FinalAssignment_python4stats.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistics For Data Science - Course Project"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Housing in Boston MA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install specific version of libraries used in lab\n",
    "#! mamba install pandas==1.3.3\n",
    "#! mamba install numpy=1.21.2\n",
    "#! mamba install scipy=1.7.1-y\n",
    "#!  mamba install seaborn=0.9.0-y\n",
    "#!  mamba install matplotlib=3.4.3-y\n",
    "#!  mamba install statsmodels=0.12.0-y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston_url = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork/labs/boston_housing.csv'\n",
    "boston_df = pd.read_csv(boston_url)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Median value of owner-occupied homes\n",
    "- For the \"Median value of owner-occupied homes\" provide a boxplot\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0     CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  \\\n",
       "0           0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0   \n",
       "1           1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0   \n",
       "2           2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0   \n",
       "3           3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0   \n",
       "4           4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0   \n",
       "\n",
       "     TAX  PTRATIO  LSTAT  MEDV  \n",
       "0  296.0     15.3   4.98  24.0  \n",
       "1  242.0     17.8   9.14  21.6  \n",
       "2  242.0     17.8   4.03  34.7  \n",
       "3  222.0     18.7   2.94  33.4  \n",
       "4  222.0     18.7   5.33  36.2  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
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       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
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       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>252.500000</td>\n",
       "      <td>3.613524</td>\n",
       "      <td>11.363636</td>\n",
       "      <td>11.136779</td>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.554695</td>\n",
       "      <td>6.284634</td>\n",
       "      <td>68.574901</td>\n",
       "      <td>3.795043</td>\n",
       "      <td>9.549407</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>12.653063</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>146.213884</td>\n",
       "      <td>8.601545</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>7.141062</td>\n",
       "      <td>9.197104</td>\n",
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       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.006320</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.460000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.385000</td>\n",
       "      <td>3.561000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>1.129600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>1.730000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>126.250000</td>\n",
       "      <td>0.082045</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.190000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.449000</td>\n",
       "      <td>5.885500</td>\n",
       "      <td>45.025000</td>\n",
       "      <td>2.100175</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>6.950000</td>\n",
       "      <td>17.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>252.500000</td>\n",
       "      <td>0.256510</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.690000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.208500</td>\n",
       "      <td>77.500000</td>\n",
       "      <td>3.207450</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>330.000000</td>\n",
       "      <td>19.050000</td>\n",
       "      <td>11.360000</td>\n",
       "      <td>21.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>378.750000</td>\n",
       "      <td>3.677082</td>\n",
       "      <td>12.500000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.624000</td>\n",
       "      <td>6.623500</td>\n",
       "      <td>94.075000</td>\n",
       "      <td>5.188425</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>16.955000</td>\n",
       "      <td>25.000000</td>\n",
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       "      <th>max</th>\n",
       "      <td>505.000000</td>\n",
       "      <td>88.976200</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>27.740000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.871000</td>\n",
       "      <td>8.780000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>12.126500</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>37.970000</td>\n",
       "      <td>50.000000</td>\n",
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      "text/plain": [
       "       Unnamed: 0        CRIM          ZN       INDUS        CHAS         NOX  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean   252.500000    3.613524   11.363636   11.136779    0.069170    0.554695   \n",
       "std    146.213884    8.601545   23.322453    6.860353    0.253994    0.115878   \n",
       "min      0.000000    0.006320    0.000000    0.460000    0.000000    0.385000   \n",
       "25%    126.250000    0.082045    0.000000    5.190000    0.000000    0.449000   \n",
       "50%    252.500000    0.256510    0.000000    9.690000    0.000000    0.538000   \n",
       "75%    378.750000    3.677082   12.500000   18.100000    0.000000    0.624000   \n",
       "max    505.000000   88.976200  100.000000   27.740000    1.000000    0.871000   \n",
       "\n",
       "               RM         AGE         DIS         RAD         TAX     PTRATIO  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     6.284634   68.574901    3.795043    9.549407  408.237154   18.455534   \n",
       "std      0.702617   28.148861    2.105710    8.707259  168.537116    2.164946   \n",
       "min      3.561000    2.900000    1.129600    1.000000  187.000000   12.600000   \n",
       "25%      5.885500   45.025000    2.100175    4.000000  279.000000   17.400000   \n",
       "50%      6.208500   77.500000    3.207450    5.000000  330.000000   19.050000   \n",
       "75%      6.623500   94.075000    5.188425   24.000000  666.000000   20.200000   \n",
       "max      8.780000  100.000000   12.126500   24.000000  711.000000   22.000000   \n",
       "\n",
       "            LSTAT        MEDV  \n",
       "count  506.000000  506.000000  \n",
       "mean    12.653063   22.532806  \n",
       "std      7.141062    9.197104  \n",
       "min      1.730000    5.000000  \n",
       "25%      6.950000   17.025000  \n",
       "50%     11.360000   21.200000  \n",
       "75%     16.955000   25.000000  \n",
       "max     37.970000   50.000000  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#MEDV \n",
    "ax = sns.boxplot(y='MEDV', data=boston_df)\n",
    "plt.title(\"Median Values of Owner-occupied Homes\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histogram for the Charles river variable\n",
    "- Provide a  histogram for the Charles river variable\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 6.79999999999999, 'Charles River Variable')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#CHAS\n",
    "ax = sns.catplot(x='CHAS',  kind='count', data=boston_df)\n",
    "plt.xlabel(\"Charles River Variable\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1\n",
    "Is there a significant difference in median value of houses bounded by the Charles river or not?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hypothesis**\n",
    "-   $H_0: µ_1 = µ_2$ (\"there is no difference in between the median value of houses bounded by Charles river and not bounded.\")\n",
    "\n",
    "-   $H_1: µ_1 ≠ µ_2$ (\"there is a difference in between the median value of houses bounded by Charles river and not bounded.\")\n",
    "\n",
    "*α = 0.05*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=3.996437466090509, pvalue=7.390623170519905e-05)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#T-Test\n",
    "import scipy\n",
    "scipy.stats.ttest_ind(boston_df[boston_df.CHAS == 1].MEDV,\n",
    "                     boston_df[boston_df.CHAS == 0].MEDV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer 1**: The p-value is less than 0.05 and statistically significant. Therefore, we reject the null hypothesis, and accept the alternative hypothesis being a significant difference in median value of houses bounded by Charles river and not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boxplot of the MEDV vs AGE \n",
    "- Provide a boxplot for the MEDV variable vs the AGE variable. (Discretize the age variable into three groups of 35 years and younger, between 35 and 70 years and 70 years and older)\n"
   ]
  },
  {
   "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>Unnamed: 0</th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "      <th>age_group</th>\n",
       "      <th>age_span</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "      <td>between 35 and 70 years</td>\n",
       "      <td>after 1940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "      <td>70 years and older</td>\n",
       "      <td>after 1940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "      <td>between 35 and 70 years</td>\n",
       "      <td>after 1940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "      <td>between 35 and 70 years</td>\n",
       "      <td>after 1940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "      <td>between 35 and 70 years</td>\n",
       "      <td>after 1940</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0     CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  \\\n",
       "0           0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0   \n",
       "1           1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0   \n",
       "2           2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0   \n",
       "3           3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0   \n",
       "4           4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0   \n",
       "\n",
       "     TAX  PTRATIO  LSTAT  MEDV                age_group    age_span  \n",
       "0  296.0     15.3   4.98  24.0  between 35 and 70 years  after 1940  \n",
       "1  242.0     17.8   9.14  21.6       70 years and older  after 1940  \n",
       "2  242.0     17.8   4.03  34.7  between 35 and 70 years  after 1940  \n",
       "3  222.0     18.7   2.94  33.4  between 35 and 70 years  after 1940  \n",
       "4  222.0     18.7   5.33  36.2  between 35 and 70 years  after 1940  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "under_35 = boston_df.loc[(boston_df['AGE'] <= 35), 'age_group'] = '35 years and younger'\n",
    "between_35_70 = boston_df.loc[(boston_df['AGE'] > 35)&(boston_df['AGE'] < 70), 'age_group'] = 'between 35 and 70 years'\n",
    "above_70 = boston_df.loc[(boston_df['AGE'] >= 70), 'age_group'] = '70 years and older'\n",
    "\n",
    "boston_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Median value of houses bounded by Charles river')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ax = sns.catplot(x='CHAS',  kind='count', data=boston_df, row= 'age_group')\n",
    "ax = sns.boxplot(x='MEDV', y='age_group', data=boston_df)\n",
    "plt.title(\"Median Value vs Age Group\")\n",
    "plt.xlabel(\"Median value of houses bounded by Charles river\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2\n",
    "- Is there a difference in median values of houses of each proportion of owner-occupied units built before 1940?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hypothesis**\n",
    "-   $H_0: µ_1 = µ_2$ (\"there is no difference in  in median values of houses of each proportion of owner-occupied units built before amd after 1940\")\n",
    "\n",
    "-   $H_1: µ_1 ≠ µ_2$ (\"there is difference in median values of houses of each proportion of owner-occupied units built before and after 1940\")\n",
    "\n",
    "*α = 0.05*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston_df.loc[(boston_df.AGE > 81), 'age_span'] = 'before 1940'\n",
    "boston_df.loc[(boston_df.AGE <= 81), 'age_span'] = 'after 1940'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=1.587082228964904, pvalue=0.2083265383143275)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#ANOVA\n",
    "scipy.stats.levene(boston_df[boston_df.age_span=='before 1940']['MEDV'],\n",
    "                  boston_df[boston_df.age_span=='after 1940']['MEDV'],\n",
    "                  center='mean')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer 2**: The p-value higher than 0.05 is statistically not significant. Therefore, we reject the alternative hypothesis, and retain the null hypothesis, being no difference in median values of houses of each proportion of owner-occupied units built before and after 1940."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relationship between Nitric oxide concentrations and the proportion of non-retail business acres per town\n",
    "- Provide a scatter plot to show the relationship between Nitric oxide concentrations and the proportion of non-retail business acres per town. What can you say about the relationship?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ax = sns.scatterplot(x='NOX', y='INDUS', data=boston_df)\n",
    "p2 = sns.lmplot(x='NOX', y='INDUS', line_kws={'color': 'r'}, data=boston_df)\n",
    "plt.title(\"Nitric Oxide Concentrations vs Non-retail Business Areas\")\n",
    "plt.xlabel(\"Concentration of Nitric Oxide (in ppm)\")\n",
    "plt.ylabel(\"Proportion of Non-retail Business Acres\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above scatter plot, there is a positive relationship between Nitric oxide concentration and the proportion of non-retail business areas per town."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3\n",
    "- Can we conclude that there is no relationship between Nitric oxide concentrations and proportion of non-retail business acres per town?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hypothesis**\n",
    "-   $H_0: there is no relationship between Nitric oxide concentrations and proportion of non-retail business acres per town.\n",
    "\n",
    "-   $H_1: there is relationship between Nitric oxide concentrations and proportion of non-retail business acres per town\n",
    "\n",
    "*α = 0.05*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.7636514469209154, 7.913361061236894e-98)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pearson \n",
    "import scipy.stats\n",
    "scipy.stats.pearsonr(boston_df['NOX'], boston_df['INDUS'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer 3**: There is a significant (p-value<0.05) strong positive correlation (r value=0.764) between Nitric oxide concentrations and non-retail business acres per town."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histogram of the pupil to teacher ratio\n",
    "- Create a histogram for the pupil to teacher ratio variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#PTRATIO\n",
    "sns.catplot(y=\"PTRATIO\", kind=\"count\", data=boston_df)\n",
    "plt.ylabel(\"Pupil to Teacher Ratio\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mariangela/anaconda3/lib/python3.6/site-packages/seaborn/distributions.py:2557: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Frequency')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Distribution plot\n",
    "sns.distplot(boston_df.PTRATIO, kde=False, bins=15)\n",
    "plt.xlabel(\"Pupil to Teacher Ratio\")\n",
    "plt.ylabel(\"Frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4\n",
    "- What is the impact of an additional weighted distance  to the five Boston employment centres on the median value of owner occupied homes? (Regression analysis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>MEDV</td>       <th>  R-squared:         </th> <td>   0.062</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.061</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   33.58</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 13 Mar 2022</td> <th>  Prob (F-statistic):</th> <td>1.21e-08</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>08:05:57</td>     <th>  Log-Likelihood:    </th> <td> -1823.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   506</td>      <th>  AIC:               </th> <td>   3652.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   504</td>      <th>  BIC:               </th> <td>   3660.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   18.3901</td> <td>    0.817</td> <td>   22.499</td> <td> 0.000</td> <td>   16.784</td> <td>   19.996</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>DIS</th>   <td>    1.0916</td> <td>    0.188</td> <td>    5.795</td> <td> 0.000</td> <td>    0.722</td> <td>    1.462</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>139.779</td> <th>  Durbin-Watson:     </th> <td>   0.570</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 305.104</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 1.466</td>  <th>  Prob(JB):          </th> <td>5.59e-67</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.424</td>  <th>  Cond. No.          </th> <td>    9.32</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   MEDV   R-squared:                       0.062\n",
       "Model:                            OLS   Adj. R-squared:                  0.061\n",
       "Method:                 Least Squares   F-statistic:                     33.58\n",
       "Date:                Sun, 13 Mar 2022   Prob (F-statistic):           1.21e-08\n",
       "Time:                        08:05:57   Log-Likelihood:                -1823.9\n",
       "No. Observations:                 506   AIC:                             3652.\n",
       "Df Residuals:                     504   BIC:                             3660.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         18.3901      0.817     22.499      0.000      16.784      19.996\n",
       "DIS            1.0916      0.188      5.795      0.000       0.722       1.462\n",
       "==============================================================================\n",
       "Omnibus:                      139.779   Durbin-Watson:                   0.570\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              305.104\n",
       "Skew:                           1.466   Prob(JB):                     5.59e-67\n",
       "Kurtosis:                       5.424   Cond. No.                         9.32\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "X = boston_df['DIS']\n",
    "y = boston_df['MEDV']\n",
    "\n",
    "X = sm.add_constant(X) \n",
    "\n",
    "model = sm.OLS(y, X).fit()\n",
    "predictions = model.predict(X)\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Answer 4**: There is an additional impact (**coefficient value = 1.0916**) of weighted distance to the five Boston employment centres on the median value of owner occupied homes."
   ]
  },
  {
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