Module3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <a href=\"http://cocl.us/DA0101EN_NotbookLink_Top\">\n",
    "         <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
    "    </a>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width = 300, align = \"center\"></a>\n",
    "\n",
    "<h1 align=center><font size = 5>Data Analysis with Python</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Welcome!</h3>\n",
    "In this section, we will explore several methods to see if certain characteristics or features can be used to predict car price. "
   ]
  },
  {
   "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",
    "Estimated Time Needed: <strong>30 min</strong>\n",
    "</div>\n",
    " \n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What are the main characteristics which have the most impact on the car price?</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">1. Import Data from Module 2</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/cognitive_class_DA0101EN_objectstorage\">HERE</a> for free storage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>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",
       "      <td>0</td>\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",
       "      <td>1</td>\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",
       "      <td>2</td>\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",
       "      <td>3</td>\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",
       "      <td>4</td>\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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To install seaborn we use the pip which is the python package manager."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": 7,
   "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",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "float64\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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."
   ]
  },
  {
   "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>"
   ]
  },
  {
   "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",
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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>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>bore</td>\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",
       "      <td>stroke</td>\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",
       "      <td>compression-ratio</td>\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",
       "      <td>horsepower</td>\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": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['bore','stroke','compression-ratio','horsepower']].corr()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()  \n",
    "\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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56242.26481222681)"
      ]
     },
     "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": [
    "# 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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87"
   ]
  },
  {
   "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>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>engine-size</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\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": 12,
     "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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xeaea69c948>"
      ]
     },
     "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=\"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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704"
   ]
  },
  {
   "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>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>highway-mpg</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xeaea70a448>"
      ]
     },
     "execution_count": 15,
     "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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",
       "      <td>peak-rpm</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\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": 16,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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",
       "      <td>stroke</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>0.08231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\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": 17,
     "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": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "#The correlation is 0.0823, the non-diagonal elements of the table.\n",
    "#code:\n",
    "df[[\"stroke\",\"price\"]].corr() \n",
    "\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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xeaee23e188>"
      ]
     },
     "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": [
    "# Write your code below and press Shift+Enter to execute \n",
    "sns.regplot(y='price',x='stroke',data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "#There is a weak correlation between the variable 'stroke' and 'price.' as such regression will not work well.  We #can see this use \"regplot\" to demonstrate this.\n",
    "\n",
    "#Code: \n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
    "\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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the relationship between \"body-style\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xeaee2521c8>"
      ]
     },
     "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": [
    "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xeaee2c9388>"
      ]
     },
     "execution_count": 20,
     "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's examine \"drive-wheels\" and \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xeaf0afd648>"
      ]
     },
     "execution_count": 21,
     "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>"
   ]
  },
  {
   "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",
    "<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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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",
       "      <td>count</td>\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",
       "      <td>mean</td>\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",
       "      <td>std</td>\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",
       "      <td>min</td>\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",
       "      <td>25%</td>\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",
       "      <td>50%</td>\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",
       "      <td>75%</td>\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",
       "      <td>max</td>\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": 22,
     "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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",
       "      <td>count</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>201</td>\n",
       "      <td>200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>unique</td>\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",
       "      <td>top</td>\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",
       "      <td>freq</td>\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": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Value Counts</h3>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fwd    118\n",
       "rwd     75\n",
       "4wd      8\n",
       "Name: drive-wheels, dtype: int64"
      ]
     },
     "execution_count": 24,
     "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 :"
   ]
  },
  {
   "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>drive-wheels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4wd</td>\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": 25,
     "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'."
   ]
  },
  {
   "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",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>fwd</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4wd</td>\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": 26,
     "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':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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",
       "      <td>fwd</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rwd</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4wd</td>\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": 27,
     "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'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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",
       "      <td>front</td>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>rear</td>\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": 28,
     "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['rwd', 'fwd', '4wd'], dtype=object)"
      ]
     },
     "execution_count": 29,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>4wd</td>\n",
       "      <td>10241.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>fwd</td>\n",
       "      <td>9244.779661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\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": 31,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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",
       "      <td>0</td>\n",
       "      <td>4wd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7603.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>12647.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>4wd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9095.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>fwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>fwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8396.387755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9811.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>fwd</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9997.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>23949.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>24202.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14337.777778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21711.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\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": 32,
     "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>"
   ]
  },
  {
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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",
       "      <td>4wd</td>\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",
       "      <td>fwd</td>\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",
       "      <td>rwd</td>\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": 33,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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",
       "      <td>4wd</td>\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",
       "      <td>fwd</td>\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",
       "      <td>rwd</td>\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": 34,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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",
       "      <td>0</td>\n",
       "      <td>convertible</td>\n",
       "      <td>21890.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>22208.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9957.441176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>sedan</td>\n",
       "      <td>14459.755319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\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": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_groupin=df[['body-style','price']]\n",
    "df_groupin1=df_groupin.groupby(['body-style'],as_index=False).mean()\n",
    "df_groupin1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\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",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you did not import \"pyplot\" let's do it again. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use a heat map to visualize the relationship between Body Style vs Price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": false
   },
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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": [
    "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">5. Correlation and Causation</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</p>\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>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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",
       "      <td>symboling</td>\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",
       "      <td>normalized-losses</td>\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",
       "      <td>wheel-base</td>\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",
       "      <td>length</td>\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",
       "      <td>width</td>\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",
       "      <td>height</td>\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",
       "      <td>curb-weight</td>\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",
       "      <td>engine-size</td>\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",
       "      <td>bore</td>\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",
       "      <td>stroke</td>\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",
       "      <td>compression-ratio</td>\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",
       "      <td>horsepower</td>\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",
       "      <td>peak-rpm</td>\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",
       "      <td>city-mpg</td>\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",
       "      <td>highway-mpg</td>\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",
       "      <td>price</td>\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",
       "      <td>city-L/100km</td>\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",
       "      <td>diesel</td>\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",
       "      <td>gas</td>\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": 44,
     "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. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \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",
    "<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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5846418222655081  with a P-value of P = 8.076488270732989e-20\n"
     ]
    }
   ],
   "source": [
    "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.809574567003656  with a P-value of P =  6.369057428259557e-48\n"
     ]
    }
   ],
   "source": [
    "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>"
   ]
  },
  {
   "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'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.690628380448364  with a P-value of P =  8.016477466158986e-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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522674  with a P-value of P = 9.200335510481516e-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)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702846  with a P-value of P =  2.1895772388936914e-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>"
   ]
  },
  {
   "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':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935489e-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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844677  with a P-value of P =  2.321132065567674e-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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.7046922650589529  with a P-value of P =  1.7495471144477352e-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",
    "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"anova\">6. ANOVA</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Drive Wheels</h3>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see if different types 'drive-wheels' impact  'price', we group the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\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>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>rwd</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>rwd</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>fwd</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4wd</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>fwd</td>\n",
       "      <td>15250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>136</td>\n",
       "      <td>4wd</td>\n",
       "      <td>7603.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    drive-wheels    price\n",
       "0            rwd  13495.0\n",
       "1            rwd  16500.0\n",
       "3            fwd  13950.0\n",
       "4            4wd  17450.0\n",
       "5            fwd  15250.0\n",
       "136          4wd   7603.0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
    "grouped_test2.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "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",
       "      <td>0</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>13495.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>rwd</td>\n",
       "      <td>convertible</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>rwd</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>fwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>13950.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4wd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>196</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>16845.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>197</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>19045.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>198</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>21485.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>199</td>\n",
       "      <td>rwd</td>\n",
       "      <td>sedan</td>\n",
       "      <td>22470.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>200</td>\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": 56,
     "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\".  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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": 57,
     "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>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "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? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Separately: fwd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "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 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4wd and rwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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>"
   ]
  },
  {
   "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",
    "<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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you for completing this notebook</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "    <p><a href=\"https://cocl.us/DA0101EN_NotbookLink_Top_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>About the Authors:</h3>\n",
    "\n",
    "This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
   ]
  }
 ],
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