Explortatory Data Analysis (EDA).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> In  Data Science, exploratory data analysis (EDA) is an approach to analyzing data sets to summarize their main characteristics, often with visual methods. In Machine Learning the same old but golden statement of <b>Garbage <em>in</em> Garbage <em>out</em></b> still applies and this is important to remember because when building models,the accuracy of our prediction depends on how much our model can learn from the data we feed it.EDA is a thorough examination meant to uncover the underlying structure of a data set and is important because it exposes trends, patterns, and relationships that are not readily apparent. </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> Let us begin</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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</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>Low</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</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>Low</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</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</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>Low</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</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>Low</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    5000.0       21          27  13495.0   \n",
       "1                9.0         111    5000.0       21          27  16500.0   \n",
       "2                9.0         154    5000.0       19          26  16500.0   \n",
       "3               10.0         102    5500.0       24          30  13950.0   \n",
       "4                8.0         115    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476                Low       0    1  \n",
       "1    11.190476                Low       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667                Low       0    1  \n",
       "4    13.055556                Low       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=pd.read_csv('clean_df.csv',index_col=0)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing individual pattern of Features\n",
    "<p> As with most machine learning project the goal is to make prediction based on certain input and corresponding ouput dataset. The predictions we make are influenced postively or negatively by the quality and also how important that feature is to the <b>Target</b>. So the need arises to understand how each feature relates to the <b> Target Variable </b> when it is not combined with other features so as to ascertain how important that feature is.</p>\n",
    "<p> One of the efficient ways of establishing this relationship is by <em><b> Visualization </b></em> and knowing what type of variable you are dealing with is important in chosing the right <em><b> Visulaization</b><em>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "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             int64\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"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to get the data type of  each column in our dataset:\n",
    "df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "  <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",
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       "      <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",
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       "    <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",
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       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075810</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>0.217300</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>0.371178</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>0.579795</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>0.615056</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",
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       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087001</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",
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       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757981</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>0.822668</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",
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       "      <td>0.001263</td>\n",
       "      <td>0.566903</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>0.098322</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",
       "  </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",
       "\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",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075810  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217300  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371178 -0.360305   \n",
       "length             0.124139           0.159733    0.579795 -0.285970   \n",
       "width              0.188829           0.189867    0.615056 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087001 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757981 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822668 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566903 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098322 -0.065713   \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",
       "\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  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\" First let's run the .corr() method to get a summary of the numerical variablew with data type int64 and float64\n",
    " we can see that going along the diagonal that the values are 1.000 this is\n",
    "because when the correlation of a feature is agianst itself the values is one\"\"\"\n",
    "df.corr().head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>bore</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566903</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>0.098322</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>-0.214489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>horsepower</td>\n",
       "      <td>0.566903</td>\n",
       "      <td>0.098322</td>\n",
       "      <td>-0.214489</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    0.566903\n",
       "stroke            -0.055390  1.000000           0.187923    0.098322\n",
       "compression-ratio  0.001263  0.187923           1.000000   -0.214489\n",
       "horsepower         0.566903  0.098322          -0.214489    1.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#to reduce the amount of information displayed at once we can select for specific features:\n",
    "df[['bore','stroke','compression-ratio','horsepower']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Continious numerical variables\n",
    "<p> This are a type of qunatitative variabe whose value occupy a certain range. They are of data type int64 or float64. A very good way of visualizing these type of variables is by making use of <b>scatterplots</b>. We can create a <b>scatterplot</b> to compare how well the individual variables realtes with the <b>Target</b> which in this case is the price column by calling the <b><em>.regplot()</em></b> function of the <B>SEABORN</B> Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56166.5951398558)"
      ]
     },
     "execution_count": 7,
     "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": [
    "# We are going to compare selected continous variables against the price column\n",
    "sns.regplot(x='engine-size',y='price', data=df)\n",
    "#this is to make 0 be the starting value for the yaxis\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> we can see that we obatined a strong and <b><em>positive</em></b> correlation. That is as  the engine size increases there is a proportionate increase in the price. I emphasized on the word <b><em>positive</em></b> because correlation can also be strong and be negative whereby in such cases we would see a corresponding increase in one variable leads to a decrease in the other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating a function to display the scatterplot based on the column names specified\n",
    "def reg_plot(x,y):\n",
    "    sns.regplot(x,y,data=df)\n",
    "    plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            horsepower     price\n",
      "horsepower    1.000000  0.809607\n",
      "price         0.809607  1.000000\n"
     ]
    },
    {
     "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": [
    "reg_plot(df['horsepower'],df['price'])\n",
    "# when this plot is displayed we notice almost the same strong and positve correlation pattern that was noticed with engine-size\n",
    "# let us run .corr() to get the value of the correlation\n",
    "print(df[['horsepower','price']].corr())\n",
    "#correlation value ranges from -1 to 1 where -1 represents a perfect negative correlation while +1 reps a perfect positvie correlation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def math(x,y):\n",
    "    mask=df.columns=='engine-size'\n",
    "    fig=plt.figure(figsize=(10,8))\n",
    "    ax0=fig.add_subplot(1,3,1)\n",
    "    ax1=fig.add_subplot(1,3,2)\n",
    "    for i in df.columns:\n",
    "        if i in df[['engine-size','horsepower']]:\n",
    "            ax0=df.plot(mask,y, kind='scatter', ax=ax0)\n",
    "            ax1=df.plot(x,y,kind='scatter', ax=ax1)\n",
    "            plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg_plot(df['peak-rpm'],df['price'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>oops from our above plot peak_rpm is not a good predictor of price due to the fact that the regression line is almost horizontal indicating a weak correlation. We can also notice how scatterd the data points are from the regression line. This implies that a lot of the variablity of the dependent variable which is <B><EM>P</EM></B> is not captured by the Peak-rpm values</p>"
   ]
  },
  {
   "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>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": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#let us the correlation value\n",
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>a value of -0.10  is a very weak negative correlation.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg_plot(df.stroke, df.price)"
   ]
  },
  {
   "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>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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['stroke','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> weak positive correlation</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Categorical variables</h3>\n",
    "\n",
    "<p>These are also known as quanlitative variables that describe a 'characteristic' of a data unit. They are usually measured using the Nominal or Oridnal scale of measurement when ranking is present in the data. 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": [
    "<p>relationship between body-style and price </p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2cd5007b2c8>"
      ]
     },
     "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.boxplot(x='body-style',y='price',data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> From the above box plot of price against body-style there seems to be significant overlap between the body style and price in such a way that we can distinctly say that a certain bodystyle produced this particular price range </p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2cd5013c8c8>"
      ]
     },
     "execution_count": 16,
     "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> The price distribution as seen from the above box plot shows a distinct value range which implies that engine-location is a good indicator of price</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2cd501ccc08>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> There is a clear distribution of price between the different drive wheels and as such we might consider it a good predictor of price</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Descriptive Statistical Analysis\n",
    "<p> Another important step in our EDA is to carry out a descriptive statistical analysis which would enable us to get better insights on how our data variables interact <p>\n",
    " we would that in the following cells below\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> The <strong>.describe()</strong> function helps us to summarize our data given us a quick overview of important measures of central tendency such as MEAN ,MEDIAN AND Standard Deviation.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#.describe() by default only returns statistical values for all numerical variables and ignores Nan and Obect type data</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>103.402985</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>37.365650</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  103.402985  5117.665368   25.179104    30.686567   \n",
       "std             4.004965   37.365650   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": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>201</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>153</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                201  \n",
       "unique                 3  \n",
       "top                  Low  \n",
       "freq                 153  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to return values for variables with data type object\n",
    "df.describe(include=['object'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### VALUE COUNT\n",
    "<p>This mehod gives us the count of how many units of each variable in a particular column.The <b><em> .value_counts()</em></b> can only be called on a pandas series.</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": [
    "#calling the .value_count on the drive_wheels column\n",
    "df['drive-wheels'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> we can convert the above series to a data frame by calling the <b>.to_frame</b> method on the <b>.value_counts()</b> method. We assign this value to the variable named drive_wheels_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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": 29,
     "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": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "drive_wheels_counts.index.name = 'drive-wheels'\n",
    "drive_wheels_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "<class 'pandas.core.series.Series'>\n"
     ]
    }
   ],
   "source": [
    "# to verify that we are dealing with a dataframe we can check the type\n",
    "print (type(drive_wheels_counts))\n",
    "print(type(df['drive-wheels']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 34,
     "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> The importance of calling the . value_counts() method is found particlularly useful here. In the above box plot where we compared engine location to price and we could identify very distinct price distribution pattern, however the fact that we only have 3 values recorded for the <b>rear</b> engine location makes the result skewed which would therefore affect any analysis we carry out.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grouping\n",
    "<p>The <b>.groupby method</b> groups data based on categories belonging to one or more columns. It is simillar to what the pivot table function in excel provides</p> For example we can use this method to calclulate the average price of cars based on their make</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['alfa-romero', 'audi', 'bmw', 'chevrolet', 'dodge', 'honda',\n",
       "       'isuzu', 'jaguar', 'mazda', 'mercedes-benz', 'mercury',\n",
       "       'mitsubishi', 'nissan', 'peugot', 'plymouth', 'porsche', 'renault',\n",
       "       'saab', 'subaru', 'toyota', 'volkswagen', 'volvo'], dtype=object)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we first determine the unique values in the make column by callling .unique\n",
    "df.make.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_price=df[['make','price','body-style']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>make</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>15498.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>audi</td>\n",
       "      <td>17859.166667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>bmw</td>\n",
       "      <td>26118.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>chevrolet</td>\n",
       "      <td>6007.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>dodge</td>\n",
       "      <td>7875.444444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>honda</td>\n",
       "      <td>8184.692308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>isuzu</td>\n",
       "      <td>8916.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>jaguar</td>\n",
       "      <td>34600.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mazda</td>\n",
       "      <td>10652.882353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>33647.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mercury</td>\n",
       "      <td>16503.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mitsubishi</td>\n",
       "      <td>9239.769231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>nissan</td>\n",
       "      <td>10415.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>peugot</td>\n",
       "      <td>15489.090909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>plymouth</td>\n",
       "      <td>7963.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>porsche</td>\n",
       "      <td>31400.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>renault</td>\n",
       "      <td>9595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>saab</td>\n",
       "      <td>15223.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>subaru</td>\n",
       "      <td>8541.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>toyota</td>\n",
       "      <td>9885.812500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>volkswagen</td>\n",
       "      <td>10077.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>volvo</td>\n",
       "      <td>18063.181818</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      price\n",
       "make                       \n",
       "alfa-romero    15498.333333\n",
       "audi           17859.166667\n",
       "bmw            26118.750000\n",
       "chevrolet       6007.000000\n",
       "dodge           7875.444444\n",
       "honda           8184.692308\n",
       "isuzu           8916.500000\n",
       "jaguar         34600.000000\n",
       "mazda          10652.882353\n",
       "mercedes-benz  33647.000000\n",
       "mercury        16503.000000\n",
       "mitsubishi      9239.769231\n",
       "nissan         10415.666667\n",
       "peugot         15489.090909\n",
       "plymouth        7963.428571\n",
       "porsche        31400.500000\n",
       "renault         9595.000000\n",
       "saab           15223.333333\n",
       "subaru          8541.250000\n",
       "toyota          9885.812500\n",
       "volkswagen     10077.500000\n",
       "volvo          18063.181818"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_price1=average_price.groupby('make').mean()\n",
    "average_price1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "#WE can also groub by on more than one column \n",
    "average_price2=average_price.groupby(['make','body-style'],as_index=False).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\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>make</th>\n",
       "      <th>body-style</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>convertible</td>\n",
       "      <td>14997.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>audi</td>\n",
       "      <td>sedan</td>\n",
       "      <td>17647.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>audi</td>\n",
       "      <td>wagon</td>\n",
       "      <td>18920.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>bmw</td>\n",
       "      <td>sedan</td>\n",
       "      <td>26118.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>chevrolet</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>5723.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>chevrolet</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6575.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>dodge</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7819.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>dodge</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7619.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>dodge</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8921.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>honda</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>7054.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>honda</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9945.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>honda</td>\n",
       "      <td>wagon</td>\n",
       "      <td>7295.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>isuzu</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>11048.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>isuzu</td>\n",
       "      <td>sedan</td>\n",
       "      <td>6785.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>jaguar</td>\n",
       "      <td>sedan</td>\n",
       "      <td>34600.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>mazda</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>10085.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>17</td>\n",
       "      <td>mazda</td>\n",
       "      <td>sedan</td>\n",
       "      <td>11464.142857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>18</td>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>convertible</td>\n",
       "      <td>35056.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>19</td>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>36788.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>20</td>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>sedan</td>\n",
       "      <td>33074.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>21</td>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>wagon</td>\n",
       "      <td>28248.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>mercury</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>16503.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>23</td>\n",
       "      <td>mitsubishi</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9597.888889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>mitsubishi</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8434.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25</td>\n",
       "      <td>nissan</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>8249.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>26</td>\n",
       "      <td>nissan</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>14409.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>27</td>\n",
       "      <td>nissan</td>\n",
       "      <td>sedan</td>\n",
       "      <td>8604.555556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>28</td>\n",
       "      <td>nissan</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9915.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>29</td>\n",
       "      <td>peugot</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15758.571429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>30</td>\n",
       "      <td>peugot</td>\n",
       "      <td>wagon</td>\n",
       "      <td>15017.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>31</td>\n",
       "      <td>plymouth</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>8130.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>32</td>\n",
       "      <td>plymouth</td>\n",
       "      <td>sedan</td>\n",
       "      <td>7150.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>33</td>\n",
       "      <td>plymouth</td>\n",
       "      <td>wagon</td>\n",
       "      <td>8921.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>34</td>\n",
       "      <td>porsche</td>\n",
       "      <td>convertible</td>\n",
       "      <td>37028.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>35</td>\n",
       "      <td>porsche</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>33278.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>36</td>\n",
       "      <td>porsche</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>22018.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>37</td>\n",
       "      <td>renault</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9895.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>38</td>\n",
       "      <td>renault</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9295.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>39</td>\n",
       "      <td>saab</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>15013.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>40</td>\n",
       "      <td>saab</td>\n",
       "      <td>sedan</td>\n",
       "      <td>15433.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>41</td>\n",
       "      <td>subaru</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>6591.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>42</td>\n",
       "      <td>subaru</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9070.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>43</td>\n",
       "      <td>subaru</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9342.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>44</td>\n",
       "      <td>toyota</td>\n",
       "      <td>convertible</td>\n",
       "      <td>17669.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>45</td>\n",
       "      <td>toyota</td>\n",
       "      <td>hardtop</td>\n",
       "      <td>9762.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>46</td>\n",
       "      <td>toyota</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9616.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>47</td>\n",
       "      <td>toyota</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9542.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>48</td>\n",
       "      <td>toyota</td>\n",
       "      <td>wagon</td>\n",
       "      <td>9836.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>49</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>convertible</td>\n",
       "      <td>11595.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>9980.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>51</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>sedan</td>\n",
       "      <td>9673.888889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>52</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>wagon</td>\n",
       "      <td>12290.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>53</td>\n",
       "      <td>volvo</td>\n",
       "      <td>sedan</td>\n",
       "      <td>18726.875000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>54</td>\n",
       "      <td>volvo</td>\n",
       "      <td>wagon</td>\n",
       "      <td>16293.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             make   body-style         price\n",
       "0     alfa-romero  convertible  14997.500000\n",
       "1     alfa-romero    hatchback  16500.000000\n",
       "2            audi        sedan  17647.000000\n",
       "3            audi        wagon  18920.000000\n",
       "4             bmw        sedan  26118.750000\n",
       "5       chevrolet    hatchback   5723.000000\n",
       "6       chevrolet        sedan   6575.000000\n",
       "7           dodge    hatchback   7819.800000\n",
       "8           dodge        sedan   7619.666667\n",
       "9           dodge        wagon   8921.000000\n",
       "10          honda    hatchback   7054.428571\n",
       "11          honda        sedan   9945.000000\n",
       "12          honda        wagon   7295.000000\n",
       "13          isuzu    hatchback  11048.000000\n",
       "14          isuzu        sedan   6785.000000\n",
       "15         jaguar        sedan  34600.000000\n",
       "16          mazda    hatchback  10085.000000\n",
       "17          mazda        sedan  11464.142857\n",
       "18  mercedes-benz  convertible  35056.000000\n",
       "19  mercedes-benz      hardtop  36788.000000\n",
       "20  mercedes-benz        sedan  33074.000000\n",
       "21  mercedes-benz        wagon  28248.000000\n",
       "22        mercury    hatchback  16503.000000\n",
       "23     mitsubishi    hatchback   9597.888889\n",
       "24     mitsubishi        sedan   8434.000000\n",
       "25         nissan      hardtop   8249.000000\n",
       "26         nissan    hatchback  14409.000000\n",
       "27         nissan        sedan   8604.555556\n",
       "28         nissan        wagon   9915.666667\n",
       "29         peugot        sedan  15758.571429\n",
       "30         peugot        wagon  15017.500000\n",
       "31       plymouth    hatchback   8130.500000\n",
       "32       plymouth        sedan   7150.500000\n",
       "33       plymouth        wagon   8921.000000\n",
       "34        porsche  convertible  37028.000000\n",
       "35        porsche      hardtop  33278.000000\n",
       "36        porsche    hatchback  22018.000000\n",
       "37        renault    hatchback   9895.000000\n",
       "38        renault        wagon   9295.000000\n",
       "39           saab    hatchback  15013.333333\n",
       "40           saab        sedan  15433.333333\n",
       "41         subaru    hatchback   6591.333333\n",
       "42         subaru        sedan   9070.600000\n",
       "43         subaru        wagon   9342.000000\n",
       "44         toyota  convertible  17669.000000\n",
       "45         toyota      hardtop   9762.333333\n",
       "46         toyota    hatchback   9616.000000\n",
       "47         toyota        sedan   9542.200000\n",
       "48         toyota        wagon   9836.000000\n",
       "49     volkswagen  convertible  11595.000000\n",
       "50     volkswagen    hatchback   9980.000000\n",
       "51     volkswagen        sedan   9673.888889\n",
       "52     volkswagen        wagon  12290.000000\n",
       "53          volvo        sedan  18726.875000\n",
       "54          volvo        wagon  16293.333333"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_price2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> we could use the .pivot_table() method to replicate the same effect we have in an excel spread sheet and it makes for grouped data to be more readable</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "pivot=average_price.pivot_table(index=['make'],columns=['body-style'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
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       "      <th>convertible</th>\n",
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       "      <th>hatchback</th>\n",
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       "      <th>wagon</th>\n",
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       "    <tr>\n",
       "      <th>make</th>\n",
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       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>14997.5</td>\n",
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       "      <td>18920.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>bmw</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>26118.750000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>chevrolet</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5723.000000</td>\n",
       "      <td>6575.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>dodge</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7819.800000</td>\n",
       "      <td>7619.666667</td>\n",
       "      <td>8921.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>honda</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7054.428571</td>\n",
       "      <td>9945.000000</td>\n",
       "      <td>7295.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>isuzu</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>11048.000000</td>\n",
       "      <td>6785.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>jaguar</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>34600.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mazda</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10085.000000</td>\n",
       "      <td>11464.142857</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mercedes-benz</td>\n",
       "      <td>35056.0</td>\n",
       "      <td>36788.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>33074.000000</td>\n",
       "      <td>28248.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mercury</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>16503.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mitsubishi</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9597.888889</td>\n",
       "      <td>8434.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>nissan</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8249.000000</td>\n",
       "      <td>14409.000000</td>\n",
       "      <td>8604.555556</td>\n",
       "      <td>9915.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>peugot</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>15758.571429</td>\n",
       "      <td>15017.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>plymouth</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8130.500000</td>\n",
       "      <td>7150.500000</td>\n",
       "      <td>8921.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>porsche</td>\n",
       "      <td>37028.0</td>\n",
       "      <td>33278.000000</td>\n",
       "      <td>22018.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>renault</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9895.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9295.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>saab</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>15013.333333</td>\n",
       "      <td>15433.333333</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>subaru</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6591.333333</td>\n",
       "      <td>9070.600000</td>\n",
       "      <td>9342.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>toyota</td>\n",
       "      <td>17669.0</td>\n",
       "      <td>9762.333333</td>\n",
       "      <td>9616.000000</td>\n",
       "      <td>9542.200000</td>\n",
       "      <td>9836.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>volkswagen</td>\n",
       "      <td>11595.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9980.000000</td>\n",
       "      <td>9673.888889</td>\n",
       "      <td>12290.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>volvo</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>18726.875000</td>\n",
       "      <td>16293.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    price                                            \\\n",
       "body-style    convertible       hardtop     hatchback         sedan   \n",
       "make                                                                  \n",
       "alfa-romero       14997.5      0.000000  16500.000000      0.000000   \n",
       "audi                  0.0      0.000000      0.000000  17647.000000   \n",
       "bmw                   0.0      0.000000      0.000000  26118.750000   \n",
       "chevrolet             0.0      0.000000   5723.000000   6575.000000   \n",
       "dodge                 0.0      0.000000   7819.800000   7619.666667   \n",
       "honda                 0.0      0.000000   7054.428571   9945.000000   \n",
       "isuzu                 0.0      0.000000  11048.000000   6785.000000   \n",
       "jaguar                0.0      0.000000      0.000000  34600.000000   \n",
       "mazda                 0.0      0.000000  10085.000000  11464.142857   \n",
       "mercedes-benz     35056.0  36788.000000      0.000000  33074.000000   \n",
       "mercury               0.0      0.000000  16503.000000      0.000000   \n",
       "mitsubishi            0.0      0.000000   9597.888889   8434.000000   \n",
       "nissan                0.0   8249.000000  14409.000000   8604.555556   \n",
       "peugot                0.0      0.000000      0.000000  15758.571429   \n",
       "plymouth              0.0      0.000000   8130.500000   7150.500000   \n",
       "porsche           37028.0  33278.000000  22018.000000      0.000000   \n",
       "renault               0.0      0.000000   9895.000000      0.000000   \n",
       "saab                  0.0      0.000000  15013.333333  15433.333333   \n",
       "subaru                0.0      0.000000   6591.333333   9070.600000   \n",
       "toyota            17669.0   9762.333333   9616.000000   9542.200000   \n",
       "volkswagen        11595.0      0.000000   9980.000000   9673.888889   \n",
       "volvo                 0.0      0.000000      0.000000  18726.875000   \n",
       "\n",
       "                             \n",
       "body-style            wagon  \n",
       "make                         \n",
       "alfa-romero        0.000000  \n",
       "audi           18920.000000  \n",
       "bmw                0.000000  \n",
       "chevrolet          0.000000  \n",
       "dodge           8921.000000  \n",
       "honda           7295.000000  \n",
       "isuzu              0.000000  \n",
       "jaguar             0.000000  \n",
       "mazda              0.000000  \n",
       "mercedes-benz  28248.000000  \n",
       "mercury            0.000000  \n",
       "mitsubishi         0.000000  \n",
       "nissan          9915.666667  \n",
       "peugot         15017.500000  \n",
       "plymouth        8921.000000  \n",
       "porsche            0.000000  \n",
       "renault         9295.000000  \n",
       "saab               0.000000  \n",
       "subaru          9342.000000  \n",
       "toyota          9836.000000  \n",
       "volkswagen     12290.000000  \n",
       "volvo          16293.333333  "
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to replace all the nan values with zero we can use .fillna()\n",
    "pivot.fillna(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> To get a pictorial representation of how what our data is saying, we are going to plot a heat map relating how the make of the car with the bodystyle impacts price</p>. We can do this by simply creating a heat map.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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": [
    "fig, ax = plt.subplots()\n",
    "im = ax.pcolor(pivot, cmap='RdBu')\n",
    "\n",
    "#label names\n",
    "# we use the .levels[1] because we not have  hierarichal columns at level 0(price) AND 1(body-style)\n",
    "row_labels = pivot.columns.levels[1]\n",
    "col_labels = pivot.index\n",
    "\n",
    "#move ticks and labels to the center\n",
    "ax.set_xticks(np.arange(pivot.shape[1]) + 0.5, minor=False)\n",
    "ax.set_yticks(np.arange(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": [
    "### CORRELATION AND CAUSATION"
   ]
  },
  {
   "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": 84,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": 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>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>0.075810</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>0.217300</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>0.371178</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>0.579795</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>0.615056</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>-0.087001</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>0.757981</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>0.822668</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>0.566903</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>0.098322</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>-0.214489</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>0.075810</td>\n",
       "      <td>0.217300</td>\n",
       "      <td>0.371178</td>\n",
       "      <td>0.579795</td>\n",
       "      <td>0.615056</td>\n",
       "      <td>-0.087001</td>\n",
       "      <td>0.757981</td>\n",
       "      <td>0.822668</td>\n",
       "      <td>0.566903</td>\n",
       "      <td>0.098322</td>\n",
       "      <td>-0.214489</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107884</td>\n",
       "      <td>-0.822192</td>\n",
       "      <td>-0.804579</td>\n",
       "      <td>0.809607</td>\n",
       "      <td>0.889482</td>\n",
       "      <td>-0.169030</td>\n",
       "      <td>0.169030</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>0.107884</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>-0.822192</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>-0.804579</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>0.809607</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>0.889482</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>-0.169030</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>0.169030</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          0.075810           0.217300    0.371178  0.579795   \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         0.615056 -0.087001     0.757981     0.822668  0.566903   \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    0.075810  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217300  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371178 -0.360305   \n",
       "length             0.124139           0.159733    0.579795 -0.285970   \n",
       "width              0.188829           0.189867    0.615056 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087001 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757981 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822668 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566903 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098322 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214489 -0.435780   \n",
       "horsepower         0.098322          -0.214489    1.000000  0.107884   \n",
       "peak-rpm          -0.065713          -0.435780    0.107884  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822192 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804579 -0.058598   \n",
       "price              0.082310           0.071107    0.809607 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889482  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169030 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169030  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        -0.822192    -0.804579  0.809607      0.889482 -0.169030   \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         0.169030  \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": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#like we have seen before\n",
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>symboling</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.483960</td>\n",
       "      <td>-0.542030</td>\n",
       "      <td>-0.404203</td>\n",
       "      <td>-0.260553</td>\n",
       "      <td>-0.529907</td>\n",
       "      <td>-0.260517</td>\n",
       "      <td>-0.181819</td>\n",
       "      <td>-0.180029</td>\n",
       "      <td>-0.011853</td>\n",
       "      <td>0.020986</td>\n",
       "      <td>-0.004021</td>\n",
       "      <td>0.290138</td>\n",
       "      <td>-0.021918</td>\n",
       "      <td>0.050444</td>\n",
       "      <td>-0.142683</td>\n",
       "      <td>0.021918</td>\n",
       "      <td>-0.211858</td>\n",
       "      <td>0.211858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>normalized-losses</td>\n",
       "      <td>0.483960</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.072600</td>\n",
       "      <td>0.045926</td>\n",
       "      <td>0.117695</td>\n",
       "      <td>-0.345880</td>\n",
       "      <td>0.123187</td>\n",
       "      <td>0.124089</td>\n",
       "      <td>-0.022405</td>\n",
       "      <td>0.108541</td>\n",
       "      <td>-0.067848</td>\n",
       "      <td>0.236603</td>\n",
       "      <td>0.241301</td>\n",
       "      <td>-0.258637</td>\n",
       "      <td>-0.209499</td>\n",
       "      <td>0.202034</td>\n",
       "      <td>0.258637</td>\n",
       "      <td>-0.096539</td>\n",
       "      <td>0.096539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>wheel-base</td>\n",
       "      <td>-0.542030</td>\n",
       "      <td>-0.072600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.913120</td>\n",
       "      <td>0.815524</td>\n",
       "      <td>0.641402</td>\n",
       "      <td>0.764638</td>\n",
       "      <td>0.645661</td>\n",
       "      <td>0.537537</td>\n",
       "      <td>0.218058</td>\n",
       "      <td>-0.119545</td>\n",
       "      <td>0.495114</td>\n",
       "      <td>-0.316128</td>\n",
       "      <td>-0.484472</td>\n",
       "      <td>-0.531121</td>\n",
       "      <td>0.681790</td>\n",
       "      <td>0.484472</td>\n",
       "      <td>0.277773</td>\n",
       "      <td>-0.277773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>length</td>\n",
       "      <td>-0.404203</td>\n",
       "      <td>0.045926</td>\n",
       "      <td>0.913120</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.889761</td>\n",
       "      <td>0.532213</td>\n",
       "      <td>0.889759</td>\n",
       "      <td>0.779691</td>\n",
       "      <td>0.639575</td>\n",
       "      <td>0.172721</td>\n",
       "      <td>-0.180277</td>\n",
       "      <td>0.660012</td>\n",
       "      <td>-0.271673</td>\n",
       "      <td>-0.661012</td>\n",
       "      <td>-0.688778</td>\n",
       "      <td>0.810331</td>\n",
       "      <td>0.661012</td>\n",
       "      <td>0.193300</td>\n",
       "      <td>-0.193300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>width</td>\n",
       "      <td>-0.260553</td>\n",
       "      <td>0.117695</td>\n",
       "      <td>0.815524</td>\n",
       "      <td>0.889761</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.370636</td>\n",
       "      <td>0.858624</td>\n",
       "      <td>0.762966</td>\n",
       "      <td>0.606621</td>\n",
       "      <td>0.237730</td>\n",
       "      <td>-0.138980</td>\n",
       "      <td>0.681364</td>\n",
       "      <td>-0.213543</td>\n",
       "      <td>-0.673376</td>\n",
       "      <td>-0.692498</td>\n",
       "      <td>0.812097</td>\n",
       "      <td>0.673376</td>\n",
       "      <td>0.236686</td>\n",
       "      <td>-0.236686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>height</td>\n",
       "      <td>-0.529907</td>\n",
       "      <td>-0.345880</td>\n",
       "      <td>0.641402</td>\n",
       "      <td>0.532213</td>\n",
       "      <td>0.370636</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.362877</td>\n",
       "      <td>0.208611</td>\n",
       "      <td>0.222777</td>\n",
       "      <td>-0.036640</td>\n",
       "      <td>0.008056</td>\n",
       "      <td>0.021625</td>\n",
       "      <td>-0.279633</td>\n",
       "      <td>-0.079883</td>\n",
       "      <td>-0.137731</td>\n",
       "      <td>0.263806</td>\n",
       "      <td>0.079883</td>\n",
       "      <td>0.295966</td>\n",
       "      <td>-0.295966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>curb-weight</td>\n",
       "      <td>-0.260517</td>\n",
       "      <td>0.123187</td>\n",
       "      <td>0.764638</td>\n",
       "      <td>0.889759</td>\n",
       "      <td>0.858624</td>\n",
       "      <td>0.362877</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.874364</td>\n",
       "      <td>0.702016</td>\n",
       "      <td>0.157342</td>\n",
       "      <td>-0.213276</td>\n",
       "      <td>0.804234</td>\n",
       "      <td>-0.247198</td>\n",
       "      <td>-0.805613</td>\n",
       "      <td>-0.830918</td>\n",
       "      <td>0.913767</td>\n",
       "      <td>0.805613</td>\n",
       "      <td>0.197509</td>\n",
       "      <td>-0.197509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>engine-size</td>\n",
       "      <td>-0.181819</td>\n",
       "      <td>0.124089</td>\n",
       "      <td>0.645661</td>\n",
       "      <td>0.779691</td>\n",
       "      <td>0.762966</td>\n",
       "      <td>0.208611</td>\n",
       "      <td>0.874364</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.697316</td>\n",
       "      <td>0.292904</td>\n",
       "      <td>-0.233197</td>\n",
       "      <td>0.818438</td>\n",
       "      <td>-0.282721</td>\n",
       "      <td>-0.722111</td>\n",
       "      <td>-0.716830</td>\n",
       "      <td>0.828417</td>\n",
       "      <td>0.722111</td>\n",
       "      <td>0.133217</td>\n",
       "      <td>-0.133217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>bore</td>\n",
       "      <td>-0.180029</td>\n",
       "      <td>-0.022405</td>\n",
       "      <td>0.537537</td>\n",
       "      <td>0.639575</td>\n",
       "      <td>0.606621</td>\n",
       "      <td>0.222777</td>\n",
       "      <td>0.702016</td>\n",
       "      <td>0.697316</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.083457</td>\n",
       "      <td>-0.169436</td>\n",
       "      <td>0.640574</td>\n",
       "      <td>-0.305171</td>\n",
       "      <td>-0.607415</td>\n",
       "      <td>-0.619292</td>\n",
       "      <td>0.645943</td>\n",
       "      <td>0.607415</td>\n",
       "      <td>0.044483</td>\n",
       "      <td>-0.044483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>stroke</td>\n",
       "      <td>-0.011853</td>\n",
       "      <td>0.108541</td>\n",
       "      <td>0.218058</td>\n",
       "      <td>0.172721</td>\n",
       "      <td>0.237730</td>\n",
       "      <td>-0.036640</td>\n",
       "      <td>0.157342</td>\n",
       "      <td>0.292904</td>\n",
       "      <td>-0.083457</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.053223</td>\n",
       "      <td>0.139188</td>\n",
       "      <td>-0.066993</td>\n",
       "      <td>-0.023552</td>\n",
       "      <td>-0.019877</td>\n",
       "      <td>0.117582</td>\n",
       "      <td>0.023552</td>\n",
       "      <td>0.320694</td>\n",
       "      <td>-0.320694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>compression-ratio</td>\n",
       "      <td>0.020986</td>\n",
       "      <td>-0.067848</td>\n",
       "      <td>-0.119545</td>\n",
       "      <td>-0.180277</td>\n",
       "      <td>-0.138980</td>\n",
       "      <td>0.008056</td>\n",
       "      <td>-0.213276</td>\n",
       "      <td>-0.233197</td>\n",
       "      <td>-0.169436</td>\n",
       "      <td>-0.053223</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.356395</td>\n",
       "      <td>-0.027306</td>\n",
       "      <td>0.475730</td>\n",
       "      <td>0.433590</td>\n",
       "      <td>-0.177579</td>\n",
       "      <td>-0.475730</td>\n",
       "      <td>0.522470</td>\n",
       "      <td>-0.522470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>horsepower</td>\n",
       "      <td>-0.004021</td>\n",
       "      <td>0.236603</td>\n",
       "      <td>0.495114</td>\n",
       "      <td>0.660012</td>\n",
       "      <td>0.681364</td>\n",
       "      <td>0.021625</td>\n",
       "      <td>0.804234</td>\n",
       "      <td>0.818438</td>\n",
       "      <td>0.640574</td>\n",
       "      <td>0.139188</td>\n",
       "      <td>-0.356395</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.102580</td>\n",
       "      <td>-0.911326</td>\n",
       "      <td>-0.885853</td>\n",
       "      <td>0.849142</td>\n",
       "      <td>0.911326</td>\n",
       "      <td>-0.163112</td>\n",
       "      <td>0.163112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>peak-rpm</td>\n",
       "      <td>0.290138</td>\n",
       "      <td>0.241301</td>\n",
       "      <td>-0.316128</td>\n",
       "      <td>-0.271673</td>\n",
       "      <td>-0.213543</td>\n",
       "      <td>-0.279633</td>\n",
       "      <td>-0.247198</td>\n",
       "      <td>-0.282721</td>\n",
       "      <td>-0.305171</td>\n",
       "      <td>-0.066993</td>\n",
       "      <td>-0.027306</td>\n",
       "      <td>0.102580</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.129449</td>\n",
       "      <td>-0.057912</td>\n",
       "      <td>-0.081912</td>\n",
       "      <td>0.129449</td>\n",
       "      <td>-0.457657</td>\n",
       "      <td>0.457657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>city-mpg</td>\n",
       "      <td>-0.021918</td>\n",
       "      <td>-0.258637</td>\n",
       "      <td>-0.484472</td>\n",
       "      <td>-0.661012</td>\n",
       "      <td>-0.673376</td>\n",
       "      <td>-0.079883</td>\n",
       "      <td>-0.805613</td>\n",
       "      <td>-0.722111</td>\n",
       "      <td>-0.607415</td>\n",
       "      <td>-0.023552</td>\n",
       "      <td>0.475730</td>\n",
       "      <td>-0.911326</td>\n",
       "      <td>-0.129449</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.968626</td>\n",
       "      <td>-0.831284</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.240686</td>\n",
       "      <td>-0.240686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>highway-mpg</td>\n",
       "      <td>0.050444</td>\n",
       "      <td>-0.209499</td>\n",
       "      <td>-0.531121</td>\n",
       "      <td>-0.688778</td>\n",
       "      <td>-0.692498</td>\n",
       "      <td>-0.137731</td>\n",
       "      <td>-0.830918</td>\n",
       "      <td>-0.716830</td>\n",
       "      <td>-0.619292</td>\n",
       "      <td>-0.019877</td>\n",
       "      <td>0.433590</td>\n",
       "      <td>-0.885853</td>\n",
       "      <td>-0.057912</td>\n",
       "      <td>0.968626</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.827265</td>\n",
       "      <td>-0.968626</td>\n",
       "      <td>0.162332</td>\n",
       "      <td>-0.162332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>-0.142683</td>\n",
       "      <td>0.202034</td>\n",
       "      <td>0.681790</td>\n",
       "      <td>0.810331</td>\n",
       "      <td>0.812097</td>\n",
       "      <td>0.263806</td>\n",
       "      <td>0.913767</td>\n",
       "      <td>0.828417</td>\n",
       "      <td>0.645943</td>\n",
       "      <td>0.117582</td>\n",
       "      <td>-0.177579</td>\n",
       "      <td>0.849142</td>\n",
       "      <td>-0.081912</td>\n",
       "      <td>-0.831284</td>\n",
       "      <td>-0.827265</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.831284</td>\n",
       "      <td>0.144657</td>\n",
       "      <td>-0.144657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>city-L/100km</td>\n",
       "      <td>0.021918</td>\n",
       "      <td>0.258637</td>\n",
       "      <td>0.484472</td>\n",
       "      <td>0.661012</td>\n",
       "      <td>0.673376</td>\n",
       "      <td>0.079883</td>\n",
       "      <td>0.805613</td>\n",
       "      <td>0.722111</td>\n",
       "      <td>0.607415</td>\n",
       "      <td>0.023552</td>\n",
       "      <td>-0.475730</td>\n",
       "      <td>0.911326</td>\n",
       "      <td>0.129449</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>-0.968626</td>\n",
       "      <td>0.831284</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.240686</td>\n",
       "      <td>0.240686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>diesel</td>\n",
       "      <td>-0.211858</td>\n",
       "      <td>-0.096539</td>\n",
       "      <td>0.277773</td>\n",
       "      <td>0.193300</td>\n",
       "      <td>0.236686</td>\n",
       "      <td>0.295966</td>\n",
       "      <td>0.197509</td>\n",
       "      <td>0.133217</td>\n",
       "      <td>0.044483</td>\n",
       "      <td>0.320694</td>\n",
       "      <td>0.522470</td>\n",
       "      <td>-0.163112</td>\n",
       "      <td>-0.457657</td>\n",
       "      <td>0.240686</td>\n",
       "      <td>0.162332</td>\n",
       "      <td>0.144657</td>\n",
       "      <td>-0.240686</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>gas</td>\n",
       "      <td>0.211858</td>\n",
       "      <td>0.096539</td>\n",
       "      <td>-0.277773</td>\n",
       "      <td>-0.193300</td>\n",
       "      <td>-0.236686</td>\n",
       "      <td>-0.295966</td>\n",
       "      <td>-0.197509</td>\n",
       "      <td>-0.133217</td>\n",
       "      <td>-0.044483</td>\n",
       "      <td>-0.320694</td>\n",
       "      <td>-0.522470</td>\n",
       "      <td>0.163112</td>\n",
       "      <td>0.457657</td>\n",
       "      <td>-0.240686</td>\n",
       "      <td>-0.162332</td>\n",
       "      <td>-0.144657</td>\n",
       "      <td>0.240686</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           0.483960   -0.542030 -0.404203   \n",
       "normalized-losses   0.483960           1.000000   -0.072600  0.045926   \n",
       "wheel-base         -0.542030          -0.072600    1.000000  0.913120   \n",
       "length             -0.404203           0.045926    0.913120  1.000000   \n",
       "width              -0.260553           0.117695    0.815524  0.889761   \n",
       "height             -0.529907          -0.345880    0.641402  0.532213   \n",
       "curb-weight        -0.260517           0.123187    0.764638  0.889759   \n",
       "engine-size        -0.181819           0.124089    0.645661  0.779691   \n",
       "bore               -0.180029          -0.022405    0.537537  0.639575   \n",
       "stroke             -0.011853           0.108541    0.218058  0.172721   \n",
       "compression-ratio   0.020986          -0.067848   -0.119545 -0.180277   \n",
       "horsepower         -0.004021           0.236603    0.495114  0.660012   \n",
       "peak-rpm            0.290138           0.241301   -0.316128 -0.271673   \n",
       "city-mpg           -0.021918          -0.258637   -0.484472 -0.661012   \n",
       "highway-mpg         0.050444          -0.209499   -0.531121 -0.688778   \n",
       "price              -0.142683           0.202034    0.681790  0.810331   \n",
       "city-L/100km        0.021918           0.258637    0.484472  0.661012   \n",
       "diesel             -0.211858          -0.096539    0.277773  0.193300   \n",
       "gas                 0.211858           0.096539   -0.277773 -0.193300   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.260553 -0.529907    -0.260517    -0.181819 -0.180029   \n",
       "normalized-losses  0.117695 -0.345880     0.123187     0.124089 -0.022405   \n",
       "wheel-base         0.815524  0.641402     0.764638     0.645661  0.537537   \n",
       "length             0.889761  0.532213     0.889759     0.779691  0.639575   \n",
       "width              1.000000  0.370636     0.858624     0.762966  0.606621   \n",
       "height             0.370636  1.000000     0.362877     0.208611  0.222777   \n",
       "curb-weight        0.858624  0.362877     1.000000     0.874364  0.702016   \n",
       "engine-size        0.762966  0.208611     0.874364     1.000000  0.697316   \n",
       "bore               0.606621  0.222777     0.702016     0.697316  1.000000   \n",
       "stroke             0.237730 -0.036640     0.157342     0.292904 -0.083457   \n",
       "compression-ratio -0.138980  0.008056    -0.213276    -0.233197 -0.169436   \n",
       "horsepower         0.681364  0.021625     0.804234     0.818438  0.640574   \n",
       "peak-rpm          -0.213543 -0.279633    -0.247198    -0.282721 -0.305171   \n",
       "city-mpg          -0.673376 -0.079883    -0.805613    -0.722111 -0.607415   \n",
       "highway-mpg       -0.692498 -0.137731    -0.830918    -0.716830 -0.619292   \n",
       "price              0.812097  0.263806     0.913767     0.828417  0.645943   \n",
       "city-L/100km       0.673376  0.079883     0.805613     0.722111  0.607415   \n",
       "diesel             0.236686  0.295966     0.197509     0.133217  0.044483   \n",
       "gas               -0.236686 -0.295966    -0.197509    -0.133217 -0.044483   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.011853           0.020986   -0.004021  0.290138   \n",
       "normalized-losses  0.108541          -0.067848    0.236603  0.241301   \n",
       "wheel-base         0.218058          -0.119545    0.495114 -0.316128   \n",
       "length             0.172721          -0.180277    0.660012 -0.271673   \n",
       "width              0.237730          -0.138980    0.681364 -0.213543   \n",
       "height            -0.036640           0.008056    0.021625 -0.279633   \n",
       "curb-weight        0.157342          -0.213276    0.804234 -0.247198   \n",
       "engine-size        0.292904          -0.233197    0.818438 -0.282721   \n",
       "bore              -0.083457          -0.169436    0.640574 -0.305171   \n",
       "stroke             1.000000          -0.053223    0.139188 -0.066993   \n",
       "compression-ratio -0.053223           1.000000   -0.356395 -0.027306   \n",
       "horsepower         0.139188          -0.356395    1.000000  0.102580   \n",
       "peak-rpm          -0.066993          -0.027306    0.102580  1.000000   \n",
       "city-mpg          -0.023552           0.475730   -0.911326 -0.129449   \n",
       "highway-mpg       -0.019877           0.433590   -0.885853 -0.057912   \n",
       "price              0.117582          -0.177579    0.849142 -0.081912   \n",
       "city-L/100km       0.023552          -0.475730    0.911326  0.129449   \n",
       "diesel             0.320694           0.522470   -0.163112 -0.457657   \n",
       "gas               -0.320694          -0.522470    0.163112  0.457657   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.021918     0.050444 -0.142683      0.021918 -0.211858   \n",
       "normalized-losses -0.258637    -0.209499  0.202034      0.258637 -0.096539   \n",
       "wheel-base        -0.484472    -0.531121  0.681790      0.484472  0.277773   \n",
       "length            -0.661012    -0.688778  0.810331      0.661012  0.193300   \n",
       "width             -0.673376    -0.692498  0.812097      0.673376  0.236686   \n",
       "height            -0.079883    -0.137731  0.263806      0.079883  0.295966   \n",
       "curb-weight       -0.805613    -0.830918  0.913767      0.805613  0.197509   \n",
       "engine-size       -0.722111    -0.716830  0.828417      0.722111  0.133217   \n",
       "bore              -0.607415    -0.619292  0.645943      0.607415  0.044483   \n",
       "stroke            -0.023552    -0.019877  0.117582      0.023552  0.320694   \n",
       "compression-ratio  0.475730     0.433590 -0.177579     -0.475730  0.522470   \n",
       "horsepower        -0.911326    -0.885853  0.849142      0.911326 -0.163112   \n",
       "peak-rpm          -0.129449    -0.057912 -0.081912      0.129449 -0.457657   \n",
       "city-mpg           1.000000     0.968626 -0.831284     -1.000000  0.240686   \n",
       "highway-mpg        0.968626     1.000000 -0.827265     -0.968626  0.162332   \n",
       "price             -0.831284    -0.827265  1.000000      0.831284  0.144657   \n",
       "city-L/100km      -1.000000    -0.968626  0.831284      1.000000 -0.240686   \n",
       "diesel             0.240686     0.162332  0.144657     -0.240686  1.000000   \n",
       "gas               -0.240686    -0.162332 -0.144657      0.240686 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.211858  \n",
       "normalized-losses  0.096539  \n",
       "wheel-base        -0.277773  \n",
       "length            -0.193300  \n",
       "width             -0.236686  \n",
       "height            -0.295966  \n",
       "curb-weight       -0.197509  \n",
       "engine-size       -0.133217  \n",
       "bore              -0.044483  \n",
       "stroke            -0.320694  \n",
       "compression-ratio -0.522470  \n",
       "horsepower         0.163112  \n",
       "peak-rpm           0.457657  \n",
       "city-mpg          -0.240686  \n",
       "highway-mpg       -0.162332  \n",
       "price             -0.144657  \n",
       "city-L/100km       0.240686  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can calcuate correlation also by using he spearmans method\n",
    "df.corr(method='spearman')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> One of the difference between the Pearson correlation and the Spearman correleation is that the Pearson is most appropriate for measurements taken fronm an interval scale, while the Spearman is more appropirate for measurements taken from ordinal scales.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "# to work with the P-value lets imports the stat mo\n",
    "\n",
    "from scipy import stats"
   ]
  },
  {
   "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": [
    "<p>Like before we are going to calculate for correlation using only contionous variables\n",
    "we are going to determine the correlation the following features have with price</p>\n",
    "<ul>\n",
    "<li>Wheel Base</li> \n",
    "<li>Horse Power</li> \n",
    "<li> Width</li> \n",
    "<li>Curb Weight </li> \n",
    "<li> Engine Size</li> \n",
    "<li> City mpg</li> \n",
    "<li> Highway mpg</li>    \n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5846418222655083  with a P-value of P = 8.076488270732873e-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": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8096068016571052  with a P-value of P =  6.273536270650862e-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": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.6906283804483644  with a P-value of P =  8.016477466158188e-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": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522665  with a P-value of P = 9.200335510484131e-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": [
    "<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": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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": [
    "## ANOVA (ANALYSIS OF VARIANCE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Analysis of Variance (ANOVA) procedures are used to compare the means of several\n",
    "populations. For example Is there a difference in the mean amount spent on vacations for the three minority groups: Asians,\n",
    "Hispanics, and African Americans? or is there a difference in the mean amount of succesful surgeries between male and female surgeons\n",
    "For our own scenario we will be calculating ANOVA for groups contained in the column \"Drive-wheel\" to see if there is a signigfant difference between the groups when related to price </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>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": [
    "### Drive-Wheels"
   ]
  },
  {
   "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": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pandas.core.groupby.generic.DataFrameGroupBy object at 0x000002CD4FC5ACC8>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wheels=df[['drive-wheels','price','make']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <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": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anova=wheels[['drive-wheels','price']].groupby(['drive-wheels'])\n",
    "anova.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": 120,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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(anova.get_group('fwd')['price'], anova.get_group('rwd')['price'], anova.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": [
    "<p> Let us then compute the anova seperately for each group</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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(anova.get_group('fwd')['price'], anova.get_group('rwd')['price'])  \n",
    " \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
     ]
    }
   ],
   "source": [
    "f_val, p_val = stats.f_oneway(anova.get_group('4wd')['price'], anova.get_group('fwd')['price'])  \n",
    "   \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "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(anova.get_group('4wd')['price'], anova.get_group('rwd')['price'])  \n",
    "   \n",
    "print( \"ANOVA results: F=\", f_val, \", P =\", p_val)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> To get a better understanding of ANOVA i will provide a link below to a Youtube tutorial video</p>\n",
    "<a href='https://www.youtube.com/watch?v=-yQb_ZJnFXw'> <b>Anova tutorial</b><a>"
   ]
  },
  {
   "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": [
    "<p>I hope you found this notebook useful. If you have any comments or questions please feel free to </p>  <a href='https://www.linkedin.com/in/adediwura/'> connect with me on Linkedin</a></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
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