30-LINEAR REGRESSION FROM SCRATCH.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0fa069c2",
   "metadata": {},
   "source": [
    "# Linear Regression From Scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42e45f10",
   "metadata": {},
   "source": [
    "Hi Guys, Welcome to [Tirendaz Academy](https://youtube.com/c/tirendazacademy) 😀\n",
    "</br>\n",
    "In this notebook, I'm going to talk about linear regression from scratch.\n",
    "</br>\n",
    "Happy learning 🐱‍🏍 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5befe775",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8276a2b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(\"data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f03e9066",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Make</th>\n",
       "      <th>Model</th>\n",
       "      <th>Year</th>\n",
       "      <th>Engine Fuel Type</th>\n",
       "      <th>Engine HP</th>\n",
       "      <th>Engine Cylinders</th>\n",
       "      <th>Transmission Type</th>\n",
       "      <th>Driven_Wheels</th>\n",
       "      <th>Number of Doors</th>\n",
       "      <th>Market Category</th>\n",
       "      <th>Vehicle Size</th>\n",
       "      <th>Vehicle Style</th>\n",
       "      <th>highway MPG</th>\n",
       "      <th>city mpg</th>\n",
       "      <th>Popularity</th>\n",
       "      <th>MSRP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>BMW</td>\n",
       "      <td>1 Series M</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium unleaded (required)</td>\n",
       "      <td>335.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>MANUAL</td>\n",
       "      <td>rear wheel drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Factory Tuner,Luxury,High-Performance</td>\n",
       "      <td>Compact</td>\n",
       "      <td>Coupe</td>\n",
       "      <td>26</td>\n",
       "      <td>19</td>\n",
       "      <td>3916</td>\n",
       "      <td>46135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>BMW</td>\n",
       "      <td>1 Series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium unleaded (required)</td>\n",
       "      <td>300.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>MANUAL</td>\n",
       "      <td>rear wheel drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Luxury,Performance</td>\n",
       "      <td>Compact</td>\n",
       "      <td>Convertible</td>\n",
       "      <td>28</td>\n",
       "      <td>19</td>\n",
       "      <td>3916</td>\n",
       "      <td>40650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BMW</td>\n",
       "      <td>1 Series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium unleaded (required)</td>\n",
       "      <td>300.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>MANUAL</td>\n",
       "      <td>rear wheel drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Luxury,High-Performance</td>\n",
       "      <td>Compact</td>\n",
       "      <td>Coupe</td>\n",
       "      <td>28</td>\n",
       "      <td>20</td>\n",
       "      <td>3916</td>\n",
       "      <td>36350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BMW</td>\n",
       "      <td>1 Series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium unleaded (required)</td>\n",
       "      <td>230.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>MANUAL</td>\n",
       "      <td>rear wheel drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Luxury,Performance</td>\n",
       "      <td>Compact</td>\n",
       "      <td>Coupe</td>\n",
       "      <td>28</td>\n",
       "      <td>18</td>\n",
       "      <td>3916</td>\n",
       "      <td>29450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BMW</td>\n",
       "      <td>1 Series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium unleaded (required)</td>\n",
       "      <td>230.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>MANUAL</td>\n",
       "      <td>rear wheel drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Luxury</td>\n",
       "      <td>Compact</td>\n",
       "      <td>Convertible</td>\n",
       "      <td>28</td>\n",
       "      <td>18</td>\n",
       "      <td>3916</td>\n",
       "      <td>34500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Make       Model  Year             Engine Fuel Type  Engine HP  \\\n",
       "0  BMW  1 Series M  2011  premium unleaded (required)      335.0   \n",
       "1  BMW    1 Series  2011  premium unleaded (required)      300.0   \n",
       "2  BMW    1 Series  2011  premium unleaded (required)      300.0   \n",
       "3  BMW    1 Series  2011  premium unleaded (required)      230.0   \n",
       "4  BMW    1 Series  2011  premium unleaded (required)      230.0   \n",
       "\n",
       "   Engine Cylinders Transmission Type     Driven_Wheels  Number of Doors  \\\n",
       "0               6.0            MANUAL  rear wheel drive              2.0   \n",
       "1               6.0            MANUAL  rear wheel drive              2.0   \n",
       "2               6.0            MANUAL  rear wheel drive              2.0   \n",
       "3               6.0            MANUAL  rear wheel drive              2.0   \n",
       "4               6.0            MANUAL  rear wheel drive              2.0   \n",
       "\n",
       "                         Market Category Vehicle Size Vehicle Style  \\\n",
       "0  Factory Tuner,Luxury,High-Performance      Compact         Coupe   \n",
       "1                     Luxury,Performance      Compact   Convertible   \n",
       "2                Luxury,High-Performance      Compact         Coupe   \n",
       "3                     Luxury,Performance      Compact         Coupe   \n",
       "4                                 Luxury      Compact   Convertible   \n",
       "\n",
       "   highway MPG  city mpg  Popularity   MSRP  \n",
       "0           26        19        3916  46135  \n",
       "1           28        19        3916  40650  \n",
       "2           28        20        3916  36350  \n",
       "3           28        18        3916  29450  \n",
       "4           28        18        3916  34500  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1ac2f366",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11914, 16)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0a143cd8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Make', 'Model', 'Year', 'Engine Fuel Type', 'Engine HP',\n",
       "       'Engine Cylinders', 'Transmission Type', 'Driven_Wheels',\n",
       "       'Number of Doors', 'Market Category', 'Vehicle Size', 'Vehicle Style',\n",
       "       'highway MPG', 'city mpg', 'Popularity', 'MSRP'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7960af0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "data.columns = data.columns.str.lower().str.replace(\" \", \"_\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d1442a38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['make', 'model', 'year', 'engine_fuel_type', 'engine_hp',\n",
       "       'engine_cylinders', 'transmission_type', 'driven_wheels',\n",
       "       'number_of_doors', 'market_category', 'vehicle_size', 'vehicle_style',\n",
       "       'highway_mpg', 'city_mpg', 'popularity', 'msrp'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c13f7fbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make                  object\n",
       "model                 object\n",
       "year                   int64\n",
       "engine_fuel_type      object\n",
       "engine_hp            float64\n",
       "engine_cylinders     float64\n",
       "transmission_type     object\n",
       "driven_wheels         object\n",
       "number_of_doors      float64\n",
       "market_category       object\n",
       "vehicle_size          object\n",
       "vehicle_style         object\n",
       "highway_mpg            int64\n",
       "city_mpg               int64\n",
       "popularity             int64\n",
       "msrp                   int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b6bc3334",
   "metadata": {},
   "outputs": [],
   "source": [
    "str_columns = list(data.dtypes[data.dtypes == \"object\"].index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "65ab90c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['make',\n",
       " 'model',\n",
       " 'engine_fuel_type',\n",
       " 'transmission_type',\n",
       " 'driven_wheels',\n",
       " 'market_category',\n",
       " 'vehicle_size',\n",
       " 'vehicle_style']"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str_columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "19110df9",
   "metadata": {},
   "outputs": [],
   "source": [
    "for col in str_columns:\n",
    "    data[col] = data[col].str.lower().str.replace(\" \", \"_\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "db602c1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>make</th>\n",
       "      <th>model</th>\n",
       "      <th>year</th>\n",
       "      <th>engine_fuel_type</th>\n",
       "      <th>engine_hp</th>\n",
       "      <th>engine_cylinders</th>\n",
       "      <th>transmission_type</th>\n",
       "      <th>driven_wheels</th>\n",
       "      <th>number_of_doors</th>\n",
       "      <th>market_category</th>\n",
       "      <th>vehicle_size</th>\n",
       "      <th>vehicle_style</th>\n",
       "      <th>highway_mpg</th>\n",
       "      <th>city_mpg</th>\n",
       "      <th>popularity</th>\n",
       "      <th>msrp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>bmw</td>\n",
       "      <td>1_series_m</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium_unleaded_(required)</td>\n",
       "      <td>335.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>manual</td>\n",
       "      <td>rear_wheel_drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>factory_tuner,luxury,high-performance</td>\n",
       "      <td>compact</td>\n",
       "      <td>coupe</td>\n",
       "      <td>26</td>\n",
       "      <td>19</td>\n",
       "      <td>3916</td>\n",
       "      <td>46135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>bmw</td>\n",
       "      <td>1_series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium_unleaded_(required)</td>\n",
       "      <td>300.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>manual</td>\n",
       "      <td>rear_wheel_drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>luxury,performance</td>\n",
       "      <td>compact</td>\n",
       "      <td>convertible</td>\n",
       "      <td>28</td>\n",
       "      <td>19</td>\n",
       "      <td>3916</td>\n",
       "      <td>40650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>bmw</td>\n",
       "      <td>1_series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium_unleaded_(required)</td>\n",
       "      <td>300.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>manual</td>\n",
       "      <td>rear_wheel_drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>luxury,high-performance</td>\n",
       "      <td>compact</td>\n",
       "      <td>coupe</td>\n",
       "      <td>28</td>\n",
       "      <td>20</td>\n",
       "      <td>3916</td>\n",
       "      <td>36350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>bmw</td>\n",
       "      <td>1_series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium_unleaded_(required)</td>\n",
       "      <td>230.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>manual</td>\n",
       "      <td>rear_wheel_drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>luxury,performance</td>\n",
       "      <td>compact</td>\n",
       "      <td>coupe</td>\n",
       "      <td>28</td>\n",
       "      <td>18</td>\n",
       "      <td>3916</td>\n",
       "      <td>29450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>bmw</td>\n",
       "      <td>1_series</td>\n",
       "      <td>2011</td>\n",
       "      <td>premium_unleaded_(required)</td>\n",
       "      <td>230.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>manual</td>\n",
       "      <td>rear_wheel_drive</td>\n",
       "      <td>2.0</td>\n",
       "      <td>luxury</td>\n",
       "      <td>compact</td>\n",
       "      <td>convertible</td>\n",
       "      <td>28</td>\n",
       "      <td>18</td>\n",
       "      <td>3916</td>\n",
       "      <td>34500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  make       model  year             engine_fuel_type  engine_hp  \\\n",
       "0  bmw  1_series_m  2011  premium_unleaded_(required)      335.0   \n",
       "1  bmw    1_series  2011  premium_unleaded_(required)      300.0   \n",
       "2  bmw    1_series  2011  premium_unleaded_(required)      300.0   \n",
       "3  bmw    1_series  2011  premium_unleaded_(required)      230.0   \n",
       "4  bmw    1_series  2011  premium_unleaded_(required)      230.0   \n",
       "\n",
       "   engine_cylinders transmission_type     driven_wheels  number_of_doors  \\\n",
       "0               6.0            manual  rear_wheel_drive              2.0   \n",
       "1               6.0            manual  rear_wheel_drive              2.0   \n",
       "2               6.0            manual  rear_wheel_drive              2.0   \n",
       "3               6.0            manual  rear_wheel_drive              2.0   \n",
       "4               6.0            manual  rear_wheel_drive              2.0   \n",
       "\n",
       "                         market_category vehicle_size vehicle_style  \\\n",
       "0  factory_tuner,luxury,high-performance      compact         coupe   \n",
       "1                     luxury,performance      compact   convertible   \n",
       "2                luxury,high-performance      compact         coupe   \n",
       "3                     luxury,performance      compact         coupe   \n",
       "4                                 luxury      compact   convertible   \n",
       "\n",
       "   highway_mpg  city_mpg  popularity   msrp  \n",
       "0           26        19        3916  46135  \n",
       "1           28        19        3916  40650  \n",
       "2           28        20        3916  36350  \n",
       "3           28        18        3916  29450  \n",
       "4           28        18        3916  34500  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c166e5f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5146c3a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_style(\"whitegrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f6c5087d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='msrp', ylabel='Count'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(data.msrp, bins=40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "dce26db0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='msrp', ylabel='Count'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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x9h0uYCIKiYKCAixduhQFBQXo6OhAXl7eiAsxGAzBcJkwYQIGBgYwffp0tLe3Y+bMmWhubsbNN98Ms9mMzZs3Q5Zl+Hw+dHV1wWQyjfj1KLRQW29svj83tsUQUdwKGxKvv/46nnjiCbS2tuLIkSMoLCzEr3/96xG/0EMPPYQVK1bAarXC7/ejoqICN954I6qrq1FTU4Ps7GwUFxcjJSUFNpsNVqsViqKgoqICWq12VM0REdHYhAyJ2tpafP7557j33ntx6623YurUqXjhhRfwn//8B0uWLBnRC+l0Orz88suXHK+rq7vkmMVigcViGdHzExHR5RfyL9M1Nzfj5ZdfRlpaGgAgMzMTL730Et5///2YFEdEROMrZEikp6cHrz76XmpqKnQ6XVSLIiKi+BAyJK666ip8/fXXQ459/fXXlwQHERElppCfSTz55JN47LHHMGvWLFx33XU4ceIEWlpasGHDhljVR0RE4yjkmcS0adOwd+9eTJ8+Hf39/fjpT3+K+vp6TJ8+PVb1ERHROAp7Caxer8f8+fNjUAoREcWbkGcSRESU3CK645rocgm3OSA3ACSKLwwJiin/YADlrx8UjteW5AFgSBDFC77dREREQgwJIiISYkgQEZEQQ4KIiIQYEkREJMSrmyiuhLpElpfHEsUeQ4LiSqhLZHl5LFHs8e0mIiISYkgQEZFQTN9u2rZtG95//334/X6UlJSgsLAQy5cvh0qlwrRp07B69Wqo1Wo4HA40NDRAo9GgtLQU8+bNi2WZRET0XzE7k2hvb8enn36K+vp62O12fPPNN1i/fj3Ky8uxd+9eKIqC/fv3o7e3F3a7HQ0NDdi5cydqamrg8/liVSYREV0gZmcSLS0tMJlMWLJkCdxuN55++mk4HA4UFhYCAIqKitDa2gq1Wo28vDxIkgRJkmA0GtHZ2Qmz2RyrUhPC+X4/5IFBAIBh8pRLrhgKKONRFRFdaWIWEufOncOJEyfw2muvobu7G6WlpVAUJfinUHU6HVwuF9xuN/R6fXCdTqeD2+0O+/yyLMPpdIac4/V6h51jmDwFfX19wnU+nw9O51dha4gnhslTUGr/GAAQCASgVg89adz20P8Ie1YUhPx6jGV8LGtH+n0Qfb8THftOLtHuO2YhMXHiRGRnZ0OSJGRnZ0Or1eKbb74Jjns8HhgMBmRkZMDj8Qw5fmFoiGi1WuTk5ISc43Q6h53T6/IiPT1duE6SpLDPHW8u7Kmvr++S/lQqCHsONTbW8bGsHen3QfT9TnTsO7mMte9wAROzzyQKCgrwwQcfQFEUnDp1Cv39/Zg1axba29sBAM3NzZgxYwbMZjM6OjogyzJcLhe6urpgMpliVSYREV0gZmcS8+bNw8cff4z77rsPiqJg1apVyMzMRHV1NWpqapCdnY3i4mKkpKTAZrPBarVCURRUVFRAq9XGqkwiIrpATC+Bffrppy85VldXd8kxi8UCi8USi5KIiCgE3kxHRERCDAkiIhLiBn90xQi1QyzAXWKJooEhQVeMUDvEAtwlliga+HYTEREJMSSIiEiIIUFEREIMCSIiEmJIEBGREEOCiIiEGBJERCTEkCAiIiGGBBERCTEkiIhIiCFBRERC3LuJEsbFGwAaJk8Z8pgbABKNHEOCEsbFGwBe/Le9uQEg0cgxJK5g5/v9kAcGhx0LKDEuhogSUsxD4syZM1iwYAF27doFjUaD5cuXQ6VSYdq0aVi9ejXUajUcDgcaGhqg0WhQWlqKefPmxbrMK4I8MIiy+k+HHdt8f25siyGihBTTkPD7/Vi1ahWuuuoqAMD69etRXl6OmTNnYtWqVdi/fz9yc3Nht9vR2NgIWZZhtVoxe/ZsSJIUy1IpAYX6o0X8vIJoeDENiQ0bNmDhwoXYvn07AODo0aMoLCwEABQVFaG1tRVqtRp5eXmQJAmSJMFoNKKzsxNmszmWpVICCvVHi/h5BdHwYhYSb775JiZNmoS5c+cGQ0JRFKhUKgCATqeDy+WC2+2GXq8PrtPpdHC73WGfX5ZlOJ3OkHO8Xu+wcwyTp6Cvr0+4zufzwen8KmwNsRaqbkVBcCwQCFwy78LxUGsv93gs117cd6j18fo9Hg3Rz3miY9/REbOQaGxshEqlQltbG5xOJyorK3H27NnguMfjgcFgQEZGBjwez5DjF4aGiFarRU5OTsg5Tqdz2Dm9Lu+Qq2AuJklS2OceD6HqVqkQHLv4Kp+Lx0OtvdzjsVx7cd+h1sfr93g0RD/niY59j359KDG7mW7Pnj2oq6uD3W5HTk4ONmzYgKKiIrS3twMAmpubMWPGDJjNZnR0dECWZbhcLnR1dcFkMsWqTCIiusC4XgJbWVmJ6upq1NTUIDs7G8XFxUhJSYHNZoPVaoWiKKioqIBWqx3PMomIkta4hITdbg/+u66u7pJxi8UCi8USy5KIiGgY3LuJiIiEGBJERCTEkCAiIiHu3USE0HdjA7wjm5IXQyKOhdrAD+AmfpdTqLuxAd6RTcmLIRHHQm3gB3ATPyKKPn4mQUREQgwJIiISYkgQEZEQQ4KIiIQYEkREJMSQICIiIV4CSxQB/ulTSlYMCaII8E+fUrLi201ERCTEkCAiIiG+3UQ0RtwckBIZQ4JojLg5ICWymIWE3+/HihUr0NPTA5/Ph9LSUkydOhXLly+HSqXCtGnTsHr1aqjVajgcDjQ0NECj0aC0tBTz5s2LVZlERHSBmIXEW2+9hYkTJ2Ljxo04d+4cfvGLX+AnP/kJysvLMXPmTKxatQr79+9Hbm4u7HY7GhsbIcsyrFYrZs+eDUmSYlUqERH9V8xC4o477kBxcXHwcUpKCo4ePYrCwkIAQFFREVpbW6FWq5GXlwdJkiBJEoxGIzo7O2E2m2NVKhER/VfMQkKn0wEA3G43li5divLycmzYsAEqlSo47nK54Ha7odfrh6xzu91hn1+WZTidzpBzvF7vsHMMk6egr69PuM7n88Hp/CpsDZdbuLoUBcLxC8cCgcAl8yJde7nHY7n24r7Hq65Y//yIfs4THfuOjph+cH3y5EksWbIEVqsV99xzDzZu3Bgc83g8MBgMyMjIgMfjGXL8wtAQ0Wq1yMnJCTnH6XQOO6fX5UV6erpwnSRJYZ87GsLVpVJBOH7hWF9f3yXzIl17ucdjufbivserrlj//Ih+zhMd+x79+lBidp/E6dOnsWjRIjz11FO47777AADTp09He3s7AKC5uRkzZsyA2WxGR0cHZFmGy+VCV1cXTCZTrMokuuy+v0RW9L/z/f7xLpFIKGZnEq+99hrOnz+PrVu3YuvWrQCAlStXYu3ataipqUF2djaKi4uRkpICm80Gq9UKRVFQUVEBrVYbqzKJLjteIktXspiFRFVVFaqqqi45XldXd8kxi8UCi8USi7KIiCgEbstBRERCvOOaaJxxG3KKZwwJonHGbcgpnvHtJiIiEmJIEBGREEOCiIiE+JkEUQI73++HPDA47Bg/FKdIMCSIEpg8MIiy+k+HHeOH4hQJhsQ4CvVbHgAElBgWQ3Ep3F+906jVGAgEhhwzTJ4SXBPqZ4h/UY8iwZAYR6F+ywOAzffnxq4YikvhtvTYfH/uJeMXbmwY6meI24VQJPjBNRERCTEkiIhIiG83EdGwuF0IAQwJIhII9ZnF7635/NA7STAkiGjE+KF38mBIRICn3USX11hu8hOtNUyegvP9/lGtjfS1kxFDIgLcpZNoZMLdgxFQgN82DH/5d7i3skRr+/r68IffzBn16wKh/3tO1oBhSBDRZRfJ/R3xthYIHW7hAiZUuA130+OF4jlg4jIkAoEAnn32Wfz73/+GJElYu3YtfvzjH493WaMS6rcP3lFNFF9ChUy4gAm3NlR4hTt7ChUy/2fyj0LWNVZxGRLvvfcefD4fXn/9dRw8eBAvvPACXn311fEua1hjOa3mHdVEBIzuzvrvbfq/P41OUf8VlyHR0dGBuXPnAgByc3Nx5MiRca5IbKynt0RE8UylKErcvemxcuVK3H777bjlllsAALfeeivee+89aDTiTDt48CC0Wm2sSiQiSgiyLCM3N1c4HpdnEhkZGfB4PMHHgUAgZEAACNkkERGNTlzu3ZSfn4/m5mYA350hmEymca6IiCg5xeXbTd9f3fTZZ59BURQ8//zzuOGGG8a7LCKipBOXIUFERPEhLt9uIiKi+MCQICIiIYYEEREJxeUlsJdTIm3x4ff7sWLFCvT09MDn86G0tBRTp07F8uXLoVKpMG3aNKxevRpqtRoOhwMNDQ3QaDQoLS3FvHnz4PV68dRTT+HMmTPQ6XTYsGEDJk2ahIMHD2LdunVISUnBnDlz8Pjjj493q8M6c+YMFixYgF27dkGj0SRF39u2bcP7778Pv9+PkpISFBYWJkXffr8fy5cvR09PD9RqNdasWZPw3/NDhw7hxRdfhN1ux7Fjx6LW6yuvvIJ//OMf0Gg0WLFiBcxmc+jClAT3t7/9TamsrFQURVE+/fRT5dFHHx3nikbvjTfeUNauXasoiqKcPXtWueWWW5RHHnlE+eijjxRFUZTq6mrl3XffVb799lvl7rvvVmRZVs6fPx/8965du5QtW7YoiqIo77zzjrJmzRpFURTl3nvvVY4dO6YEAgHlN7/5jXLkyJHxaTAEn8+nPPbYY8rtt9+ufPHFF0nR90cffaQ88sgjyuDgoOJ2u5UtW7YkRd+Koih///vflaVLlyqKoigtLS3K448/ntC9b9++Xbn77ruVX/7yl4qiKFHr9ciRI4rNZlMCgYDS09OjLFiwIGxtCf9205W0xUc4d9xxB377298GH6ekpODo0aMoLCwEABQVFeHDDz/E4cOHkZeXB0mSoNfrYTQa0dnZOeRrUVRUhLa2Nrjdbvh8PhiNRqhUKsyZMwdtbW3j0l8oGzZswMKFCzF58mQASIq+W1paYDKZsGTJEjz66KO49dZbk6JvAMjKysLg4CACgQDcbjc0Gk1C9240GlFbWxt8HK1eOzo6MGfOHKhUKvzoRz/C4OAgzp49G7K2hA8Jt9uNjIyM4OOUlBQMDAyMY0Wjp9PpkJGRAbfbjaVLl6K8vByKokClUgXHXS4X3G439Hr9kHVut3vI8QvnXvj1+f54PHnzzTcxadKk4H8IAJKi73PnzuHIkSN4+eWX8dxzz+HJJ59Mir4BID09HT09PbjzzjtRXV0Nm82W0L0XFxcP2VUiWr2O5muQ8J9JjGaLj3h28uRJLFmyBFarFffccw82btwYHPN4PDAYDJf07PF4oNfrhxwPNddgMMSuoQg0NjZCpVKhra0NTqcTlZWVQ377SdS+J06ciOzsbEiShOzsbGi1WnzzzTfB8UTtGwB2796NOXPmYNmyZTh58iQefPBB+P3+4Hgi9w4AavX//v5+OXtNTU0d9jlC1nK5mopXibTFx+nTp7Fo0SI89dRTuO+++wAA06dPR3t7OwCgubkZM2bMgNlsRkdHB2RZhsvlQldXF0wmE/Lz89HU1BScW1BQgIyMDKSmpuL48eNQFAUtLS2YMWPGuPU4nD179qCurg52ux05OTnYsGEDioqKEr7vgoICfPDBB1AUBadOnUJ/fz9mzZqV8H0DgMFgCP6f14QJEzAwMJAUP+vfi1av+fn5aGlpQSAQwIkTJxAIBDBp0qSQtST8HdeJtMXH2rVr8de//hXZ2dnBYytXrsTatWvh9/uRnZ2NtWvXIiUlBQ6HA6+//joURcEjjzyC4uJi9Pf3o7KyEr29vUhNTcWmTZtw9dVX4+DBg3j++ecxODiIOXPmoKKiYhy7DM1ms+HZZ5+FWq1GdXV1wvf9u9/9Du3t7VAUBRUVFcjMzEyKvj0eD1asWIHe3l74/X488MADuPHGGxO69+7ubjzxxBNwOBz46quvotZrbW0tmpubEQgE8Mwzz4QNyoQPCSIiGr2Ef7uJiIhGjyFBRERCDAkiIhJiSBARkRBDgoiIhBgSREQkxJAgIiKhK3d/CqJx9uabb+LAgQPwer3o7e3FAw88gP379+Pzzz/H008/jffeew/Hjx+HLMt4+OGHcdddd+Huu+/G9ddfD0mSkJWVhS+//BJnzpzB+fPnUVVVFbd3AFPyYkgQjYHH48GuXbuwb98+7N69Gw6HA+3t7Xj11Vdx/PhxNDY2AgBaW1sBAH19fXjssccwffp01NbW4qqrrsIf//hHfP7551i2bBneeuut8WyH6BIMCaIxyMnJAQDo9XrccMMNUKlUmDBhAjQaDaqrq1FdXQ2324177703uCYrKyv475tvvhkAMG3aNJw+fTq2xRNFgJ9JEI3B99s5D+fo0aP4/e9/j+3bt2Pjxo3BLeov3OHz6NGjAIDPPvsM11xzTXSLJRoFnkkQRUlvby/mz5+P9PR0LFq0aNgt6p1OJx588EH09/djzZo141AlUWjc4I9onNTW1uKHP/whSkpKxrsUIiG+3UREREI8kyAiIiGeSRARkRBDgoiIhBgSREQkxJAgIiIhhgQREQn9f9oKKeHrPFzdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(data.msrp[data.msrp<100000], bins=40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4c4cc710",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "814a8e25",
   "metadata": {},
   "outputs": [],
   "source": [
    "log_data = np.log1p(data.msrp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a571e798",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='msrp', ylabel='Count'>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(log_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "3e391561",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "make                    0\n",
       "model                   0\n",
       "year                    0\n",
       "engine_fuel_type        3\n",
       "engine_hp              69\n",
       "engine_cylinders       30\n",
       "transmission_type       0\n",
       "driven_wheels           0\n",
       "number_of_doors         6\n",
       "market_category      3742\n",
       "vehicle_size            0\n",
       "vehicle_style           0\n",
       "highway_mpg             0\n",
       "city_mpg                0\n",
       "popularity              0\n",
       "msrp                    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e8627aca",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = len(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "097cb148",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_val = int(0.15 * n)\n",
    "n_test = int(0.15 * n)\n",
    "n_train = n - (n_val + n_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "f5c1aa08",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b4c36823",
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = np.arange(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "1c2c5fdb",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.shuffle(idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "af167efe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3995, 7474, 7300, ..., 5390,  860, 7270])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "5390916c",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_shuffled = data.iloc[idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "474e7082",
   "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>make</th>\n",
       "      <th>model</th>\n",
       "      <th>year</th>\n",
       "      <th>engine_fuel_type</th>\n",
       "      <th>engine_hp</th>\n",
       "      <th>engine_cylinders</th>\n",
       "      <th>transmission_type</th>\n",
       "      <th>driven_wheels</th>\n",
       "      <th>number_of_doors</th>\n",
       "      <th>market_category</th>\n",
       "      <th>vehicle_size</th>\n",
       "      <th>vehicle_style</th>\n",
       "      <th>highway_mpg</th>\n",
       "      <th>city_mpg</th>\n",
       "      <th>popularity</th>\n",
       "      <th>msrp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3995</th>\n",
       "      <td>gmc</td>\n",
       "      <td>envoy_xl</td>\n",
       "      <td>2005</td>\n",
       "      <td>regular_unleaded</td>\n",
       "      <td>275.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>automatic</td>\n",
       "      <td>rear_wheel_drive</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>large</td>\n",
       "      <td>4dr_suv</td>\n",
       "      <td>18</td>\n",
       "      <td>13</td>\n",
       "      <td>549</td>\n",
       "      <td>29695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7474</th>\n",
       "      <td>volkswagen</td>\n",
       "      <td>passat</td>\n",
       "      <td>2016</td>\n",
       "      <td>regular_unleaded</td>\n",
       "      <td>170.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>automatic</td>\n",
       "      <td>front_wheel_drive</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>midsize</td>\n",
       "      <td>sedan</td>\n",
       "      <td>38</td>\n",
       "      <td>25</td>\n",
       "      <td>873</td>\n",
       "      <td>30495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7300</th>\n",
       "      <td>honda</td>\n",
       "      <td>odyssey</td>\n",
       "      <td>2016</td>\n",
       "      <td>regular_unleaded</td>\n",
       "      <td>248.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>automatic</td>\n",
       "      <td>front_wheel_drive</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>large</td>\n",
       "      <td>passenger_minivan</td>\n",
       "      <td>28</td>\n",
       "      <td>19</td>\n",
       "      <td>2202</td>\n",
       "      <td>37650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3148</th>\n",
       "      <td>chevrolet</td>\n",
       "      <td>cruze</td>\n",
       "      <td>2015</td>\n",
       "      <td>regular_unleaded</td>\n",
       "      <td>138.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>manual</td>\n",
       "      <td>front_wheel_drive</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>midsize</td>\n",
       "      <td>sedan</td>\n",
       "      <td>36</td>\n",
       "      <td>25</td>\n",
       "      <td>1385</td>\n",
       "      <td>16170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>747</th>\n",
       "      <td>volvo</td>\n",
       "      <td>740</td>\n",
       "      <td>1991</td>\n",
       "      <td>regular_unleaded</td>\n",
       "      <td>162.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>automatic</td>\n",
       "      <td>rear_wheel_drive</td>\n",
       "      <td>4.0</td>\n",
       "      <td>luxury,performance</td>\n",
       "      <td>midsize</td>\n",
       "      <td>sedan</td>\n",
       "      <td>20</td>\n",
       "      <td>17</td>\n",
       "      <td>870</td>\n",
       "      <td>2000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            make     model  year  engine_fuel_type  engine_hp  \\\n",
       "3995         gmc  envoy_xl  2005  regular_unleaded      275.0   \n",
       "7474  volkswagen    passat  2016  regular_unleaded      170.0   \n",
       "7300       honda   odyssey  2016  regular_unleaded      248.0   \n",
       "3148   chevrolet     cruze  2015  regular_unleaded      138.0   \n",
       "747        volvo       740  1991  regular_unleaded      162.0   \n",
       "\n",
       "      engine_cylinders transmission_type      driven_wheels  number_of_doors  \\\n",
       "3995               6.0         automatic   rear_wheel_drive              4.0   \n",
       "7474               4.0         automatic  front_wheel_drive              4.0   \n",
       "7300               6.0         automatic  front_wheel_drive              4.0   \n",
       "3148               4.0            manual  front_wheel_drive              4.0   \n",
       "747                4.0         automatic   rear_wheel_drive              4.0   \n",
       "\n",
       "         market_category vehicle_size      vehicle_style  highway_mpg  \\\n",
       "3995                 NaN        large            4dr_suv           18   \n",
       "7474                 NaN      midsize              sedan           38   \n",
       "7300                 NaN        large  passenger_minivan           28   \n",
       "3148                 NaN      midsize              sedan           36   \n",
       "747   luxury,performance      midsize              sedan           20   \n",
       "\n",
       "      city_mpg  popularity   msrp  \n",
       "3995        13         549  29695  \n",
       "7474        25         873  30495  \n",
       "7300        19        2202  37650  \n",
       "3148        25        1385  16170  \n",
       "747         17         870   2000  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_shuffled.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "626ba54f",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_train = data_shuffled.iloc[:n_train].copy()\n",
    "data_val = data_shuffled.iloc[n_train:n_train+n_val].copy()\n",
    "data_test = data_shuffled.iloc[n_train+n_val:].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "351681d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8340, 16)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "765412c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train = np.log1p(data_train.msrp.values)\n",
    "y_val = np.log1p(data_val.msrp.values)\n",
    "y_test = np.log1p(data_test.msrp.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "c6eeb89c",
   "metadata": {},
   "outputs": [],
   "source": [
    "del data_train[\"msrp\"]\n",
    "del data_test[\"msrp\"]\n",
    "del data_val[\"msrp\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "7374347a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['make', 'model', 'year', 'engine_fuel_type', 'engine_hp',\n",
       "       'engine_cylinders', 'transmission_type', 'driven_wheels',\n",
       "       'number_of_doors', 'market_category', 'vehicle_size', 'vehicle_style',\n",
       "       'highway_mpg', 'city_mpg', 'popularity'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_train.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "5743ab1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_linear_regression(X, y):\n",
    "    ones = np.ones(X.shape[0])\n",
    "    X = np.column_stack([ones, X])\n",
    "    XTX = X.T.dot(X)\n",
    "    XTX_inv = np.linalg.inv(XTX)\n",
    "    w = XTX_inv.dot(X.T).dot(y)\n",
    "    return w[0], w[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "c7451443",
   "metadata": {},
   "outputs": [],
   "source": [
    "base = [\"engine_hp\", \"engine_cylinders\", \"highway_mpg\", \"city_mpg\",\"popularity\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "13581126",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_num = data_train[base]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "b148dc91",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_num = data_num.fillna(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "5250668d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "engine_hp           0\n",
       "engine_cylinders    0\n",
       "highway_mpg         0\n",
       "city_mpg            0\n",
       "popularity          0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_num.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "274d22e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = data_num.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "6476471b",
   "metadata": {},
   "outputs": [],
   "source": [
    "w_0, w = train_linear_regression(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "674d5e2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = w_0 + X_train.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "5533b6a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rmse(y, y_pred):\n",
    "    error = y_pred-y\n",
    "    mse  = (error**2).mean()\n",
    "    return np.sqrt(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "595ebb04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7534764940614554"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse(y_train, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "92a66de3",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_num = data_val[base]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "80c5514a",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_num = data_num.fillna(0)\n",
    "X_val = data_num.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "c2979826",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = w_0 + X_val.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "e25f0107",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7396293330627383"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse(y_val, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "a0a0dfbf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_X(data):\n",
    "    data_num = data[base]\n",
    "    data_num = data_num.fillna(0)\n",
    "    X = data_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "3105d537",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "w_0, w = train_linear_regression(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "7950ee97",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation: 0.7396293330627383\n"
     ]
    }
   ],
   "source": [
    "X_val = prepare_X(data_val)\n",
    "y_pred = w_0 + X_val.dot(w)\n",
    "print(\"Validation:\", rmse(y_val, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "1cca8430",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_X(data):   \n",
    "    data = data.copy()\n",
    "    feature = base.copy()\n",
    "    data[\"age\"] = 2017-data.year\n",
    "    feature.append(\"age\")\n",
    "    data_num = data[feature]\n",
    "    data_num = data_num.fillna(0)\n",
    "    X = data_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "bae09341",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "w_0, w = train_linear_regression(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "fe75c294",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation: 0.5062765673626448\n"
     ]
    }
   ],
   "source": [
    "X_val = prepare_X(data_val)\n",
    "y_pred = w_0 + X_val.dot(w)\n",
    "print(\"Validation:\", rmse(y_val, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "cede938d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0    8353\n",
       "2.0    3160\n",
       "3.0     395\n",
       "Name: number_of_doors, dtype: int64"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.number_of_doors.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "33e667fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_X(data):   \n",
    "    data = data.copy()\n",
    "    features = base.copy()\n",
    "    data[\"age\"] = 2017-data.year\n",
    "    features.append(\"age\")  \n",
    "    for v in [2,3,4]:\n",
    "        feature = \"num_doors_%s\" %v\n",
    "        data[feature] = (data[\"number_of_doors\"] == v).astype(int)\n",
    "        features.append(feature)      \n",
    "    for v in ['chevrolet', 'ford', 'volkswagen', 'toyota', 'dodge']:\n",
    "        feature = 'is_make_%s' % v\n",
    "        data[feature] = (data['make'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "    data_num = data[features]\n",
    "    data_num = data_num.fillna(0)\n",
    "    X = data_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "da7782bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation: 0.49498138000463826\n"
     ]
    }
   ],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "w_0, w = train_linear_regression(X_train, y_train)\n",
    "X_val = prepare_X(data_val)\n",
    "y_pred = w_0 + X_val.dot(w)\n",
    "print(\"Validation:\", rmse(y_val, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "27aed94c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def prepare_X(df):\n",
    "    df = df.copy()\n",
    "    features = base.copy()\n",
    "\n",
    "    df['age'] = 2017 - df.year\n",
    "    features.append('age')\n",
    "    \n",
    "    for v in [2, 3, 4]:\n",
    "        feature = 'num_doors_%s' % v\n",
    "        df[feature] = (df['number_of_doors'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    for v in ['chevrolet', 'ford', 'volkswagen', 'toyota', 'dodge']:\n",
    "        feature = 'is_make_%s' % v\n",
    "        df[feature] = (df['make'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    for v in ['regular_unleaded', 'premium_unleaded_(required)', \n",
    "              'premium_unleaded_(recommended)', 'flex-fuel_(unleaded/e85)']:\n",
    "        feature = 'is_type_%s' % v\n",
    "        df[feature] = (df['engine_fuel_type'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    for v in ['automatic', 'manual', 'automated_manual']:\n",
    "        feature = 'is_transmission_%s' % v\n",
    "        df[feature] = (df['transmission_type'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    for v in ['front_wheel_drive', 'rear_wheel_drive', 'all_wheel_drive', 'four_wheel_drive']:\n",
    "        feature = 'is_driven_wheens_%s' % v\n",
    "        df[feature] = (df['driven_wheels'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    for v in ['crossover', 'flex_fuel', 'luxury', 'luxury,performance', 'hatchback']:\n",
    "        feature = 'is_mc_%s' % v\n",
    "        df[feature] = (df['market_category'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    for v in ['compact', 'midsize', 'large']:\n",
    "        feature = 'is_size_%s' % v\n",
    "        df[feature] = (df['vehicle_size'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    for v in ['sedan', '4dr_suv', 'coupe', 'convertible', '4dr_hatchback']:\n",
    "        feature = 'is_style_%s' % v\n",
    "        df[feature] = (df['vehicle_style'] == v).astype(int)\n",
    "        features.append(feature)\n",
    "\n",
    "    df_num = df[features]\n",
    "    df_num = df_num.fillna(0)\n",
    "    X = df_num.values\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "d2c048d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation: 115.11918034528615\n"
     ]
    }
   ],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "w_0, w = train_linear_regression(X_train, y_train)\n",
    "X_val = prepare_X(data_val)\n",
    "y_pred = w_0 + X_val.dot(w)\n",
    "print(\"Validation:\", rmse(y_val, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "d44d9f90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8340, 38)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "7d9f7f51",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_linear_regression_reg(X, y, r=0.0):\n",
    "    ones = np.ones(X.shape[0])\n",
    "    X = np.column_stack([ones, X])\n",
    "    XTX = X.T.dot(X)\n",
    "    reg = r*np.eye(XTX.shape[0])\n",
    "    XTX = XTX + reg\n",
    "    XTX_inv = np.linalg.inv(XTX)\n",
    "    w = XTX_inv.dot(X.T).dot(y)\n",
    "    return w[0], w[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "15f77ffa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.001, 7.45, -0.09, 1.90\n",
      " 0.01, 7.43, -0.09, 1.90\n",
      "  0.1, 7.28, -0.09, 1.86\n",
      "    1, 6.35, -0.09, 1.62\n",
      "   10, 4.52, -0.07, 1.13\n"
     ]
    }
   ],
   "source": [
    "for r in [0.001, 0.01, 0.1, 1 ,10]:\n",
    "    w_0, w = train_linear_regression_reg(X_train, y_train, r = r)\n",
    "    print(\"%5s, %.2f, %.2f, %.2f\" %(r, w_0, w[13], w[21]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "c5bc7827",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation: 0.44945183047679926\n"
     ]
    }
   ],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "w_0, w = train_linear_regression(X_train, y_train, r = 0.001)\n",
    "X_val = prepare_X(data_val)\n",
    "y_pred = w_0 + X_val.dot(w)\n",
    "print(\"Validation:\", rmse(y_val, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "9be1ba61",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 1e-06 0.44945191116666916\n",
      "0.0001 0.4494540231230776\n",
      " 0.001 0.44945183047679926\n",
      "  0.01 0.4494304408972553\n",
      "   0.1 0.4492687917985319\n",
      "     1 0.4497447786658369\n",
      "     5 0.45487047516713214\n",
      "    10 0.46017016344932754\n"
     ]
    }
   ],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "X_val = prepare_X(data_val)\n",
    "for r in [0.000001, 0.0001, 0.001, 0.01, 0.1, 1, 5, 10]:\n",
    "    w_0, w = train_linear_regression_reg(X_train, y_train, r=r)\n",
    "    y_pred = w_0 + X_val.dot(w)\n",
    "    print('%6s' %r, rmse(y_val, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "0e6f17d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation: 0.4494304408972553\n"
     ]
    }
   ],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "w_0, w = train_linear_regression(X_train, y_train, r = 0.01)\n",
    "X_val = prepare_X(data_val)\n",
    "y_pred = w_0 + X_val.dot(w)\n",
    "print(\"Validation:\", rmse(y_val, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "a79ff7dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation: 0.4646065014921197\n"
     ]
    }
   ],
   "source": [
    "X_train = prepare_X(data_train)\n",
    "y_pred = w_0 + X_train.dot(w)\n",
    "print(\"Validation:\", rmse(y_train, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "b84e555b",
   "metadata": {},
   "outputs": [],
   "source": [
    "ad = {\n",
    "'city_mpg': 18,\t\n",
    "'driven_wheels': 'all_wheel_drive',\n",
    "'engine_cylinders': 6.0,\n",
    "'engine_fuel_type': 'regular_unleaded',\n",
    "'engine_hp': 268.0,\n",
    "'highway_mpg': 25,\n",
    "'make': 'BMV',\n",
    "'market_category': 'crossover,performance',\n",
    "'model': 'venza',\n",
    "'number_of_doors': 4.0,\n",
    "'popularity': 2031,\n",
    "'transmission_type': 'automatic',\n",
    "'vehicle_size': 'midsize',\n",
    "'vehicle_style': 'wagon',\n",
    "'year': 2017\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "8e72fa1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_test = pd.DataFrame([ad])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "891df940",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test = prepare_X(data_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "bc99a4e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = w_0 + X_test.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "f371a4a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([46350.75865698])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict = np.expm1(y_pred)\n",
    "predict"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b671c3c0",
   "metadata": {},
   "source": [
    "Don't forget to follow us on [YouTube](http://youtube.com/tirendazacademy) | [Medium](http://tirendazacademy.medium.com) | [Twitter](http://twitter.com/tirendazacademy) | [GitHub](http://github.com/tirendazacademy) | [Linkedin](https://www.linkedin.com/in/tirendaz-academy) | [Kaggle](https://www.kaggle.com/tirendazacademy) 😎"
   ]
  }
 ],
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