AnaJaved-L04-AutoHypothesis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lesson 4 Assignment - Automobile Price Hypothesis Testing\n",
    "## Author - Ana Javed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Instructions\n",
    "Test hypotheses for the price of automobiles:\n",
    "\n",
    "1. Compare and test the normality of the distributions of **price** and **log price**. <br/>\n",
    "Use both a graphical method and a formal test. Hint: remember these relationships will always be approximate.\n",
    "\n",
    "2. Test significance of **price (or log price)** stratified by \n",
    "a) **fuel type**, b) **aspiration**, and c) **rear vs. front wheel drive**. <br />Use both graphical methods and the formal test.\n",
    "\n",
    "3. Apply ANOVA and Tukey's HSD test to the auto price data to compare the **price (or log price** if closer to a normal distribution) of autos stratified by **body style**.\n",
    "\n",
    "4. Graphically explore the differences between the price conditioned by the categories of each variable. <br/>\n",
    "Hint: Make sure you have enough data for each category and drop categories with insufficient data.\n",
    "\n",
    "5. Use standard ANOVA and Tukey HSD to test the differences of these groups.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note: \n",
    "Please clearly outline the results of these tests with markdown text. Be sure your discussion includes narrative for your figures and tables so it is clear to the reader the importance of each bit of evidence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries & packages required \n",
    "import pandas as pd\n",
    "import numpy as np \n",
    "from scipy import stats\n",
    "import scipy.stats as ss\n",
    "import statsmodels.stats.weightstats as ws\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from statistics import mean\n",
    "import numpy.random as nr\n",
    "from statsmodels.stats.multicomp import pairwise_tukeyhsd \n",
    "\n",
    "# Declaring inline visualizations \n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cleaned up Dataset location\n",
    "fileName = \"https://library.startlearninglabs.uw.edu/DATASCI410/Datasets/Automobile%20price%20data%20_Raw_.csv\"\n",
    "\n",
    "# Reading file into a Pandas Dataframe \n",
    "Auto = pd.read_csv(fileName)\n",
    "\n",
    "### Some Exploratory Data Analysis \n",
    "# print(Auto.describe()) # Summary Statistics\n",
    "\n",
    "# print(Auto.shape) # DF dimensions\n",
    "\n",
    "# Auto.head(5) # Top 5 rows\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Compare and test Normality the distributions of price and log price Use both a graphical method and a formal test. Hint: Remember these relationships will always be approximate. Use the distribution that fits best for the rest of this exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#### Creating New Column: Log Price\n",
    "\n",
    "# Converting Unknown \"?\" Values in Price Column \n",
    "Auto.loc[:,'price'] = pd.to_numeric(Auto.loc[:,'price'], errors='coerce')    \n",
    "HasNan1 = np.isnan(Auto.loc[:,'price'])\n",
    "Auto.loc[HasNan1,'price'] = np.nanmedian(Auto.loc[:,'price'])\n",
    "\n",
    "## Creating New Log Price Column from Price Column\n",
    "Auto.loc[:, \"LogPrice\"] = np.log(Auto.loc[:, \"price\"])\n",
    "\n",
    "#### Verifying Output looks correct\n",
    "# print(Auto.loc[:, \"price\"].value_counts()) \n",
    "# print(Auto.loc[:, \"LogPrice\"].value_counts()) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Value')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Creating a Histogram of Price and LogPrice Distributions \n",
    "\n",
    "plt.figure(figsize=(10, 9))\n",
    "\n",
    "x = np.linspace(min(Auto.loc[:,'price']), max(Auto.loc[:,'price']), 100) #start, stop, num of samples \n",
    "x1 = np.linspace( min(Auto.loc[:,'LogPrice']), max(Auto.loc[:,'LogPrice']), 100) #start, stop, num of samples \n",
    "\n",
    "#### Testing Normality of Price Column \n",
    "plt.subplot(2, 2, 1) # The first plot # Rows, Column, Index \n",
    "plt.hist(Auto.loc[:,'price'], bins = \"auto\", density=True)\n",
    "plt.axvline(mean(Auto.loc[:,'price']), color = 'red')\n",
    "\n",
    "plt.plot(x, \n",
    "         norm.pdf(x, mean(Auto.loc[:,'price']), \n",
    "                  np.std(Auto.loc[:,'price'])), \n",
    "         color = 'black')\n",
    "\n",
    "plt.ylabel('Price Frequency')\n",
    "plt.xlabel('Value')\n",
    "\n",
    "\n",
    "#### Testing Normality of Price Column \n",
    "plt.subplot(2,2, 2) # The next plot # nrows=1, ncols=1,\n",
    "plt.hist(Auto.loc[:,'LogPrice'], bins = \"auto\", density=True)\n",
    "plt.axvline(mean(Auto.loc[:,'LogPrice']), color = 'Orange')\n",
    "\n",
    "plt.plot(x1, \n",
    "         norm.pdf(x1, mean(Auto.loc[:,'LogPrice']), \n",
    "                      np.std(Auto.loc[:,'LogPrice'])), \n",
    "         color = 'black')\n",
    "\n",
    "plt.ylabel('Log Price Frequency')\n",
    "plt.xlabel('Value')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histogram Plot Explanation\n",
    "\n",
    "The left plot is a histogram the Automobile Price column. As we see, the mean is around 13150 and the data appears to be skewed to the right of the mean. The black line is a normal curve laid ontop of the distribution. It is cutoff on the left side. \n",
    "\n",
    "The right plot is a histogram the Automobile LogPrice column. As we see, the mean is around 9.3 and the data also appears to be skewed to the right of the mean. This distribution appears closer to a normal distribution, since the normal curve laid ontop of it is nearly a complete bell curve - but let's verify with statistics from conducting a t-test. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Creating a Q-Q Plot for a Normal Distribution\n",
    "\n",
    "## Function to Create Q-Q Plot \n",
    "def qq_plot(vec1, vec2):\n",
    "    import matplotlib.pyplot as plt\n",
    "    import scipy.stats as ss\n",
    "    \n",
    "    plt.figure(figsize=(10, 8)).gca() # define axis\n",
    "    \n",
    "    ax1 = plt.subplot(221) ## setup the left subplot\n",
    "    ss.probplot(vec1, plot = ax1, dist ='norm') ## Plot the left subplot\n",
    "    ax1.set_title(\"Probplot for Price Column\")\n",
    "    \n",
    "    ax1 = plt.subplot(222) ## Set up the right subplot\n",
    "    ss.probplot(vec2, plot = ax1, dist = 'norm') ## Plot the right subplot\n",
    "    ax1.set_title(\"Probplot for LogPrice Column\")\n",
    "    \n",
    "# Passing Price and LogPrice Columns to the Q-Q Plot Function\n",
    "qq_plot(Auto.loc[:, 'price'], Auto.loc[:, 'LogPrice'])    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these q-q plots, we visually see a greater distance at the top and bottom for Price column. The LogPrice column also has this curvature, but it is not as large. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---- Price Column (After Normalizing): ----\n",
      "KS-statistic = 0.160931935149899\n",
      "P-value = 4.174734746658962e-05\n",
      "\n",
      "\n",
      "---- LogPrice Column (After Normalizing): ----\n",
      "KS-statistic = 0.09982085789407613\n",
      "P-value = 0.031318982399451856\n"
     ]
    }
   ],
   "source": [
    "### Calculating the KS Statistics to exactly Measure the Maximum Distance \n",
    "\n",
    "def ks_test(dat, dist = 'norm'):  # KS Test Function \n",
    "    from scipy.stats import kstest \n",
    "    from sklearn.preprocessing import scale\n",
    "    \n",
    "    ks_statisic, pvalue = kstest(scale(dat), dist)  # Scaling/Normalizing Variable \n",
    "    print('KS-statistic = ' + str(ks_statisic))\n",
    "    print('P-value = ' + str(pvalue))\n",
    "  \n",
    "\n",
    "print(\"---- Price Column (After Normalizing): ----\")\n",
    "ks_test(Auto.loc[:, 'price'])  \n",
    "print(\"\\n\")\n",
    "\n",
    "print(\"---- LogPrice Column (After Normalizing): ----\")\n",
    "ks_test(Auto.loc[:, 'LogPrice'])  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KS Statistic & P-value Analysis\n",
    "\n",
    "For the Price column, we see that the KS statistic is small, and the P value is quite small. \n",
    "\n",
    "For the LogPrice column, we see that the KS statistic is smaller than the Price column, and the P value is small, but larger than the Price column's P value. \n",
    "\n",
    "When compared to each other (and assuming alpha = 0.05 or cutoff is 5%), each P-value is small enough to reject the null hypothesis that these distributions are the same as a normal distribution. \n",
    "\n",
    "When comparing the KS-statistic, which measures the maximum distance between the two cumulative density functions, the Price column has a larger value than LogPrice column. This means that there is a bigger difference in the Price column, so LogPrice column is closer to a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Test significance of price (or log price) stratified by a) fuel type, b) aspiration, and c) rear vs. front wheel drive.  Use both graphical methods and the formal test. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Defining Functions to assist conducting the T-test and Plotting Results \n",
    "\n",
    "## Histogram Plot \n",
    "def hist_plot(vec, bins):\n",
    "    import matplotlib.pyplot as plt\n",
    "    from statistics import mean\n",
    "    plt.hist(vec, bins = bins)\n",
    "    plt.axvline(mean(vec), color = 'red')\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.xlabel('Value')\n",
    "    \n",
    "## Confidence Interval on Histogram \n",
    "def hist_mean_ci(vec, t_test, bins):\n",
    "    import matplotlib.pyplot as plt\n",
    "    from statistics import mean\n",
    "    upper = mean(vec) + t_test[5] - t_test[1]\n",
    "    lower = mean(vec) + t_test[4] - t_test[1]\n",
    "    plt.hist(vec, bins = bins)\n",
    "    plt.axvline(mean(vec), color = 'red')\n",
    "    plt.axvline(upper, color = 'red', linestyle='--')\n",
    "    plt.axvline(lower, color = 'red', linestyle='--')\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.xlabel('Value')\n",
    "    \n",
    "## Function to Plot T-Tests \n",
    "def plot_t(a, b, t_test, cols=['A', 'B'], nbins = 20):\n",
    "    import matplotlib.pyplot as plt\n",
    "    plt.figure(figsize=(7, 8))\n",
    "    minx = min([min(a), min(b)])\n",
    "    maxx = max([max(a), max(b)])\n",
    "    stepx = (maxx - minx)/(nbins + 1)\n",
    "    bins = [minx + i * stepx for i in range(nbins + 1)]\n",
    "    plt.subplot(2, 1, 1) # The first plot\n",
    "    hist_mean_ci(a, t_test, bins)\n",
    "    plt.title('Histogram of ' + cols[0] + ' and ' + cols[1])\n",
    "    plt.subplot(2, 1, 2) # The next plot\n",
    "    hist_plot(b, bins)\n",
    "    \n",
    "## Function for Non-paired T Tests\n",
    "def t_test(a, b, alpha, alternative='two-sided'):\n",
    "    from scipy import stats\n",
    "    import scipy.stats as ss\n",
    "    import pandas as pd\n",
    "    import statsmodels.stats.weightstats as ws\n",
    "    \n",
    "    diff = a.mean() - b.mean()\n",
    "\n",
    "    res = ss.ttest_ind(a, b, equal_var=False)\n",
    "      \n",
    "    means = ws.CompareMeans(ws.DescrStatsW(a), ws.DescrStatsW(b))\n",
    "    confint = means.tconfint_diff(alpha=alpha, alternative=alternative, usevar='unequal') \n",
    "    degfree = means.dof_satt()\n",
    "\n",
    "    index = ['DegFreedom', 'Difference', 'Statistic', 'PValue', 'Low95CI', 'High95CI']\n",
    "    return pd.Series([degfree, diff, res[0], res[1], confint[0], confint[1]], index = index)   \n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DegFreedom    23.423234\n",
      "Difference    -0.232111\n",
      "Statistic     -2.017983\n",
      "PValue         0.055188\n",
      "Low95CI       -0.469812\n",
      "High95CI       0.005591\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Paired T-Test LogPrice & Fuel-type\n",
    "\n",
    "# Examining the different groups:\n",
    "# print(Auto.loc[:, \"fuel-type\"].value_counts())\n",
    "    # gas       185\n",
    "    # diesel     20\n",
    "    \n",
    "# Separating the categories \n",
    "gas = Auto.loc[Auto.loc[:, 'fuel-type'] == 'gas', 'LogPrice']\n",
    "diesel = Auto.loc[Auto.loc[:, 'fuel-type'] == 'diesel', 'LogPrice']\n",
    "\n",
    "# Applying the t-test\n",
    "Fuel_type = t_test(gas, diesel, alpha = 0.05)\n",
    "print(Fuel_type)\n",
    "\n",
    "# Plotting results in a histogram \n",
    "plot_t(gas, diesel, Fuel_type, cols=[\"Gas\", \"Diesel\"]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DegFreedom    66.240183\n",
      "Difference    -0.326451\n",
      "Statistic     -4.416153\n",
      "PValue         0.000038\n",
      "Low95CI       -0.474032\n",
      "High95CI      -0.178871\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Paired T-Test LogPrice & Aspiration  + Historgram \n",
    "\n",
    "# Examining the different groups:\n",
    "# print(Auto.loc[:, \"aspiration\"].value_counts())\n",
    "#     # std      168\n",
    "#     # turbo     37\n",
    "\n",
    "# Separating the categories \n",
    "std = Auto.loc[Auto.loc[:, 'aspiration'] == 'std', 'LogPrice']\n",
    "turbo = Auto.loc[Auto.loc[:, 'aspiration'] == 'turbo', 'LogPrice']\n",
    "\n",
    "# Applying the t-test\n",
    "Aspiration_type = t_test(std, turbo, alpha = 0.05)\n",
    "print(Aspiration_type)\n",
    "\n",
    "# Plotting results in a histogram \n",
    "plot_t(std, turbo, Aspiration_type, cols=[\"Std\", \"Turbo\"]) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DegFreedom    1.240960e+02\n",
      "Difference   -7.075543e-01\n",
      "Statistic    -1.217148e+01\n",
      "PValue        6.500851e-23\n",
      "Low95CI      -8.226133e-01\n",
      "High95CI     -5.924954e-01\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Paired T-Test LogPrice & Drive-wheels  \n",
    "\n",
    "# Examining the different groups:\n",
    "# print(Auto.loc[:, \"drive-wheels\"].value_counts())\n",
    "    # fwd    120\n",
    "    # rwd     76\n",
    "    # 4wd      9\n",
    "    \n",
    "# Separating the categories \n",
    "fwd = Auto.loc[Auto.loc[:, 'drive-wheels'] == 'fwd', 'LogPrice']\n",
    "rwd = Auto.loc[Auto.loc[:, 'drive-wheels'] == 'rwd', 'LogPrice']\n",
    "\n",
    "# Applying the t-test\n",
    "Drive_Wheels_type = t_test(fwd, rwd, alpha = 0.05)\n",
    "print(Drive_Wheels_type)\n",
    "\n",
    "# Plotting results in a histogram \n",
    "plot_t(fwd, rwd, Drive_Wheels_type, cols=[\"Front Wheel\", \"Rear Wheel Drive\"]) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysis of the 3 T-tests conducted above:\n",
    "\n",
    "\n",
    "-- For Fuel Type, the t-test conducted on the gas and diesel groups showed a p-value of 0.055 which is larger than 0.05 cutoff, has a small t statistic, has a small difference in means, and the CI staddles 0. From this we cannot reject the null hypothesis. There is a good chance that the difference in price means between the groups is from random variation.\n",
    "\n",
    "\n",
    "-- For Aspiration type, the t-test conducted on the std and turbo groups showed a small p-value of 0.00004, a small difference in means, a large t-statistic, and a CI that did not contain 0. From this we can reject the null hypothesis (since p < alpha) and there is a good chance that the difference in price means between the groups is not from random fluctuation. \n",
    "\n",
    "\n",
    "\n",
    "-- For Drive Wheels, the t-test conducted on the front wheel and rear wheel drive groups showed a very small p value, a small T-statistic, a small difference in the means, and the CI does not straddle 0. From this we can reject the null hypothesis (p < alpha) and there is a good chance that the difference in price means between the groups is not due to random variation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Apply ANOVA and Tukey's HSD test to the auto price data to compare the price (or log price, if closer to a Normal distribution) of autos stratified by body style."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Box Plot of Different Body Style Prices')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### ANOVA & F-Statistic: LogPrice and Body Style\n",
    "\n",
    "# Examining the different groups in the Body Style Column\n",
    "# print(Auto.loc[:, \"body-style\"].value_counts())\n",
    "    # sedan          96\n",
    "    # hatchback      70\n",
    "    # wagon          25\n",
    "    # hardtop         8\n",
    "    # convertible     6\n",
    "    \n",
    "## Separating out the Categories to their own dataset \n",
    "sedan = Auto.loc[Auto.loc[:, 'body-style'] == 'sedan', 'LogPrice']\n",
    "hatchback = Auto.loc[Auto.loc[:, 'body-style'] == 'hatchback', 'LogPrice']\n",
    "wagon = Auto.loc[Auto.loc[:, 'body-style'] == 'wagon', 'LogPrice']\n",
    "hardtop = Auto.loc[Auto.loc[:, 'body-style'] == 'hardtop', 'LogPrice']\n",
    "convertible = Auto.loc[Auto.loc[:, 'body-style'] == 'convertible', 'LogPrice']\n",
    "\n",
    "## Quick Boxplot Visualization for the different categories \n",
    "\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.boxplot([sedan, hatchback, wagon, hardtop, convertible], \n",
    "            labels = [\"Sedan\", \"Hatchback\", \"Wagon\", \"Hardtop\", \"Convertible\"])\n",
    "\n",
    "plt.ylabel('Log Price')\n",
    "plt.xlabel('Body Style')\n",
    "plt.title('Box Plot of Different Body Style Prices')\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F statistic = 8.548650407843674\n",
      "P-value = 2.180028605224779e-06\n"
     ]
    }
   ],
   "source": [
    "## Calculating the F Statistic / ANOVA to determine if there is a statistically significant difference \n",
    "\n",
    "f_statistic, p_value = ss.f_oneway(sedan, hatchback, wagon, hardtop, convertible) \n",
    "\n",
    "print('F statistic = ' + str(f_statistic))\n",
    "print('P-value = ' + str(p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The F statistic is quite large and the p-value is very small. We can reject the null hypothesis that the 5 Body Style categories have the same mean or price. The probability of the differences being due to random chance is low. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Multiple Comparison of Means - Tukey HSD, FWER=0.05     \n",
      "============================================================\n",
      "   group1     group2  meandiff p-adj   lower   upper  reject\n",
      "------------------------------------------------------------\n",
      "convertible   hardtop  -0.0966    0.9  -0.787  0.5937  False\n",
      "convertible hatchback  -0.7596 0.0015 -1.3034 -0.2158   True\n",
      "convertible     sedan  -0.4561 0.1384  -0.994  0.0819  False\n",
      "convertible     wagon  -0.5399 0.0826  -1.121  0.0412  False\n",
      "    hardtop hatchback   -0.663 0.0016 -1.1401 -0.1859   True\n",
      "    hardtop     sedan  -0.3594 0.2227 -0.8298   0.111  False\n",
      "    hardtop     wagon  -0.4433 0.1335 -0.9625   0.076  False\n",
      "  hatchback     sedan   0.3035  0.001  0.1026  0.5045   True\n",
      "  hatchback     wagon   0.2197 0.2551 -0.0781  0.5176  False\n",
      "      sedan     wagon  -0.0838    0.9 -0.3709  0.2032  False\n",
      "------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "## Tukey HSD for Auto Body Styles \n",
    "body_styles = Auto.loc[:, [\"body-style\", \"LogPrice\"]]\n",
    "body_styles.columns = [\"bodystyle\", \"logprice\"]\n",
    "\n",
    "Tukey_HSD = pairwise_tukeyhsd(body_styles.logprice, body_styles.bodystyle)\n",
    "print(Tukey_HSD)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When examining the pairwise groups CI intervals, there are three pairs that are truly different from each other and do not have zero included in the upper and lower CI range. \n",
    "These groupings are: \n",
    "- convertible and hatchback\n",
    "- hardtop and hatchback\n",
    "- hatchback and sedan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Graphically explore the differences between the price conditioned (grouped) by the categories of each variable. If any of these relationships are statistically significant, are they large enough to be important to your client? Is this importance evident in your graphics?\n",
    "Hint: Make sure you have enough data for each category and drop categories with insufficient data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/anajaved/opt/miniconda3/lib/python3.8/site-packages/statsmodels/sandbox/stats/multicomp.py:775: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax1.set_yticklabels(np.insert(self.groupsunique.astype(str), 0, ''))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Remaining categorical columns that we haven't explored yet are: \n",
    "## 'symboling', 'make', 'num-of-doors', 'engine-location', 'fuel-system'. I conduct analysis\n",
    "## on all the columns above except engine-location, since it did not have enough \"front\" samples\n",
    "\n",
    "## Examining unique values in the column\n",
    "# print(Auto.loc[:, \"symboling\"].value_counts())\n",
    "    #  0    67\n",
    "    #  1    54\n",
    "    #  2    32\n",
    "    #  3    27\n",
    "    # -1    22\n",
    "    # -2     3\n",
    "    \n",
    "## Isolating the Columns needed \n",
    "Symboling = Auto.loc[:, [\"symboling\", \"LogPrice\"]]\n",
    "\n",
    "## Removing -2 group since low number of samples\n",
    "Symboling = Symboling[Symboling.symboling != -2]\n",
    "\n",
    "## Tukey Visualtion of the different Groups: \n",
    "Tukey_HSD = pairwise_tukeyhsd(Symboling.LogPrice, Symboling.symboling)\n",
    "# print(Tukey_HSD)\n",
    "Tukey_HSD.plot_simultaneous()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stratifying Symboling Analysis\n",
    "\n",
    "This visualization compares the different categories of symboling to the log price column in the data frame. According to this dataset's documentation, \"a value of +3 indicates that the auto is risky, -3 that it is probably pretty safe\". \n",
    "\n",
    "The means of the groups vary, indicated by the dot. Also the price ranges also vary for each category. The following group pairings are different from each other: \n",
    "- Group -1 and Group 1\n",
    "- Group -1 and Group 2\n",
    "\n",
    "- Group 0 and Group 1\n",
    "- Group 0 and Group 2\n",
    "\n",
    "- Group 1 and Group 3\n",
    "- Group 2 and Group 3\n",
    "\n",
    "These are a lot of groups that are different from each other, and they are all statistically significant since their adjusted p-score is under the 0.05 cutoff. I would suggest to explore these categories relationships to my clients since a relationship is present. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Examining unique values in the Make column\n",
    "# print(Auto.loc[:, \"make\"].value_counts())\n",
    "\n",
    "    # toyota           32\n",
    "    # nissan           18\n",
    "    # mazda            17\n",
    "    # mitsubishi       13\n",
    "    # honda            13\n",
    "    # subaru           12\n",
    "    # volkswagen       12\n",
    "    # peugot           11\n",
    "    # volvo            11\n",
    "    # dodge             9\n",
    "    # bmw               8\n",
    "    # mercedes-benz     8\n",
    "    # audi              7\n",
    "    # plymouth          7\n",
    "    # saab              6\n",
    "    # porsche           5\n",
    "    # isuzu             4\n",
    "    # jaguar            3\n",
    "    # alfa-romero       3\n",
    "    # chevrolet         3\n",
    "    # renault           2\n",
    "    # mercury           1\n",
    "\n",
    "    \n",
    "## Isolating the Columns needed \n",
    "df = Auto.loc[:, [\"make\", \"LogPrice\"]]\n",
    "\n",
    "## Removing groups with low number of samples\n",
    "df = df[df.make != 'mercury']\n",
    "df = df[df.make != 'renault']\n",
    "df = df[df.make != 'chevrolet']\n",
    "df = df[df.make != 'alfa-romero']\n",
    "df = df[df.make != 'jaguar']\n",
    "df = df[df.make != 'isuzu']\n",
    "df = df[df.make != 'porsche']\n",
    "df = df[df.make != 'saab']\n",
    "\n",
    "## Tukey Visualtion of the different Groups: \n",
    "Tukey_HSD = pairwise_tukeyhsd(df.LogPrice, df.make)\n",
    "# print(Tukey_HSD)\n",
    "Tukey_HSD.plot_simultaneous()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stratifying Make Analysis \n",
    "\n",
    "There were multiple makes that had under 7 samples, so those 8 categories had been removed. From the table and graph, we can see that there are multiple groups that are significantly different from each other. They are:\n",
    "- Audi and Dodge\n",
    "- Audi and Honda\n",
    "- Audi and Mazda\n",
    "- Audi and mercedes-benz\n",
    "- Audi and mitsubishi\n",
    "- Audi and Nissan\n",
    "- Audi and plymouth\n",
    "- Audi and subaru\n",
    "- Audi and toyota\n",
    "- Audi and volkswagen\n",
    "- bmw and dodge\n",
    "- bmw and honda\n",
    "- bmw and mazda \n",
    "- bmw and mitsubishi\n",
    "- bmw and nissan \n",
    "- bmw and peugot \n",
    "- bmw and plymouth \n",
    "- bmw and subaru \n",
    "- bmw and toyota \n",
    "- bmw and volkswagen \n",
    "- dodge and mitsubishi \n",
    "- dodge and peugot \n",
    "- dodge and volkswagen\n",
    "- honda and mercedes-benz \n",
    "- honda and peugot\n",
    "- honda and volvo\n",
    "- mazda and mercedes-benz\n",
    "- mazda and peugot\n",
    "- mazda and volvo\n",
    "- mercedes-benz and mitsubishi\n",
    "- mercedes-benz and nissan\n",
    "- mercedes-benz and peugot\n",
    "- mercedes-benz and plymouth\n",
    "- mercedes-benz and subaru\n",
    "- mercedes-benz and toyota\n",
    "- mercedes-benz and volkswagen\n",
    "- mercedes-benz and volvo\n",
    "- mitsubishi and peugot\n",
    "- mitsubishi and volvo\n",
    "- nissan and peugot\n",
    "- nissan and volvo \n",
    "- peugot and plymouth\n",
    "- peugot and subaru\n",
    "- peugot and toyota\n",
    "- plymouth and volvo\n",
    "- subaru and volvo\n",
    "- toyota and volvo\n",
    "- volkswagen and volvo\n",
    "\n",
    "There is certainly a patter and trend which vehicles are more likely to be related than others. In the Tukey HSD plot it is apparent that there are groups of cars that are in the same price range of each other than other cars, indicating a correlation of automobile make and price. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjlYcrqrqgKp6wVpWBmBPNjMzk+np6eyzzz6Znp7OzMzMelcJWAOrGbk6IIlwBbATZmZmsmXLlszOzqa1ltnZ2WzZskXAgj1QtdZWtmHVm5Ick+RzST6Z5JTW2qlVdUqSK1prz6mq45Pcu7X2O1X135M8Z9z9ta21VyxV/saNG9uOHTt29jwAuti0adOalLt9+/Zcf/31N1t+u9vdLkceeeSaHPO0005bk3KBpKrOaq1tXGjdakauXpbk8621hyR5X5KfGJffI8nh4++PTPKRqnpokmcneViSI5M8t6p+ZIGKbamqHVW149JLL11FVQB2LwsFq6WWA7uvfXdyv48kOaGqDk/y2SQHVtXdkzw8yYsyjFid0lr7ZpJU1dszhLFPThbSWtuWZFsyjFztZF0Aulmr0Z7p6enMzs7ebPnU1JQRJtjD7NSnBVtrX0lyYJLHJflwhrD1tCTXtNauTlLdagiwB9i6dWs2bNhwk2UbNmzI1q1b16lGwFpZTbi6OskdJx7/a5ITcmO4esn4b8Zlx1bVhqraP8mTJtYB7HU2b96cbdu2ZWpqKlWVqampbNu2LZs3b17vqgGdrXhasLV2eVV9tKrOSfKeDGHpMa21C6pqNsldxmVprX2iql6X5GPj7q9trX1yoXIB9habN28WpmAvsOJPC641nxYEAHYXvT4tCADAMoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6EKwCAjoQrAICOhCsAgI6WDVdV9aKqOreqZnZFhQAAdmcrGbl6QZKjW2ubd/YgNTBKBrCOZmZmMj09nX322SfT09OZmfGeGdbCkoGnql6T5D5JTq2qF1fVO6rq7KraXlUPHrd5eVW9ZGKfc6pqevw5t6peneQTSe61licCwOJmZmayZcuWzM7OprWW2dnZbNmyRcCCNbDvUitba8+vqsclOSrJ7yX5ZGvt2Kr6ySSvT/KQZcr/wSTPbq29oEdlAfZ0mzZtWpNyt2/fnuuvv/4my6699tocf/zxOfHEE9fkmKeddtqalAu3dquZqntkkpOTpLX2oSQHVdWdl9lntrW2fbGVVbWlqnZU1Y5LL710FVUBYDXmB6vllgM7b8mRq3lqgWUtyQ25aUjbb+L3by5VYGttW5JtSbJx48a2iroA7JHWarRneno6s7OzN1s+NTVlhAk6W83I1YeTbE6SqtqU5LLW2lVJLkxyxLj8iCT37lpDAG6xrVu3ZsOGDTdZtmHDhmzdunWdagR7rtWEq5cn2VhVZyf5oyTHjcvfluQuVfWpJL+S5N97VhCAW27z5s3Ztm1bpqamUlWZmprKtm3bsnnzTn8QHFhEtXbrmI3buHFj27Fjx3pXAwBgWVV1Vmtt40LrfPcUAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHwhUAQEfCFQBAR8IVAEBHaxququqwqjqjqj5dVadX1cFreTyAOTMzM5mens4+++yT6enpzMzMrHeVgL3Erhi5ekZr7UFJzkjy/F1wPGAvNzMzky1btmR2djattczOzmbLli0CFrBL7LuWhbfWzpt4uF+Sy9fyeOtl06ZN610FYML27dtz/fXX32TZtddem+OPPz4nnnjiOtUKWMhpp5223lXobk3D1ZyqemySxyV5+LzlW5JsSZJDDz10V1QF2AvMD1bLLQfoqVpra3uAqn2SfCnJUa218xfbbuPGjW3Hjh1rWhdg7zA9PZ3Z2dmbLZ+amsqFF1646ysE7HGq6qzW2saF1u2Ke64OSfKNpYIVQE9bt27Nhg0bbrJsw4YN2bp16zrVCNib7IpwdUWSF++C4wAkSTZv3pxt27ZlamoqVZWpqals27YtmzdvXu+qAXuBXTEteEiSV7bWnrLUdqYFAYDdxVLTgmt+Q3tr7eIkSwYrAIA9hW9oBwDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoSLgCAOhIuAIA6Ei4AgDoaN/1PHhVbUmyZXx4TVV9bj3rsxs4OMll612J3Yw2Wz1ttnrabPW02epps9VbyzabWmxFtdbW6Jj0VlU7Wmsb17seuxNttnrabPW02epps9XTZqu3Xm1mWhAAoCPhCgCgI+Fq97JtvSuwG9Jmq6fNVk+brZ42Wz1ttnrr0mbuuQIA6MjIFQBAR8LVrUBV/XpVfaaqzqmqN1bVfvPWb6qqb1TVp8af351Y97iq+lxVXVBVL9v1tV8fK2iz35hor3Oq6rtVdZdx3YVV9elx3Y71OYNdr6p+bWyLz1TVCQusr6p65diXzq6qIybW7a39bLk22zy21dlVdUZV/fDEOv1s4TZzPZtnBW2211/PqurvquprVXXOxLK7VNUHqur88d8DF9l3wX610v13SmvNzzr+JLlHki8muf34+C1JnjVvm01J3rXAvt+X5PNJ7pPktkn+Lcnh631Ot4Y2m7f9E5N8aOLxhUkOXu/z2MVt9kNJzkmyIcP3230wyf3mbXN0kvckqSRHJjlzL+9nK2mzRyQ5cPz98XNtpp8t2WauZ6tss3nb75XXsySPSnJEknMmlv1JkpeNv78syR+vpl+tZP+d/TFydeuwb5LbV9W+GV5gF69wvx9LckFr7QuttW8neVOSY9aojrc2q2mzpyd54y6p1a3XA5Jsb61d21q7IcnpSZ40b5tjkry+DbYnOaCq7p69t58t22attTNaa1eMD7cnuecuruOtzUr62WL0s5W12V55PWutfTjJ1+ctPibJSePvJyU5doFdl+pXK9l/pwhX66y19pUkf5bkS0m+muQbrbX3L7Dpw6vq36rqPVX1wHHZPZJcNLHNl8dle7RVtFmqakOSxyV522QRSd5fVWeN/0vA3uCcJI+qqoPGNjk6yb3mbbNYf9or+1lW1maTjs8w8jdHP1u8zVzPbrTifuZ6djM/0Fr7apKM/951gW2W6lcr2X+nrOt/f0MyzvEek+TeSa5M8o9V9YzW2hsmNvtEkqnW2jVVdXSSdyS5X4bpm/n2+I9/rrDN5jwxyUdba5PveH68tXZxVd01yQeq6rzxXdEeq7V2blX9cZIPJLkmw9D4DfM2W6w/7ZX9bIVtliSpqqMyhKtHTizWzxZuM9ezCavpZ3E92xnr0q+MXK2/n07yxdbapa217yR5e4b7OL6ntXZVa+2a8fd3J7lNVR2cIYFPvsO5Z1Y+pbg7W7bNJvxC5g2ht9YuHv/9WpJTMgwb7/Faa3/bWjuitfaoDMPr58/bZLH+tLf2s5W0WarqwUlem+SY1trlE/vqZwu0mevZza2kn41cz27qkvHWhYz/fm2BbZbqVyvZf6cIV+vvS0mOrKoNVVVJfirJuZMbVNXdxnWpqh/L8LxdnuTjSe5XVfeuqttmeOGduktrvz6WbbMkqao7J3l0kn+aWLZ/Vd1x7vckj8kwLL/HG9/ZpqoOTfLk3Py+jVOTPLMGR2aYbv1q9t5+tmybjcvfnuSXWmv/PrFcP1u8zVzP5lnBa9P1bGGnJjlu/P24TLTNhKX61Ur23ymmBddZa+3MqnprhqHyG5J8Msm2qnr+uP41SZ6S5Feq6oYk1yX5hTZ8vOGGqvrVJO/L8ImIv2utfWY9zmNXWmGbJcNNoe9vrX1zYvcfSHLKeG3fN8k/tNbeu8sqv77eVlUHJflOkhe21q6Y12bvznC/xwVJrk3y7HHdXtnPRsu12e8mOSjJq8c+dUMb/pNY/WzxNnM9u7nl2izZy69nVfXGDJ80Pbiqvpzk95L8UZK3VNXxGd50P3Xc9pAkr22tHb3M9WvB/bvUd+jTAAD0YFoQAKAj4QoAoCPhCgCgI+EKAKAj4QoAoCPhCgCgI+EKAKAj4QoAoKP/Dya3/QHMHitEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Examining unique values in the Number of Doors column\n",
    "# print(Auto.loc[:, \"num-of-doors\"].value_counts())\n",
    "    # four    114\n",
    "    # two      89\n",
    "    # ?         2\n",
    "    \n",
    "## Isolating the Columns needed \n",
    "df = Auto.loc[:, [\"num-of-doors\", \"LogPrice\"]]\n",
    "df.columns = [\"numofdoors\", \"logprice\"]\n",
    "\n",
    "# ## Tukey Visualtion of the different Groups: \n",
    "Tukey_HSD = pairwise_tukeyhsd(df.logprice, df.numofdoors)\n",
    "# print(Tukey_HSD)\n",
    "Tukey_HSD.plot_simultaneous()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stratifying Number of Door Analysis\n",
    "\n",
    "The number of doors on a car do not contain statistically significant differences in prices. This is evident by the two and four CI overlapping and having p scores above the cutoff. I would not recommend further examining this attribute to my organization to identify potential correlation with prices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Examining unique values in Fuel System column\n",
    "# print(Auto.loc[:, \"fuel-system\"].value_counts())\n",
    "        # mpfi    94\n",
    "        # 2bbl    66\n",
    "        # idi     20\n",
    "        # 1bbl    11\n",
    "        # spdi     9\n",
    "        # 4bbl     3\n",
    "        # spfi     1\n",
    "        # mfi      1\n",
    "    \n",
    "## Isolating the Columns needed \n",
    "df = Auto.loc[:, [\"fuel-system\", \"LogPrice\"]]\n",
    "df.columns = [\"fuelsystem\", \"logprice\"]\n",
    "\n",
    "## Removing categories with small sample size\n",
    "df = df[df.fuelsystem != 'mfi']\n",
    "df = df[df.fuelsystem != 'spfi']\n",
    "df = df[df.fuelsystem != '4bbl']\n",
    "df = df[df.fuelsystem != 'spdi']\n",
    "\n",
    "## Tukey Visualtion of the different Groups: \n",
    "Tukey_HSD = pairwise_tukeyhsd(df.logprice, df.fuelsystem)\n",
    "# print(Tukey_HSD)\n",
    "Tukey_HSD.plot_simultaneous()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stratifying Fuel Systems Analysis\n",
    "\n",
    "The Tukey HSD plot displays a subgrouping within the categories. mpfi and idi are similar prices to each other, and 2bbl and 1bbl have similar prices to each other. Thus, the following groups are identified as being significantly different from each other: \n",
    "\n",
    "- 1bbl    idi\n",
    "- 1bbl   mpfi\n",
    "- 2bbl    idi\n",
    "- 2bbl   mpfi\n",
    "\n",
    "Since these groups are different from each other and there is a low chance this is from random fluctuation, I would recommend to my client/organization to look into an automobile's fuel system as it relates to price. "
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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