EDA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1e8922f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ad77d2d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "        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>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e6e84b6",
   "metadata": {},
   "source": [
    "## 1. Analyzing Individual Feature Patterns Using Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae0124b4",
   "metadata": {},
   "source": [
    "+ choose the right visualization method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "29148feb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symboling              int64\n",
      "normalized-losses      int64\n",
      "make                  object\n",
      "aspiration            object\n",
      "num-of-doors          object\n",
      "body-style            object\n",
      "drive-wheels          object\n",
      "engine-location       object\n",
      "wheel-base           float64\n",
      "length               float64\n",
      "width                float64\n",
      "height               float64\n",
      "curb-weight            int64\n",
      "engine-type           object\n",
      "num-of-cylinders      object\n",
      "engine-size            int64\n",
      "fuel-system           object\n",
      "bore                 float64\n",
      "stroke               float64\n",
      "compression-ratio    float64\n",
      "horsepower           float64\n",
      "peak-rpm             float64\n",
      "city-mpg               int64\n",
      "highway-mpg            int64\n",
      "price                float64\n",
      "city-L/100km         float64\n",
      "horsepower-binned     object\n",
      "diesel                 int64\n",
      "gas                    int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "561d346e",
   "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>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#calculate the correlation between variables of type \"int64\" or \"float64\"\n",
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9040afcb",
   "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>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055390           0.001263    0.566936\n",
       "stroke            -0.055390  1.000000           0.187923    0.098462\n",
       "compression-ratio  0.001263  0.187923           1.000000   -0.214514\n",
       "horsepower         0.566936  0.098462          -0.214514    1.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "##correlation between the following columns: bore, stroke, compression-ratio, and horsepower.\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07c1e8d4",
   "metadata": {},
   "source": [
    "## Continuous Numerical Variables\n",
    "\n",
    "### Positive Linear Relationship"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "64b8050c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "431904bd",
   "metadata": {},
   "source": [
    "As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. \n",
    "    Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fc68b594",
   "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>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.872335</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872335\n",
       "price           0.872335  1.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c41b2853",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e34cd4fc",
   "metadata": {},
   "source": [
    "As highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. \n",
    "    Highway mpg could potentially be a predictor of price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6a553ecb",
   "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>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg     price\n",
       "highway-mpg     1.000000 -0.704692\n",
       "price          -0.704692  1.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"highway-mpg\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8597214",
   "metadata": {},
   "source": [
    "### Weak Linear Relationship"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e867fd1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "306b6b80",
   "metadata": {},
   "source": [
    "Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. \n",
    "Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore, it's not a reliable variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "77c3637f",
   "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>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.101616\n",
       "price    -0.101616  1.000000"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1155c3c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5d05302",
   "metadata": {},
   "source": [
    "There is a weak correlation between the variable 'stroke' and 'price.' as such regression will not work well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3b734050",
   "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>stroke</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.08231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.08231</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         stroke    price\n",
       "stroke  1.00000  0.08231\n",
       "price   0.08231  1.00000"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['stroke','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf81de16",
   "metadata": {},
   "source": [
    "## categorical Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "602f1bd8",
   "metadata": {},
   "source": [
    "+ These are variables that describe a 'characteristic' of a data unit, and are selected from a small group of categories. The categorical variables can have the type \"object\" or \"int64\". A good way to visualize categorical variables is by using boxplots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "cd1e1407",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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etTUWuDMibodsCN0UezWvipmZ2fDQ1xbJCrLEUTAW+O7gV8fMzIabviaSMRHxSuFJmj6qpwKSTpb0sKRnJa2TdG2K3yjpl5JWp8fFRWWul9Qm6SeSLiyKT5O0Ns1rSiMlkkZTvDfFV0ma2I99NzOzQdDXRPJrSX9QeCJpGrCzlzJ7gb+KiDcAZwNXS5qS5i2IiKnpsTStcwowGziDbGz3W9IpNIBbgblkw+9OTvMB5gAvRcQkYAFwUx/3x8zMBklfr5F8HPi6pE3p+QTgip4KpLHWN6fpHZKeBep7KHIJsCgidgPPp+Fzz5K0ETgmIlYCSLobuJRsuN1LgBtT+fuAL0iSx203M6ucPrVIIuIJ4HSysdM/CrwhIp7s60bSKac3A6tS6GOS1ki6U9JxKVYPvFBUrD3F6tN093iXMhGxF9gOHNTLm6S5kloltXZ0dPS12mZm1gc9JhJJ56e/fwq8C3g92amld6VYryQdDXwD+HhE/IrsNNVpwFSyFsvnC4uWKB49xHsq0zUQcVtETI+I6XV1dX2ptpmZ9VFvp7b+GHiILIl0F8A3eyosqYYsifxbRHwTICK2FM2/HXggPW0HTi4q3gBsSvGGEvHiMu3p1/bHAi/2sk9mZjaIekwkEXGDpBFAS0Qs7s+K051VdwDPRsTNRfEJ6foJwHuAZ9L0EuCrkm4GTiJr+TweEfsk7ZB0NtmpsSuBhUVlGoGVwGXAQ74+YmZWWb1ebI+I/ZI+BvQrkZB18vhBYK2k1Sn2aeB9kqaStWg2kv1SnohYJ2kxsJ7sjq+rI2JfKncVcBfZ71da0gOyRHVPujD/ItldX2ZmVkF9vWtruaS/Bu4Ffl0IRsQhTyNFxPcpfQ1jaQ9l5gPzS8RbgTNLxHcBl/dYczMzy1VfE8lfkrUgPtot/ruDWx0zMxtu+ppIppAlkbeRJZTHgC/mVSkzMxs++ppImskGtWpKz9+XYu/No1JmZjZ89DWR/F5EvKno+cOSns6jQmZmNrz0ta+tp9LttwBI+kPgB/lUyczMhpO+JpI/BH4oaWPq+2ol8MepR941udXODnudnZ1cc801bNu2rdpVMbMB6uuprYt6X8Ss/5qbm1mzZg3Nzc1cd9111a6OmQ1AXztt/HlPj7wraYenzs5OWlpaiAhaWlrcKjEbpvp6asts0DU3N1Po0Wb//v00NzdXuUZmNhBOJFY1y5cvZ8+ePQDs2bOHZcuWVblGZjYQTiRWNTNmzKCmpgaAmpoaZs6cWeUamdlAOJFY1TQ2NpJ1Eg0jRoygsbGxyjUys4FwIrGqqa2tZdasWUhi1qxZjB9/0OCWZjYM9PX2X7NcNDY2snHjRrdGzIYxJxKrqtraWhYuXNj7gmY2ZPnUlpmZlSW3RCLpZEkPS3pW0jpJ16b48ZKWS9qQ/h5XVOZ6SW2SfiLpwqL4tNQdS5ukpjSML5JGS7o3xVdJmpjX/piZWWl5tkj2An8VEW8AzgauljQF+BSwIiImAyvSc9K82cAZZF2y3CJpZFrXrcBcsnHcJ3Ogy5Y5wEsRMQlYANyU4/6YmVkJuSWSiNgcET9O0zuAZ4F64BKysUxIfy9N05cAiyJid0Q8D7QBZ0maABwTESsj+xn03d3KFNZ1H3BBobViZmaVUZGL7emU05uBVcCJEbEZsmQj6YS0WD3wo6Ji7Sm2J013jxfKvJDWtVfSdmA80Nlt+3PJWjSccsopg7ZfdkBTUxNtbW39Ltfenv1rGxoa+lVu0qRJzJs3r9/bMxsM7e3tbH91Bw8/t6jaVRk0L7+6lWjfOaCyuV9sl3Q08A3g4xHxq54WLRGLHuI9lekaiLgtIqZHxPS6urreqmwVtHPnTnbuHNiL18yGhlxbJJJqyJLIv0XEN1N4i6QJqTUyAdia4u3AyUXFG4BNKd5QIl5cpl3SKOBY4MVcdsZ6NNDWQaFcU1NTL0uaDR0NDQ1o9zbOO312tasyaB5+bhH1DQP7UXCed20JuAN4NiJuLpq1BCj8+qwRuL8oPjvdiXUq2UX1x9NpsB2Szk7rvLJbmcK6LgMeikJ3smZmVhF5tkjeCnwQWCtpdYp9GvgssFjSHOAXwOUAEbFO0mJgPdkdX1dHxL5U7irgLmAs0JIekCWqeyS1kbVEDp+vB2aHgYFcOxvodTPwtbNqyS2RRMT3KX0NA+CCQ5SZD8wvEW8FziwR30VKRGZ2ePA1s+HHXaSYWW4G0jrwdbPhx12kmJlZWZxIzMysLD61ZdaDgf7Qsr82bNgADPw26v7yRWkbTE4kZj1oa2vjqXVPwbicN7Q/+/PUL5/KeUPAy/lvwo4sTiRmvRkH+8/dX+1aDJoRj/iMtg0uv6LMzKwsbpEk7e3tjHh1O2PWP1DtqgyaEa9uo719b7WrYWaHObdIzMysLG6RJA0NDWzZPYpdU95Z7aoMmjHrH6Ch4XXVroaZHebcIjEzs7I4kZiZWVmcSMzMrCxOJGZmVhZfbDezPnF3MXYouSUSSXcC7wS2RsSZKXYj8GGgIy326YhYmuZdD8wB9gHzIuLBFJ/GgUGtlgLXRkRIGg3cDUwDtgFXRMTGvPbH7EjX1tbGc6tXk/d9gIXTJC+vXp3zluC/ct/CkSHPFsldwBfIPuyLLYiIfyoOSJpCNrrhGcBJwHclvT6NkHgrMBf4EVkiuYhshMQ5wEsRMUnSbOAm4Ir8dsfMXgfMOeR4dcPPHXhk7sGQ2zWSiHiUbPjbvrgEWBQRuyPieaANOEvSBOCYiFiZxmK/G7i0qExzmr4PuCCN6W5mZhVUjYvtH5O0RtKdko5LsXrghaJl2lOsPk13j3cpExF7ge3A+FIblDRXUquk1o6OjlKLmJnZAFU6kdwKnAZMBTYDn0/xUi2J6CHeU5mDgxG3RcT0iJheV1fXrwqbmVnPKppIImJLROyLiP3A7cBZaVY7cHLRog3AphRvKBHvUkbSKOBY+n4qzczMBklFb/+VNCEiNqen7wGeSdNLgK9KupnsYvtk4PGI2Cdph6SzgVXAlcDCojKNwErgMuChdB1lwEa8+mJFev/Vrl8BEGOOyXU7I159EXK/x8bMjnR53v77NeBcoFZSO3ADcK6kqWSnoDYCHwGIiHWSFgPrgb3A1emOLYCrOHD7b0t6ANwB3COpjawlMruc+k6aNKmc4v2yYcMOACaflveH/Osqul9mdmTKLZFExPtKhO/oYfn5wPwS8VbgzBLxXcDl5dSxWCV/kFTYVlNTU8W2aWaWF3eRYmZmZXEiMTOzsjiRmJlZWZxIzMysLE4kZmZWFicSMzMrixOJmZmVxYnEzMzK4hES7SCVGgkPKjsankfCM8uHE4kdpK2tjZ8+82NOOXpf7wuX6b/tyRrFuzY+ket2fvHKyFzXb3YkcyIpw0C/uQ/0W3glv1GfcvQ+PjP9lYpsqxL+vvXoaldh2Gtvb2cHh9eogpuBV9rbe13OeuZEUgVjx46tdhXMzAaNE0kZfL7djiQNDQ283Nl52I3ZPq6hofcFrUdOJGY9aG9vh+0w4pHD6AbHl6E9fDrHBs9h9O4wM7NqcIvErAcNDQ10qIP95+6vdlUGzYhHRtBQ79M5Nnhya5FIulPSVknPFMWOl7Rc0ob097iieddLapP0E0kXFsWnSVqb5jVJUoqPlnRviq+SNDGvfTEzs0PL89TWXcBF3WKfAlZExGRgRXqOpClkQ+WekcrcIqlw4/+twFyycdwnF61zDvBSREwCFgA35bYnZmZ2SLklkoh4lGws9WKXAM1puhm4tCi+KCJ2R8TzQBtwlqQJwDERsTIiAri7W5nCuu4DLii0VszMrHIqfbH9xIjYDJD+npDi9cALRcu1p1h9mu4e71ImIvYC24HxpTYqaa6kVkmtHR0dg7QrZmYGQ+eurVItiegh3lOZg4MRt0XE9IiYXldXN8AqmplZKZW+a2uLpAkRsTmdttqa4u3AyUXLNQCbUryhRLy4TLukUcCxHHwqzcwsFy+/upWHn1uU6zZe2fUSAEePOa6XJcv38qtbqS99UqdXlU4kS4BG4LPp7/1F8a9Kuhk4ieyi+uMRsU/SDklnA6uAK4GF3da1ErgMeChdRzEzy9WkSZMqsp0NG7LvxvWnDewDvj/qGT/g/cotkUj6GnAuUCupHbiBLIEsljQH+AVwOUBErJO0GFgP7AWujohC17NXkd0BNhZoSQ+AO4B7JLWRtURm57UvZmbFKtU9UmE7TU1NFdneQOWWSCLifYeYdcEhlp8PzC8RbwXOLBHfRUpENrja29v59Y6Rh1WPuT/fMZLfci+vZrkYKhfbzcxsmHIXKXaQhoYGdu3dfNiNRzLGvbya5cKJxMysAgYyEF45Q1FXciA8JxKz3rxcgW7kC42/SlyWepkDP+vtp/8i/xESt6W/+d+nlO3PuApsZ6CGyyB4TiRmPajcbZ7ZN8/J9ZPz31j9wParUseiIx2LcZPzPxbjqNx+Hc4D4TmRmPXAt3ke4GNhh+K7tszMrCxOJGZmVhaf2jKz3BzOdyrZAU4kZjakDJc7lewAJxIr6RevVKaLlC2vZmdXTzwq3zHRf/HKSF6f6xasFLcOjgxOJHaQSt0OCfCbdBpjzMR8b/V8PZXdL7MjiROJHaSS3yJ9q6fZ8Oe7tszMrCxOJGZmVpaqnNqStBHYAewD9kbEdEnHA/cCE4GNwHsj4qW0/PXAnLT8vIh4MMWncWDQq6XAtR4l0arNt7zakaaaLZLzImJqRExPzz8FrIiIycCK9BxJU8hGPzwDuAi4RdLIVOZWYC7Z0LyT03yzYWfs2LG+7dWGraF0sf0SsqF5AZqBR4D/leKLImI38HwaWves1Ko5JiJWAki6G7iUA0PxWgUN5Fs4DPyb+FD+Fj5U62WWl2q1SAJYJulJSXNT7MSI2AyQ/p6Q4vXAC0Vl21OsPk13jx9E0lxJrZJaOzo6BnE3rFz+Jm42/FWrRfLWiNgk6QRguaTnelhWJWLRQ/zgYMRtwG0A06dP9zWUHPhbuNmRqyotkojYlP5uBf4dOAvYImkCQPq7NS3eDpxcVLwB2JTiDSXiZmZWQRVPJJJ+S9JvF6aBmcAzwBKgMS3WCNyfppcAsyWNlnQq2UX1x9Pprx2SzpYk4MqiMmZmViHVOLV1IvDv2Wc/o4CvRsR3JD0BLJY0B/gFcDlARKyTtBhYD+wFro6IfWldV3Hg9t8WfKHdzKzidKT97GL69OnR2tpa7WqYmQ0rkp4s+rlGF/5lu5mZlcWJxMzMyuJEYmZmZXEiMTOzshxxF9sldQA/r3Y9gFqgs9qVGCJ8LDI+Dgf4WBwwVI7F70REXakZR1wiGSoktR7qDogjjY9FxsfhAB+LA4bDsfCpLTMzK4sTiZmZlcWJpHpuq3YFhhAfi4yPwwE+FgcM+WPhayRmZlYWt0jMzKwsTiRmZlYWJ5IhRNI4SR8ten6SpPvS9IckfeEQ5V7JqT4TJT3Tj+UvlTSll2XOlfTAIeZtlFTb33qWWE8uxyNv/T3eNrQN9v+z8LpO6/3zwVrvYHAiGSIkjQTGAa8lkojYFBGXVa1S/Xcp0GMiMbPeSeppiI+JgBPJUCXpSklrJD0t6R5JvyNpRYqtkHRKWu4uSU2SfijpPyVdluL3Srq4aH13SfozSSMlfU7SE2ldH0nzz5X0sKSvAmuBzwKnSVqdlu/+jeZkSd+R9BNJNxxiH/6maDt/NwiHZaSk2yWtk7RM0lhJH07beFrSNyQdJemPgHcDn0v1P03SJEnfTcv9WNJpaZ1HS7pP0nOS/i0NTFbwN5IeT49JaZ/eJWmVpKfS+k5M8aMl/auktWl//6zbsaiVtFLSnwzCceizNHjbf6T9fkbSFZKmSfqepCclPagDo4FOS8utBK4uWsdESY+l4/bjdHwLr5lHejh+Q4KkT0qal6YXSHooTV8g6SuSbpXUml5Xf1dU7uK0X99P77EHUvx4Sd9K/+cfSXpjit8o6c50TP6zsM0hpE/vH3jt8+JmSQ8DN0k6Nb1+n5D0/4rW+VngnPQ++4SkMUXvg6cknZfW9yFJ96uXz4xBERF+ZHeunQH8BKhNz48Hvg00pud/CXwrTd8FfJ0sEU8B2lL8PUBzmv5vwAtkg27NBT6T4qOBVuBU4Fzg18Cpad5E4JmiOr32HPgQsBkYn9b5DDA9zXsl/Z1JdqugUt0eAN5exjGZSDaY2NT0fDHwAWB80TJ/D1xTdFwuK5q3CnhPmh4DHJX2eTvZ0MgjgJXA29IyG4G/TdNXAg+k6eM4cIfh/wA+n6ZvAv65aHvHFY4H2QBqq4AZVXgt/Rlwe9HzY4EfAnXp+RXAnWl6DfDHafpzRf/vo4AxaXoy0JqmD3n8htIDOBv4epp+DHgcqAFuAD4CHJ/mjQQeAd6YXiMvFL0fvlb0GlgI3JCmzwdWp+kb07EdTdaVyDagptr7X8b75wFgZHq+BLgyTV/Ngff5uYXjkp7/FfCvafp0soEBx9DDZ8ZgP9wiOeB84L6I6ASIiBeBtwBfTfPvAd5WtPy3ImJ/RKwn+9CCbITG8yWNBmYBj0bETrIP+CslrSb7cBtP9uEA2bDBz/exjssjYlta5ze71Ye0nZnAU8CPyV5UkynP8xGxOk0/SfbmODN9W14LvJ8sCXehbDjl+oj4d4CI2BURr6bZj0dEe0TsB1andRZ8rejvW9J0A/Bg2t7fFG3vHcC/FApGxEtpsgZYAXwyIpYPYJ/LtRZ4h6SbJJ0DnAycCSxPr4HPAA2SjgXGRcT3Url7itZRA9ye9vnrdD1l2NPxGyqeBKal18FusoQ3HTiHLLG8V9KPyV6rZ5Dt3+nAfxa9H75WtL63kY5PRDwEjE/HD+A/ImJ3eu9u5cD7cSjo7/vn63FgBNi3cuAYFL82uis+Ns+R9SX4+jSvt8+MQVGNoXaHKgG9/aimeP7ubmWJiF2SHgEuJPvW+bWi+ddExINdNiidS9Yi6avu9ev+XMA/RMSX+rHO3hTv5z6ybzZ3AZdGxNOSPkT2Dam7nk63dF9n8eswSkwvBG6OiCXpmN1YtI1S/7O9ZG/aC4HvlZifq4j4qaRpwMXAPwDLgXUR8Zbi5SSN49CvuU8AW4A3kbU8dhXN6+n4DQkRsUfSRuAvyFoMa4DzgNOAncBfA/89Il6SdBfZN+ieXjOl5hWO3VA+Hv19/3T/POjLD/16Om69fWYMCrdIDlhB9i1pPGTnZMneALPT/PcD3+/DehaRvXnOAQqJ40HgKkk1ad2vl/RbJcruAH67h3XPSOeKx5Jd2P5Bt/kPAn8p6ei0nXpJJ/Shzv3128DmtD/vL4q/Vv+I+BXQLunSVJfRhXPBvbii6O/KNH0s8Ms03Vi07DLgY4Unko5Lk0F2KvJ0SZ/q4z4NGkknAa9GxFeAfwL+EKiT9JY0v0bSGRHxMrBdUuFbYvGxPBbYnFodHyQ7BTTcPEqWMB4la4X8T7IW1DFkH5jblV3vmpWWfw74XUkT0/Mruq3r/fDaF7DO9Bobjg71/unuB3T9/Cno/jlRfGxeD5xCdpoeev/MGBROJElErAPmA9+T9DRwMzAP+AtJa8jezNf2YVXLgLcD342I36TYl4H1wI+VXTz/EiW+NUXENuAHyi7Qfq7Eur9P1oRdDXwjIlq7lV9GdipuZWo230fPiWmg/jfZKbrlZG/+gkVkF8ufUnZh/YPAvHT8fgi8rg/rHi1pFdmx/kSK3Qh8XdJjdO1O+++B49LxeprsGy8A6fTAbOA8Fd1SXSG/DzyeTmP9LfB/gMvILqA+Tfb/+6O07F8A/6LsYvvOonXcAjRK+hHZaYr+tFyHiseACcDKiNhC1qp6LCKeJjultQ64k/Thlk6/fBT4jqTvk7XItqd13QhMT6+lz9L1C8Vwc6j3T3fXAldLeoLsi0XBGmBvulj/CbLXysj0nr8X+FBEFFpCPX5mDBZ3kWJmQ4akoyPiFUkiu/61ISIWVLtew1E6bTY9Ij7W27LlcovEzIaSD6eW3Dqyb+GDeb3PcuIWiZmZlcUtEjMzK4sTiZmZlcWJxMzMyuJEYtYHKqMnV/XQ43E/1/PxvvwWR8O092MbvpxIzIaPj5P1wWU2pDiRmPXdKEnNynqgvU9Zr8cXpB9grlXWC+1oAEkXKfViC/xpio2QtEFSXdHzNnUbg0Wlew+eB5wEPKysx+g5khYUlfmwpJu7V1iD3xu02UGcSMz67veA2yLijcCvgOvI+k26IiJ+n6y3gqskjQFuB95F1lXO6wBSdydf4UB3F+8Ani50FFrkImBTRLwpIs4EvhMRTcAm4LyIOI+sF4F3F7rdIfuF/L8Wr0TSTLJOO88CppJ1ovj2wTgQZsWcSMz67oWIKPRV9BXgArLeXX+aYs1k3eOcnuIbIvuh1leK1nEnWRf5kPUH1uXDP+nSe3BEbO++QET8GngIeKek08m6Tl/bbbE8eoM2O8hQ6iXTbKjrz693Sy4bES9I2iLpfLLOHN8v6WSysW8AvhgRXyzuPVjSsoj4vyVW92Xg02T9NZVKSHn0Bm12ELdIzPrulEIPvsD7gO8CE5VGciTrpPJ7ZB/sp+rAiJDv67aeL5O1UhZHxL6IeCEipqbHF0v0HvwHqVyXXl8jYhXZWCd/TtexOwoq1Ru0HeHcIjHru2fJeuT9ErCBrHfWH5H1TDwKeIKsRbFb0lzgPyR1kvXAembRepaQtSBKtSIg6z34c5L2A3uAq1L8NqBF0uZ0nQSyUfemFg3q9ZqIWCbpDWS9QUM2cuQHyAZ/Mhs07mvLrMIkTQcWRMQ5g7CuB9K6VpRfM7OB8aktswpKA219A7i+zPWMk/RTYKeTiFWbWyRmZlYWt0jMzKwsTiRmZlYWJxIzMyuLE4mZmZXFicTMzMry/wFu3kw8j/czlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"body-style\", y=\"price\", data=df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eac52909",
   "metadata": {},
   "source": [
    "We see that the distributions of price between the different body-style categories have a significant overlap, so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d6382286",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0ebd536",
   "metadata": {},
   "source": [
    "Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "07d40ce9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# drive-wheels\n",
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57001a52",
   "metadata": {},
   "source": [
    "Here we see that the distribution of price between the different drive-wheels categories differs. As such, drive-wheels could potentially be a predictor of price."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9635971e",
   "metadata": {},
   "source": [
    "## 2. Descriptive Statistical Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "45c9fab9",
   "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>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.00000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>197.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "      <td>201.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.840796</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>98.797015</td>\n",
       "      <td>0.837102</td>\n",
       "      <td>0.915126</td>\n",
       "      <td>53.766667</td>\n",
       "      <td>2555.666667</td>\n",
       "      <td>126.875622</td>\n",
       "      <td>3.330692</td>\n",
       "      <td>3.256904</td>\n",
       "      <td>10.164279</td>\n",
       "      <td>103.405534</td>\n",
       "      <td>5117.665368</td>\n",
       "      <td>25.179104</td>\n",
       "      <td>30.686567</td>\n",
       "      <td>13207.129353</td>\n",
       "      <td>9.944145</td>\n",
       "      <td>0.099502</td>\n",
       "      <td>0.900498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.254802</td>\n",
       "      <td>31.99625</td>\n",
       "      <td>6.066366</td>\n",
       "      <td>0.059213</td>\n",
       "      <td>0.029187</td>\n",
       "      <td>2.447822</td>\n",
       "      <td>517.296727</td>\n",
       "      <td>41.546834</td>\n",
       "      <td>0.268072</td>\n",
       "      <td>0.319256</td>\n",
       "      <td>4.004965</td>\n",
       "      <td>37.365700</td>\n",
       "      <td>478.113805</td>\n",
       "      <td>6.423220</td>\n",
       "      <td>6.815150</td>\n",
       "      <td>7947.066342</td>\n",
       "      <td>2.534599</td>\n",
       "      <td>0.300083</td>\n",
       "      <td>0.300083</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.000000</td>\n",
       "      <td>65.00000</td>\n",
       "      <td>86.600000</td>\n",
       "      <td>0.678039</td>\n",
       "      <td>0.837500</td>\n",
       "      <td>47.800000</td>\n",
       "      <td>1488.000000</td>\n",
       "      <td>61.000000</td>\n",
       "      <td>2.540000</td>\n",
       "      <td>2.070000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4150.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>5118.000000</td>\n",
       "      <td>4.795918</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>101.00000</td>\n",
       "      <td>94.500000</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>2169.000000</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>3.150000</td>\n",
       "      <td>3.110000</td>\n",
       "      <td>8.600000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>4800.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>7775.000000</td>\n",
       "      <td>7.833333</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>122.00000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>0.832292</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>54.100000</td>\n",
       "      <td>2414.000000</td>\n",
       "      <td>120.000000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.290000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>95.000000</td>\n",
       "      <td>5125.369458</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>10295.000000</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>137.00000</td>\n",
       "      <td>102.400000</td>\n",
       "      <td>0.881788</td>\n",
       "      <td>0.925000</td>\n",
       "      <td>55.500000</td>\n",
       "      <td>2926.000000</td>\n",
       "      <td>141.000000</td>\n",
       "      <td>3.580000</td>\n",
       "      <td>3.410000</td>\n",
       "      <td>9.400000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>5500.000000</td>\n",
       "      <td>30.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>16500.000000</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>256.00000</td>\n",
       "      <td>120.900000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>59.800000</td>\n",
       "      <td>4066.000000</td>\n",
       "      <td>326.000000</td>\n",
       "      <td>3.940000</td>\n",
       "      <td>4.170000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>262.000000</td>\n",
       "      <td>6600.000000</td>\n",
       "      <td>49.000000</td>\n",
       "      <td>54.000000</td>\n",
       "      <td>45400.000000</td>\n",
       "      <td>18.076923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        symboling  normalized-losses  wheel-base      length       width  \\\n",
       "count  201.000000          201.00000  201.000000  201.000000  201.000000   \n",
       "mean     0.840796          122.00000   98.797015    0.837102    0.915126   \n",
       "std      1.254802           31.99625    6.066366    0.059213    0.029187   \n",
       "min     -2.000000           65.00000   86.600000    0.678039    0.837500   \n",
       "25%      0.000000          101.00000   94.500000    0.801538    0.890278   \n",
       "50%      1.000000          122.00000   97.000000    0.832292    0.909722   \n",
       "75%      2.000000          137.00000  102.400000    0.881788    0.925000   \n",
       "max      3.000000          256.00000  120.900000    1.000000    1.000000   \n",
       "\n",
       "           height  curb-weight  engine-size        bore      stroke  \\\n",
       "count  201.000000   201.000000   201.000000  201.000000  197.000000   \n",
       "mean    53.766667  2555.666667   126.875622    3.330692    3.256904   \n",
       "std      2.447822   517.296727    41.546834    0.268072    0.319256   \n",
       "min     47.800000  1488.000000    61.000000    2.540000    2.070000   \n",
       "25%     52.000000  2169.000000    98.000000    3.150000    3.110000   \n",
       "50%     54.100000  2414.000000   120.000000    3.310000    3.290000   \n",
       "75%     55.500000  2926.000000   141.000000    3.580000    3.410000   \n",
       "max     59.800000  4066.000000   326.000000    3.940000    4.170000   \n",
       "\n",
       "       compression-ratio  horsepower     peak-rpm    city-mpg  highway-mpg  \\\n",
       "count         201.000000  201.000000   201.000000  201.000000   201.000000   \n",
       "mean           10.164279  103.405534  5117.665368   25.179104    30.686567   \n",
       "std             4.004965   37.365700   478.113805    6.423220     6.815150   \n",
       "min             7.000000   48.000000  4150.000000   13.000000    16.000000   \n",
       "25%             8.600000   70.000000  4800.000000   19.000000    25.000000   \n",
       "50%             9.000000   95.000000  5125.369458   24.000000    30.000000   \n",
       "75%             9.400000  116.000000  5500.000000   30.000000    34.000000   \n",
       "max            23.000000  262.000000  6600.000000   49.000000    54.000000   \n",
       "\n",
       "              price  city-L/100km      diesel         gas  \n",
       "count    201.000000    201.000000  201.000000  201.000000  \n",
       "mean   13207.129353      9.944145    0.099502    0.900498  \n",
       "std     7947.066342      2.534599    0.300083    0.300083  \n",
       "min     5118.000000      4.795918    0.000000    0.000000  \n",
       "25%     7775.000000      7.833333    0.000000    1.000000  \n",
       "50%    10295.000000      9.791667    0.000000    1.000000  \n",
       "75%    16500.000000     12.368421    0.000000    1.000000  \n",
       "max    45400.000000     18.076923    1.000000    1.000000  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e031e34c",
   "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>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>engine-type</th>\n",
       "      <th>num-of-cylinders</th>\n",
       "      <th>fuel-system</th>\n",
       "      <th>horsepower-binned</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>201</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>22</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>toyota</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>ohc</td>\n",
       "      <td>four</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>32</td>\n",
       "      <td>165</td>\n",
       "      <td>115</td>\n",
       "      <td>94</td>\n",
       "      <td>118</td>\n",
       "      <td>198</td>\n",
       "      <td>145</td>\n",
       "      <td>157</td>\n",
       "      <td>92</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          make aspiration num-of-doors body-style drive-wheels  \\\n",
       "count      201        201          201        201          201   \n",
       "unique      22          2            2          5            3   \n",
       "top     toyota        std         four      sedan          fwd   \n",
       "freq        32        165          115         94          118   \n",
       "\n",
       "       engine-location engine-type num-of-cylinders fuel-system  \\\n",
       "count              201         201              201         201   \n",
       "unique               2           6                7           8   \n",
       "top              front         ohc             four        mpfi   \n",
       "freq               198         145              157          92   \n",
       "\n",
       "       horsepower-binned  \n",
       "count                200  \n",
       "unique                 3  \n",
       "top                  Low  \n",
       "freq                 115  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1072ca73",
   "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>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              value_counts\n",
       "drive-wheels              \n",
       "fwd                    118\n",
       "rwd                     75\n",
       "4wd                      8"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
    "drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "a14cb591",
   "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>value_counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-location</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>front</th>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rear</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 value_counts\n",
       "engine-location              \n",
       "front                     198\n",
       "rear                        3"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# engine-location as variable\n",
    "engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
    "engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
    "engine_loc_counts.index.name = 'engine-location'\n",
    "engine_loc_counts.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "738dae1f",
   "metadata": {},
   "source": [
    "we see that engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, so this result is skewed. Thus, we are not able to draw any conclusions about the engine location."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f818f285",
   "metadata": {},
   "source": [
    "## 3. Grouping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "9b5a8f3c",
   "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>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12647.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  drive-wheels   body-style         price\n",
       "0          4wd    hatchback   7603.000000\n",
       "1          4wd        sedan  12647.333333\n",
       "2          4wd        wagon   9095.750000\n",
       "3          fwd  convertible  11595.000000\n",
       "4          fwd      hardtop   8249.000000"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest = df[['drive-wheels','body-style','price']]\n",
    "grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
    "grouped_test1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "86d6c8c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#This grouped data is much easier to visualize when it is made into a pivot table. \n",
    "#A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. \n",
    "#We can convert the dataframe to a pivot table using the method \"pivot\" to create a pivot table from the groups.\n",
    "\n",
    "grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.pcolor(grouped_pivot, cmap='RdBu')\n",
    "\n",
    "#label names\n",
    "row_labels = grouped_pivot.columns.levels[1]\n",
    "col_labels = grouped_pivot.index\n",
    "\n",
    "#move ticks and labels to the center\n",
    "ax.set_xticks(np.arange(grouped_pivot.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(grouped_pivot.shape[0]) + 0.5, minor=False)\n",
    "\n",
    "#insert labels\n",
    "ax.set_xticklabels(row_labels, minor=False)\n",
    "ax.set_yticklabels(col_labels, minor=False)\n",
    "\n",
    "#rotate label if too long\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "fig.colorbar(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4eabe573",
   "metadata": {},
   "source": [
    "+ What are the main characteristics which have the most impact on the car price?\n",
    "+ To get a better measure of the important characteristics, we look at the correlation of these variables with the car price. In other words: how is the car price dependent on this variable?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2f8b879",
   "metadata": {},
   "source": [
    "## 4. Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "6edc3f46",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5846418222655081  with a P-value of P = 8.076488270732989e-20\n"
     ]
    }
   ],
   "source": [
    "# Let's calculate the Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'\n",
    "\n",
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c15b9167",
   "metadata": {},
   "source": [
    "#### conclusion:\n",
    "+ Since the p-value is  <  0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "bf393537",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.809574567003656  with a P-value of P =  6.369057428259557e-48\n"
     ]
    }
   ],
   "source": [
    "# Horsepower vs. Price\n",
    "\n",
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "555a1cff",
   "metadata": {},
   "source": [
    "#### conclusion:\n",
    "+ Since the p-value is  <  0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1).\n",
    "\n",
    "\n",
    "+ try to calculate the following ;) :\n",
    "    - Length vs. Price\n",
    "    - Width vs. Price\n",
    "    - Curb-Weight vs. Price\n",
    "    - Engine-Size vs. Price\n",
    "    - Bore vs. Price\n",
    "    - City-mpg vs. Price\n",
    "    - Highway-mpg vs. PriceHighway-mpg vs. Price"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80aa8efa",
   "metadata": {},
   "source": [
    "## 5. ANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "8817f529",
   "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>drive-wheels</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  drive-wheels   body-style    price\n",
       "0          rwd  convertible  13495.0\n",
       "1          rwd  convertible  16500.0\n",
       "2          rwd    hatchback  16500.0\n",
       "3          fwd        sedan  13950.0\n",
       "4          4wd        sedan  17450.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "f72e9649",
   "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>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rwd</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>rwd</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>fwd</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4wd</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>15250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>4wd</td>\n",
       "      <td>7603.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels    price\n",
       "0            rwd  13495.0\n",
       "1            rwd  16500.0\n",
       "3            fwd  13950.0\n",
       "4            4wd  17450.0\n",
       "5            fwd  15250.0\n",
       "136          4wd   7603.0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "e6a39344",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4      17450.0\n",
       "136     7603.0\n",
       "140     9233.0\n",
       "141    11259.0\n",
       "144     8013.0\n",
       "145    11694.0\n",
       "150     7898.0\n",
       "151     8778.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2.get_group('4wd')['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "415dc14e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 67.95406500780399 , P = 3.3945443577151245e-23\n"
     ]
    }
   ],
   "source": [
    "# ANOVA\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'], grouped_test2.get_group('4wd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b67f358c",
   "metadata": {},
   "source": [
    "This is a great result with a large F-test score showing a strong correlation and a P-value of almost 0 implying almost certain statistical significance. But does this mean all three tested groups are all this highly correlated?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "04bd122b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 130.5533160959111 , P = 2.2355306355677845e-23\n",
      "ANOVA results: F= 8.580681368924756 , P = 0.004411492211225333\n",
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "#fwd and rwd\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'])   \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val )\n",
    "\n",
    "#4wd and rwd\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)  \n",
    "\n",
    "#4wd and fwd\n",
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price'])  \n",
    "print(\"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ba50ec",
   "metadata": {},
   "source": [
    "<p>We now have a better idea of what our data looks like and which variables are important to take into account when predicting the car price. I have narrowed it down to the following variables:</p>\n",
    "\n",
    "Continuous numerical variables:\n",
    "\n",
    "<ul>\n",
    "    <li>Length</li>\n",
    "    <li>Width</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Horsepower</li>\n",
    "    <li>City-mpg</li>\n",
    "    <li>Highway-mpg</li>\n",
    "    <li>Wheel-base</li>\n",
    "    <li>Bore</li>\n",
    "</ul>\n",
    "\n",
    "Categorical variables:\n",
    "\n",
    "<ul>\n",
    "    <li>Drive-wheels</li>\n",
    "</ul>\n",
    "\n",
    "<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>"
   ]
  }
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