100}</td>\n",
       "      <td>-16.816150</td>\n",
       "      <td>1.928269</td>\n",
       "      <td>-15.887528</td>\n",
       "      <td>0.408765</td>\n",
       "      <td>0.728427</td>\n",
       "      <td>0.010639</td>\n",
       "      <td>0.746370</td>\n",
       "      <td>0.003302</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              params  mean_test_neg_mean_squared_error  \\\n",
       "5       {'alpha': 1}                        -10.311579   \n",
       "4    {'alpha': 0.01}                        -10.324647   \n",
       "3   {'alpha': 0.001}                        -10.325194   \n",
       "2   {'alpha': 1e-08}                        -10.325255   \n",
       "1   {'alpha': 1e-10}                        -10.325255   \n",
       "0   {'alpha': 1e-15}                        -10.325255   \n",
       "6       {'alpha': 5}                        -10.748886   \n",
       "7      {'alpha': 10}                        -11.562892   \n",
       "8      {'alpha': 20}                        -12.975287   \n",
       "9      {'alpha': 30}                        -13.992610   \n",
       "10     {'alpha': 35}                        -14.391300   \n",
       "11     {'alpha': 40}                        -14.735030   \n",
       "12     {'alpha': 45}                        -15.034035   \n",
       "13     {'alpha': 50}                        -15.296310   \n",
       "14     {'alpha': 55}                        -15.528123   \n",
       "15    {'alpha': 100}                        -16.816150   \n",
       "\n",
       "    std_test_neg_mean_squared_error  mean_train_neg_mean_squared_error  \\\n",
       "5                          1.188781                          -8.997841   \n",
       "4                          1.207556                          -8.960110   \n",
       "3                          1.207806                          -8.960106   \n",
       "2                          1.207834                          -8.960106   \n",
       "1                          1.207834                          -8.960106   \n",
       "0                          1.207834                          -8.960106   \n",
       "6                          1.219759                          -9.534904   \n",
       "7                          1.326397                         -10.395192   \n",
       "8                          1.505755                         -11.853305   \n",
       "9                          1.624592                         -12.905215   \n",
       "10                         1.669341                         -13.319704   \n",
       "11                         1.707275                         -13.678410   \n",
       "12                         1.739857                         -13.991603   \n",
       "13                         1.768157                         -14.267306   \n",
       "14                         1.792977                         -14.511818   \n",
       "15                         1.928269                         -15.887528   \n",
       "\n",
       "    std_train_neg_mean_squared_error  mean_test_r2  std_test_r2  \\\n",
       "5                           0.227491      0.833080     0.013757   \n",
       "4                           0.228133      0.832808     0.014722   \n",
       "3                           0.228133      0.832799     0.014732   \n",
       "2                           0.228133      0.832798     0.014733   \n",
       "1                           0.228133      0.832798     0.014733   \n",
       "0                           0.228133      0.832798     0.014733   \n",
       "6                           0.222334      0.826193     0.011669   \n",
       "7                           0.225373      0.813162     0.010949   \n",
       "8                           0.256120      0.790437     0.010691   \n",
       "9                           0.290738      0.774032     0.010622   \n",
       "10                          0.305883      0.767597     0.010602   \n",
       "11                          0.319423      0.762048     0.010590   \n",
       "12                          0.331501      0.757220     0.010583   \n",
       "13                          0.342300      0.752984     0.010580   \n",
       "14                          0.351995      0.749239     0.010580   \n",
       "15                          0.408765      0.728427     0.010639   \n",
       "\n",
       "    mean_train_r2  std_train_r2  \n",
       "5        0.856352      0.002217  \n",
       "4        0.856955      0.002210  \n",
       "3        0.856955      0.002210  \n",
       "2        0.856955      0.002210  \n",
       "1        0.856955      0.002210  \n",
       "0        0.856955      0.002210  \n",
       "6        0.847772      0.002255  \n",
       "7        0.834032      0.002323  \n",
       "8        0.810753      0.002617  \n",
       "9        0.793961      0.002892  \n",
       "10       0.787346      0.002994  \n",
       "11       0.781621      0.003075  \n",
       "12       0.776623      0.003137  \n",
       "13       0.772223      0.003185  \n",
       "14       0.768321      0.003221  \n",
       "15       0.746370      0.003302  "
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_cv_results = pd.DataFrame(ridge_regressor.cv_results_)\n",
    "ridge_cv_results = ridge_cv_results.iloc[:, [5, 11, 12, 19, 20, 26, 27, 34, 35]]\n",
    "ridge_cv_results.sort_values(by = 'mean_test_neg_mean_squared_error', ascending = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Elastic Net Regression - L1 + L2 Regularization "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=5, estimator=ElasticNet(),\n",
       "             param_grid={'alpha': [1e-15, 1e-10, 1e-08, 0.001, 0.01, 1, 5, 10,\n",
       "                                   20, 30, 35, 40, 45, 50, 55, 100]},\n",
       "             refit='neg_mean_squared_error', return_train_score='True',\n",
       "             scoring=['neg_mean_squared_error', 'r2'])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "\n",
    "elastic_net = ElasticNet()\n",
    "cv_parameters = {'alpha':[1e-15,1e-10,1e-8,1e-3,1e-2,1,5,10,20,30,35,40,45,50,55,100]}\n",
    "elastic_net_regressor = GridSearchCV(estimator = elastic_net,\n",
    "                               param_grid=cv_parameters,\n",
    "                               cv = 5,\n",
    "                               scoring = ['neg_mean_squared_error', 'r2'],\n",
    "                               refit = 'neg_mean_squared_error',\n",
    "                               return_train_score = 'True')\n",
    "elastic_net_regressor.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-10.31409424026328"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elastic_net_regressor.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "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>params</th>\n",
       "      <th>mean_test_neg_mean_squared_error</th>\n",
       "      <th>std_test_neg_mean_squared_error</th>\n",
       "      <th>mean_train_neg_mean_squared_error</th>\n",
       "      <th>std_train_neg_mean_squared_error</th>\n",
       "      <th>mean_test_r2</th>\n",
       "      <th>std_test_r2</th>\n",
       "      <th>mean_train_r2</th>\n",
       "      <th>std_train_r2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>{'alpha': 0.001}</td>\n",
       "      <td>-10.314094</td>\n",
       "      <td>1.203238</td>\n",
       "      <td>-8.961214</td>\n",
       "      <td>0.228115</td>\n",
       "      <td>0.832990</td>\n",
       "      <td>0.014535</td>\n",
       "      <td>0.856937</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>{'alpha': 0.01}</td>\n",
       "      <td>-10.318062</td>\n",
       "      <td>1.180566</td>\n",
       "      <td>-9.053588</td>\n",
       "      <td>0.227097</td>\n",
       "      <td>0.833024</td>\n",
       "      <td>0.013005</td>\n",
       "      <td>0.855461</td>\n",
       "      <td>0.002230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>{'alpha': 1e-08}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>{'alpha': 1e-10}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>{'alpha': 1e-15}</td>\n",
       "      <td>-10.325255</td>\n",
       "      <td>1.207834</td>\n",
       "      <td>-8.960106</td>\n",
       "      <td>0.228133</td>\n",
       "      <td>0.832798</td>\n",
       "      <td>0.014733</td>\n",
       "      <td>0.856955</td>\n",
       "      <td>0.002210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>{'alpha': 1}</td>\n",
       "      <td>-19.238840</td>\n",
       "      <td>2.156398</td>\n",
       "      <td>-18.652332</td>\n",
       "      <td>0.551440</td>\n",
       "      <td>0.689262</td>\n",
       "      <td>0.010353</td>\n",
       "      <td>0.702279</td>\n",
       "      <td>0.002549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>{'alpha': 5}</td>\n",
       "      <td>-19.279019</td>\n",
       "      <td>2.056187</td>\n",
       "      <td>-18.675318</td>\n",
       "      <td>0.550807</td>\n",
       "      <td>0.688381</td>\n",
       "      <td>0.011487</td>\n",
       "      <td>0.701910</td>\n",
       "      <td>0.002638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>{'alpha': 10}</td>\n",
       "      <td>-19.357039</td>\n",
       "      <td>1.937242</td>\n",
       "      <td>-18.725360</td>\n",
       "      <td>0.551982</td>\n",
       "      <td>0.686811</td>\n",
       "      <td>0.013657</td>\n",
       "      <td>0.701112</td>\n",
       "      <td>0.002630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>{'alpha': 20}</td>\n",
       "      <td>-19.614181</td>\n",
       "      <td>1.738789</td>\n",
       "      <td>-18.919355</td>\n",
       "      <td>0.556708</td>\n",
       "      <td>0.681990</td>\n",
       "      <td>0.019624</td>\n",
       "      <td>0.698015</td>\n",
       "      <td>0.002606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>{'alpha': 30}</td>\n",
       "      <td>-19.916798</td>\n",
       "      <td>1.641253</td>\n",
       "      <td>-19.198035</td>\n",
       "      <td>0.534225</td>\n",
       "      <td>0.676522</td>\n",
       "      <td>0.025332</td>\n",
       "      <td>0.693553</td>\n",
       "      <td>0.002678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>{'alpha': 35}</td>\n",
       "      <td>-19.985865</td>\n",
       "      <td>1.643331</td>\n",
       "      <td>-19.315088</td>\n",
       "      <td>0.493238</td>\n",
       "      <td>0.675307</td>\n",
       "      <td>0.026587</td>\n",
       "      <td>0.691659</td>\n",
       "      <td>0.003390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>{'alpha': 40}</td>\n",
       "      <td>-20.016228</td>\n",
       "      <td>1.608388</td>\n",
       "      <td>-19.425199</td>\n",
       "      <td>0.472107</td>\n",
       "      <td>0.674745</td>\n",
       "      <td>0.026909</td>\n",
       "      <td>0.689875</td>\n",
       "      <td>0.004738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>{'alpha': 45}</td>\n",
       "      <td>-20.038605</td>\n",
       "      <td>1.566990</td>\n",
       "      <td>-19.507322</td>\n",
       "      <td>0.465681</td>\n",
       "      <td>0.674339</td>\n",
       "      <td>0.026780</td>\n",
       "      <td>0.688546</td>\n",
       "      <td>0.005629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>{'alpha': 100}</td>\n",
       "      <td>-20.058676</td>\n",
       "      <td>1.433613</td>\n",
       "      <td>-19.755629</td>\n",
       "      <td>0.351034</td>\n",
       "      <td>0.673915</td>\n",
       "      <td>0.026115</td>\n",
       "      <td>0.684528</td>\n",
       "      <td>0.006339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>{'alpha': 50}</td>\n",
       "      <td>-20.064423</td>\n",
       "      <td>1.526058</td>\n",
       "      <td>-19.557337</td>\n",
       "      <td>0.465675</td>\n",
       "      <td>0.673875</td>\n",
       "      <td>0.026695</td>\n",
       "      <td>0.687743</td>\n",
       "      <td>0.005839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>{'alpha': 55}</td>\n",
       "      <td>-20.090183</td>\n",
       "      <td>1.491687</td>\n",
       "      <td>-19.609408</td>\n",
       "      <td>0.462656</td>\n",
       "      <td>0.673424</td>\n",
       "      <td>0.026580</td>\n",
       "      <td>0.686905</td>\n",
       "      <td>0.006102</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              params  mean_test_neg_mean_squared_error  \\\n",
       "3   {'alpha': 0.001}                        -10.314094   \n",
       "4    {'alpha': 0.01}                        -10.318062   \n",
       "2   {'alpha': 1e-08}                        -10.325255   \n",
       "1   {'alpha': 1e-10}                        -10.325255   \n",
       "0   {'alpha': 1e-15}                        -10.325255   \n",
       "5       {'alpha': 1}                        -19.238840   \n",
       "6       {'alpha': 5}                        -19.279019   \n",
       "7      {'alpha': 10}                        -19.357039   \n",
       "8      {'alpha': 20}                        -19.614181   \n",
       "9      {'alpha': 30}                        -19.916798   \n",
       "10     {'alpha': 35}                        -19.985865   \n",
       "11     {'alpha': 40}                        -20.016228   \n",
       "12     {'alpha': 45}                        -20.038605   \n",
       "15    {'alpha': 100}                        -20.058676   \n",
       "13     {'alpha': 50}                        -20.064423   \n",
       "14     {'alpha': 55}                        -20.090183   \n",
       "\n",
       "    std_test_neg_mean_squared_error  mean_train_neg_mean_squared_error  \\\n",
       "3                          1.203238                          -8.961214   \n",
       "4                          1.180566                          -9.053588   \n",
       "2                          1.207834                          -8.960106   \n",
       "1                          1.207834                          -8.960106   \n",
       "0                          1.207834                          -8.960106   \n",
       "5                          2.156398                         -18.652332   \n",
       "6                          2.056187                         -18.675318   \n",
       "7                          1.937242                         -18.725360   \n",
       "8                          1.738789                         -18.919355   \n",
       "9                          1.641253                         -19.198035   \n",
       "10                         1.643331                         -19.315088   \n",
       "11                         1.608388                         -19.425199   \n",
       "12                         1.566990                         -19.507322   \n",
       "15                         1.433613                         -19.755629   \n",
       "13                         1.526058                         -19.557337   \n",
       "14                         1.491687                         -19.609408   \n",
       "\n",
       "    std_train_neg_mean_squared_error  mean_test_r2  std_test_r2  \\\n",
       "3                           0.228115      0.832990     0.014535   \n",
       "4                           0.227097      0.833024     0.013005   \n",
       "2                           0.228133      0.832798     0.014733   \n",
       "1                           0.228133      0.832798     0.014733   \n",
       "0                           0.228133      0.832798     0.014733   \n",
       "5                           0.551440      0.689262     0.010353   \n",
       "6                           0.550807      0.688381     0.011487   \n",
       "7                           0.551982      0.686811     0.013657   \n",
       "8                           0.556708      0.681990     0.019624   \n",
       "9                           0.534225      0.676522     0.025332   \n",
       "10                          0.493238      0.675307     0.026587   \n",
       "11                          0.472107      0.674745     0.026909   \n",
       "12                          0.465681      0.674339     0.026780   \n",
       "15                          0.351034      0.673915     0.026115   \n",
       "13                          0.465675      0.673875     0.026695   \n",
       "14                          0.462656      0.673424     0.026580   \n",
       "\n",
       "    mean_train_r2  std_train_r2  \n",
       "3        0.856937      0.002210  \n",
       "4        0.855461      0.002230  \n",
       "2        0.856955      0.002210  \n",
       "1        0.856955      0.002210  \n",
       "0        0.856955      0.002210  \n",
       "5        0.702279      0.002549  \n",
       "6        0.701910      0.002638  \n",
       "7        0.701112      0.002630  \n",
       "8        0.698015      0.002606  \n",
       "9        0.693553      0.002678  \n",
       "10       0.691659      0.003390  \n",
       "11       0.689875      0.004738  \n",
       "12       0.688546      0.005629  \n",
       "15       0.684528      0.006339  \n",
       "13       0.687743      0.005839  \n",
       "14       0.686905      0.006102  "
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "elastic_net_cv_results = pd.DataFrame(elastic_net_regressor.cv_results_)\n",
    "elastic_net_cv_results = elastic_net_cv_results.iloc[:, [5, 11, 12, 19, 20, 26, 27, 34, 35]]\n",
    "elastic_net_cv_results.sort_values(by = 'mean_test_neg_mean_squared_error', ascending = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Negative Mean Squared Error scores for test datasets in Cross Validation - \n",
      "Linear Regression = -10.325\n",
      "Lasso (L1) Regression = -10.299\n",
      "Ridge (L2) Regression = -10.312\n",
      "Elastic Net (L1 + L2) Regression = -10.314\n"
     ]
    }
   ],
   "source": [
    "# summary\n",
    "print(\"Negative Mean Squared Error scores for test datasets in Cross Validation - \")\n",
    "print(\"Linear Regression =\", format(linear_regressor_cv_results.test_neg_mean_squared_error.mean(), '.3f'))\n",
    "print(\"Lasso (L1) Regression =\", format(lasso_regressor.best_score_, '.3f'))\n",
    "print(\"Ridge (L2) Regression =\", format(ridge_regressor.best_score_, '.3f'))\n",
    "print(\"Elastic Net (L1 + L2) Regression =\", format(elastic_net_regressor.best_score_, '.3f'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why was OLS not significantly outperformed by Regularization?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- What we saw above is that while scores did improve in case of Regularization, the improvement was extremely insignificant.\n",
    "- The reason for this is, as mentioned in documentation, that the regularization techniques come handy when OLS overfits our data or we have little data to work with (which also results in overfitting) - \n",
    "    > **OLS is ideal when the underlying relationship is Linear and we have `n >> p` *(where `n` is the number of samples and `p` is the number of features)*.**  \n",
    "    > But if `n` is not much larger than `p` or `p > n` (unfeasible for OLS), there can be a lot of variability in the fit which can result in either overfitting and very poor predictive ability.\n",
    "- This is where Regularization techniques such as L1, L2 etc. can be used to improve model performance by eliminating overfit. \n",
    "- Our dataset has 398 observations and 6 variables. Therefore, we are in the case n>>p where OLS is said to be ideal. Further, there isn't much differecne between R squared values for Test and Train sets as seen in CV which also means our model is not overfitting. In other words, we don't have the problem that Regularization is intended to solve.\n",
    "- Regularization is not a magical technique to drastically improve an underperforming OLS, it is simply an extension of OLS making the model fit poorly on training data, penalizing feature dependency and, thus, making the model more robust. That slight change, while good to combat overfitting, is an effort in vain otherwise."
   ]
  }
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