DA0101EN-Exploratory-data-analysis.ipynb

{
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   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%203/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Data Analysis with Python\n",
    "\n",
    "Estimated time needed: **30** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "-   Explore features or charecteristics to predict price of car\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of content</h2>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "<ol>\n",
    "    <li><a href=\"#import_data\">Import Data from Module</a></li>\n",
    "    <li><a href=\"#pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</a></li>\n",
    "    <li><a href=\"#discriptive_statistics\">Descriptive Statistical Analysis</a></li>\n",
    "    <li><a href=\"#basic_grouping\">Basics of Grouping</a></li>\n",
    "    <li><a href=\"#correlation_causation\">Correlation and Causation</a></li>\n",
    "    <li><a href=\"#anova\">ANOVA</a></li>\n",
    "</ol>\n",
    "\n",
    "</div>\n",
    " \n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics which have the most impact on the car price?</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">1. Import Data from Module 2</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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",
   "metadata": {},
   "source": [
    "<h2 id=\"pattern_visualization\">2. Analyzing Individual Feature Patterns using Visualization</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn we use the pip which is the python package manager.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! pip install seaborn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import visualization packages \"Matplotlib\" and \"Seaborn\", don't forget about \"%matplotlib inline\" to plot in a Jupyter notebook.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How to choose the right visualization method?</h4>\n",
    "<p>When visualizing individual variables, it is important to first understand what type of variable you are dealing with. This will help us find the right visualization method for that variable.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "# list the data types for each column\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h3>Question  #1:</h3>\n",
    "\n",
    "<b>What is the data type of the column \"peak-rpm\"? </b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df['peak-rpm'].dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "float64\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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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": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagonal elements are always one; we will study correlation more precisely Pearson correlation in-depth at the end of the notebook.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2: </h1>\n",
    "\n",
    "<p>Find the correlation between the following columns: bore, stroke,compression-ratio , and horsepower.</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[['bore','stroke' ,'compression-ratio','horsepower']]</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['bore','stroke' ,'compression-ratio','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 56347.026562786035)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='highway-mpg', ylabel='price'>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='peak-rpm', ylabel='price'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore it's it is not a reliable variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  3 a): </h1>\n",
    "\n",
    "<p>Find the correlation  between x=\"stroke\", y=\"price\".</p>\n",
    "<p>Hint: if you would like to select those columns  use the following syntax: df[[\"stroke\",\"price\"]]  </p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute\n",
    "df[['stroke','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "\n",
    "#The correlation is 0.0823, the non-diagonal elements of the table.\n",
    "\n",
    "df[[\"stroke\",\"price\"]].corr()\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  3 b):</h1>\n",
    "\n",
    "<p>Given the correlation results between \"price\" and \"stroke\" do you expect a linear relationship?</p> \n",
    "<p>Verify your results using the function \"regplot()\".</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='stroke', ylabel='price'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ym6keU9Whyu2aYRjGVKyIZO1RlEUiIv+FoEz7XU7UDXy3QvtkGIZh1BHFurZuBC4BBgFU9TXAHgkMwzCMohVJQlWT4QdXabexaqsYhmEYeSlWkfy7iPwp0Coi/yfwP4F/qdxuGYZhGPVCsYrkFuAI8BJwA/Aw8GeV2inDMAyjfig2a6sV+JaqfgMyLXRbAatLYBjGvGLVf2uPYi2SxwkUR0gr8Fj5d8cwDKMwu/b1c9uDe+kfGmdJa5z+oXFue3CvVf+tMsUqkhZVHQ4/uOW26QaIyBoR+TcReUVE9orIzU7+WRF5Q0RecK8PZo25VUT2i8jPReTXs+QXishLbt0drlMirpviA07+jIisLeHYDcOoM+7a3UM8KrQ1xRAJ3uNR4a7dPdXetYamWEUyIiIXhB9E5EJgbIYxaeAPVfUs4GLgRhE52637iqqe714Pu+88m6DD4TkEvd2/7lxoAHcCWwna725w6wGuBwZU9QzgK8C2Io/HMIw6pHdglNZ4NEfWGo/SN2Be9mpSbIzk08D/FJE33edVwMemG+B6rR9yy0Mi8gqwepohVwL3q2oCOODa514kIgeBTlV9CkBE7gWuImi3eyXwWTd+J/A1ERHr224sVBo9PrBmaRv9Q+O0NU3cusZSHt1Lp3WQGBWmKItEVX8MbCTonf5fgbNU9bli/4hzOb0TeMaJPiUiPxWRb4nIUidbDfRmDetzstVuebI8Z4yqpoGTwLI8f3+riOwRkT1HjhwpdrcNo6aw+ADccOl6Up4ymkyjGrynPOWGS9dXe9cammkViYhc5t7/L+A3gDMJXEu/4WQzIiLtwD8Bn1bVQQI31enA+QQWy1+Hm+YZrtPIpxuTK1DdrqqbVHXTihUritltw6g5LD4Q1Nm6/Ypz6Opo4eRYiq6OFm6/4pyGsspqkZlcW78GPEGgRCajwD9PN1hE4gRK5B9U9Z8BVPVw1vpvAA+5j33Amqzh3cCbTt6dR549ps/Ntl8MHJ/hmAyjLukdGGVJazxH1ojxASvaWHtMq0hU9S9EJAI8oqo7Svlil1l1N/CKqn45S77KxU8APgK87JYfBP5RRL4MvI3A8nlWVT0RGRKRiwlcY9cCf5s15jrgKWAL8ITFR4yFSjXjA40emzGmZ8YYiar6wKdm8d2XAB8HLpuU6vvfXSrvT4H3Av+P+zt7gR3Az4BHgRtV1XPf9Ungm8B+4D8IAu0QKKplLjD/BwQz8A1jQVKt+IDFZoyZkGIe4EXkzwnSfR8ARkK5qtadG2nTpk26Z8+eau+GYcyK0DLoGxile54sg2u2Pz3FEhpNpunqaOE7Wy+u6N82agcReU5VN+VbV2z67+8SxET+6yS5pUoYxjxSjfiAxWaMmSh2QuLZwP8AXgReIIhRnFOhfTIMo4ZYs7SNsZSXI7O5G0Y2xSqSe4CzgDsIlMhZTmYYxgLH5m4YM1Gsa+uXVPW8rM//JiIvVmKHDMOorSypzRu7uB3mPTZj1A/FWiQ/cem3AIjIu4H/rzK7ZBiNTS1nSVluvZGPYhXJu4EfichBV/vqKeDXstJ4DcMoE7U2g72WFZtRGxTr2rp85k0MwyiVfC6sWsuSylZsAG1NMUaTae7a3WPuLQMoUpGo6uuV3hHDaDTCJ/14VHKe9DuaY4ylvJqpcFtris2oPYp1bRmGUWYKubBUtaaypCz915gJUyRGw7FrXz/XbH+a92x7gmu2P101X3+hJk0jSa+mKtxa+q8xE8XGSAxjQVDInXQ7zPuNeroijIVmsFcjLdjSf42ZMEViNBS1FDi+4dL13PbgXkaTaVrjUcZS3rRP+rv29fPHO19kaDxN2vc5OpTgj3e+yBe3nDcvysQUh1EIc20ZDUUt9fwutUnTtkf3MTCaQoFYNIICA6Mptj26b1732zAmYxaJ0VDUWs/vUp70e46OEBGISNAYVARUlJ6jIzOMNIzKYhaJ0VBY4Ngwyo8pEqOhqOee3+uWteEr+L6iqvi+4msgN4xqUjHXloisAe4FVgI+sF1VvyoipxA0yFoLHAR+S1UH3JhbgesBD7hJVb/v5BcC3wZagYeBm1VVRaTZ/Y0LgWPAx1T1YKWOyVgY1Gvg+JYPnMUf7XyR4UQaz1eiEWFJc5xbPnBWtXfNaHAqaZGkgT9U1bOAi4EbReRsgna4j6vqBuBx9xm37mqCPieXA18XkTAqeiewlaCP+wYmSrZcDwyo6hnAV4BtFTwew6gqmzd28aUt5/HONUtZ2dnCO9cs5UvTZGzVynwZY+FTMYtEVQ8Bh9zykIi8AqwGrgQ2u83uAXYBn3Hy+1U1ARxwfdgvckUiO1X1KQARuRe4iqBv+5XAZ9137QS+JiKixfQPNow6pFhrqpbmyxgLn3mJkYjIWuCdwDPAqU7JhMomvKpXA71Zw/qcbLVbnizPGaOqaeAksCzP398qIntEZM+RI0fKdFSGUbvUWgVhY2FT8fRfEWkH/gn4tKoOiktdzLdpHplOI59uTK5AdTuwHWDTpk1mrRgLHiu0aMwFz1cSaY9Eyifp+Xj+9LfNiioSEYkTKJF/UNV/duLDIrJKVQ+JyCogdNz2AWuyhncDbzp5dx559pg+EYkBi4HjFTkYw5hH7njsVb755AFGkh6LmqJ84j3ruOn9ZxY9vtzzZWqpY6NRXjxfSab9QHGkfRIpn7Tv52wTj07vvKqYa0sC0+Nu4BVV/XLWqgeB69zydcD3suRXi0iziKwjCKo/69xfQyJysfvOayeNCb9rC/CExUeMeueOx17lq0/sZyzlEYsECuCrT+znjsdeLfo7yjlfxhpbLRx8XxlLepwYTdI/OE7v8VFePzbCoZNjHB9JMpJIT1EixVBJi+QS4OPASyLygpP9KfAFYIeIXA/8AvgogKruFZEdwM8IMr5uVNWwdvUnmUj/fcS9IFBU97nA/HGCrC/DqDlKeaL/5pMHiAjEIsFzXkQg7ft888kDRVsl5Sy0WEv1yYzi8X0l6QUWRmhtpLzSlUQxVDJr60nyxzAA3ldgzOeBz+eR7wHOzSMfxykiw6hVSs2gGkl6RFDGU15OwM/z07P6+3M10Wst3mJutqmoauCWCl1UqcopjXxYrS3DqDB37e4h5XkcG06T9HyaohE6W2MFn+ibYxFGk94UuWpwEw3HTHdDLWf6by3VJ7O05uorjXxYiRTDqDCv9Q9xdChJ2s1GT/vK0aEkr/UP5d3+lNb8z3cCmfTdmeIW5Uz/LVe8pRwTJBstrdn3A8v05FiKI0MJ+gZGOXhslDdPjHFsOMHweLrqSgTMIjGMipNM+zCpaq8vQaZMXiJTn+8iQDQqGXfSTHGLcrqjNm/sYkvfiSlZZMVaALv29bPt0X282j9MPCqc2tE8a0ui1txs5STt+RlLI+niGbWgJIrBLBLDqDDxaKBAsostAjRF84cQ1yxtoyUWoTkWoTUepTUeJR6NEI1Ixp00U1+VcvZZ37Wvn/uefp1k2kcIFOB9T79elEURWk4Hjo4QFVAf3jw5TtrTWVkSC6V/vKqzNEZT9A+O84tjo/zi+CiHB8c5MZp0Vl99KBEwRWIYFefMUztZtqiJWFTwVIlFhWWLmthwamfe7W+4dD0dLTE8X/F8P3ip0t4cy7iTZrqhljP9dy4NtULLyVMlEpHghXB0ODErS6Je2wCkPJ/hRJqjwwneODE24Z4aSTA8y5TbWsIUiWFUmBsuXU9TLMrKxS380qkdrFzcQlMsWvDmt3ljF1/cch4butoREUSEM1YsyinQONMNdfPGLrZcsJojQwleeWuII0MJtlywelYB6eyGWoIQESEiFNVQK7ScmqKRidnSns9o0uPYSKJkS6Ie2gBkz9U47KyN3uOj9A+OMziWIpHyWGjT3SxGYiwYajUtdLZzOpa0NbGiI533WGb6zl37+tn5/Bus6GjmNNcPfufzb/CO7iXzek7CjK/25hiHhxIZuQKHBxNc867TSv7OWmsDEM4KH3fzNQrGvhYwpkjmkVq90S0Eaj0ttJSb33THAhR1DZVzEuG6ZW3sPzKC+Bq091XwFc5YPrM1ccOl67ntwb0MjCanrlR45OW3Sir9Um3Snp81yS9QHDPVoWoETJHME7V+o6s2c1Wypc7VqCUmH/uJ0WTeY9n26D5Gkl5R19BsspsK/QalNNTK9x23X3EOv3PPj4Fgln5UhFg0guf7NdtvPpyrkfLCDCo1pTENFiOZJxot/70UylHLqdS5GrVCvmP/+eEh+gcTU45lv0ufLeYaKjW7abrfoNiGWoW+A6ApGqEpKjTHosRmKAA436Q8n5FEOqf+1IGjI7x5YowjQwlOjqUYTaZNiUyDWSTzxELOf58r5XDDlDxXo0bId+wAnkLTpGNJ+zptym82oUtpNJmm1cVIpstumuk3KMY1N913zMU9Vg5UlZQX1J4K3VMpT0mlffwFFviuBqZI5olaKjNRa5RDycajwlgqyJgJb1RQeK5GrZDv2EPCWltCMEcxKsE1U8w1VGqAv3dglKhAz5HhjDtteXtTSb/BdL/j5648d976zau6YoWuJPp4yiPt5vAYlcEUyTxR6hNiI1EOJXvmqZ0cODrM0PhEXKGjJc665e2V2OWyke/YYxEh6WmgQZwmUR/etrQ1k/JbzDVUSoC/vSnKvsPDmc8pz2Pk+BgbTy3+/E33O4busXJUI84mlVEYwbmop9ngCwlTJPPEXMtMLGTKoWTD71i5OFaTirpQIDvfsfuqRF0Z+dC68lRZ1BTllg+cVfabMcCRrNTcYuT5mOl3nEvabtrzSbuy6MmsEiIWt6gNTJHME7WS11+LlKN3Rjn7b5SbmTL2Ju/3ybEUi5qiHB1OZqyrle3NjCS9is2hOD6WmlZeTFZdOX6DcNJiMm1xjHqiYopERL4FfBjoV9VzneyzwH8BjrjN/lRVH3brbgWuBzzgJlX9vpNfyERTq4eBm1VVRaQZuBe4EDgGfExVD1biWMox/8OaA01POW6QtTZRLaTUQPY125+mf2ic9Ssm3EqjyTRdHS0V28fwPi2SKwtL1xebul7sb5BMB+1cU57i+YFLKl+LV6N6JNM+Q+MpBsfTjOVpa5BNJS2SbwNfI7jZZ/MVVf1StkBEzibobngO8DbgMRE503VIvBPYCjxNoEguJ+iQeD0woKpniMjVwDbgY+U+iHLN/7Csrcal1N++GvG0tqZo0AMljO7rhHwuD0GhSyrlTczFSKTq28J4tuc49/+4l0ODY6zqbOXqd63hovWnVHu38hIUh/QZHE8xPJ5mcDzF0HiawfE0Q5nl4D1UGkNjwfJ4CRmPleyQuFtE1ha5+ZXA/aqaAA641rkXichBoFNVnwIQkXuBqwgUyZXAZ934ncDXRERm6tnu+crJ0RQSCWsHuXeXOhrWFIpEgkezclkSlrXVuJT621fDTfd7l67nbx5/DV/JKJGIBPIdz/XNqAjDtq7ZMYzkAnRJPdtznK8+8RqxiNDZEuPYSIKvPvEaN7OhosrEV2U04WUpgkk3/1A+NrE8lAiWU17lf4NqxEg+JSLXAnuAP1TVAWA1gcUR0udkKbc8WY577wVQ1bSInASWAUcn/0ER2Upg1bC6ew3HRooLIIoIB44O09kSz8xHEAmyal4/NsKx4QTRSFBULyIQjUhGKUVlQi4ilrXVwMzmty+Hm64Ul2xYpmRyMshN7z+Tp3qOZxShqqLAaCLNqZ0tHB4czwS+G4H7f9xLKu1xIumR8nzi0QiLmqLc/+PeohSJ52tw8x8LlMFwIss6GMunIILl4USacuQVCNDeEqOjJUZHS5yO5hidrXE6WmJ0hrJwfXOcztZAdsqiJk7fVvh751uR3Al8juCZ53PAXwO/S/7e7jqNnBnW5QpVtwPbAd5x/gVF/xyqysrOVo6NJDITwVSDp8mw+mixvH35Im7cfDr3/7iXt06OsXJxK7/97tP4pVUdHB4cRyBH8UQEBEEiZNZlW08SrpeJ9dFIbc+ZaFSqYWHMxiV70/vP5MbLNgRlQTyftKf0D46z5cLV/PW/vkoy7dMSjzCeCtxVWy7oZiQxuz7y9crBY8MMJ9Kgwf/BVNpnIO0zlhrkkZcOTXIZTbUY8rVQng3RiNDRPKEQOltjtDulECqEyYqhsyXOoubYrO4T8RmqEcyrIlHVw+GyiHwDeMh97APWZG3aDbzp5N155Nlj+kQkBiwGjpd7n69+1xq++sRrjKW8nP9EV79rzcyDs1BV3rXuFN61LvepZaYgVqlEnEKRLAsplEWEoB9ElgtvwqU3ocSM8jPfiQCFXLJ/9+//wSUblpP2lLQfKIuU55PyC2dHvfO0pdx02YbgIWhwjJU1HhcolqD8vhe4gMYKxw4mrIQ0J8fSE0+rWadqJOnzxX99teR9aI5FMjf5jjw3/o4cpTChNFrj0Zr6vzqvikREVqnqIffxI8DLbvlB4B9F5MsEwfYNwLOq6onIkIhcDDwDXAv8bdaY64CngC3AEzPFR2bDRetP4Wbq5z+Rr4o/B59oPssns5xlAYX2oGQZhpKR5f++oITJJIsr629EzKqaE0EjLMVX5fXjIyxuiZN2LiclcLcePDZC7/HSEzx+/tYgr/UPMZbyGBpP8/O3Bkv+P1CpILXnK8OJrNjAJEsg20WUHUMYHE+VxV0Ucmpnc447KOfmHyqJ1kBBtDcHrqTmSSVv6pVKpv9+B9gMLBeRPuAvgM0icj7BdX0QuAFAVfeKyA7gZ0AauNFlbAF8kon030fcC+Bu4D4XmD9OkPVVES5af0rNKo5yE/rAqxkklSyLaeq6qduF8ShFc52bWcou2wU4aXWWAsxVdsKEkiNrebIbshR8P6iZ5asG6bX5vbFuXfA7qB+8exqM88PPvrqaVTrl9+pqb8lxyULgkl3Z2VrS/gLc96OD3PP06y4OCIm0xz1Pvw7Ax391bVHfUUyQOuX5mRt+rkWQL4YwsTxcJvdaRMi4h4IYwSQLoTXOv7xwiBNjCcZTwWTIeFRob47SvbSdL3/svLLsRz0ijVZ/5h3nX6Df/cHuau+GMYl6SqmczGQrLpAF7+F/r0I3/ELM9Xw823Oczz20l9GUnwk2tsUj/PmHzyn5vP7G3z5JIu0RjUz4yT3fpzkW5V9+/z0524bl14MMolTmZn/3kwcYHE8REcH3A6WY8pSICB0tMYbG01OqFc+WWEQyN/7Olhjtzkoo5CoK3UhtzdG8Dy/ZZCvEbFf3zZdVNmur2sSjEU5btug5Vd2Ub73NbDeqTrVSKstFua24cpyPn781mFEiEFg3oym/aJdUdrrpaNJDIGeyoAAjSY8/++7LU9xHpaabFlIgLfHIlJt/e07sYGI5I2uN0xKLVCx+UG+u7vnCFIlRde7/cS+xiGTcMGGKbLEplQuNcpyPHc/1EY1MuOWUwK32jz/uZeWS1qmxg5y5CFPTTSerhvDzj/7j2Iz70t4cy1TgDd2FEFhpSxc18Yn3rJtQBlkxhKZYbfUtCSnk6q5nq3qumCIxqs6hwTE6W3IvxZZ4hLcGx6q0R9Xl0OAYUYHegURmrsKS1hhvnAgaLk1OL83EC8YmlMJIJhswVwV4aZ//9si+suxnSyzCB9+xKhNLCILMWdZBc5z2liDd9BPf/jGvHx/NuP9UwUdZ0hLj8nNXZr7z2Z7j3PHY/pq+GedTGEBdW9VzxRSJUXVWTZqrAzCe8mcVGK5lVDWT9TRldvJYbtZR9nyDtO8zlgp6nl9/z54578ey9qasm/3UgHLnpNjBzQ/8hFTa4+TYRH+UJW0xmmNRPvXeM4r6myMpj1M7mxkYTWWU49K2Jkaz3Fr14OJ8tuc4276/jxHXV2VgJMm274+wtDXe0Fa1KRKj6pRrrs584asykkgXLE2RPf9geNLEtHKVPRcgFhWWtzezcnELnZMCyC/3neBHPcddZtlER8L/+1feXnSmVcjqxW0cG0nQ1ZGbAbZsUXPR3xE+LKzJKgszlvLoyvqOenBxbv9hD4NjKSIRIRoVVAmSCsZSrF+xKGfbRrKqTZEYVadaAcy05zM4ns4pZldw/kGW0hgeTxdI2i0NATqyAsihJfCj/zhKNCIkUj6eauYJPekpLfEoTVGhtSmaUbgfu3DqufrYu9Zw348OsuO5PsZSHq3xKL91YXfJSgQCRb/t+/s4PDSO7yuRiLCoKcaNm4uzRsLvmOlhoR5cnL0Dozmp6SKAKCk/sKIXulVdCFMkRk0wl7k6iZQ3Y2mKjKLImotQrnTTqLvRd4QTzVpzs4mOjyT591ePEIsKrfEIaU/xgZsv28DFpy+b8n1/8MCLeeeAjI0kaY5Fin5i//ivrp2V4iiIKys/Gy1azMNCPbs4YxFI+1o3VnW5MUVi1ASqykjSKzw7eSyPdZAIZMkSyl1PR3MskskcygSQJ5WmmFroLk5LfPp00z944EXiURhOpDkxGsQH2puj7NjTl1eRFHp6j0cFz/dzgvBL2+Jle2KPRiSn2kA46XLHc710tsQ4tbMlM4kzaMzWx+W/HATKJ+bJBL+llzVhMlz37tOX8e7TlxXsnV4PLs41S1p5/fgo+JrjMnz7KW1svfT0hk0LNkVilBXP11xXUSI3hvBa/zCvHBpkJOkRiwhtTVFSXlARtVzlKtqaolkWQW5piry1i9x7pdJNXz8+wtBYCokE7QnSvjIwkiLtj+TdvtDT+/Yf9vD6sZGgXlpE8Hzl8GCCdcsX0RKPuvYHubXTwtpqUbcumkfhZbdNyEf/UCLIIjs+munYuLy9icOD4yxpa5rx+KerQqyZGf5w2iltLO9o4hs/PMAbA6O8bUkb11+ylkvOXIE6JYWrBpA98993H/ysSZ/ZE0HD6gHZ+iv7UitlUvbWS08Pgu3JdMbN19kUZ+ulpzdUBYzJmCIx8pLdHS2/lZDffTSSKN5dlISC1VAjQlbmUHZm0VRZthspTDetJZJp35VemfCre6LTWlIXrT+FXz1jObGoEIsK8UiEu5/sCcZrWN5FMm0N3rakcu6fjuYYr/UPE40EtdDSvvLGiXE2dLXPOHamKsSSVQ0AhPefvZL3n71ymm+sLJOVymTl8/Zli+jqaGb7DycqOX/i/1jHr/1SV57tcxWYKpkyN5PL3oSWW46SdE9WYTmcWsYUyQJGVRlP+wyOTQSSK9EdbTriUcnc8I8OBS6ZoLBg4EppiQvLFrVw43tPn6hx1BKnrWnmchX1QjwqJNLBjSF0hwCZoHk0EiiKqFMY0YgQj8oUd9lY2qd7aWtWL3fJ9HKvJEPjKdKuRphARlEX8yR/1+4eUp7HseF0xprpbI3xhUdemXP76kow+ZznuwQvO/tULjv71Hnaown8sEYbuUoH8ltemaoGqlnLZKy6iXETv6XmjFfC8nUz/V80RVIHlNIdbTgxt3IVhWiNR3NmH2fPP8jnPgrfm7PKVfzmnT8ikfKC1El3Qx1P+gxGU2xauzBdAiLC+uXt9A6MMpLIvpk2sW55O6sWF29JhJ0WJ/dyb4pGuGb70xW5Ke/a18+hwcC1FbiSAvfl8vZ4UQrstf4hTo66dFlnzRw+mXAuOZ1T++pGIxIRInnbMFUfUyTzyOTuaNntMOe9O5qbddyZrRyyYgeT+yPM1NimGGbj4qkXwhL4TbEI8WiEpliEJvd+0/s2cNuDe+lsjc+pO2a+TouDYykUSHp+RW7Kd+3uISqQ8sPjDCySoXGPM7o6Zxyf7zcPn3rfOjmeY6WU2r7aqB1MkcyCnHTTRDqnNEW+FNRht1wuF0R2umlHVtA4tA7am+Msbp0aQ5htd7RyMZ2Lp16IRSJOWQhxpyzi0ci057VcHRLzfU88IqR8ndLAajY35XxB8df6h0h5ua4R31M8KU4RxqPCWCr3Nw+/K+1rxko5OpQk5Q2VtL9G7dCwiiQsVxHEBYrrjhYulzPdNDtInLeaaR10RyuWtcva6RsYYSSn33WM7qWLZh48z+RTGE3RyLTZTdNRrg6Jk7/nPdueYElrPGeb1niUvoHSmlcVCoqHFs9kYhEp6njOPLWTA0eHg/83zvpIerl+dxHwnWVaSp95o3ZoOEVy4OgIv3nnj8parqJQumnuXISF2x2tWMIZ0p4zRTxVPKWq8wREhOZYhOZYZMItNQeFMd+EcZPQIoFgjkd3VimSYijUmrdQjK3YkvmhO27l4ljGHddzZIRoZKplqqr88c4XGRpPk/Z9jg4l+OOdL/LFLeeZMqlxKtkh8VvAh4F+VT3XyU4BHgDWEnRI/C1VHXDrbgWuBzzgJlX9vpNfyESHxIeBm1VVRaQZuBe4EDgGfExVD860X0nPZ2A0NUUedkfLn3IaTkALG+VkN82JEStD/KBRSHk+ybS7c/hKU3R+4iMiQiwiOQojeE3Njqon8sVNZhN/6R0YzWvZFFIX+YzyQtbElr4TfPPJA4wkPRY1Rele2spwIsXJsSD2FxFY3BojkVYGRlNEI0IsGkEVBkZTbHt0X10okka2pippkXwb+BrBzT7kFuBxVf2CiNziPn9GRM4maJV7DkHP9sdE5EzXbvdOYCvwNIEiuZyg3e71wICqniEiVwPbgI/NtFNdHc382YfOymmMU2x3NGNubP9hD2NJz928gyfRsaTH9h/2lHUiV0SCoHfmFY3kZI8tJMoVfylk2USEgokedzz2Kje9/0ygsGtsS98Jdj7/Bis6mjnNKbr+wXFGkl6Q5uy+f3DcQ30lFpXcwLwoPUfzT9ysJWaaL7PQqZgiUdXdIrJ2kvhKgj7uAPcAu4DPOPn9qpoADrg+7BeJyEGgU1WfAhCRe4GrCBTJlcBn3XftBL4mIqIzJLcvbWvisgb4YWuRQgXvekv054fEIpFgsp5zR8VjQlM0UtMWYiWeWssRfylk2SxqijJUYJLpN588kFEkoWss7SkHTo6Q9HyiEeHv/r2HxW2xnHkkKc8nKrh4SSDraIlxeCgxp2OoJoVcg42SiTbfMZJTVfUQgKoeEpHwDK8msDhC+pws5ZYny8Mxve670iJyElgGHJ38R0VkK4FVw+ru2qnbYxSHhBaGS6dtjs2cKVWL7NrXX7MxgEKWzV27e3iqJ38XxOFEOrPcOzDK4GiCwcSEzyvozQ6JQY+Y+73SvpL0lKiQMx9GVTk2nMRXkEl1rM5YXlq8pxr0DowSFeg5MpxTRqbUpId6pVaC7fnuCDqNfLoxU4Wq24HtAO84/4LarjWwgFmzpJWDx0ZJZfX+jgBrl01MysvOlsp2TdWLW2o6i2Pbo/tqOgZQyLIppEhyfhPfz1EiAGGc3lNoyrJChanusrGUxxld7bwxMMpw0svETtqbotzygbNmfUzzxVzKyCwE5tsHcFhEVgG4934n7wOyTYVu4E0n784jzxkjIjFgMXC8YntuzJlfO3MFk2O0PvDr565k5eIW3r5sEacta2Pl4haWtTfT0RKnOVY/qc6hn7x/aDzHT75rX3CZ9xwdybj2hInCirUcA9i8sYuWWP7z3xafkB8fS+fdJsT3NSi86KwNgNcOD/HKoZO8dniIwbEUHzh3JU3xaO6DRJ1kNmp2XZKsUvulFISsZ+ZbkTwIXOeWrwO+lyW/WkSaRWQdsAF41rnBhkTkYgnuJtdOGhN+1xbgiZniI0Z1EBGa41FeenOQUzubaItHiEVgUVOUVYubeaH3JG1NtVdssVTCulJvnRzn54eHeOvkOCnP467dPdXetTmxbnl7zo0iIrCkNca5q5dmZIWKbwJEJejm6GkQTO9siRGNAK5UPW62+8MvHSIWkUyF4qjLtKuH8zec9Fi9pCXnOFcvaal4HbRaoZLpv98hCKwvF5E+4C+ALwA7ROR64BfARwFUda+I7AB+BqSBG13GFsAnmUj/fcS9AO4G7nOB+eMEWV9GDRC6pJpj0cwcDRHhrcFxVrS30NUxoTBUdcH4kfPVlcqesb1uWRv7j4zUVQxg175+Dh4dzrEkfTc7vdgU40hEWLm4JRPE7xsYY0VHM8vbWzLbjCbTwbkRiBAok7SnHBtJkvYGy3tQFaBQHbSujpZpRi0cKpm1dU2BVe8rsP3ngc/nke8Bzs0jH8cpImP+iUh2iZDA5x+PyrTxjHJNnqtVkmk/KPntBVVZw3hAWAnhlg+cxR/tfJHhRDAZNhoRljTHazoG8GfffYmx9FRDf3AGV1Y2LTHhyFAiM4+kORaZ0u+9NR7FC9N/I1kz3l1wvtYp13yeeqVWgu1GDRONCM2xaJalEZlVEceF/p/NV5/se97EjO1AkWze2MWXtpw35zkfs2G2acdvnBzPK1fISW2NukZb+Uh60L10Yh5J38AYx0YSORbJWMoj5koM+5o1412pWMOxclKu+Tz1iikSI4dYJEJz3E3ic+/lmpeRb5bzJ96zbsH8Z0uk8s/SH8+Sl6vmVikUm3acT9lMF3V8rX+iyGI8Al6BIgWnLIrnzK9Y2hbn+EiKtqZYzgPF6csX0T+U4MRYKpO1taQ1zoaujrKch0pTjd+2VjBF0sDEoxM1psKYRiUD3rv29XPf06+TTPsIQZG++55+nXd0L1kQ/wEL6JGC8vli26P7OD6SzMQ2PN8nNZLMSTveta8/x+12dDjBH+18kQhMybQLGRqfcG81xaIk0ukp+fcCU9xYy9ubSXs+XR0tOU/vP+07wVef2J8z4/3keJpfadD2tfWEKZIGIVQaoYuqOTb/hQm3PbqPo8PJrDLiPonhZM3Mo6hX7njs1SlWXjjjHGB//3Cuy41gbsf+/uGM7AuPvMKJ0RRR199dfTgxmiqoRAASWQW3mmIRYq6XfCaRwA96Ao+lvClxsQ2ndvKdrRfnfN9du3tY0d6UUym4oyXGUz3HuWnWZ8eYD0yRLECylUbonqqFaravHh6a8sSqTm7kUmxM447HXuWrT+wnIhCLBDfprz6xHyCjTNIFYhfZ8gPHXPmarEC3FlEdO6y3taGrg4PHhhkcy+oCuSjO4pY4oym/qLhY78Aoy9ubWZGV6bSQsvoWMrUfxTIKEs7P6GiJs6y9mbctaWXtskWsOaWNrs4WFrfFaYlHa0KJABRKvqmDpJyiKPSfqdT/ZDNNbMzmm08ecEokQkQi7j2QhxQ6veU47X/z+Gvc8dir3HDpeuLRoB1zUzRCIu1zfCTFB395FbdfcQ5dHS2cHEvR1dHC7Veck1cprlnaxlgqd97FQsrqW8iYRVInhG1cw3pT9VY6pBFYvbSV3oGxvPJSKKUA4EjSY3JSU0QoeSLc+uWLeK1/GNHcOS4xNx+mEL7C3+3u4We3X86FL/Tx3RcOZWobdbbE2Pn8G7yje8kUN1Y+FnpW30LGFEkNMjkIXusVbY2AsWT+uRWF5IXoHRglmfI4cHQkk720fFFT3s6ci5qiDI6nCdr4TNDZUtp/7c9cvnEis8vziUUiLG2L8/GL386du/bnnUsSMpr02LWvn4dfPkwsGkzGVIXhhEdzPFJ0BdxGT6GtZ0yRVJmmSQHwWolnGKVzbGRqw7Tp5JA/FiJA/3ASIXiyVw0+r8lj2XQ2h4pkqrwUNm/s4osF5ri8o3sJX3jkFfYdHi44/q7dPcGEwkhQR0wEfJSToyn6IsXHOBo5hbaeMUUyT4hIphBdc7S2guDzRWdLjKHx3BRRATpKfHquVUqNRRSa33FyLJV33NHhqf06+k7m7+GRLS+UwjvZxi10Ew/la2/53wWOJLCimmMR0t5EUUYRSHi+xTgagIXxP7jGsHhGfj7xnnWZDKOw856vgbwRKVRWPu3rlJt/BGZdKiQei5BM+1MUeLzEGeNCfqUoBIHytOdzbCQJfqBEPFVikYjFOBoAUyRzxOIZxROmo04356GeKfbJPyS7rDxMtJbFfY9A5u7tA22zLBUSFouMysQcD0+VdctKsxQyZUvyyMNA+bJFwTyQRDrokHjj5tPNVdUAmCIpknx9wBvNNVUObnr/mQtGcUymXE/+IZr5J+CU1tn9dy1Xscj25hgjicA1mV2UclFzzALlDY4pkjyEXfoyAfBZFik0GotSn/wLlZWPR4QlbTGOjUzUnFq2KI5EZncNbt7YxbUXvz2wBD2P1miEay9+e8k3+dA1GS3gmrRAeePS0IpkcgA8VB713mDJqA63fOAsbvrO83lbxebLzipkKaxobybp+axcPKGACvW2aIkJ43lSc7O7Gu7a18/O599gRcdEBd5wfkcpN/6F7po0Zk9VFImIHASGCJLf06q6SUROAR4A1gIHgd9S1QG3/a3A9W77m1T1+05+IRNNrx4Gbp6pS2I0IqzoaF6QAfDZlgo3KstP+06w8/k3iEclZ6b67Veck7esPMAf73yRNwbGSPvBnI6Olhh//qGzp3x3oas9W17KBMeZWMiuSWP2VNMiea+qHs36fAvwuKp+QURucZ8/IyJnE3Q/PAd4G/CYiJzpOijeCWwFniZQJJcz0UExL9GI0NESL//RVJmwrMaUmxWYMpkntj26j9GUTzwaybiqRlM+f7e7h1WLW/LeyL+z9eIpv8+uff1BaGRSK9p8JApkcmXLewdGWdKae823xqNWw8ooG7Xk+L8SuMct3wNclSW/X1UTqnoA2A9cJCKrgE5VfcpZIfdmjWk4sp86RYL3eLQ++l0vFLKzsAQhIkJEgpnfrfHcCYLT3cjv2t3DYteHY+PKTjZ0dbC4NZ73t8yesxG+suVgNayMylMtRaLAv4rIcyKy1clOVdVDAO49fExbDfRmje1zstVuebJ8CiKyVUT2iMieI0eOlPEwaofegdGSblbG/CGulHo2093IS/ktVy8O4iaqE69sOQSpuSlPGU2mUQ3erYaVUU6qpUguUdULgA8AN4rIpdNsmy+IodPIpwpVt6vqJlXdtGLFitL3tg6wp87qs25ZW5DJ5Cuqiu8rvsLqzuaSbuSl/JZ/ddUv09kcJcwPiUhQHuWvrvrlzDabN3YVXYHXMGZDVWIkqvqme+8Xkf8FXAQcFpFVqnrIua3Cmtl9wJqs4d3Am07enUfekFjl1OpTKAvrrz7yDqD4ORal/JabN3ZxxzUXzPjdlpprVBKZIcmp/H9QZBEQUdUht/wD4HbgfcCxrGD7Kar6JyJyDvCPBMrmbcDjwAZV9UTkx8DvA88QBNv/VlUfnu7vb9q0Sffs2VOx46smYdaWTQirHuX6Dey3NGoNEXlOVTflXVcFRbIe+F/uYwz4R1X9vIgsA3YApwG/AD6qqsfdmP8X+F0gDXxaVR9x8k1MpP8+Avz+TOm/C1mRGIZhVIqaUiTVxhSJYRhG6UynSGop/dcwDMOoQ0yRGIZhGHPCFIlhGIYxJ0yRGIZhGHOi4YLtInIEeH2SeDlwNM/mxgR2jqbHzs/M2Dmanlo/P29X1bwzuhtOkeRDRPYUykYwAuwcTY+dn5mxczQ99Xx+zLVlGIZhzAlTJIZhGMacMEUSsL3aO1AH2DmaHjs/M2PnaHrq9vxYjMQwDMOYE2aRGIZhGHPCFIlhGIYxJxpGkYjIGhH5NxF5RUT2isjNebYREblDRPaLyE9F5IJq7Gs1KPL8bBaRkyLygnvdVo19rRYi0iIiz4rIi+4c/WWebRr5Girm/DT0NQQgIlER+YmIPJRnXV1eP1VpbFUl0sAfqurzItIBPCciP1DVn2Vt8wFgg3u9G7jTvTcCxZwfgB+q6oersH+1QAK4TFWHRSQOPCkij6jq01nbNPI1VMz5gca+hgBuBl4BOvOsq8vrp2EsElU9pKrPu+Uhgh9yco/3K4F7NeBpYInr1rjgKfL8NDTuuhh2H+PuNTlbpZGvoWLOT0MjIt3Ah4BvFtikLq+fhlEk2YjIWuCdBJ0Vs1kN9GZ97qMBb6bTnB+AX3Gui0dc98qGwrklXiBoBf0DVbVrKIsizg809jX0N8CfAH6B9XV5/TScIhGRduCfCDotDk5enWdIQz1RzXB+nieot3Me8LfAd+d596qOqnqqej7QDVwkIudO2qShr6Eizk/DXkMi8mGgX1Wfm26zPLKav34aSpE4v+0/Af+gqv+cZ5M+YE3W527gzfnYt1pgpvOjqoOh60JVHwbiIrJ8nnezJlDVE8Au4PJJqxr6GgopdH4a/Bq6BLhCRA4C9wOXicjfT9qmLq+fhlEkIiLA3cArqvrlAps9CFzrMicuBk6q6qF528kqUsz5EZGVbjtE5CKC6+fY/O1ldRGRFSKyxC23Au8H9k3arJGvoRnPTyNfQ6p6q6p2q+pa4GrgCVX97Umb1eX100hZW5cAHwdecj5cgD8FTgNQ1b8DHgY+COwHRoHfmf/drBrFnJ8twCdFJA2MAVdrY5VGWAXcIyJRghvgDlV9SER+D+waorjz0+jX0BQWwvVjJVIMwzCMOdEwri3DMAyjMpgiMQzDMOaEKRLDMAxjTpgiMQzDMOaEKRLDMAxjTpgiMYx5QEQ+LSJtJY5ZKyIvV2qfDKNcmCIxjPnh00BeReLmXRhG3WKKxDDKjIgsEpH/7QoTviwifwG8Dfg3Efk3t82wiNwuIs8QFDH8A7ftyyLy6Tzfud71sHiXiJwuIo+KyHMi8kMR2Ti/R2gYuTTSzHbDmC8uB95U1Q8BiMhighnK71XVo26bRcDLqnqbiFzo1r+boGjfMyLy78CAG/9LBLWZfkdVXxCRx4HfU9XXROTdwNeBy+bx+AwjB5vZbhhlRkTOBL4P7AAeUtUfukJ9m0JF4kqENKuqJ0E3ymWqeptb9zngCEHdpWcIFMpvqupeV535CPDzrD/ZrKpnzdPhGcYUzCIxjDKjqq86K+ODwH8TkX/Ns9m4qnpuOV/p8JCTBP0pLgH2ErijT7hS7YZRE1iMxDDKjIi8DRhV1b8HvgRcAAwBHQWG7AauEpE2EVkEfAT4oVuXBK4iqAj7n1yPmAMi8lH3t0REzqvc0RjGzJhFYhjl55eBL4qID6SATwK/AjwiIodU9b3ZG6vq8yLybeBZJ/qmqv7EdapEVUdcU6QfiMgI8J+BO0Xkzwja2d4PvDgPx2UYebEYiWEYhjEnzLVlGIZhzAlTJIZhGMacMEViGIZhzAlTJIZhGMacMEViGIZhzAlTJIZhGMacMEViGIZhzIn/Hx7lUa85U+BMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "\n",
    "#There is a weak correlation between the variable 'stroke' and 'price.' as such regression will not work well. We can see this using \"regplot\" to demonstrate this.\n",
    "\n",
    "#Code: \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Categorical variables</h3>\n",
    "\n",
    "<p>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.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='body-style', ylabel='price'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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=\"body-style\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We see that the distributions of price between the different body-style categories have a significant overlap, and so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='engine-location', ylabel='price'>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"engine-location\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>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.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine \"drive-wheels\" and \"price\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='drive-wheels', ylabel='price'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>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.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's first take a look at the variables by utilizing a description method.</p>\n",
    "\n",
    "<p>The <b>describe</b> function automatically computes basic statistics for all continuous variables. Any NaN values are automatically skipped in these statistics.</p>\n",
    "\n",
    "This will show:\n",
    "\n",
    "<ul>\n",
    "    <li>the count of that variable</li>\n",
    "    <li>the mean</li>\n",
    "    <li>the standard deviation (std)</li> \n",
    "    <li>the minimum value</li>\n",
    "    <li>the IQR (Interquartile Range: 25%, 50% and 75%)</li>\n",
    "    <li>the maximum value</li>\n",
    "<ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can apply the method \"describe\" as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "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": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Value-counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column 'drive-wheels'. Don’t forget the method \"value_counts\" only works on Pandas series, not Pandas Dataframes. As a result, we only include one bracket \"df['drive-wheels']\" not two brackets \"df[['drive-wheels']]\".</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can convert the series to a Dataframe as follows :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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",
       "    </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": [
       "     drive-wheels\n",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].value_counts().to_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column  'drive-wheels' to 'value_counts'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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",
       "  </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",
       "fwd           118\n",
       "rwd            75\n",
       "4wd             8"
      ]
     },
     "execution_count": 24,
     "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Now let's rename the index to 'drive-wheels':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the above process for the variable 'engine-location'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": 26,
     "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",
   "metadata": {},
   "source": [
    "<p>Examining the value counts of the 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, this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The \"groupby\" method groups data by different categories. The data is grouped based on one or several variables and analysis is performed on the individual groups.</p>\n",
    "\n",
    "<p>For example, let's group by the variable \"drive-wheels\". We see that there are 3 different categories of drive wheels.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['drive-wheels'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>If we want to know, on average, which type of drive wheel is most valuable, we can group \"drive-wheels\" and then average them.</p>\n",
    "\n",
    "<p>We can select the columns 'drive-wheels', 'body-style' and 'price', then assign it to the variable \"df_group_one\".</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_group_one = df[['drive-wheels','body-style','price']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then calculate the average price for each of the different categories of data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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>4wd</td>\n",
       "      <td>10241.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>fwd</td>\n",
       "      <td>9244.779661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>rwd</td>\n",
       "      <td>19757.613333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  drive-wheels         price\n",
       "0          4wd  10241.000000\n",
       "1          fwd   9244.779661\n",
       "2          rwd  19757.613333"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
    "df_group_one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
    "\n",
    "<p>You can also group with multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combinations 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8396.387755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9811.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>23949.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>24202.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14337.777778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21711.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>rwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16994.222222</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\n",
       "5           fwd    hatchback   8396.387755\n",
       "6           fwd        sedan   9811.800000\n",
       "7           fwd        wagon   9997.333333\n",
       "8           rwd  convertible  23949.600000\n",
       "9           rwd      hardtop  24202.714286\n",
       "10          rwd    hatchback  14337.777778\n",
       "11          rwd        sedan  21711.833333\n",
       "12          rwd        wagon  16994.222222"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping results\n",
    "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot \" to create a pivot table from the groups.</p>\n",
    "\n",
    "<p>In this case, we will leave the drive-wheel variable as the rows of the table, and pivot body-style to become the columns of the table:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  NaN           NaN   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Often, we won't have data for some of the pivot cells. We can fill these missing cells with the value 0, but any other value could potentially be used as well. It should be mentioned that missing data is quite a complex subject and is an entire course on its own.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "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",
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"5\" halign=\"left\">price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>body-style</th>\n",
       "      <th>convertible</th>\n",
       "      <th>hardtop</th>\n",
       "      <th>hatchback</th>\n",
       "      <th>sedan</th>\n",
       "      <th>wagon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>drive-wheels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4wd</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7603.000000</td>\n",
       "      <td>12647.333333</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fwd</th>\n",
       "      <td>11595.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>8396.387755</td>\n",
       "      <td>9811.800000</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rwd</th>\n",
       "      <td>23949.6</td>\n",
       "      <td>24202.714286</td>\n",
       "      <td>14337.777778</td>\n",
       "      <td>21711.833333</td>\n",
       "      <td>16994.222222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   price                                            \\\n",
       "body-style   convertible       hardtop     hatchback         sedan   \n",
       "drive-wheels                                                         \n",
       "4wd                  0.0      0.000000   7603.000000  12647.333333   \n",
       "fwd              11595.0   8249.000000   8396.387755   9811.800000   \n",
       "rwd              23949.6  24202.714286  14337.777778  21711.833333   \n",
       "\n",
       "                            \n",
       "body-style           wagon  \n",
       "drive-wheels                \n",
       "4wd            9095.750000  \n",
       "fwd            9997.333333  \n",
       "rwd           16994.222222  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
    "grouped_pivot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question 4:</h1>\n",
    "\n",
    "<p>Use the \"groupby\" function to find the average \"price\" of each car based on \"body-style\" ? </p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>convertible</td>\n",
       "      <td>21890.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>hardtop</td>\n",
       "      <td>22208.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>hatchback</td>\n",
       "      <td>9957.441176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>sedan</td>\n",
       "      <td>14459.755319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>wagon</td>\n",
       "      <td>12371.960000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    body-style         price\n",
       "0  convertible  21890.500000\n",
       "1      hardtop  22208.500000\n",
       "2    hatchback   9957.441176\n",
       "3        sedan  14459.755319\n",
       "4        wagon  12371.960000"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df_group_two = df[['body-style','price']]\n",
    "df_group_two = df_group_two.groupby(['body-style'],as_index=False).mean()\n",
    "df_group_two"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# grouping results\n",
    "df_gptest2 = df[['body-style','price']]\n",
    "grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index= False).mean()\n",
    "grouped_test_bodystyle\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\" let's do it again. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Variables: Drive Wheels and Body Style vs Price</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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": [
    "#use the grouped results\n",
    "plt.pcolor(grouped_pivot, cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
    "\n",
    "<p>The default labels convey no useful information to us. Let's change that:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEmCAYAAABoGYshAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAeSElEQVR4nO3daZRkVZnu8f+TVQgoFCKTSKEgliLigCCCDI3SauGEA9rlRaEVRW1UtPs6Lr222qi4rnO3AzYq4kjbtuKAyIVWRoFCaZlESkApQRFExKGAqnzuh7MDooqsysjMyDwV+zy/tc7KiB0RJ96oynxz57v32Vu2iYiI+oy1HUBERMyOJPiIiEolwUdEVCoJPiKiUknwERGVmt92AP00fyNrw03bDmO4Kp2l9PBF27cdwtAtu/6PbYcwK7bZ4t5thzArrrvy0ptsbzWTc4wtWGhWrhjouf7rzafaXjyT95tr61eC33BT7rXL89oOY6jGV97Rdgiz4qTvfrjtEIbuWe88re0QZsVrX7xb2yHMitftu9MvZ3ySlSuY/7BnDfTUOy/+7JYzfr85tl4l+IiIOSWhsXltRzFrkuAjosPE2Px7tR3ErEmCj4juSg8+IqJOAjQvCT4ioj4SY+nBR0TUKSWaiIgapQYfEVEnIcbmb9B2GLMmCT4iuis9+IiIeiXBR0TUSMo0yYiIGon04CMi6qQx5mWpgoiICik9+IiIKonMoomIqFYSfEREjTIPPiKiVknwERFVksTYBplFExFRn5RoIiLqlQQfEVGpsTG1HcKsSYKPiM6ShJLgIyLqNG/eWNshzJok+IjoLpEefEREjZrVJJPgIyIqJMaUBB8RUZ+UaCIi6pUEHxFRIQnmzU+Cj4iokiquwc/JBFBJB0j69ly8V0TEoCQxNjbYMYqm1YNX8ytPtseHHE9ExJyquQY/cA9e0g6SrpD0ceBq4PjSfrSkq8vtnSSdXW4vlvSzcv+5sxB7RMSMaUwDHes8h7S9pP8uOfIySUeX9vtJOk3SVeXr5n2veYukZZKulPTUvvbdJV1SHvto6VAjaUNJXy3t50vaYbLPNtUSzcOAzwN7A7uWtv2AmyVtB+wLnCVpI+DTwDPL4/ef4vtERMw+wZg00DGJlcA/2X44sBdwlKRdgDcDp9teBJxe7lMeWwI8AlgMfFxSb1nLTwBHAovKsbi0HwHcYvshwIeAYycLaqoJ/pe2f2T7N8AmkjYFtge+BOxPk8zPAnYGrrF9lW0DX1jbCSUdKWmppKVeuWKK4URETJ8QY/PHBjrWxfYNtn9cbt8GXAFsBxwMnFCedgLw7HL7YOArtm+3fQ2wDNhT0rbAAtvnldz5+TVe0zvX14ADe737tZlqgv9z3+3zgJcAV9Ik9f1oevbn9D7zICe0fZztPWzvofkbTTGciIgZEFMZZN2y1xktx5ETnrIpnewGnA9sY/sGaH4JAFuXp20HXNf3suWlbbtye8321V5jeyVwK7DFuj7eTKZJngm8qxw/AZ4I/NX2rZJ+BuwoaSfbvwBeOIP3iYiYNVOYJnmT7T0mOdcmwH8Cr7P9x3Wce6IHvI72db1mrWYyTfIsmvLMmbZX0fxmORvA9gqaGtJ3yiDrL2fwPhERs6JZbGywY9JzSRvQJPcv2v56af5tKbtQvt5Y2pfT5M+ehcD1pX3hBO2rvUbSfGAz4PfrimngHrzta7l7YJXSM1ff/aes8fzv0dTiIyLWTxrOjk6lFn48cIXtD/Y9dDJwOPC+8vWbfe1fkvRB4AE0g6kX2F4l6TZJe9GUeA4DPrbGuc4DDgHOKHX6tcqVrBHRYWJsOBt+7AO8GLhE0sWl7a00if0kSUcAvwKeD2D7MkknAZfTzMA5qlRCAF4FfA7YGDilHND8AjlR0jKanvuSyYJKgo+IztKQevC2z2biGjnAgWt5zTHAMRO0L6WvWtLXvoLyC2JQSfAR0Wk1X8maBB8RnSXBvCT4iIg6JcFHRFRIKAk+IqJGEtxrkmUIRlkSfER0lgTz04OPiKiPSA0+IqJOSg0+IqJKTQ8+NfiIiCqlBx8RUaExKbNoIiJqNW/w9eBHThJ8RHRWliqIiKhYEnxERIVyoVNERKVEBlkjIqqUGnxERKWyVEFERK3Sg4+IqFPWg4+IqFgSfEREhcay4UdERKVSg4+IqJNQ1qKJiKjVWBJ8RER9BMyrN78nwUdEhwnGUoOPiKiPgA2yZV9ERH1SoplDuz10O849/T1thzFcF3yz7QhmxxXfaDuCobvqDTu3HcKs8Ngf2g5hVrxuGCeRUqKJiKiRyCyaiIhqpUQTEVEhCTaYl0HWiIjqpEQTEVGxlGgiIiokVHUPvt7iU0TEZMpqkoMck55K+oykGyVd2tf2z5J+Lenicjyt77G3SFom6UpJT+1r313SJeWxj0rNbyBJG0r6amk/X9IOk8WUBB8RndXU4Ac7BvA5YPEE7R+y/ZhyfBdA0i7AEuAR5TUflzSvPP8TwJHAonL0znkEcIvthwAfAo6dLKAk+IjorN5SBYMck7F9JvD7Ad/6YOArtm+3fQ2wDNhT0rbAAtvn2TbweeDZfa85odz+GnBgr3e/NknwEdFdgnljgx3AlpKW9h1HDvgur5b001LC2by0bQdc1/ec5aVtu3J7zfbVXmN7JXArsMW63jiDrBHRWVOcJnmT7T2m+BafAN4NuHz9APDS8tZr8jrameSxCSXBR0SHze6OTrZ/e9c7SZ8Gvl3uLge273vqQuD60r5wgvb+1yyXNB/YjElKQinRRERn9XrwgxzTOn9TU+95DtCbYXMysKTMjNmRZjD1Ats3ALdJ2qvU1w8Dvtn3msPL7UOAM0qdfq3Sg4+IzmqWKhhOD17Sl4EDaGr1y4F3AAdIegxNKeVa4BUAti+TdBJwObASOMr2qnKqV9HMyNkYOKUcAMcDJ0paRtNzXzJZTEnwEdFpw6rQ2H7hBM3Hr+P5xwDHTNC+FNh1gvYVwPOnElMSfER02tiEY5d1SIKPiM4Sw+vBr4+S4COi0yre0CkJPiI6TOnBR0RUSbM8D75tSfAR0Wkp0UREVKri/J4EHxHdlS37IiIqVnF+T4KPiG6reUGuJPiI6CyVLftqlQQfEZ2WEk1ERIVESjQREdWaZFvTkZYEHxHdpVzoFBFRJQFD2u9jvZQEHxGdVnOJZkrjC5JeK+kKSV+c4uuulbTl1EKLiJhdzZWsgx2jaKo9+H8ADrJ9zWwEExEx10Y0dw9k4B68pE8CDwZOlmQ17itpXNL+5TlnSXqIpC0kfV/STyR9irr/DSNiZIkxDXaMooETvO1XAtcDTwROBXYB9gUuAvaTtCGw0PYymt3Ez7a9G3Ay8MC1nVfSkZKWSlr6u5tvnv4niYiYqrLhxyDHKJruHP+zgP3L8V6aRP844MLy+P7AFwBsfwe4ZW0nsn2c7T1s77HVFltMM5yIiKmTjcZXDXSMopkk+P2APYHvAvcFDgDO7HuOZxJYRMRckMcHOkbRdBP8+cATgHHbK4CLgVfQJH5oEv2hAJIOAjafWZgREbPB4PHBjhE0rQRv+3bgOuBHpeksYFPgknL/ncD+kn4MPAX41QzjjIiYHfZgxwia0jRJ2zv03d6v7/aXgC/13b+ZJrH3vH76IUZEzBJ7ZHvng8iVrBHRaaNaXx9EEnxEdJhhfGXbQcyaJPiI6C6TEk1ERJ0M40nwERFVSg0+IqJWSfARERWyYUSXIRhEEnxEdFpKNBERVcqFThER9ao4wU93sbGIiNHn4S02Jukzkm6UdGlf2/0knSbpqvJ1877H3iJpmaQrJT21r313SZeUxz6qsmmspA0lfbW0ny9ph8liSoKPiM4SQ10u+HPA4jXa3gycbnsRcHq5j6RdgCXAI8prPi5pXnnNJ4AjgUXl6J3zCOAW2w8BPgQcO1lASfAR0WGGVasGOyY7k30m8Ps1mg8GTii3TwCe3df+Fdu3lz2ulwF7StoWWGD7PNsGPr/Ga3rn+hpwYK93vzapwUdEd01tqYItJS3tu3+c7eMmec02tm8AsH2DpK1L+3bcvdw6wPLSdme5vWZ77zXXlXOtlHQrsAVw09rePAk+IjptCtMkb7K9x7DedoI2r6N9Xa9Zq5RoIqLDZn1Hp9+Wsgvl642lfTmwfd/zFgLXl/aFE7Sv9hpJ84HNuGdJaDVJ8BHRbbOb4E8GDi+3Dwe+2de+pMyM2ZFmMPWCUs65TdJepb5+2Bqv6Z3rEOCMUqdfq5RoIqK7hrhUgaQvAwfQ1OqXA+8A3gecJOkImq1Ln9+8rS+TdBJwObASOMp2L5BX0czI2Rg4pRwAxwMnSlpG03NfMllMSfAR0WHGK+8czpnsF67loQPX8vxjgGMmaF8K7DpB+wrKL4hBJcFHRHeZLDYWEVEjYzzAHPdRlQQfEd1lsqNTRESdsh58RESdPLxB1vVREnxEdJhxevARERXKLJqIiFo5g6wREVUymSYZEVGnzKKJiKhTZtFERNQqPfg586uLr+DozR7bdhgxgA9+7dVthzB0f93zkLZDmBWbXHVm2yGsvzKLJiKiTsY4s2giIiqUHnxERKVsfOcdbUcxa5LgI6LDcqFTRES9UqKJiKiQs9hYRES1MosmIqJGNl6VBB8RUR3bjN+5su0wZk0SfER0l0kPPiKiVknwEREVss141oOPiKhTZtFERNQos2giIuqUWTQRERUbTw8+IqJCmSYZEVGp1OAjIupkMosmIqJONuN3ZJA1IqI+hvH04CMi6mNSg4+IqJPBFS9VMNZ2ABER7TEeHx/omIykayVdIuliSUtL2/0knSbpqvJ1877nv0XSMklXSnpqX/vu5TzLJH1Ukqb76ZLgI6K7yjz4QY4BPdH2Y2zvUe6/GTjd9iLg9HIfSbsAS4BHAIuBj0uaV17zCeBIYFE5Fk/34yXBR0Rn2WbVHSsHOqbpYOCEcvsE4Nl97V+xfbvta4BlwJ6StgUW2D7PtoHP971mypLgI6LDplSi2VLS0r7jyHucDL4v6aK+x7axfQNA+bp1ad8OuK7vtctL23bl9prt05JB1ojorqktVXBTX+llIvvYvl7S1sBpkn62judOVFf3OtqnJQk+IrrL4FXTzp+rn8q+vny9UdJ/AXsCv5W0re0bSvnlxvL05cD2fS9fCFxf2hdO0D4tKdFERGcZM75qfKBjXSTdR9KmvdvAU4BLgZOBw8vTDge+WW6fDCyRtKGkHWkGUy8oZZzbJO1VZs8c1veaKUsPPiK6y+DxofTgtwH+q8xonA98yfb3JF0InCTpCOBXwPMBbF8m6STgcmAlcJTt3oT8VwGfAzYGTinHtAyc4MsUnqXAr20/Y6pvJOlPtjeZ6usiImaLDavumPmFTravBh49QfvNwIFrec0xwDETtC8Fdp1xUEytB380cAWwYBhvHBHROntoNfj10UA1eEkLgacD/17uby3ponL70ZIs6YHl/i8k3VvSjpLOk3ShpHfP1geIiJiJ8VUe6BhFgw6yfhh4IzAOzSgxsJGkBcB+NKWb/SQ9CLjR9l+AjwCfsP044DfDDjwiYsaGfyXremXSBC/pGTRJ+6I1HjoX2AfYH3hP+bofcFZ5fB/gy+X2ies4/5G9CwdWUO+iPxGx/jEwPu6BjlE0SA1+H+BZkp4GbAQskPQF4Ps0Cf1BNNN43kTz7/XtvtdO+q9i+zjgOICttOFo/itGxGiyhzLIur6atAdv+y22F9regWZxnDNsvwg4E3gRcJXtceD3wNOAc8pLzynPBzh02IFHRMyUy4VOgxyjaNoXOtm+ttw8s3w9G/iD7VvK/aOBo8o80M2mHWFExGypPMFP6UIn2z8AftB3/4F9t99DU4vv3b8G2Lvv5e+bbpAREbPDk16lOspyJWtEdNfwrmRdLyXBR0RnGUZ2jvsgkuAjortsxiueRZMEHxGdZacHHxFRrUE21B5VSfAR0V0e3XVmBpEEHxHdNcQdndZHSfAR0VlmSnuyjpwk+IjoLptVdyTBR0RUx4Zxp0QTEVGlVUnwERH1MVDxGGsSfER0W3rwEREVGjfckcXGIiLqlBJNRESFjFOiiYioUQZZIyIqlgQfEVEhO7NoIiKqZDKLJiKiSqnBR0RULCWaiIgKNTX4tqOYPUnwEdFp6cFHRFTIQL2rwSfBR0SHGWcWTUREjZpZNEnwERH1qXyQdaztACIi2tLrwQ9yTEbSYklXSlom6c2zH/3k0oOPiE4bRg9e0jzg34AnA8uBCyWdbPvymZ99+pLgI6KzxhnaUgV7AstsXw0g6SvAwUCrCV5ejwYYJP0O+OUcvd2WwE1z9F5zpcbPBPlco2QuP9ODbG81kxNI+h5NzIPYCFjRd/8428eV8xwCLLb9snL/xcDjbb96JvHN1HrVg5/pf9ZUSFpqe4+5er+5UONngnyuUTJqn8n24iGdShOdfkjnnrYMskZEzNxyYPu++wuB61uK5S5J8BERM3chsEjSjpLuBSwBTm45pvWrRDPHjms7gFlQ42eCfK5RUuNnmpTtlZJeDZwKzAM+Y/uylsNavwZZIyJieFKiiYioVBJ8RESlkuAjIiqVBB8RUalOzaKRtC+wyPZnJW0FbGL7mrbjmilJjwX2pbmw4hzbP245pBmTdJDtU9Zoe6XtT7YV0zBIegKwA30/e7Y/31pAQ1LWYtmG1T/Xr9qLKKBDs2gkvQPYA3iY7YdKegDwH7b3aTm0GZH0f4DnA18vTc+m+Vz/0lpQQyDpXOBtts8o998EHGD7oHYjmz5JJwI7ARcDq0qzbb+2taCGQNJrgHcAv+XuDZJs+1HtRRXQrQR/MbAb8GPbu5W2n476N6GkK4DdbK8o9zem+YwPbzeymZG0JfBt4A3AYmBnYIntO1sNbAbK/9UuruyHTtIymnVXbm47llhdl2rwd5QfLANIuk/L8QzLtTSLIPVsCPyinVCGx/ZNwLNolmB9AHDIKCf34lLg/m0HMQuuA25tO4i4py7V4E+S9CngvpJeDrwU+HTLMQ3D7cBlkk6j+eX1ZOBsSR8FGLU//yXdRvM5VL7eC3gwcIgk217QZnwztCVwuaQLaP7fALD9rPZCGoqrgR9I+g6rf64PthdSQIdKNACSngw8hSZ5nGr7tJZDmjFJh6/rcdsnzFUssW6S/maidts/nOtYhqmMb92D7XfOdSyxuk4l+FqVxY0eWu5eWUEpA0nPAc6wfWu5f1+aQdZvtBlXrJ2kTWkGV//UdizRqD7B9/3Jf4+HaL4ZR/lPfiQdAJxAU4sXzZKlh9s+s72oZk7SxbYfs0bbT3oD5KNI0l7Ax4CH05Se5gF/ruB7cFfgROB+pekm4LD1YbGtrqu+Bm9707ZjmGUfAJ5i+0oASQ8Fvgzs3mpUMzfRBIBR/379V5plZP+DZsruYcCiViMajuOAf7T933BXp+PTwBNajCkY/R+YKVnjgqCzbf+k5ZCGYYNecgew/XNJG7QZ0JAslfRBmlk0Bl4DXNRuSDNne5mkebZXAZ8t8/1H3X16yR3A9g8qmqU20jozTbJcEHQCsAXNbIbPSXpbu1ENxVJJx0s6oByfpoJESJPQ7wC+StPjXQEc1WpEM/eXMl5ysaT3S3o9UEMivFrS2yXtUI63ASN/hXgNqq/B91R8QdCGNIlvX5oa/JnAv9m+o9XA4h4kPQi4EdgAeD2wGfBx28taDWyGJG0OvJPVvwf/2fYtrQYWnUrwpwAvtP2Hcv++wBdsP6PNuGZK0tG2PzJZ26gpawW9EXgEfRdy2X5Sa0FFjJjqa/CSPkZTw53wgqA2YxuSw4E1k/nfT9A2ar5IU555BvBKms/5u1YjmiZJlzDxTC4AKlgu41vc8/PdCiwFPtX7qznmXvU9+FovBJL0QuB/0fxZfFbfQ5sCq2z/bSuBDYmki2zv3r9ekKQf2p7wYqH1WSnNwN1jCCeWr4cCf7H9rrmPangkfQTYimb2FsDfAb8BNgYW2H5xW7F1XfU9+FFN4AM4F7iBZsD4A33ttwE/bSWi4epdrHWDpKcD1wMLW4xn2mz/EkDSPmusXvpmSecAI53gaca29u+7/y1JZ9reX1Lmwreo+gQv6STbL1jbn8mj+udxSRq/BPZuO5ZZ8i+SNgP+iebioAU0A5Oj7D6S9rV9Nty1NnwNs2i2kvTA3vrvkh5I0/GAZiZUtKQLJZptbd/Q92fyanq9q1Gzjit0ARj1qyNrJGl34DM0s2dMU6d+6ahv0CLpacAnaVYxFbAj8A/AD4CX2/5wa8F1XPUJvkfSsbbfNFnbqJH0Lpp654k0P1yHApvafn+rgc2QpAfTDBTvTbOJxHnA621f3WpgQyBpAc3PXjVL7JbpujvTfA/+LAOr64cuJfgf237sGm01bPhxvu3HT9Y2aiT9iOYq1t7A3RLgNaP8uSRtA7wHeIDtgyTtAuxt+/iWQ5uxsh7NLqw+pXXktyIcddVfySrpVaX+vrOkn/Yd11DHYOQqSYdKmidpTNKh3L0d3CiT7RNtryzHF1hHSWpEfA44lWYDE4CfA69rK5hhKcsFf6wcTwTeT7NZS7Ss+h58GajbHHgv8Oa+h26z/ft2ohoeSTvQlDL2oWy6DbzO9rUthjVtknorEr4R+APwFZrP9XfAhrbf3VJoMybpQtuP618Vc6JVM0dN6UA9GviJ7UeXv1T+3fYzWw6t86qfRWP71jIg+chRHVBdGzU72R9l++C2Yxmii7h7RyeAV/Q9ZmBkEzzwZ0lbcPe2kXtRx1Z3K2yPS1pZxhdupNmFK1pWfYIHKN98/9M/lasGtleVmRnVsL1j2zHMon8ETgZ2KvPftwIOaTekobiwLP3RW+juT8AFrUYUQEcSfLEtzVIFFwB/7jVWsB/mTySdTLPiYv/n+np7IQ1HmSe+A33fpyM+cLcTcBDNpizPAx5PHT+DmwLPp5kW+T2aq1drGN8aedXX4Hsq3g/zsxM02/ZL5zyYIZJ0Ik1CvJi7B409apuI9+vN2pK0L81smg8Abx3lmUEAkp5Es2TGfjSlmYuBM0d9wbsadCbBw11rgiyy/f8k3RuYZ/u2tuOKeyrLO+/iir5Be4Orkt4LXGL7S6O+DWFPGQ96HM0smlcCf7W9c7tRRQ1/Hg5E0suBI2n2jdwJ2I7m6rsD24xrpiRtBBzBPZfVHekePHApcH+a9XZq8WtJnwL+Fji2XBw08lOVJZ1Os+TCeTQL3z3O9o3tRhVQwTfXFBxFM5XwjwC2rwK2bjWi4TiRJhE+FfghzYJcI/tXiaRvlTGFLYHLJZ0q6eTe0XZ8M/QCmnnwi8u+BPcD3tBqRMPxU5o1Z3YFHgXsWjbUiZZ1pkTTu7qz78/k+TQ7Oo36lay9z9Or724AnDqqG2OsbaykZ9THTGomaRPgJcD/Bu5ve8OWQ+q8zpRogB9KeiuwsaQn0yyG9K2WYxqG3rK6fyiXi/+GZubJSOolcEk7AjesscXiNm3GFhOT9GqaAdbdaVY4/Qyr71EQLelSD36Mplb9FJqLaE6ludpupP8BJL0M+E/gkTSXwm8CvN32p9qMa6YkLQWe0NtbVs1m1efYfly7kcWaJL2BZh/Wi2yvbDueuFuXEvxzgO/avr3tWIapDNQ9j6bXvkFpdgW7BN3jEn5J/2P70S2FFDFyujTI+izg55JOlPT0UoOvwTeBg4GVNFcQ/om+C55G2O8k3XURmqSDgZtajCdi5HSmBw9QBiAPolm4al/gNNsvazeqmZF0qe1d245j2CTtRLPxdm/lxeXAi23/or2oIkZLLb3Ygdi+U9IpNIs9bUzT8x3pBA+cK+mRti9pO5AhG7e9V5mZIdu3lYHXiBhQZ3rwkhbTbBrxRJo1M74KfH9UB4X69pidDywCrgZupxlAdgXTPyfaoOUi21UtrhYxm7rUg/97mrXFX1HJQOsz2g5gNkjameaq3M0kPbfvoQX0XakbEZPrTIK3vaTtGIaptrXt+zyM5pfXfYH+DSNuA17eRkARo6pLJZrnAsfSLE8g7i5lLGg1sJiQpL1tn9d2HBGjrEsJfhnwTNtXtB1LTK7iRdQi5kyX5sH/Nsl9pFS1iFpEG7rUg/8ITcL4Bs1sE6COnY9qVNsiahFt6MwgK80sjL/QrEXTYyAJfv1U1SJqEW3oTIK3/ZK2Y4gpOU7S5sDbaDaq3gR4e7shRYyWLpVoFgIfo9n0w8DZwNG2l7caWEyo1kXUIuZSlwZZP0vTE3wAzXZ93yptsX6qdRG1iDnTpR78RMvP3qMt1g+1LqIWMZe61IO/SdKLJM0rx4uAm9sOKtbqXEmPbDuIiFHWpR78A4F/BfamqcGfC7zW9q9aDSxWU/siahFzqUsJ/gTgdbZvKffvB/zfXBm5fpH0oHU9XvEaPBFD15lpksCjeskdwPbvJe3WZkBxT0ngEcPTpRr8WJlXDdzVg+/SL7iI6JguJbgP0AzcfY2mxvsC4Jh2Q4qImD2dqcEDSNoFeBLNgN3pti9vOaSIiFnTqQQfEdElXarBR0R0ShJ8RESlkuAjIiqVBB8RUan/D8tnM2IAuFOfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
   "metadata": {},
   "source": [
    "<p>Visualization is very important in data science, and Python visualization packages provide great freedom. We will go more in-depth in a separate Python Visualizations course.</p>\n",
    "\n",
    "<p>The main question we want to answer in this module, is \"What are the main characteristics which have the most impact on the car price?\".</p>\n",
    "\n",
    "<p>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?</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">5. Correlation and Causation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Correlation</b>: a measure of the extent of interdependence between variables.</p>\n",
    "\n",
    "<p><b>Causation</b>: the relationship between cause and effect between two variables.</p>\n",
    "\n",
    "<p>It is important to know the difference between these two and that correlation does not imply causation. Determining correlation is much simpler  the determining causation as causation may require independent experimentation.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</p>\n",
    "\n",
    "<p>The Pearson Correlation measures the linear dependence between two variables X and Y.</p>\n",
    "<p>The resulting coefficient is a value between -1 and 1 inclusive, where:</p>\n",
    "<ul>\n",
    "    <li><b>1</b>: Total positive linear correlation.</li>\n",
    "    <li><b>0</b>: No linear correlation, the two variables most likely do not affect each other.</li>\n",
    "    <li><b>-1</b>: Total negative linear correlation.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Pearson Correlation is the default method of the function \"corr\".  Like before we can calculate the Pearson Correlation of the of the 'int64' or 'float64'  variables.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " sometimes we would like to know the significant of the correlation estimate. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \n",
    "\n",
    "<p>What is this P-value? The P-value is the probability value that the correlation between these two variables is statistically significant. Normally, we choose a significance level of 0.05, which means that we are 95% confident that the correlation between the variables is significant.</p>\n",
    "\n",
    "By convention, when the\n",
    "\n",
    "<ul>\n",
    "    <li>p-value is $<$ 0.001: we say there is strong evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.05: there is moderate evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.1: there is weak evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $>$ 0.1: there is no evidence that the correlation is significant.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.584641822265508  with a P-value of P = 8.076488270733218e-20\n"
     ]
    }
   ],
   "source": [
    "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",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>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)</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8095745670036562  with a P-value of P =  6.369057428259195e-48\n"
     ]
    }
   ],
   "source": [
    "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",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>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)</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Length vs Price</h3>\n",
    "\n",
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'length' and 'price'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.6906283804483639  with a P-value of P =  8.016477466159328e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522675  with a P-value of P = 9.200335510481123e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (~0.751).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702843  with a P-value of P =  2.189577238894065e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-size vs Price</h3>\n",
    "\n",
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'engine-size' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622198389e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626603  with a P-value of P =   8.049189483935261e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844678  with a P-value of P =  2.321132065567641e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of ~ -0.687 shows that the relationship is negative and moderately strong.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.704692265058953  with a P-value of P =  1.7495471144476358e-31\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['highway-mpg'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\">6. ANOVA</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>ANOVA: Analysis of Variance</h3>\n",
    "<p>The Analysis of Variance  (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
    "\n",
    "<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
    "\n",
    "<p><b>P-value</b>:  P-value tells how statistically significant is our calculated score value.</p>\n",
    "\n",
    "<p>If our price variable is strongly correlated with the variable we are analyzing, expect ANOVA to return a sizeable F-test score and a small p-value.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
    "\n",
    "<p>Let's see if different types 'drive-wheels' impact  'price', we group the data.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 48,
     "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": 49,
   "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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22625.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>201 rows × 3 columns</p>\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\n",
       "..           ...          ...      ...\n",
       "196          rwd        sedan  16845.0\n",
       "197          rwd        sedan  19045.0\n",
       "198          rwd        sedan  21485.0\n",
       "199          rwd        sedan  22470.0\n",
       "200          rwd        sedan  22625.0\n",
       "\n",
       "[201 rows x 3 columns]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_gptest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain the values of the method group using the method \"get_group\".  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2.get_group('4wd')['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can use the function 'f_oneway' in the module 'stats'  to obtain the <b>F-test score</b> and <b>P-value</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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",
   "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? \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 130.5533160959111 , P = 2.2355306355677845e-23\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine the other groups \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 8.580681368924756 , P = 0.004411492211225333\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('rwd')['price'])  \n",
    "   \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>4wd and fwd</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price'])  \n",
    " \n",
    "print(\"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Conclusion: Important Variables</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "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. We 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",
    "<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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
    "\n",
    "Bahare Talayian\n",
    "\n",
    "Eric Xiao\n",
    "\n",
    "Steven Dong\n",
    "\n",
    "Parizad\n",
    "\n",
    "Hima Vasudevan\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                 |\n",
    "| ----------------- | ------- | ---------- | ---------------------------------- |\n",
    "| 2020-10-30        | 2.1     | Lakshmi    | changed URL of csv                 |\n",
    "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab |\n",
    "\n",
    "<hr>\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
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