Linear Regression Mini Project - Boston Housing Prices.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression in Python\n",
    "\n",
    "***\n",
    "This is a very quick run-through of some basic statistical concepts, adapted from [Lab 4 in Harvard's CS109](https://github.com/cs109/2015lab4) course. Please feel free to try the original lab if you're feeling ambitious :-) The CS109 git repository also has the solutions if you're stuck.\n",
    "\n",
    "* Linear Regression Models\n",
    "* Prediction using linear regression\n",
    "\n",
    "Linear regression is used to model and predict continuous outcomes with normal random errors. There are nearly an infinite number of different types of regression models and each regression model is typically defined by the distribution of the prediction errors (called \"residuals\") of the type of data. Logistic regression is used to model binary outcomes whereas Poisson regression is used to predict counts. In this exercise, we'll see some examples of linear regression as well as Train-test splits.\n",
    "\n",
    "The packages we'll cover are: `statsmodels`, `seaborn`, and `scikit-learn`. While we don't explicitly teach `statsmodels` and `seaborn` in the Springboard workshop, those are great libraries to know.\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img width=600 height=300 src=\"https://imgs.xkcd.com/comics/sustainable.png\"/>\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# special IPython command to prepare the notebook for matplotlib and other libraries\n",
    "%matplotlib inline \n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "# special matplotlib argument for improved plots\n",
    "from matplotlib import rcParams\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"poster\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# Part 1: Introduction to Linear Regression\n",
    "### Purpose of linear regression\n",
    "***\n",
    "<div class=\"span5 alert alert-info\">\n",
    "\n",
    "<p> Given a dataset containing predictor variables $X$ and outcome/response variable $Y$, linear regression can be used to: </p>\n",
    "<ul>\n",
    "  <li> Build a <b>predictive model</b> to predict future values of $\\hat{Y}$, using new data $X^*$ where $Y$ is unknown.</li>\n",
    "  <li> Model the <b>strength of the relationship</b> between each independent variable $X_i$ and $Y$</li>\n",
    "    <ul>\n",
    "      <li> Many times, only a subset of independent variables $X_i$ will have a linear relationship with $Y$</li>\n",
    "      <li> Need to figure out which $X_i$ contributes most information to predict $Y$ </li>\n",
    "    </ul>\n",
    "   <li>It is in many cases, the first pass prediction algorithm for continuous outcomes. </li>\n",
    "</ul>\n",
    "</div>\n",
    "\n",
    "### A Brief Mathematical Recap\n",
    "***\n",
    "\n",
    "[Linear Regression](http://en.wikipedia.org/wiki/Linear_regression) is a method to model the relationship between a set of independent variables $X$ (also knowns as explanatory variables, features, predictors) and a dependent variable $Y$.  This method assumes the relationship between each predictor $X$ is **linearly** related to the dependent variable $Y$. The most basic linear regression model contains one independent variable $X$, we'll call this the simple model. \n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1 X + \\epsilon$$\n",
    "\n",
    "where $\\epsilon$ is considered as an unobservable random variable that adds noise to the linear relationship. In linear regression, $\\epsilon$ is assumed to be normally distributed with a mean of 0. In other words, what this means is that on average, if we know $Y$, a roughly equal number of predictions $\\hat{Y}$ will be above $Y$ and others will be below $Y$. That is, on average, the error is zero. The residuals, $\\epsilon$ are also assumed to be \"i.i.d.\": independently and identically distributed. Independence means that the residuals are not correlated -- the residual from one prediction has no effect on the residual from another prediction. Correlated errors are common in time series analysis and spatial analyses.\n",
    "\n",
    "* $\\beta_0$ is the intercept of the linear model and represents the average of $Y$ when all independent variables $X$ are set to 0.\n",
    "\n",
    "* $\\beta_1$ is the slope of the line associated with the regression model and represents the average effect of a one-unit increase in $X$ on $Y$.\n",
    "\n",
    "* Back to the simple model. The model in linear regression is the *conditional mean* of $Y$ given the values in $X$ is expressed a linear function.  \n",
    "\n",
    "$$ y = f(x) = E(Y | X = x)$$ \n",
    "\n",
    "![conditional mean](images/conditionalmean.png)\n",
    "http://www.learner.org/courses/againstallodds/about/glossary.html\n",
    "\n",
    "* The goal is to estimate the coefficients (e.g. $\\beta_0$ and $\\beta_1$). We represent the estimates of the coefficients with a \"hat\" on top of the letter.  \n",
    "\n",
    "$$ \\hat{\\beta}_0, \\hat{\\beta}_1 $$\n",
    "\n",
    "* Once we estimate the coefficients $\\hat{\\beta}_0$ and $\\hat{\\beta}_1$, we can use these to predict new values of $Y$ given new data $X$.\n",
    "\n",
    "$$\\hat{y} = \\hat{\\beta}_0 + \\hat{\\beta}_1 x_1$$\n",
    "\n",
    "* Multiple linear regression is when you have more than one independent variable and the estimation involves matrices\n",
    "    * $X_1$, $X_2$, $X_3$, $\\ldots$\n",
    "\n",
    "\n",
    "* How do you estimate the coefficients? \n",
    "    * There are many ways to fit a linear regression model\n",
    "    * The method called **least squares** is the most common methods\n",
    "    * We will discuss least squares\n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1 X_1 + \\ldots + \\beta_p X_p + \\epsilon$$ \n",
    "    \n",
    "### Estimating $\\hat\\beta$: Least squares\n",
    "***\n",
    "[Least squares](http://en.wikipedia.org/wiki/Least_squares) is a method that can estimate the coefficients of a linear model by minimizing the squared residuals: \n",
    "\n",
    "$$ \\mathscr{L} = \\sum_{i=1}^N \\epsilon_i = \\sum_{i=1}^N \\left( y_i - \\hat{y}_i \\right)^2  = \\sum_{i=1}^N \\left(y_i - \\left(\\beta_0 + \\beta_1 x_i\\right)\\right)^2 $$\n",
    "\n",
    "where $N$ is the number of observations and $\\epsilon$ represents a residual or error, ACTUAL - PREDICTED.  \n",
    "\n",
    "#### Estimating the intercept $\\hat{\\beta_0}$ for the simple linear model\n",
    "\n",
    "We want to minimize the squared residuals and solve for $\\hat{\\beta_0}$ so we take the partial derivative of $\\mathscr{L}$ with respect to $\\hat{\\beta_0}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{align}\n",
    "\\frac{\\partial \\mathscr{L}}{\\partial \\hat{\\beta_0}} &= \\frac{\\partial}{\\partial \\hat{\\beta_0}} \\sum_{i=1}^N \\epsilon^2 \\\\\n",
    "&= \\frac{\\partial}{\\partial \\hat{\\beta_0}} \\sum_{i=1}^N \\left( y_i - \\hat{y}_i \\right)^2 \\\\\n",
    "&= \\frac{\\partial}{\\partial \\hat{\\beta_0}} \\sum_{i=1}^N \\left( y_i - \\left( \\hat{\\beta}_0 + \\hat{\\beta}_1 x_i \\right) \\right)^2 \\\\\n",
    "&= -2 \\sum_{i=1}^N \\left( y_i - \\left( \\hat{\\beta}_0 + \\hat{\\beta}_1 x_i \\right) \\right) \\hspace{25mm} \\mbox{(by chain rule)} \\\\\n",
    "&= -2 \\sum_{i=1}^N y_i - \\hat{\\beta}_0 - \\hat{\\beta}_1 x_i \\\\\n",
    "&= -2 \\left[ \\left( \\sum_{i=1}^N y_i \\right) - n \\hat{\\beta_0} - \\hat{\\beta}_1 \\left( \\sum_{i=1}^N x_i\n",
    "\\right) \\right] \\\\\n",
    "& 2 \\left[ n \\hat{\\beta}_0 + \\hat{\\beta}_1 \\sum_{i=1}^N x_i - \\sum_{i=1}^N y_i \\right] = 0 \\hspace{20mm} \\mbox{(Set equal to 0 and solve for $\\hat{\\beta}_0$)} \\\\\n",
    "& n \\hat{\\beta}_0 + \\hat{\\beta}_1 \\sum_{i=1}^N x_i - \\sum{i=1}^N y_i = 0 \\\\\n",
    "& n \\hat{\\beta}_0 = \\sum_{i=1}^N y_i - \\hat{\\beta}_1 \\sum_{i=1}^N x_i \\\\\n",
    "& \\hat{\\beta}_0 = \\frac{\\sum_{i=1}^N y_i - \\hat{\\beta}_1 \\sum_{i=1}^N x_i}{n} \\\\\n",
    "& \\hat{\\beta}_0 = \\frac{\\sum_{i=1}^N y_i}{n} - \\hat{\\beta}_1 \\frac{\\sum_{i=1}^N x_i}{n} \\\\\n",
    "& \\boxed{\\hat{\\beta}_0 = \\bar{y} - \\hat{\\beta}_1 \\bar{x}}\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using this new information, we can compute the estimate for $\\hat{\\beta}_1$ by taking the partial derivative of $\\mathscr{L}$ with respect to $\\hat{\\beta}_1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{align}\n",
    "\\frac{\\partial \\mathscr{L}}{\\partial \\hat{\\beta_1}} &= \\frac{\\partial}{\\partial \\hat{\\beta_1}} \\sum_{i=1}^N \\epsilon^2 \\\\\n",
    "&= \\frac{\\partial}{\\partial \\hat{\\beta_1}} \\sum_{i=1}^N \\left( y_i - \\hat{y}_i \\right)^2 \\\\\n",
    "&= \\frac{\\partial}{\\partial \\hat{\\beta_1}} \\sum_{i=1}^N \\left( y_i - \\left( \\hat{\\beta}_0 + \\hat{\\beta}_1 x_i \\right) \\right)^2 \\\\\n",
    "&= 2 \\sum_{i=1}^N \\left( y_i - \\left( \\hat{\\beta}_0 + \\hat{\\beta}_1 x_i \\right) \\right) \\left( -x_i \\right) \\hspace{25mm}\\mbox{(by chain rule)} \\\\\n",
    "&= -2 \\sum_{i=1}^N x_i \\left( y_i - \\hat{\\beta}_0 - \\hat{\\beta}_1 x_i \\right) \\\\\n",
    "&= -2 \\sum_{i=1}^N x_i y_i - \\hat{\\beta}_0 x_i - \\hat{\\beta}_1 x_i^2 \\\\\n",
    "&= -2 \\sum_{i=1}^N x_i y_i - \\left( \\bar{y} - \\hat{\\beta}_1 \\bar{x} \\right) x_i - \\hat{\\beta}_1 x_i^2 \\\\\n",
    "&= -2 \\sum_{i=1}^N x_i y_i - \\bar{y}x_i + \\hat{\\beta}_1\\bar{x}x_i - \\hat{\\beta}_1 x_i^2 \\\\\n",
    "&= -2 \\left[ \\sum_{i=1}^N x_i y_i - \\bar{y} \\sum_{i=1}^N x_i + \\hat{\\beta}_1\\bar{x} - \\hat{\\beta}_1 x_i^2 \\right] \\\\\n",
    "&= -2 \\left[ \\hat{\\beta}_1 \\left\\{ \\bar{x} \\sum_{i=1}^N x_i - \\sum_{i=1}^N x_i^2 \\right\\} + \\left\\{ \\sum_{i=1}^N x_i y_i - \\bar{y} \\sum_{i=1}^N x_i \\right\\}\\right] \\\\\n",
    "& 2 \\left[ \\hat{\\beta}_1 \\left\\{ \\sum_{i=1}^N x_i^2 - \\bar{x} \\sum_{i=1}^N x_i \\right\\} + \\left\\{ \\bar{y} \\sum_{i=1}^N x_i - \\sum_{i=1}^N x_i y_i \\right\\} \\right] = 0 \\\\\n",
    "& \\hat{\\beta}_1 = \\frac{-\\left( \\bar{y} \\sum_{i=1}^N x_i - \\sum_{i=1}^N x_i y_i \\right)}{\\sum_{i=1}^N x_i^2 - \\bar{x}\\sum_{i=1}^N x_i} \\\\\n",
    "&= \\frac{\\sum_{i=1}^N x_i y_i - \\bar{y} \\sum_{i=1}^N x_i}{\\sum_{i=1}^N x_i^2 - \\bar{x} \\sum_{i=1}^N x_i} \\\\\n",
    "& \\boxed{\\hat{\\beta}_1 = \\frac{\\sum_{i=1}^N x_i y_i - \\bar{x}\\bar{y}n}{\\sum_{i=1}^N x_i^2 - n \\bar{x}^2}}\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solution can be written in compact matrix notation as\n",
    "\n",
    "$$\\hat\\beta =  (X^T X)^{-1}X^T Y$$ \n",
    "\n",
    "We wanted to show you this in case you remember linear algebra, in order for this solution to exist we need $X^T X$ to be invertible. Of course this requires a few extra assumptions, $X$ must be full rank so that $X^T X$ is invertible, etc. Basically, $X^T X$ is full rank if all rows and columns are linearly independent. This has a loose relationship to variables and observations being independent respective. **This is important for us because this means that having redundant features in our regression models will lead to poorly fitting (and unstable) models.** We'll see an implementation of this in the extra linear regression example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "# Part 2: Exploratory Data Analysis for Linear Relationships\n",
    "\n",
    "The [Boston Housing data set](https://archive.ics.uci.edu/ml/datasets/Housing) contains information about the housing values in suburbs of Boston.  This dataset was originally taken from the StatLib library which is maintained at Carnegie Mellon University and is now available on the UCI Machine Learning Repository. \n",
    "\n",
    "\n",
    "## Load the Boston Housing data set from `sklearn`\n",
    "***\n",
    "\n",
    "This data set is available in the [sklearn](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_boston.html#sklearn.datasets.load_boston) python module which is how we will access it today.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "import pandas as pd\n",
    "\n",
    "boston = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'feature_names', 'DESCR'])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO'\n",
      " 'B' 'LSTAT']\n"
     ]
    }
   ],
   "source": [
    "# Print column names\n",
    "print(boston.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston House Prices dataset\n",
      "===========================\n",
      "\n",
      "Notes\n",
      "------\n",
      "Data Set Characteristics:  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive\n",
      "    \n",
      "    :Median Value (attribute 14) is usually the target\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "http://archive.ics.uci.edu/ml/datasets/Housing\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      "**References**\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "   - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Print description of Boston housing data set\n",
    "print(boston.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's explore the data set itself. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "        0     1     2    3      4      5     6       7    8      9     10  \\\n",
       "0  0.00632  18.0  2.31  0.0  0.538  6.575  65.2  4.0900  1.0  296.0  15.3   \n",
       "1  0.02731   0.0  7.07  0.0  0.469  6.421  78.9  4.9671  2.0  242.0  17.8   \n",
       "2  0.02729   0.0  7.07  0.0  0.469  7.185  61.1  4.9671  2.0  242.0  17.8   \n",
       "3  0.03237   0.0  2.18  0.0  0.458  6.998  45.8  6.0622  3.0  222.0  18.7   \n",
       "4  0.06905   0.0  2.18  0.0  0.458  7.147  54.2  6.0622  3.0  222.0  18.7   \n",
       "\n",
       "       11    12  \n",
       "0  396.90  4.98  \n",
       "1  396.90  9.14  \n",
       "2  392.83  4.03  \n",
       "3  394.63  2.94  \n",
       "4  396.90  5.33  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos = pd.DataFrame(boston.data)\n",
    "bos.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are no column names in the DataFrame. Let's add those. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\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>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\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>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\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>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\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>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\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>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos.columns = boston.feature_names\n",
    "bos.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have a pandas DataFrame called `bos` containing all the data we want to use to predict Boston Housing prices.  Let's create a variable called `PRICE` which will contain the prices. This information is contained in the `target` data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506,)\n"
     ]
    }
   ],
   "source": [
    "print(boston.target.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>PRICE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\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>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\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>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\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>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\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>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\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>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  PRICE  \n",
       "0     15.3  396.90   4.98   24.0  \n",
       "1     17.8  396.90   9.14   21.6  \n",
       "2     17.8  392.83   4.03   34.7  \n",
       "3     18.7  394.63   2.94   33.4  \n",
       "4     18.7  396.90   5.33   36.2  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos['PRICE'] = boston.target\n",
    "bos.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EDA and Summary Statistics\n",
    "***\n",
    "\n",
    "Let's explore this data set.  First we use `describe()` to get basic summary statistics for each of the columns. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>PRICE</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",
       "      <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",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.593761</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>356.674032</td>\n",
       "      <td>12.653063</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.596783</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>91.294864</td>\n",
       "      <td>7.141062</td>\n",
       "      <td>9.197104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\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>0.320000</td>\n",
       "      <td>1.730000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\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>375.377500</td>\n",
       "      <td>6.950000</td>\n",
       "      <td>17.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\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>391.440000</td>\n",
       "      <td>11.360000</td>\n",
       "      <td>21.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.647423</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>396.225000</td>\n",
       "      <td>16.955000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\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>396.900000</td>\n",
       "      <td>37.970000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     3.593761   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.596783   23.322453    6.860353    0.253994    0.115878    0.702617   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.082045    0.000000    5.190000    0.000000    0.449000    5.885500   \n",
       "50%      0.256510    0.000000    9.690000    0.000000    0.538000    6.208500   \n",
       "75%      3.647423   12.500000   18.100000    0.000000    0.624000    6.623500   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean    68.574901    3.795043    9.549407  408.237154   18.455534  356.674032   \n",
       "std     28.148861    2.105710    8.707259  168.537116    2.164946   91.294864   \n",
       "min      2.900000    1.129600    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.025000    2.100175    4.000000  279.000000   17.400000  375.377500   \n",
       "50%     77.500000    3.207450    5.000000  330.000000   19.050000  391.440000   \n",
       "75%     94.075000    5.188425   24.000000  666.000000   20.200000  396.225000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT       PRICE  \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": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bos.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scatterplots\n",
    "***\n",
    "\n",
    "Let's look at some scatter plots for three variables: 'CRIM' (per capita crime rate), 'RM' (number of rooms) and 'PTRATIO' (pupil-to-teacher ratio in schools).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2d5309b9048>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ixo0b+PDDDyGVSnHhwgWkp6eDz+cjISEBH330EQDg8ePHrM8r/0x99913+O6771iV0dbW\nVmUbU1NTpXp0dRwcHAD8d4PUxo4dOwBU3Zxv3ryJn376CR07dsTq1avrvOGp4+vri/bt2+PUqVOY\nOnUqKisrcebMGUyYMIHTcXg8HioqKvDDDz/gzp07SEtLQ2pqqiKPi6nRPsTn81U+X/Lvkfy7IG/c\n79ixo8r5nnvuOU4BZP78+YoeVDweD2ZmZnBxcdHYdVfd37gmeW6Nuipu+YNhbm4uCgoKUFBQoDH4\nA1XV29UfbOtCAeRfHh4e6Nevn+Ln4cOHIyQkBAsWLEBRURFCQ0MV6+QfwokTJyIoKEjt8SwtLTWe\na8OGDfjxxx/Rvn179OzZEwMHDkTnzp2RmpqKpUuXci57zS+FunU1g4um9pnq3nrrLQwfPhwXLlzA\nlStXcO3aNfzwww/YvHkzIiIilPJm2BxPE3WBT/7llT8t16a2cwsEAsUNdfjw4RgzZoza7eo6T1BQ\nEJYvX47o6Gi4u7tDLBajb9++inLGxsYqgmVwcLDS78DmvPK/09y5c1XqweVq3ui0vebe3t6wtLTE\njRs3at0uKSkJixYtwujRo1XaVKp/VwYOHIiAgABMnjwZEyZMwL59+9ChQwfO5Ro6dCi2bt2Kp0+f\nIikpCfn5+Zwb8GNiYjB9+nRYWlqiT58+GD58OEQiEdq1a6e2LYVLG0Z5ebnKMq4Pe/IOM2xVf+PR\nhM1Dmryc/v7+eO+99+p1vuoogGhgYWGBdevWYdSoUVixYgU6d+6saIhu164dgKovcPUvElD1ITt/\n/rzaJ3Kg6ily3bp16NOnD7Zt26Z48geALVu2aFVWV1dXpKSkQCwWq9yM5a/+zs7OnI6Zn5+P+/fv\nw8vLC6NHj8bo0aPBMAxOnjyJDz/8EDt37lQKIPXx+PFjlS/Vw4cPYWJiAldX1zr3T0lJUXmqevjw\nIXg8Hjp06ICKigoAVUlbNf9eDMPg9OnTcHFxqfUc7du3h4eHB65cuYLs7Gy0adNG8STZqlUrXL16\nFYWFhejYsSPc3d0BQHFMNueVf6bMzc1Vts3NzcVff/3F6lqwYWpqiiFDhuDo0aM4f/48Bg8erHa7\nQ4cO4datW6yqo3r27In58+fj66+/xqxZs3Do0CG1Dwa1GTZsGLZs2YIzZ87g/v37EIlEat8ua/PZ\nZ5/B0tISJ06cUHp6V9crjy15MExKSlKpYnr8+LHWx9UV+WcoOTlZ8dmT+/rrr2FlZYVZs2ahRYsW\nKCoqUvl8AVXVdNbW1qwe2Kqjbry1cHZ2xueffw6pVIoFCxYo6k99fX3h4uKCQ4cO4cmTJ0r7bNu2\nDXPmzMH58+fVHrOgoAAMw6BTp05KwSM/P1/RXbN6FYT8KbO2J50XX3wRRUVF2L59u9LyR48e4fff\nf4erqyvnxKOYmBhMnDgRBw4cUCzj8XiKnjtcn1Rqs3v3bqWhYm7fvo3Lly9jwIABSu0qmhw4cEDp\nKez27du4dOkS+vXrh5YtW8Le3h7du3fH+fPn8b///U9p399++w2zZ8/GoUOHFMs0XfOgoCDExcXh\nypUr6NOnD3g8Hng8Hvr06YOYmBhcu3ZN6WbL5bwBAQFo0aIFfvrpJxQWFiptu2rVKsycOVPlGPUx\nZ84cWFhY4LPPPsP9+/dV1p8/fx47d+6Ek5MT3nzzTVbHnDhxIgYMGIB79+7hhx9+4Fymzp07w83N\nDadOncK5c+c0tiHWJi8vD3Z2dkrBQyqVIiIiAoB27T4vvPAChEIhtm3bpvQ5TUpK0vg9NyT5G+/u\n3buVlt+9exd79+5FTk4OBAIBgoODkZCQoJLXc+3aNbz77rsIDw/nfG56A6nDiBEjcPr0aZw+fRrf\nfvstvvzySwgEAnz55Zd499138dprr2H8+PFwdnbGjRs3cOzYMXTu3Flj3a27uzvat2+PgwcPwtTU\nFB4eHnjy5AkOHz6MgoICAFBqRJW3VWzduhUBAQFqnwbffvttREVFYc2aNbh79y569eqFzMxM/Pzz\nz+Dz+fjmm284/97BwcHo3Lkz1q5di9TUVPj6+qKwsBAHDx6EUChU5KTowuPHjzF+/HiMGjUKeXl5\n2L17N1q2bIkFCxaw2v/p06cICQnBq6++iszMTOzevRtWVlZK44999tlneOuttxASEoLx48fD3d0d\nCQkJOHjwIFxcXPD+++8rttV0zYOCgrBlyxbcvXtXqSNBv379FDkMNf8+bM9rY2ODJUuWYPHixRg5\nciTGjBmDNm3a4OLFizh//jwGDhyIF198UYurq56zszM2bNiAWbNm4fXXX8ewYcPQtWtXSCQSxMXF\nITIyEm3atMHGjRtZd8cFgGXLluHll1/Gjh07EBQUpNR9nI2hQ4cqbmRcq68AYPDgwTh27BhmzZqF\nAQMGoKioCMePH8f9+/fB5/NZJzdW5+zsjA8//BArV67E+PHjMXLkSBQVFWHPnj1o2bKl0TPkAwMD\nMXToUOzbtw9Pnz5FYGAg8vLysHfvXtja2mLWrFkAgI8//hjXr1/H7Nmz8frrr8PX1xePHz/Gvn37\nYGNjg08++YTzuSmAsPD555/jzz//xIEDBxAcHIzAwED0798f+/fvx6ZNm7B//36UlpbC2dkZb7/9\nNqZNm6bxS2dqaoqtW7fiu+++w9GjR1FeXg5HR0cEBwdj6tSpGDZsGKKjoxEWFgYAePPNN3H9+nUc\nPHgQMTExagOIpaUl9u7di82bN+PUqVOIjIyEjY0NAgMD8d5773GuBgCqMvAjIiKwceNGXLx4Eb/9\n9hvMzc3h5+eHb7/9Ft26deN8TE0WLFiAv//+G2vXroVQKERgYCA+/PBD1lU2X375Jc6ePYtVq1aB\nYRj07dsX8+bNU2r09PLywpEjR7B+/XocP34c+fn5cHBwwBtvvIH33ntPqRFT0zXv2rWrYkiN6lVm\n8ioBe3t7lYQ3Lud9/fXX4ezsjG3btmHHjh2QSCRwdXXFRx99hNDQUM7VC3UJCAjA77//jr179+Ly\n5cuIiopCeXk52rVrh6lTp+Ltt9/mnBcg73wxf/58LFy4EEePHuWUWDhs2DCEh4crGtW5+uyzz2Bj\nY4PIyEhcuHABdnZ28PHxwddff40vv/wSf/75J+eGYqCqk03btm0RERGBNWvWKPK/KioqtHpy17XV\nq1eja9euOHz4MFasWIHWrVtjwIABmDNnjuIz5ujoiMOHD2PDhg24cOECfv31V9ja2iI4OBjvv/++\nVmNr8ZjaWmAJ0aMjR45g4cKFWLlypcaxlQghDRe1gRBCCNEKBRBCCCFaoQBCCCFEK9QGQgghRCv0\nBkIIIUQrzaYbb13DNhBCCFFP06gTzSaAAJovQm0SEhIAVI0fRKrQNVFG10MVXRNljfl61PbwTVVY\nhBBCtEIBhBBCiFaMWoWVl5eHPn36qCx/6aWX8OOPP4JhGISHh+PAgQPIy8tD9+7dsWTJEpURJ/Wl\noEyMlZcycT+7DKXSx2jVwhTPt2uFIZ0dEffwGf55WgALoQC9OrXBOwPd0cJU9XJKpDJEJ+Ygo7Ac\ndlam4AHILhYr/b9TS3MEeNhBKOArbW9vZQoGQE6NbQghpCEwagC5e/cugKr5tKvPn9GqVSsAVfNm\nbNmyBfPmzYOLiws2bdqEyZMn48SJE6xGadVWXrEYg7+/gPwy5XH288rK8Ci3DMfi05WWxzx8hnXn\nEiFysMaRGf3QwtQE4koZlp1IQExiDpKyiyGrpbO0gA90tLWEiYCPSpkMj3JKIK0x+C6fB7jbWyHA\nww6LR3hTICGEGJ1RA8i9e/dgZ2eHgIAAlXXFxcWIiIjAzJkzFZM59ezZE4MHD8ahQ4dUpm/VlYIy\nMXp9cxaV3OaJgYwB7mYWoe/yc7j0yWDM2HsT0Yk5YJNkI5UBidmqU23WPP6DrGIk/vtvx5ReFEQI\nIUZl1DvQvXv34OnpqXZdfHw8SktLFWPdA1VDXvv7++Py5ct6K9OglRc4B4/qCsoqMWjlBdbBgysG\nQHRiDpYdT9DD0QkhhD2jB5CysjKMHz8ezz//PAYOHIht27aBYRgkJycDgMqQ3u3atVOs07WCMjHy\nyuqeHrIueWUSvQQPOXkQkdSs5yKEEAMyWhWWVCpFUlISLCwsMH/+fDg7O+PChQv4/vvvUV5eDqFQ\nCFNTU5VpMS0tLbWaFAb4ry+2JqsuZ2p1XGN4mF2M/edvoqcL+7kWdKWsrAxA3dezuaDroYquibKm\nej2M2gYSHh4OZ2dnxZzDvXv3RmlpKbZt24Z3331X44T3mpbX19PC+r99GIqUAXJLuU/PSQghumK0\nACIQCJRmdZMbMGAA9u/fDwsLC4jFYkgkEqW5w0tKSrTugVVXFqjX32VIyEmvdZuGQsAH/Lw6wlvk\nYPBzN+asWn2g66GKromyxnw9GmQmemZmJg4cOIBnz54pLa+oqABQ1WDOMAzS0tKU1qelpSlNVapL\nn4/01ctx9aGTnRX6udsZuxiEkGbMaAFELBZj6dKlOHbsmNLy06dPw83NDS+88ALMzMwQGRmpWFdQ\nUIDr16+rfXPRBRsLU7S2ENa9YR1aWwihn0q2KjyAkgoJIUZntCosV1dXvPzyy1i7di14PB7c3d1x\n6tQpnDlzBhs2bIClpSVCQkKwdu1a8Pl8uLm5ITw8HFZWVhgzZozeynXhk0Ho+sVZrfe3sTDBhU8G\nccoD4UIePBaPaHyvwoSQpsWojejLli3Dxo0bsXPnTmRnZ8Pd3R3r1q1T5H7MnTsXfD4f27dvR2lp\nKfz8/LBixQq9ZqG3MDWBraUQuSXcGtT5PChlou+Y0gvLjicgmmUmeic7Swj4fEhlDB7mFKvNRPdw\nqKq2okx0QkhDYNQAYm5ujrlz52Lu3Llq15uYmGDevHmYN2+ewcoUnZjDOXiM6tYWy1/rojQWllDA\nx+cjfSCRyhCTlIPMgnLYWpuCBx5yiiqU/t/Rxhz93P8bC0u+vZ21GRgwyC0SK21DCCENQbOaD4SN\njMJyzvuM7OasdiBFoCqQBHLoKcV1e0IIMRZ6nK3BqaU55wbw3CKxXspCCCENGQWQGgI87OBkY856\nez4PcOSwPSGENBUUQGoQCvh4wduR9fbu9pSPQQhpniiAqLFguBdMBXVXZFE+BiGkOaM7nxrfnroH\nsbTuDA4nG3PKxyCENFsUQGqQSGWIScxhta2lqUDPpSGEkIaLAkgN8sQ/Nh7mlCAmiV2wIYSQpoYC\nSA0ZheW1Zo1XJ2OAzALueSOEENIUUACpwc7KtO6NqrG15rY9IYQ0FRRAauCaRMjT67i7hBDScFEA\nqSGzsILT9toMfUIIIU0BBZAacoq5BZBnxTSMCSGkeaIAUoOtlRm37S2pDYQQ0jxRAKnBqSW3AELj\nYBFCmisKIDVI2Pbh/Rej8zkHCSGkcaAAUsOumGRO29NQ7oSQ5ooCSDUSqQzJOaWc9qEqLEJIc0UB\npJroxBxkFnHrltvNtZWeSkMIIQ0bBZBqMgrLIZVx22fugVv6KQwhhDRwFECqcWppzvmCxCTlQsI1\n6hBCSBNAAaQartPZAkCZRIbLD7L1VCJCCGm4KIBUIxTwMaQz++ls5aJZzh9CCCFNCQWQGhYM8+I8\nPKKUY+4IIYQ0BRRAavj21D3OqYGtW9BwJoSQ5ocCSDVcprOtzsGa2/AnhBDSFFAAqSY6MQcPc9hN\nZ1td1N1s6olFCGl2KIBUo00eCACcTcjElB1xFEQIIc0KBZBqnFqaQ6DlFYlOzMGy4wm6LRAhhDRg\nFECqCfCwQyc7K632ZVAVROgthBDSXFAAqUYo4CPAw07r/R/mFCMmiXJCCCHNQ4MIIGKxGMOGDcOC\nBQsUyxiGwaZNmzBo0CB07doVU6ZMQVJSkt7LsniEN3zattRqX6kMyCygOdIJIc1Dgwgg69evx8OH\nD5WWbdiwAZs2bUJYWBhWr16NoqIiTJ48GUVFRXoti1DAx8H3+sLGwoTzvgI+De9OCGk+jB5A7ty5\ng927d6N169aKZcXFxYiIiMDMmTMRGhqK4OBgREREoKSkBIcOHdJ7mVqYmmBUNxfO+3Wys0I/d+2r\nwAghpDExagCprKzEokWLMHXqVDg6/jcGVXx8PEpLSxEcHKxYZmNjA39/f1y+fFnv5ZJIZUjM4pYP\nwkNVI7zyQ0FjAAAgAElEQVRQ225chBDSyBj1brd161ZIJBJMnz5daXlycjIAwNXVVWl5u3btFOv0\n6evjCYhNymW9vTx4LB7hrb9CEUJIA8O9ol9HkpKSEB4ejp9++gmmpspjSRUXF8PU1FRluaWlJYqL\nuWeKyyUk1J2nUSljcP72E9bjYbVvaYJuzi0wrZc1Eu/f07psjUlZWRkAdtezOaDroYquibKmej2M\nEkBkMhkWL16MN954A35+firrGYYBj6d+TFxNy3XlVnoZnhRKWG3LBzC1ly3821nqtUyEENIQGSWA\n7N69G+np6diyZQsqKysVyxmGQWVlJaytrSEWiyGRSCAUChXrS0pKYG1trfV5vb3rrmKKL06BlMlg\ndTwZAItWDvD2bq91mRoj+VMUm+vZHND1UEXXRFljvh43btzQuI5TG0hJSQnWr1+PN954A/3798ef\nf/6Jv//+G0uWLEFaWhrr40RGRiIjIwO9evWCj48PfHx8cPfuXfz222/w8fGBiYkJGIZROWZaWho6\nduzIpciccRnOhLrtEkKaM9YB5NmzZ3j99dexadMmVFZWIjc3FxKJBM+ePcPhw4cxbtw4PHr0iNWx\nvvjiCxw6dEjpn5ubGwYPHoxDhw5hxIgRMDMzQ2RkpGKfgoICXL9+HX379uX+W3IQ4GEHKzN2L2ZW\nZibUbZcQ0myxrsJatWoVcnJycOTIEdjb26Nfv34AgEGDBuHgwYOYNm0afvjhB6xdu7bOY3Xq1Ell\nmbm5OVq1aoXnn38eABASEoK1a9eCz+fDzc0N4eHhsLKywpgxY9gWmRBCiB6xDiDnz59HSEgIPD09\nkZeXp7TO19cXISEh2Ldvn84KNnfuXPD5fGzfvh2lpaXw8/PDihUr6tUGwkZ0Yg4Kyyrr3hBAYVkl\nYpJyEChy0GuZCCGkIWIdQEpLS5WS/WqysbGpVxfbo0ePKhfMxATz5s3DvHnztD6mNjIKy1l34WVA\nY18RQpov1m0gHh4eGrPAZTIZTpw4AXd3d50VzFjsrLjNb25jKax7I0IIaYJYB5Dp06cjKioKn376\nKW7evAkAyM7ORnR0NN5++23cvHkTkyZN0ltBDYVrlsnB6+x7nxFCSFPCugrrpZdewueff46VK1cq\nBjScP38+GIaBUCjEhx9+iJEjR+qtoIaSXSzmtP3/nhRAIpXRGFiEkGaHUyLh+PHj8fLLLyMmJgYp\nKSmQyWRo27YtAgIC0KZNG32V0aBat+BWJZVVVEEN6YSQZolTACktLUVkZCRefPFFtGjRAgBw7Ngx\nnDt3DqNGjVIZu6ox+t+TAk7bU0M6IaS5Yl3vkp6ejtGjR2PhwoVKkz/Fxsbi008/xbhx4/Ds2TO9\nFNKQbj7Oq3ujGigbnRDSHLEOIKtWrUJhYSF27NgBX19fxfLly5dj7969yMjIwOrVq/VSSENqwTIL\nvbpebk2j+o4QQrhgHUBiY2MRFhaGPn36qKzr0aMHQkNDcenSJZ0WzhhG+3GfifDqQ/ZzhxBCSFPB\nOoBUVFTAxETz07mFhYXe5ys3BKmMbRrhfyIusxsDjBBCmhLWAaRLly745ZdfUFpaqrKuoqICR44c\ngY+Pj04LZwwRlx/WvVENj3JKIJHK9FAaQghpuFhX+M+YMQOTJ0/GK6+8gldffRXt21fNgZGamorf\nf/8dT548wY4dO/RWUEN5mFPCeZ+MwnLqyksIaXZYB5CePXti27ZtWLlyJTZs2KC0ztPTE1u3bkWv\nXr10XkBDkkhlkGrxJiFjqCsvIaT54dTlqE+fPjhy5Ahyc3Px9OlTyGQyODk51TrIYmMSnZiDEgn3\nNhCaWIoQ0hxpNaWtra0tbG1tdV0Wo8so1O4topOdFU0sRQhpdjQGkOHDh+OTTz7BoEGDFD/Xhcfj\n4fjx4zornKHZcxyJVy7Aw47GwiKENDsaA4itrS3MzMyUfm7quFdeAQIesHiEt87LQgghDZ3GALJ7\n926lnxcuXAgvLy/w+U33STuH40i8AODu0ILePgghzRLrO9/UqVPxww8/6LMsRufUkntDuI1F4x9A\nkhBCtME6gIjF4ibT20qTAA87tOXYm+ppfjklERJCmiXWAWTmzJnYsmULTp8+jczMTH2WyWiEAj5e\n8OYWJOVJhIQQ0tyw7sZ79OhRFBYWYs6cOQAAgUAAgUCgtA2Px8OtW7d0W0IDmz7QDbuuPma9vVRG\nSYSEkOaJdQDx8vKCt3fT72304uqLnPehJEJCSHPEOoCsWLFCn+VoEErFlSit5L4fJRESQpqjOgNI\nfHw8bt68CalUis6dO6Nv376GKJdRbL6YxHkfAQ/UjZcQ0ixpDCBlZWWYPXs2Ll++DIapSrHj8Xjw\n9vbGpk2bmmSPrD+TuU9n2629jR5KQgghDZ/GALJx40ZcunQJw4cPx7Bhw8Dn8xEbG4v9+/dj0aJF\niIiIMGQ5DcJcyP1Nokf71nooCSGENHwaA8jp06cxatQofPvtt4plwcHBaNOmDdatW4f8/Hy0atXK\nIIU0FB9nG5y7m81pn9O3M7BoROOfSIsQQrjS+MidkZGBnj17qiwfMmQIGIZBSkqKXgtmDNr0pnr8\njBIJCSHNk8YAIhaLYW6uekO1t7cHALVT2zZ2Ti3N6t5Ijcg7TTOxkhBCaqN19yF5w3pTou1vtPVS\nok7LQQghjQH1P60ms7BCq/0Ss7nPo04IIY1drXkgZ8+exePHysN6lJeXg8fj4ejRo7hx44bSOh6P\nhxkzZrA+uVgsxoYNG3Ds2DHk5eWhS5cumD9/Pnx8qhqlGYZBeHg4Dhw4gLy8PHTv3h1LliyBu7s7\n63NwkV2k3ZAkZWIZJFIZ5YMQQpqVWgPImTNncObMGbXrfvvtN5VlXAPI8uXLcfToUcybNw8dOnTA\nrl27EBoaimPHjsHFxQUbNmzAli1bMG/ePLi4uGDTpk2YPHkyTpw4AWtra9bnYSuvhPt8IAAgkTG4\n9CALwV5OysulMkQn5iCjsBxOLc1p5kJCSJOiMYCcO3dOrycuKirCwYMH8dFHH2HChAkAgB49eqB3\n7944evQoQkNDERERgZkzZyI0NBQA0LNnTwwePBiHDh3ClClTdF4mPp+n9b4xD3IVAURcKcOyEwmI\nSczBw5xiSGWAgF81d3qAhx0Wj/CmQEIIafQ0BhAXFxe9ntjCwgK//PKL0nlMTEzA4/EgFosRHx+P\n0tJSBAcHK9bb2NjA398fly9f1ksA6d3JFjui2Y/EW12lrKoJXiKVIeynOEQn5ig1yktlwIOsYiT+\n+2/HlF4URAghjZrR7mAmJibo3LkzbGxsIJPJkJqaikWLFoHH42HkyJFITk4GALi6uirt165dO8U6\nXRPW4w2ksFwCAPj6eIJK8KiOARCdmINlxxO0PhchhDQErEfj1aeNGzdi3bp1AIAPPvgAnTp1wtmz\nZ2FqagpTU+UpYy0tLVFcXKzVeRISar9p/+9+oVbHBYCCggL87/YdnL/9pM7uwAyAqNtP8Lo7Dyb1\nCFrGUlZWBqDu69lc0PVQRddEWVO9Hg0igAwZMgT+/v64du0aNm7cCIlEAnNzc/B46m+umpbXl62l\n9pejnY0pbqWX4UmhhNX2TwoluJVehp4uLbQ+JyGEGFODCCBeXl4AAH9/f5SUlCAiIgLz5s2DWCyG\nRCKBUChUbFtSUqJ1D6y6JsTyEMnw2bmTkHHMKDThAwtG++NY/FNImQxW+0gZwMzGHt7e7bmdrAGQ\nP0U1hwnG2KDroYquibLGfD1qpmtUZ7Q2kOzsbBw+fFilOsrb2xtisRg2NjZgGAZpaWlK69PS0tCx\nY0e9lUubBHsPe2u0MDWBU0tzsG0XF/BpJkNCSOPG+g1k/fr1ta7n8XgQCoWwtbWFj4+P4q1Ck8LC\nQixatAgA8PrrryuWR0dHw9bWFkOGDIGZmRkiIyMxbdo0AFXtDNevX8fMmTPZFpuT2hq/azP3pecA\nAAEeduhkZ4UHWXW30XSys9LJTIaUa0IIMRbWAWTTpk1gGEbxrzp5m0T1iaeGDx+O7777Dny++puZ\nu7s7XnrpJXz77beQSCRwdXXFmTNncPToUXzzzTewsrJCSEgI1q5dCz6fDzc3N4SHh8PKygpjxozR\n9vetVUahdpno+SVV7R5CAR8BHnZIzCquNRDxgHrf6CnXhBBibKwDyOHDhxEaGop+/fohLCwMnTp1\ngqmpKR4/fow9e/bgt99+w5o1a+Do6IiTJ09i+/btEIlEeOeddzQe89tvv8X69euxZcsWZGVlwcPD\nA2vXrsXQoUMBAHPnzgWfz8f27dtRWloKPz8/rFixQi9Z6ADg1FK7KqXqVVGLR3gjMatY49uMPHgs\nHqF9XSjXXBN6SyGE6AOPYTmsbkhICKytrbFp0ya16z/44APk5+dj165dAIBPP/0UcXFxOHXqlO5K\nWw83btxAjx49at1GIpXhucUnOR/7wbJhSjfkkopKvL4pBknZxZBI/7u8QgEP7vZWOPJ+P7Qw1b7/\nwmfHbmNXTHKdbzkhfTqAz+fp/C2lMTcI6gNdD1V0TZQ15utR272T9d3jf//7HwYMGKBxfZ8+fRAf\nH6/4uUuXLkhPT+dQTOPTxVO5RCrDO7tv4F5GkVLwqFrH4F5GEabvuqH1JFQSqQwxLNpqGACHbqRh\nV0wyHmRVBQ/gv7eUnTHJmLIjjibDIoRojfUd097evtbuXH/99Rdat/5vfvDs7GylnxuL1i24vxm8\nsu6K4kas70z06H/fJtgok0gpI54QojesA8iYMWNw/PhxfPHFF3j06BEqKysBAKmpqVi5ciX++OMP\nvPbaawCqBmLcu3cv+vXrp59S65G9NfdZCe9mFGHS9usoFVeyfjuITszR6uk/o7AcunppqE85CCGE\n9eP29OnTkZOTg59//hn79+8Hj8cDj8eDTFZ18xk/fjxmzpyJsrIyzJgxA66urpg9e7beCq4vnk7W\nuJ/JfYKomKRcfLDvJuu3g4c5xYhJykGgyIHTeeS5Jrq652tbDkIIYR1AeDweFi9ejNDQUJw7dw6p\nqamorKyEq6srgoKC0KlTJ8W2O3fuhJ+fn8o4Vo1B13at8Hs8u2zymv5Oy2d9Y5fKgMwC7t2GueSa\n6LMchBDCucLf1dUVkydP1rjewsICvXv3rk+ZjOr20wKt980uEoPPA6uhULTNRGeba8IWZcQTQrTF\nKYA8fPgQp06dQm5uLqRSqcp6Ho+Hzz77TGeFM4ZyifZ1QwwAeyszZBXVPbd6fTLR68o1AQALIR9l\nLH4XXWXEE0KaH9YB5NSpU5g7d66izUOdphBA4lPztN5XwAe6utog8k6WXjPRhQI+dkzphWX/9viq\nnuPhbl8VEGQMg92xj/WeEU8Iab5YB5ANGzbAxcUF33//Pby8vBpl+wYbRWWVWu/byc4Ka8f7Yfqu\nG3rNRAeqgsjnI32q8kKScpBZUA5HG3P0c7dTZJ8/zC7RezkIIc0X60fPx48fY/LkyejSpUuTDR4A\nwKvHw7i9lRmuP3qGLaE9MKmfG55zsIJ8vig+D/Cwt0SwtwOGP++ks+6zQgEfgSIHjO3VHoEiB8Xb\nhPwtRV4O+UuGgA+IHK0wqZ8bTatLCKkX1m8gzs7OWs8E2Jj4tW+Ni/dztdo35mEuriXnoqOtJUwE\nfMgYmWJ4eBkDPH5WiqTsEkQmZBlk4MO63lIIIaQ+WAeQsLAwrF27FsOGDUP79o1vEiS2JvTuoHUA\nAaq6xSZmq88jqT60iaaBD/VB/pZCCCG6xDqAJCYmwtTUFMOHD4dIJELr1q1Vhmrn8XjYsmWLzgtp\nSD06GHb4lepDinw+0seg5yaEkPpgHUAiIyPB4/Hg4OCA/Px85Ofnq2yjr7nKDSl021WDn7P6kCJU\ntUQIaSxYB5CoqCh9lqNBkEhluJPBfRgTXaAhRQghjQ097lZz8X6W0c5NQ4oQQhobjW8gw4cPxyef\nfIJBgwYpfq4Lj8fD8ePHdVY4Q4tOzDHauWlIEUJIY6MxgNja2sLMzEzp56ZOxmYQKz3R9ZAiNI0t\nIUTfNAaQ3bt31/pzU2RtITTauQV8nk5u8OJKGZadSND5NLaEEFIT59F4xWKxIhO9oKAAZ86cgYmJ\nCYYMGQJra2udF9CQisokRjt3pVRW715YEqkMYT/FqQxfYsicE0JI88H6LlJYWIhp06YhJCQEAFBU\nVITRo0dj6dKlWLhwIUaMGIHU1FS9FdQQaua1GNKj3BLEJNWvDUbf0+kSQkh1rO+Yq1evRmxsLAYO\nHAgAOHz4MJ4+fYr58+dj9+7dEAgE+OGHH/RWUEPo06mN0c5d315YEqlM79PpEkJIdawDSFRUFEJD\nQzFz5kwAwOnTp2FnZ4fJkyejV69eePPNNxEdHa23ghqCCd+4iZB2WszHLicf1p0Nec4JIYTUB+sA\nkp+fD3d3dwBAXl4e4uPjMWDAAMX6Vq1aoaKi7omUGrLsYrFRz8/UY47BjMJyvU+nSwgh1bEOIG3b\ntkViYiIA4MSJE2AYBsHBwYr10dHRaNeune5LaEBOLY2bh5FbpH0Ac2ppDrbt4pRzQgjRBda9sEaM\nGIHNmzcjOTkZV69ehaOjIwYOHIiUlBQsX74cFy5cwIIFC/RZVr0L8DDe1K58HpBZVIH9cSla5W0E\neNihk50VHmTVXY1F09gSQnSBdQD54IMPYGJiguPHj6N79+74+OOPYWpqiuLiYvz111+YOXMmJk2a\npM+yNmkCPg9rzt6HjNEub0Mo4CPAww6JWcV1VoQJjNzWQwhpGjjlgbz//vt4//33lZZ5e3sjNjbW\nqF1gdcWYQ5nUZ64Qeda5yNEKndu2xO30wlrPdS+jCFN2xFE+CCGkXlgHkNxcdpMsNeYhT57mlxm7\nCErqmitEU9a5qYAHsVTzewjNQUII0QXWASQgIIDVfB8JCY03SS2n2LC9yHgAp7yN6m8LtWWdS1n0\n5qI5SAgh9cU6gMyYMUMlgEilUuTm5uLy5cswMzPDBx98oPMCGpKtlfZ5GFyZC/mokLDrd6turpC6\nss61PS4hhLDFOoDMmjVL47rS0lKMHz8eDx8+5HRyqVSKXbt24ZdffkF6ejqcnZ0xYcIEvPXWW+Dx\neGAYBuHh4Thw4ADy8vLQvXt3LFmyRJGPomsurSz0clx1ylkGD0A1b4Nt1jnX4xJCCBc6qbto0aIF\nxo4di19++YXTfhs3bsTq1asxcuRIbNq0CcOGDcM333yDbdu2AQA2bNiATZs2ISwsDKtXr0ZRUREm\nT56MoqIiXRRbhTG78damZt4Gl6xzLsclhBAuOI/Gq0lxcTEKC2vv/VOdVCrFjh07MHXqVLz33nsA\ngL59++LZs2fYvn073nzzTURERGDmzJkIDQ0FAPTs2RODBw/GoUOHMGXKFF0VXaGhtgXUzNvgknXO\n5biEEMIF6wDy999/q10uFotx9+5dbNu2DV27dmV94uLiYrz66qt48cUXlZZ37NgRz549w9WrV1Fa\nWqqU7W5jYwN/f39cvnxZLwGkIQ4wyANUkgrlWef1Ka664xJCCBesA8jYsWM19sJiGAZ2dnZYuHAh\n6xPb2Nhg6dKlKsvPnz8PJycnZGZmAgBcXV2V1rdr1w5RUVGsz8OFMfNA1JHf5BeP8FZaziXrXNNx\nO7dtieccrXDhXhYFEkKIVlgHkOXLl6tdzufzYW9vD39/f5iY1K9G7ODBg4iJicGSJUtQXFwMU1NT\nxeRVcpaWligu1u7GWVcX41v32VfBGUJvVwvM72uNxPv3VNZ5t+EjMavubsA1mQkAoYCHhPRCLP71\nHwh4gEtLIbq1tcC0XrasRiQuK6vKl2nMXbZ1ia6HKromyprq9WB9xx89erQ+y4Fjx47hs88+w0sv\nvYSQkBBs3rxZ4xsPm3wUbdha6qxJSCf6uFpqvKFP62WLlAIxbqVz60VVIQUqqme9M0BKgQSpBRKk\nFIjx1ZC2Rh/WnhDSOHC6Y8pkMvz66684d+4c0tPTIRQK4ejoiEGDBmH06NFaD2eyY8cOfPvttwgK\nCsKqVavA4/FgbW0NsVgMiUQCofC/ucpLSkq0njrX29u71vUeIhk+jTyp1bF1jQfAz6sjvGvJ0Tjo\n5YWvfr+DfXEpSkOhaIMBEJ9ejsNJDD4f2bnWbeVPUXVdz+aCrocquibKGvP1uHHjhsZ1rANIeXk5\npk2bhri4OFhZWaF9+/aoqKhATEwMIiMjcfjwYfz0008qVU51Wb16NTZv3oxXX30Vy5YtU1SDdejQ\nAQzDIC0tDR07dlRsX/NnXWpI7QD21mZ19pASCvj48lVfgAfsin1c73NSdjohhAvWd4n169fjzz//\nxIIFCxAbG4sjR47g6NGjuHr1KubPn4+bN29i06ZNnE6+c+dObN68GaGhoVixYoVSG4qfnx/MzMwQ\nGRmpWFZQUIDr16+jb9++nM7DVkPqhdXGUohNFxKx99pjXLiXVWvZPn25M/p72EEXFU81ZyuUSGW4\ncC8L++NS6iwHIaR5Yf0GcuLECbzxxhuYPHmy0nKhUIjJkycjMTERf/zxB2bPns3qeFlZWVi1ahVE\nIhFGjBiB+Ph4pfW+vr4ICQnB2rVrwefz4ebmhvDwcFhZWWHMmDFsi81JQ+qFdTejGHczHgCoqs5y\nt7dE/+fs1Q7vLhTwsWNKLyz7d3iT6gMruttbwc7KDDFJ7AbDlGenaxqosZOdFbzb8DGtV+MdNJMQ\nohusA0hWVhY6d9ZcN+7j44Njx46xPvGVK1cgFotx//59jBs3TmV9bGws5s6dCz6fj+3bt6O0tBR+\nfn5YsWKF1m0gdckobJjDejAAErNLqv5pGN5dKODj85E+VcOcJOUgs6Acjjbm6Oduh+jEHFx7lMsq\nb0TAr5qbXdNAjVXDzAMpBWIc9PKiqi5CmjHWAcTZ2Rk3b97Em2++qXb9jRs34OjoyPrEr732Gl57\n7bU6t5s3bx7mzZvH+rj1Yewpbdmoaxh2oYCvGBxRPk/Ik/wyOFqb4ymLca862Vnh/N3sWgdqlDe4\n03DwhDRvnLrx/vjjj2jXrh3CwsJgZWUFoCqjPCIiAsePH8eMGTP0VlBDaKhjYVXHALjyILvWhm51\n1U9s2kd4APq62yI2KVfrYeYJIc0H6wAyffp03L59Gxs3bkR4eLhi4qjc3FzIZDIMGjQI7777rt4K\naghCAR+tzQXIK5cauyi1SswuwdjwGLzR0xUurSyUMsk1zRNSV0CQZ70PFNlh7zV2PbpoOHhCmjfW\nAUQgEGD9+vW4ePEioqKi8PTpUzAMAxcXFwwePBiDBg3SYzENp7OLDaKTnhm7GHW6mVqAm6kF4POq\nGsrlQ56wnSdEPpmVvKG9n3vV/of/SmM9xhYNB09I88Y59TowMBCBgYH6KEuD8CSv1NhF4ETG/Dd/\n+v3MImQVlrMa3qStjTlmBnvApZUF+rn/9wbDZaBGQw0HL2/LySgsh1NLcxq7i5AGQmMAiYuL0+qA\nvXr10rowDUFeWaWxi6AVBkBMUi7rXJDMonK4tLJQqX7iMlCjvoeDr60rsfyNiwIJIcajMYBMnDiR\n05hTDMOAx+M1+sHCyisaZwCRYzugiabqJ6GAjwAPOyRmFdd6LH0PB1/bnO/yNy5NXZoJIYahMYCo\nG323pKQEX3/9NaZOnQoPDw+9FswYJFIZ6jmkVKNRW/XT4hHeSMwq1tiWwgPQra25yjDzulRXW468\nFxh1JSbEeDQGEHWj7+bl5eHrr79G//799TaciDFFJ+agspkEkNqqn+rKbPdqXZWJrs+3DzZzvlNX\nYkKMq2GNX25kDTUTnQt576q6tqmr+qm2zHZ185PoEpc536krMSHGQwGkmsaQiV4XDwcr2FubaUwG\n1DTLoSbyzHZ5T6jDf6VBUlCKbm0tdFru6rjM+U5didWjnmvEECiAVBPgYYcWpnyUio0/4qypgAcx\nxwaZ6sFBU/WTPN+D7c1EbU+of2cxDEpi9NITqiF2JW4sqOcaMSQKINUIBXz07miL8/eyjV2UegWP\n2qqfuNw8NPaE+ncWw50xyXrpCdWQuhI3JtRzjRiaVp8ifU0p2xD8ML6bsYvAWVsbM0zq56ZyY5BX\nP43t1R6BIgfONw0uPaF0Sd6VuK5Pmb67Ejc2xvp7keZL4xtIly5dNAaKadOmqZ2+lsfj4datW7or\nnRH8mdzwhzGpyc3OUuddWY3dE4pNV2IubTlNnbH/XqR50hhAhg8f3qTfNDS5kshu4qWG5HFOKesb\nAtvGVWP3hKqrKzHXtpymzth/L9I8aQwgK1asMGQ5GgyZrPElgjwtKMf7e/7CxpDunIZ419S4Kq6U\nYfPFh0bvCaWrtpzmgHquEWOgRvQaWrUQGrsIWjmbkIkpO+LUNpByaVwFgLCf4hD7kP2bmL57QlWf\nJIuoRz3XiDFQAKnBzsrM2EXQ2pXEHHz1+x18+aqv0nIujavy/+eitp5QlI9gGNRzjRgDBZAa8krF\nxi5CvRy8kYYFw73QwrTqT8u1cZVhGNYDMgKae0JRPoJhNZRBMEnzQgGkhtYtTI1dhHopk0gx6+e/\nMLGvGzIKy5FVWI6kbHaNq0nZxWA4NgGp6wlF+QjGQT3XiKFRAKkht6TC2EWotwv3snH+XjZkTFWi\nD9u8eq79BwLcbdUGARpJ1zio5xoxNAogNeSVNO4qLABKQ9JzGZSFzwMYht2cInwA0wM7qW2wp3wE\n46Gea8SQKIDUwOc3v9wXOXd7KzAMg8Tskjq3dWlpgkqpDPvjUpQaxykfoWGgnmvEECiA1BDgYYcd\n0Y+NXQyDk9ePA0BSdkmdbxB55VJM331DpXH8OUcrykcgpJmgAFJDoMgBLc0FKCyXGrsoBtXX3VbR\nuFpbQ6xcsfi/tdUbxzu3tQafx649hfIRCGncqFK0BqGAD2ebFsYuhsF5OFhBKOArGmIn9XPDcw5W\nkFebC/hAK4vanzcYAHfSi2Btzu65hPIRCGnc6A2kBolUhkrG+POBGFpsUq6iQVtdQ6yttSmWn7iL\n/AbVEVoAACAASURBVLLKWo/DtiMX5SMQ0vjRt7eG6MQcPMqpuxG5IeHzAKGgfo3/8gbt6qoPBy/g\n8Vlfl+KKSvg4t9Q4HHtjykeQSGW4cC8L++NScOFeFiRsG3gIaQboDaQGLoPSNQSd21rjoxdF+O7U\nfdzNLNL6OFIZsOXiQ43dPbkO1tfLrTV6tG+N2Ie5inwEPg9wsjGHWxtLTAnooHVZDYEy6QmpGwWQ\nGrgMSmdsFkIB9k3vgxl7b+JePYKHXHRSrsYBGblel12xj+Fub4W+7raY95IIu2KS8Si3FJmF5Xia\nX45rybnoZGeFvp1sEehph+xicYMZK4sy6UlToe+x6CiA1MBlUDpj6+fRBqvPPqizxxQX0Yk5+OqP\nOwjyclD60HG9LjLmv5vtsVtPkV8mUVovvxk/yCrGrqtV3aYbyhM+ZdKTxs5Qb9ANJoCcO3cO8+bN\nw82bNxXLGIZBeHg4Dhw4gLy8PHTv3h1LliyBu7u73srBdlA6tpxtzPH+YHdcvJeDRznFeJRborO3\nmwEedlgT+UBnwQOoujnuu56CPVcfQ8Yof+j6uttyvi4MoBI8NGkIT/jaZNIT0pAY8g26Qbx///XX\nX/j4449Vlm/YsAGbNm1CWFgYVq9ejaKiIkyePBlFRfWvrqnN4hHeiqS6+uABeNHHCSF93LB1Uk+c\nnDMQ2yf3whvdXXRy7Igrj1BQR68obUikjCKPQ/6h2xmTjMSsYvR1t61zrvL6Mubc3dpk0hPSkHB5\ng64vowYQsViMrVu3IjQ0FCYmyi9DxcXFiIiIwMyZMxEaGorg4GBERESgpKQEhw4d0mu55LkQoX07\nwEyg3THU9TSS92p6uasz6vtgLRTwkJpnuCxuBlVdfT3srfCKV0u0txHqNZAY6wmfZvYjjZmh36CN\nGkAuXbqELVu24JNPPkFISIjSuvj4eJSWliI4OFixzMbGBv7+/rh8+bLeyyYU8PHlKF/sH++G3u0s\n4GBtprhhCviAyNEKoX07ILRPB5WEO5GjFSb1c9P4iihvT6gPsVSXFVfsMABiH+ZiWi9bbBjZDlMC\n3PR6PmM84cs7C7BBmfSkoTH0G7RR20Cef/55nDt3Di1btsS6deuU1iUnJwMAXF1dlZa3a9cOUVFR\nhioizE34+Dy4LTxEnhpHN+U68qmu21kM6WFOMW6lW6GnSwsMFNlhZ2yy3nqsGeMJX5uZ/RLvs5/+\nlxB9MvQbtFEDiKOjo8Z1xcXFMDU1hamp8gRPlpaWKC7WrodUQgL3Or+ysjIAQOL9e3AA4GAFQFqi\nctOobZ06r7vzcOuROeLTyxtVEJHKgOuPC5CeXwqHliVwthYitYBdIzlXAh5QUZCNhATDJnZ6t+Ej\nMav2rHqefLv79xSfEW0+X01VY7wmlTIGt9LLkFtSCVtLE3RrawETHY3ObajrISkohYCnPKWDJrr4\nfjWYXlg1MQwDHk/9H0/T8sbEhM/DV0PaYmtcLm6ll+FJoYTVH70h+ONBGRiUQcArhIVQf38Ll5ZC\ndGtrobfjazKtly1SCsQagzsPQLe25pjWy1bt/vq8ERHdk0gZbPtT+Xso4P33+ZvWy7bR/P26tbWA\nS0shUlg81Oni+9VgA4i1tTXEYjEkEgmEQqFieUlJCaytrbU6prc396Ez5E8M2uzLxipPGb764w7O\nJWTiqREbZNk+tQD/PZlLGeVRedXhAbCxELLuylt9vyAfFzzv05nTfrpy0MuL9cx+8s+I+3OelL3+\nL31/b3RFIpVhyo44RCcWKnd5ZYCUAglSCyR4Vmla7y6vhrweQUkMdsYk1/kGzfb7dePGDY3rGmwA\n6dChAxiGQVpaGjp27KhYXvNnfZM/TcYXp+g8k1NTf21jEPB5kNbzFcjGwgTFFZUqN9tPhnpi+Ym7\nOBb/hFW344YwVhbXmf0qZQxlrzdCTTFpdPEI71qnZNDl96vBBhA/Pz+YmZkhMjIS06ZNAwAUFBTg\n+vXrmDlzpt7PL8/kPH/7yb+vtRk6f5qs68NrSLro1WVvZYY147ohp6hC6WYrkcrwKKcEhXUEj4Y4\ndzfbmf22xuWqPMVW1xhvRE1dU51+WZ6GwPYNuj4abACxtLRESEgI1q5dCz6fDzc3N4SHh8PKygpj\nxozR67kNkcnJ9sNrDNXfJHhgP0T7o9wSCPg8jO3VXmk520AZ5OmIjSHdG8WXtDr5W2pTuxE1dU15\n+mWub9DaarABBADmzp0LPp+P7du3o7S0FH5+flixYoXWbSBsGeK1lsuH19AcrM2xepwncovEuJtR\nhO3Ryaz2k3cLrD6Am52VKaITs1kFoeTcxjWMvpy88ZWNxnYjasqaQ9Io2zdobTWYADJr1izMmjVL\naZmJiQnmzZuHefPmGawchnqtbcjDxj/MKcadp0WwtzZDqxZC1lPU8nnA2YRMbL38SPHazOUNprHe\nXHNLKll3QGisN6KmiMsI05Q0ql6DCSANhaFeaxvysPFSGfD9mfsAqr44Aj4PMhZ3SDMTASLvZCkF\nDC5VdI315mpracK+730dNyJ9D79N/qNN0ihRRgGkBkO91nL58JoL+SiXGCfSSGWAlGUYKJNI63Wu\nxvqUx6XvvaYbEU1gZXhsR4Sg6Zc1oytSg6HGQpJ/eNmkJ5mZNPw/k4Ww/mVsrE95JnweurW1qPNv\nqelGJO+0sSsmGQ+yihUPMNVHQp6yI46GjtcD+cjbTWH6ZWNo+HcmAwvwsIOVGbsXMyszk3rd8Nh8\neH3atkRxhe6HbNeWUMBTfGjkA0cO8XaAuJ43t8b+lDetl63WNyJDDr9NlMm7vE7q58Z5UFRCVVhG\nVVd/7d4dbZGYVdSg2klkDIMQv9ZoYyGAn1dH9HO3w+G/0hCZkKX1MZvCU54Jn6dV3/ummovQmBiq\ny2tTRAGkhujEHBSVs3viLyqvrHevIU0f3l5ubTB91w3EPnzG6Xg25iYoYFl+bUhlQBsLAV56riW8\n//29uXYIkPfqaoiJg/WhzY2oKeciNDb67vLaFFEAqSGjsJxVl1Wg6iaoq15DNT+8nx27jehEbmP1\nO9uYY+nIzpix9y+9vbUI+IBtC+WPDZcOAR72lpg/1Auxj3IBBujnYYtAkUOjDx7VcbkRNYdcBNJ0\nUQCpoSH0DdcmS10+fW6wlyPrm7k2OtlZqYzgyWV+ExMBHytP31NU8eyMTW7WPY0awueNEG01r28r\nC1xmC9RXryFtstSr34DZ9u7iSt5WoW5o67o6BABAKwsh7mUUUU+jahrC540QbVEAqYHtDVifvYa4\nZqkHuNsq9RRh1TXR3Rb93G1ZB5q6Grrr6s3i5WSNgjJJo+5pJJHKcOFeFvbHpeDCvSydBLuG8Hlr\nzPTxNyHsURWWGoYcDlkdLtUafB4wPbCT0o2F7WicAFS24aGqq65EyoABt4bu2joEjFof3Wh7GtWV\n5Pe6O69eEw4Z+/PWGFHiZcNAAUSN6jfgKMVw7obrNcSlUVpenprY9gjSdMOPS36mdXfGmo3IF+5l\nNdqeRmxGZr71yBxfDWmr9TkMOfx2U2CI0bIJOxRANJDfgF935+FWehnMbOwN1jdcl0MssOkRpG4b\nXd7AG3NPIzZJfvHp5dgal4sf6zHNB+UisNcUJ4FqrCiA1MGEz0NPlxbw9m5f98Y61JSqNRprTyMu\nSX630st0UvVGuQi1o8TLhoWubAPVlIZYaKw9jbj0hntSKEFMEre8HcKdNomX5P/tnXlUVEf2x78s\nDSOigIqIwXGlW6BZmlUUgYYRRUlcJggR3MAoxmgiyDKYqLhEFHUUFEUERdxwJTFRTBR0QFBEjA7G\nLUAUFVzYZFO2+v3h9Pv5aHaRlqY+5/Q5/e57r96t+6r7Vt3aPhy0BfIRIy1hja666mmbQm8dOKmU\n0jRdORwqjVAH0gWQhrBGVwzJtSn0JvPxhN6kma4aDpVWPo6qHkXq6YohubaE3j7pzfloQm/STFcN\nh0ortAVC6TS6WkiuLaE3I80eH2UepI2uGg6VVqgDoXQ6XSkk15rQm5Hm3/ClWd/OVq3b0hXDodIK\ndc8USjO0JvS2+h+a7zUTndI2umI4VFqhLRAKpQVaCr3dufPxrt8lrXS1cKi0Qh0IhdJKulLorbtA\n34lkoa6aQqFQKO2COhAKhUKhtAsZQkhbNr7rsly/fl3SKlAoFEqXxMTEpFF5t3EgFAqFQulYaAiL\nQqFQKO2COhAKhUKhtAvqQCgUCoXSLqgDoVAoFEq7oA6EQqFQKO2COhAKhUKhtAvqQCgUCoXSLqgD\noVAoFEq7oA6EQqFQKO2COpAWOHr0KBwcHGBgYAAXFxfcuHFD0ip1CnV1ddi7dy8cHR1hZGSEiRMn\n4sCBAxAtXEAIwc6dO2FrawtDQ0PMnTsX2dnZEta686iuroajoyMCAgIYWXe0SVpaGpydnWFgYACh\nUIjQ0FDU1dUB6J72qKurQ2RkJMaNGweBQABnZ2ekpaUx56XOJoTSJCdPniQjR44kYWFh5OLFi8TT\n05MIBALy6NEjSav2wQkNDSV8Pp+Eh4eT1NRUEhoaSnR0dMju3bsJIYSEhYURfX19EhMTQ86fP0/+\n+c9/EisrK/Lq1SsJa945bN68mXC5XOLv78/IuptNMjIyiJ6eHvH39yepqakkMjKS8Pl8EhYWRgjp\nfvYghJCIiAiio6NDdu7cSS5fvky8vb2Jnp4euX37NiFE+mxCHUgT1NfXE6FQSFasWMHIqquriZ2d\nHVmzZo0ENfvw1NbWEoFAQP7973+z5KtWrSKjRo0iZWVlxMjIiERERDDnSkpKiEAgINHR0Z2tbqdz\n+/ZtYmRkRCwsLBgH0h1t8sUXX5D58+ezZCEhIcTd3b1b2oMQQiZMmEB8fX2Z49raWmJjY0OCgoKk\n0iY0hNUEDx8+xJMnT2BnZ8fIOBwObG1tkZycLEHNPjzl5eWYMmUKHBwcWPKhQ4eiqKgIV65cQWVl\nJezt7ZlzKioqMDc3l3rb1NbWIjAwEJ6entDQ0GDkN2/e7FY2KSoqQmZmJqZPn86SL1u2DLGxsd3O\nHiKqq6uhrKzMHMvJyaFXr14oLS2VSptQB9IEf/31FwBg8ODBLPmgQYPw6NEjJs4rjaioqGDFihXQ\n1dVlyZOSkjBgwAA8e/YMwFtbvIuWlhZjN2klMjISNTU1mD9/Pksuynd3scm9e/dACIGSkhK8vLyg\nr68PS0tLhIWFob6+vtvZQ4Sbmxt+/PFHpKWloaysDDExMXjw4AEmTpwolTahW9o2QXl5OQCgZ8+e\nLHnPnj1RX1+PqqoqVk1D2jl27BhSU1Px3Xffoby8HAoKClBQUGBd07NnT8Zu0kh2djZ27dqFffv2\nieW9u9mkuLgYAODn5wcnJyfMmTMH165dw86dO6GoqAhCSLeyh4gvvvgCV65cwZw5cxjZt99+C3t7\ne0REREidTagDaQLyv9FGMjIyjZ5vSi6N/PTTT1i5ciXGjx8Pd3d3REREdDu71NfXY/ny5fj8888h\nEAjEzhNCupVNampqAABWVlbw9/cHAIwaNQrFxcXYuXMn5s+f363sAbwtA56ensjOzsbKlSsxfPhw\npKamYseOHejdu7dUlhHqQJqgV69eAICKigr069ePkVdUVEBOTk6sZSKt7N27Fxs2bICdnR02bdoE\nGRkZ9OrVC9XV1aipqQGHw2GuraioYOwmbcTGxiI/Px+7d+9GbW0tIyeEoLa2ttvZRFT+x44dy5KP\nHj0aBw8eRO/evbuVPYC3u55ev34dW7duhaOjIwDAwsICdXV1CAkJwdKlS6XOJrQPpAlEfR95eXks\neV5eHoYMGSIBjTqfLVu2IDg4GJMnT0ZoaCjT9B48eDAIIXj8+DHr+sePH2Po0KGSUPWDc/78eRQU\nFMDMzAx6enrQ09PD3bt3ER8fDz09PcjLy3crm/z9738H8P8tEREi59rd7AEABQUFAAAjIyOW3MTE\nBFVVVZCRkZE6m1AH0gRDhgyBpqYmzp8/z8hqampw8eJFWFpaSlCzziEmJgYRERGYNWsWgoODIS//\n/41VgUAARUVFlm1KS0uRnp4utbYJCgrC8ePHWZ8hQ4ZAKBTi+PHjmDRpUreyyYgRI6ChoYGEhASW\n/NKlS+jfv3+3swcApmKZmZnJkt+8eRPy8vJwcHCQOpvIrVq1apWklfgYkZGRAYfDQXh4OGpqalBd\nXY3169cjJycHGzZsgIqKiqRV/GA8f/4cXl5eGD58OBYsWIBnz56hoKCA+QwcOBAVFRXYvXs3FBUV\nUVxcjBUrVqCmpgbr1q2DoqKipLPQ4aipqUFDQ4P1OX78OAYNGgQ3NzcoKCigrKys29hERkYGampq\niIyMxMuXL/G3v/0NR48excGDB+Hn5wdjY+NuZQ8A6N+/P7KysnDkyBEoKSmhsrISJ0+eRGRkJGbN\nmoUJEyZInU1oH0gzuLm54c2bN9i/fz/27dsHHR0dREVFiQ3DkzZSUlJQXV2N+/fvw8XFRex8Wloa\nvL29ISsri+joaFRWVkIgECA4OLjLxnI7gu5mkylTpkBeXh4RERE4efIkNDU1ERQUxJSZ7mYPANi2\nbRu2bt2KXbt2obS0FIMHD8by5cvh6uoKQPpsIkNEw40oFAqFQmkDtA+EQqFQKO2COhAKhUKhtAvq\nQCgUCoXSLqgDoVAoFEq7oA6EQqFQKO2COhAKhUKhtAvqQDqIgIAA8Hg81kdXVxdmZmaYM2cOrl69\nKmkVO5THjx+Dx+Nh9+7dLHnDpV8kgZ2dHTw9PSWtxnvTUbYMCwsDj8fDixcvOiS9xvgY3ntrKS0t\nxZgxY/DgwQOW/NWrV4iIiMBnn30GgUAAY2NjzJw5kzVzXISdnZ3Y753H48HY2BiTJ0/Gvn370HCG\nRMNyKXovPB4Pubm5TeprY2MDHo+HsLAwAG/XX5s6darYKgCSgE4k7GA2btzIfK+vr0dhYSEOHDgA\nDw8PxMTEwNTUVILadRx9+vTBxo0bWXuGeHh4QEtLC6tXr5agZkBgYGCXX+xyx44dOHPmDH755RdJ\nq9Iix48fR3BwMDIyMiStSqvYsmULRo8eDW1tbUb24MEDeHl54cWLF5gyZQpcXV1RUVGB06dPY9Gi\nRfDx8RHbA2bYsGHw8vJiyQoKCnDixAmsX78eb968wYIFC1qlU1JSUqPrYWVlZTFrbImQkZHBkiVL\nEBQUBGtraygpKbU26x0OdSAdzOTJk8Vktra2cHJyws6dOxEVFSUBrToeJSUlsbxevny50Znrnc0/\n/vEPSavw3ly5cqXLbFqWkZGBN2/eSFqNVpGdnY1jx47h9OnTjKyqqgqLFi1CVVUVTp06heHDhzPn\nPDw8sHDhQmzevBkCgQBmZmbMuX79+jX6e3dzc8OECRMQFRWFuXPniu3/0RAtLS0kJSXBw8ND7NyF\nCxegpqbG7L8iQigUYsuWLYiOjsbXX3/d6vx3NDSE1QmMGDEC2trauHHjhqRVoVC6NYcOHYK2tjbL\nSRw8eBAPHz5EYGAgSw683ZJ2xYoVkJWVRVxcXKueoaysDHt7e5SWliInJ6fF64VCITIzM1FaWip2\n7vz58xAKhY3eN3HiRBw5ckRsReTOhDqQTkJOTk6sRnn48GE4OTmBz+dj7Nix+OGHH1BRUcGcP3ny\nJHg8Hn799VfY2NhAIBDg4MGDTT4jPz8ffn5+GD16NIyNjeHu7i4WVjh9+jRcXV1hbGwMPp+P8ePH\nIzIykhWvtbOzw+rVqxEbG8s8d+7cubhz5w5zzbt9IKLvABAXFwcej8csWZ2TkwMfHx9YWVmBz+fD\n0tISPj4+zLa4zdFSfmbOnImvvvoK69evh6GhIaysrPDs2TOxWDOPx0NMTAy2b98OKysrGBkZwcvL\nC4WFhcjMzISzszMMDQ3x6aef4vLlyywdKisrsWHDBtjY2IDP58PR0bHZd9CSboQQxMbGYtq0aTAy\nMoKBgQE+/fRTnDhxgmX/9PR05Obmgsfj4eTJk8y5lspMc9y7dw+urq7Q19eHg4MDYmJimHNJSUng\n8XiIj48Xu2/KlCmsHfYa5vPUqVOorq5mxekB4OzZs5g2bRr09fVhYWEBHx8fPHnyBMDbHQ11dHSw\nadMmVnrTpk2Drq4ua4e+8+fPg8fjISsri/lN3L9/H4sXL4axsTFMTU3h7+8vVktvSFVVFeLj48X+\nkM+ePQtlZWVmD4+GaGlp4eeff2aFp1uiLWEle3t71NbW4j//+Q9LnpeXh/v37zfZohYKhXjx4gV+\n++23Vj+ro6EOpBN4/vw5cnJyoKOjw8i2bNmCoKAgjBw5EsuXL4ejoyMOHTqEefPmsTYsAt7G9KdP\nn44vv/wSFhYWjT6jqKgIzs7OOH/+PJydneHj44OysjJ4enoyf/xHjhzBsmXLoKGhAX9/fyxbtgxK\nSkrYtGmTWKw9MTERW7ZswZQpU7Bw4UI8ePAA7u7uje7dLOoPAd7uSrdx40b06dMHz58/h6urK7Ky\nsuDh4YHvv/8etra2OHPmDAIDA5u1WWvyA7xd2PHSpUsICAiAi4sLNDQ0Gk0vKioKCQkJWLhwIZyd\nnXHx4kUsWrQICxcuxKhRo+Dr64vCwkJ88803TE2wtrYWX375JY4cOYJJkyYhMDAQ2traWL16tdgf\nX2M0ptuWLVuwbt068Pl8LF++HIsXL8abN28QGBjItFADAwMxbNgwqKurY+PGjUzYpC1lpjEWL16M\n/v37IyAgAIMGDcIPP/yA8PBwAG93FlRVVRXrmM3NzcWdO3cwadKkRtP08vKCqakpOBwONm7ciHHj\nxgF4ux3At99+C0VFRfj6+sLV1RVJSUmYPn068vPzoaamBj6fj/T0dCat8vJy3L17F3V1dfj9998Z\neWpqKvr16wc9PT1GNn/+fNTV1cHPzw8TJ05EfHx8i31vmZmZKC8vZ22CVV9fj7t370JPTw9ycnJN\n3jt8+HDIyrbu77K+vh4pKSlQUlJq1d5BI0aMwKBBg5CUlMSSX7hwARoaGtDX12/0vpEjR6J///5I\nTk5ulV4fBELpEPz9/QmXyyWFhYXM5+nTpyQ5OZlMnTqVcLlc8uuvvxJCCMnNzSU8Ho9s376dlUZS\nUhLhcrnk+PHjhBBCTpw4QbhcLlm5cmWLzw8ODiYjR44kWVlZjKy4uJiYmJgQf39/QgghEyZMILNn\nz2bdV1ZWRvh8PlmyZAkjEwqFhMvlkpSUFEaWk5NDdHV1ybJlywghhOTl5REul0siIiKYa7hcLvn+\n+++Z44iICKKjo0Py8vJYz/T29iY8Ho9UVFS8V37c3d0Jl8slN2/eZN0rFAqJh4cHSy9TU1NSUlLC\nyGbMmEG4XC6Ji4tjZCJ7JycnE0IIOXr0KOHxeCQ9Pb1R3R4+fNik/o3pVl1dTQQCAQkMDGRdm5OT\nQ7hcLtmwYQPr/vHjxzPHrS0zjREaGkq4XC4JCAhgZHV1dWTWrFnEwMCAvHr1ihBCyHfffUf4fD4p\nKytjrtuxYwfR09MjxcXFTabv7+9P+Hw+c1xUVEQMDAyIu7s7qa2tZeS3bt0iI0eOZMrQtm3biK6u\nLvO8pKQkoqenR0aNGkW2bt3K3Ofg4MC8c9E78vX1Zeng6elJ9PT0SHV1dZN6btu2jXC5XFb+CgsL\nCZfLJUuXLm3yvsYQCoXExcWF9Xt/8eIFuXXrFvHx8SFcLpfs2LFD7J53y6XovTx//pysW7eOmJqa\nkpqaGua8u7s7WblyJXn+/DnhcrkkNDRUTA9PT0/i4ODQJt07EtoC6WAsLS2Zj62tLTw9PfHkyROs\nWLGCqZ0lJiaCEAKhUIiioiLmY2BgAFVVVVy6dImVZmN7cDfk0qVLEAgErFqaqqoqDh8+jGXLlgEA\nfvzxR1aIAQBevnwJZWVlVFZWsuS6uroYM2YMczx06FBYW1uL6dYc8+fPR0pKCrS0tBhZWVkZOBwO\nCCGoqqp6r/wAAIfDAZ/Pb1EXExMT1h4uopqhnZ0dIxPtQvny5UsAb2uAAwYMwPDhw1nvyd7eHvX1\n9WIhh4Y01I3D4SA1NZXV+iKEMB3QDd/Bu7S1zDTGu2E9WVlZuLu74/Xr18wQ80mTJqG6uhqJiYnM\ndWfPnsXo0aOhqqraYvoi0tLS8Pr1a8ydO5dVq9fX18eYMWOQlJQEQgisrKxQW1uL69evAwDS09PB\n5/NhbGzMyJ4+fYq//voL1tbWrGc4ODiwjnV0dFBTU4OysrIm9crLy4OqqiqUlZVZdgDQrgELN27c\nYP3ex4wZg88//xyZmZlYvnw5vvrqq1anZWdnh1evXjEh2uLiYly/fh329vbN3jdo0CAmLCgJ6Cis\nDmbv3r3Md3l5eaipqWHYsGGsH9KjR48AAFOnTm00jfz8fNbxwIEDW3zu06dPYWhoKCZ/d6iigoIC\nrl69ijNnziA7Oxu5ubl49eoVgLfN7ncZNmyYWFqDBw9GYmIiKz7dEq9fv8bmzZtx+/Zt5ObmIj8/\nn+lvafjMtuYHADQ0NFoVWujbty/rWPQ+3pWLZCK9Hj16hPz8/CZ3i2v4nhrSmG4KCgpISEhAYmIi\ncnJykJubyziO5uzR1jLTEBkZGWYbWhGifW1E/VXm5uZQV1fHuXPn8NlnnyE7Oxv3799v85waUXqN\nhW+GDx+O5ORklJWVwdDQECoqKrh69SpsbGyQnp4OCwsLqKmpYfv27aitrcXly5chJyfHqswAb8Om\n7yIa6dScIygpKWE5DwBQUVEBh8NBUVFRm/IIvO1bCwgIAPD2D3///v148OABfH19m+xPaQpTU1Oo\nqKggMTERo0aNwqVLl9CjRw9YWFg02rkuQllZGTU1NSgvLxfLW2dAHUgHM3r06BavEf1RREZGsraK\nFdFwDgOHw2kxzdbUoDZs2IDo6GgYGBjA0NAQzs7OMDMzw9y5c8WubWzooegZzcWK3+XWrVuYNWsW\nlJWVMXr0aFhaWsLAwACXL19GRETEe+cHaJ1tgKZ1lpGRaVYHbW3tJvtrNDU126QbIQRLly7FEMR7\nsAAAB8tJREFUuXPnYGZmBgsLC8yaNQvm5uZNjrQR0dYy0xhN2UAkl5WVhaOjI+Li4lBRUYGEhAQo\nKip26LBo0XvlcDiQk5ODpaUl0tPTUV5ejj/++ANff/011NTUUFVVhT/++AOpqakwMDAQ2wG0tf0R\n7yLak7yhTCAQICsrC7W1tY3aFgD8/PzQo0cPrFq1iikzKioqrN/7uHHjMGfOHHh7e0NOTk6sldQc\n8vLysLa2RlJSEgIDA3HhwgXY2Ni0OARYVC7aY4+OgDoQCSD649HS0hKr6Z89exb9+vVrV5qimt+7\nREZGoqysDNOnT0d0dDRcXFxYnY11dXUoKSkRu6+xmcWPHj2Curo6evTo0SqdQkJC0LNnT/zyyy+s\nP4DWTI5rKT/e3t6t0uF9GDhwIP78809YWlqyHE1RUREyMjLaPIHr2rVrSEhIgLe3N2uCWWtmiL9v\nmSGE4OnTp6zdNEUDIt5tmTg5OWH//v1IS0tDUlISrK2t21yz/eSTTwC87YBvqGtubi569+7NlCEr\nKyusXLkSycnJIITA2NgYSkpKUFJSQnp6OtLS0jB79uw2Pb8p+vbt2+hkx3HjxiE9PR0JCQlwcnIS\nO19QUICff/4ZJiYmzVY4FBQUsHnzZjg5OSEwMBAGBgYYMGBAq/Wzs7PD6dOncffuXaSkpGDdunUt\n3lNSUsLYSxLQPhAJIKptRkZGsuS//fYbvv3223YNy7O2tkZmZib+/PNPRlZaWoro6Gg8efKEaQY3\n/EGfOHEClZWVYjX+jIwM3L17lznOzs5GcnJyszFZWVlZVg2vpKQE6urqLOfx7NkzJn/NtTJayk9n\nYGtri+fPn4sNbQ0PD8fixYvbvHyHyFE3nGtw4MABAGx7NLRlR5SZ48ePM9/r6uoQGxuLXr16sSbH\nGRoaYtCgQfjpp59w+/ZtTJw4scV0G+pqaWkJBQUF7Nu3j5Wn27dvIzU1FTY2Noxs7NixqKurQ2Rk\nJLS1tdG7d2/Iy8vDyMgIhw8fRnFxsVj/R3vR1NRERUWFWD+Ji4sLNDU1sWHDBrElRV6/fg0/Pz/U\n1dWJzTpv6hl+fn4oKytDUFBQm/SztrYGh8NBSEgIampqWpXvgoKCNjmpjoa2QCTAyJEj4eLigri4\nOBQWFsLGxgYFBQU4cOAABg8eDDc3tzanuWDBAiQkJMDNzQ0zZ86Eqqoq4uLi8Pr1ayxatAhaWlrQ\n1NREeHg4Kisr0a9fP1y7dg2nT5+GoqKi2FwCDoeDOXPmMOP/Y2JioKam1uys1z59+iAtLQ3Hjh2D\ng4MDrK2tsWfPHvj6+sLc3BxPnz7F0aNHmWc1N3+hpfx0Bq6urjh16hSWL1+O33//Hbq6usjMzER8\nfDwcHBzavCyNsbExevbsiTVr1uDRo0fo0aMHLl26hIsXL4LD4bDs0adPH1y/fh0xMTEYM2bMe5cZ\nGRkZHDlyBKWlpeByuUhISEBGRgbWrFkjVnudNGkSdu3aBSUlpRZDayJda2pqEB4eDisrKxgYGOCb\nb75BSEgI3N3d4ejoiKKiIsTGxkJFRQVLly5l7h0wYAC0tbVx+/ZtuLu7M3JTU1Nm+O67y+W8D+bm\n5tixYwdu3brF6lNRVFREWFgYPD09MXXqVEyePBk6Ojp4+fIl4uPjkZeXh0WLFon1wzTF9OnTER8f\nj8TERCQkJGDChAmtuk9ZWRnm5uZISUnB2LFjW9Xyy8rKapWT/1DQFoiECAoKwr/+9S88fvwY69ev\nR3x8PCZMmIDY2Ng2jXgRoa6ujsOHD8PS0hIxMTHYunUr+vfvj0OHDmHYsGFQUFBAREQEdHV1ERUV\nhU2bNuHhw4fYvHkzZsyYgTt37rBqZubm5vDy8kJsbCz27NkDMzMzHDlyBOrq6k3qsHTpUlRUVGDt\n2rW4f/8+lixZgtmzZ+Pq1atYu3Ytzpw5AycnJ+zbtw8Aml1gsqX8dAaKiorYv38/ZsyYgYsXL2Lt\n2rW4ceMGFi9e3Kp5IA3p168fIiIiMGDAAISFhSE0NBQVFRWIioqCUChERkYGE9P28PDAJ598gpCQ\nEFy4cAHA+5UZWVlZREZG4tatW1i/fj1evnyJkJAQTJ8+Xexa0ZwPoVDYqnCli4sLdHV1ER4ezkyI\nnDdvHkJCQvD69WuEhITg6NGjsLe3x8mTJ5kQlwjRvAwTExNGJmoVjR07ttmwUVsQhcdEI7zeRV9f\nH/Hx8XB2dkZ6ejqCg4MRHR0NLS0t7N69G0uWLGn1c2RkZLBmzRpwOBysXbu22ZFhDRG18FvT75Sd\nnY2SkhJYWVm1Ov2ORoY07FWidHvs7OwwdOhQqVm3i9I2Hjx4ACcnJ4SHh7c4jLSrsWLFCly7dg1n\nz56VtCrvTWhoKI4ePYrExMQWO9s/FLQFQqFQWMTFxaFv374d1vfwMTFnzhzk5ubiv//9r6RVeS8I\nITh9+jRmzpwpMecBUAdCoVD+x8aNGzFv3jzExsZi1qxZrR4i3ZUYNmwYpk6dij179khalffi3Llz\nqKqqald/aUdCHQiFQgHwdpWAjIwMTJ06tdGlxaUFX19fpKen4969e5JWpV0QQrBjxw4EBgZKZPLg\nu9A+EAqFQqG0C9oCoVAoFEq7oA6EQqFQKO2COhAKhUKhtAvqQCgUCoXSLqgDoVAoFEq7oA6EQqFQ\nKO3i/wCOe9bqzyHDYQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d530778080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(bos.CRIM, bos.PRICE)\n",
    "plt.xlabel(\"Per capita crime rate by town (CRIM)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between CRIM and Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 2 Checkup Exercise Set I</h3>\n",
    "\n",
    "<p><b>Exercise:</b> What kind of relationship do you see? e.g. positive, negative?  linear? non-linear? Is there anything else strange or interesting about the data? What about outliers?</p>\n",
    "\n",
    "\n",
    "<p><b>Exercise:</b> Create scatter plots between *RM* and *PRICE*, and *PTRATIO* and *PRICE*. Label your axes appropriately using human readable labels. Tell a story about what you see.</p>\n",
    "\n",
    "<p><b>Exercise:</b> What are some other numeric variables of interest? Why do you think they are interesting? Plot scatterplots with these variables and *PRICE* (house price) and tell a story about what you see.</p>\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# your turn: describe relationship\n",
    "The relationship between CRIM and Housing Price tend to err on a negative correlation where the higher the crime rate, the lower the median price of homes. Though there are also homes that have no crime that have low prices as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2d530abb2e8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oLEe+SAxHGwu4NbPW6vyoMqyTeiIEkyPgcRU/hKSkUhNLozs1x8PG9ozZF5/L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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5307411d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: scatter plot between *RM* and *PRICE*dd\n",
    "plt.scatter(bos.RM, bos.PRICE)\n",
    "plt.xlabel(\"Number of Rooms (RM)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between RM and Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relations between the number of rooms and price have a stronger positive correlation. As the number of rooms grows larger, the median housing price tends to be more expensive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2d531d46da0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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m/RuC8vJyLDxFLTW0KfXh2mJq34BR93A2btyIxo0by/N9d+7cGUKhEJs3b8an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\nCASCSSAKh0AgEAgm4f8B0jeL7IkxCyQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d531cf46a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: scatter plot between *PTRATIO* and *PRICE*\n",
    "plt.scatter(bos.PTRATIO, bos.PRICE)\n",
    "plt.xlabel(\"Pupil Teacher Ratio (PTRATIO)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between PTRATIO and Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pupil teacher ratio appears to have a overall negative correlation as more pupils per teacher tend to drop in housing price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2d531ddf518>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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orKwknfvaa68BUGxTQ4YMIZXb3d0d7u7uKC4u1lhnQqEQZ8+ehbW1NYYPHy4/LnvWoUOH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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d531d1bcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: create some other scatter plots\n",
    "plt.scatter(bos.AGE, bos.PRICE)\n",
    "plt.xlabel(\"Age of Property\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between Age of Property and Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The age of the property has a very slight negative correlation between the age of the property and the price. Age seems to not be a huge deterining factor of house median prices until the houses are older than 80-100 years old. However, this may also not be taking into consideration if the homes were renovated or not. This may not be a key metric in determining overall value of the home."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scatterplots using Seaborn\n",
    "***\n",
    "\n",
    "[Seaborn](https://stanford.edu/~mwaskom/software/seaborn/) is a cool Python plotting library built on top of matplotlib. It provides convenient syntax and shortcuts for many common types of plots, along with better-looking defaults.\n",
    "\n",
    "We can also use [seaborn regplot](https://stanford.edu/~mwaskom/software/seaborn/tutorial/regression.html#functions-to-draw-linear-regression-models) for the scatterplot above. This provides automatic linear regression fits (useful for data exploration later on). Here's one example below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2d531dc4898>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UKvBoHz8QTaEnkgRgua4kSmCvrwRAW0jFYEzLkT+pJjzn/9NKwJynm1sV/mxL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\nfmMSISIiv/0/qhjGhumMFDIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d531dd7048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(y=\"PRICE\", x=\"RM\", data=bos, fit_reg = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histograms\n",
    "***\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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E8PBwJCQkoKKiAqGhoaioqFBz5UREpNGvX244iomIiMArr7wCAHB1dUVpaSnS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\nRK3KBDzuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d531e5f550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.log(bos.CRIM))\n",
    "plt.title(\"CRIM\")\n",
    "plt.xlabel(\"Crime rate per capita\")\n",
    "plt.ylabel(\"Frequencey\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 2 Checkup Exercise Set II</h3>\n",
    "\n",
    "<p><b>Exercise:</b> In the above histogram, we took the logarithm of the crime rate per capita. Repeat this histogram without taking the log. What was the purpose of taking the log? What do we gain by making this transformation? What do you now notice about this variable that is not obvious without making the transformation?\n",
    "    \n",
    "    <p><b></b>\n",
    "\n",
    "<p><b>Exercise:</b> Plot the histogram for *RM* and *PTRATIO* against each other, along with the two variables you picked in the previous section. We are looking for correlations in predictors here.</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The purpose of taking log is to normalize the data and to scale it to a more Gaussian distribution. This will make it easier to fit the data into a regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xPDQ15DFJT0+vdtkzeyZjbW0NQRBw48YNtfYbN26gc+fOAB5O8t+9exelpaXV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\nRMOQISIi0TBkiIhINP8fioPuRfiisrcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d531e5c940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#your turn\n",
    "plt.hist(bos.CRIM)\n",
    "plt.title(\"CRIM\")\n",
    "plt.xlabel(\"Crime rate per capita\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FITw8HMHBwUhPT0dFRQV27tzZrHESkfnRunibNGkSPv/8c/z111/6iIeIqFGa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\nAww9Iu/XPIncAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d532005e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "\n",
    "_ = plt.subplot(1,2,1)\n",
    "plt.hist(np.log(bos.CRIM), bins =20)\n",
    "plt.title(\"RM\")\n",
    "plt.xlabel(\"RM\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "\n",
    "_ = plt.subplot(1,2,2)\n",
    "plt.hist(bos.PTRATIO,  bins =20)\n",
    "plt.title(\"PTRATIO\")\n",
    "plt.xlabel(\"PTRATIO\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: Linear Regression with Boston Housing Data Example\n",
    "***\n",
    "\n",
    "Here, \n",
    "\n",
    "$Y$ = boston housing prices (called \"target\" data in python, and referred to as the dependent variable or response variable)\n",
    "\n",
    "and\n",
    "\n",
    "$X$ = all the other features (or independent variables, predictors or explanatory variables)\n",
    "\n",
    "which we will use to fit a linear regression model and predict Boston housing prices. We will use the least-squares method to estimate the coefficients.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use two ways of fitting a linear regression. We recommend the first but the second is also powerful in its features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting Linear Regression using `statsmodels`\n",
    "***\n",
    "[Statsmodels](http://statsmodels.sourceforge.net/) is a great Python library for a lot of basic and inferential statistics. It also provides basic regression functions using an R-like syntax, so it's commonly used by statisticians. While we don't cover statsmodels officially in the Data Science Intensive workshop, it's a good library to have in your toolbox. Here's a quick example of what you could do with it. The version of least-squares we will use in statsmodels is called *ordinary least-squares (OLS)*. There are many other versions of least-squares such as [partial least squares (PLS)](https://en.wikipedia.org/wiki/Partial_least_squares_regression) and [weighted least squares (WLS)](https://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\kj.park\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "# Import regression modules\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  PRICE   R-squared:                       0.741\n",
      "Model:                            OLS   Adj. R-squared:                  0.734\n",
      "Method:                 Least Squares   F-statistic:                     108.1\n",
      "Date:                Mon, 26 Feb 2018   Prob (F-statistic):          6.95e-135\n",
      "Time:                        18:10:07   Log-Likelihood:                -1498.8\n",
      "No. Observations:                 506   AIC:                             3026.\n",
      "Df Residuals:                     492   BIC:                             3085.\n",
      "Df Model:                          13                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     36.4911      5.104      7.149      0.000      26.462      46.520\n",
      "CRIM          -0.1072      0.033     -3.276      0.001      -0.171      -0.043\n",
      "ZN             0.0464      0.014      3.380      0.001       0.019       0.073\n",
      "INDUS          0.0209      0.061      0.339      0.735      -0.100       0.142\n",
      "CHAS           2.6886      0.862      3.120      0.002       0.996       4.381\n",
      "NOX          -17.7958      3.821     -4.658      0.000     -25.302     -10.289\n",
      "RM             3.8048      0.418      9.102      0.000       2.983       4.626\n",
      "AGE            0.0008      0.013      0.057      0.955      -0.025       0.027\n",
      "DIS           -1.4758      0.199     -7.398      0.000      -1.868      -1.084\n",
      "RAD            0.3057      0.066      4.608      0.000       0.175       0.436\n",
      "TAX           -0.0123      0.004     -3.278      0.001      -0.020      -0.005\n",
      "PTRATIO       -0.9535      0.131     -7.287      0.000      -1.211      -0.696\n",
      "B              0.0094      0.003      3.500      0.001       0.004       0.015\n",
      "LSTAT         -0.5255      0.051    -10.366      0.000      -0.625      -0.426\n",
      "==============================================================================\n",
      "Omnibus:                      178.029   Durbin-Watson:                   1.078\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              782.015\n",
      "Skew:                           1.521   Prob(JB):                    1.54e-170\n",
      "Kurtosis:                       8.276   Cond. No.                     1.51e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.51e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "# statsmodels works nicely with pandas dataframes\n",
    "# The thing inside the \"quotes\" is called a formula, a bit on that below\n",
    "m = ols('PRICE ~ CRIM + ZN + INDUS + CHAS + NOX + RM + AGE + DIS + RAD +TAX +PTRATIO + B + LSTAT',bos).fit()\n",
    "print(m.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interpreting coefficients\n",
    "\n",
    "There is a ton of information in this output. But we'll concentrate on the coefficient table (middle table). We can interpret the `RM` coefficient (9.1021) by first noticing that the p-value (under `P>|t|`) is so small, basically zero. This means that the number of rooms, `RM`, is a statistically significant predictor of `PRICE`. The regression coefficient for `RM` of 9.1021 means that *on average, each additional room is associated with an increase of $\\$9,100$ in house price net of the other variables*. The confidence interval gives us a range of plausible values for this average change, about ($\\$8,279, \\$9,925$), definitely not chump change. \n",
    "\n",
    "In general, the $\\hat{\\beta_i}, i > 0$ can be interpreted as the following: \"A one unit increase in $x_i$ is associated with, on average, a $\\hat{\\beta_i}$ increase/decrease in $y$ net of all other variables.\"\n",
    "\n",
    "On the other hand, the interpretation for the intercept, $\\hat{\\beta}_0$ is the average of $y$ given that all of the independent variables $x_i$ are 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  `statsmodels` formulas\n",
    "***\n",
    "This formula notation will seem familiar to `R` users, but will take some getting used to for people coming from other languages or are new to statistics.\n",
    "\n",
    "The formula gives instruction for a general structure for a regression call. For `statsmodels` (`ols` or `logit`) calls you need to have a Pandas dataframe with column names that you will add to your formula. In the below example you need a pandas data frame that includes the columns named (`Outcome`, `X1`,`X2`, ...), but you don't need to build a new dataframe for every regression. Use the same dataframe with all these things in it. The structure is very simple:\n",
    "\n",
    "`Outcome ~ X1`\n",
    "\n",
    "But of course we want to to be able to handle more complex models, for example multiple regression is doone like this:\n",
    "\n",
    "`Outcome ~ X1 + X2 + X3`\n",
    "\n",
    "In general, a formula for an OLS multiple linear regression is\n",
    "\n",
    "`Y ~ X1 + X2 + ... + Xp`\n",
    "\n",
    "This is the very basic structure but it should be enough to get you through the homework. Things can get much more complex. You can force statsmodels to treat variables as categorical with the `C()` function, call numpy functions to transform data such as `np.log` for extremely-skewed data, or fit a model without an intercept by including `- 1` in the formula. For a quick run-down of further uses see the `statsmodels` [help page](http://statsmodels.sourceforge.net/devel/example_formulas.html).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how our model actually fit our data. We can see below that there is a ceiling effect, we should probably look into that. Also, for large values of $Y$ we get underpredictions, most predictions are below the 45-degree gridlines. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 3 Checkup Exercise Set I</h3>\n",
    "\n",
    "<p><b>Exercise:</b> Create a scatterplot between the predicted prices, available in `m.fittedvalues` (where `m` is the fitted model) and the original prices. How does the plot look? Do you notice anything interesting or weird in the plot? Comment on what you see.</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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rr/aEeuQsCyvPi/8bqJTDbOVRqDMhIkiFYLXc5XlVad/x3Jq4h0r0ZjAMEBag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\n9g5Z1k7P4ppmZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5320626a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(m.fittedvalues, bos.PRICE, data=bos, fit_reg = True)\n",
    "plt.xlabel(\"Predicted Price from Model\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between Predicted Price and Housing Price\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting Linear Regression using `sklearn`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "X = bos.drop('PRICE', axis = 1)\n",
    "\n",
    "# This creates a LinearRegression object\n",
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### What can you do with a LinearRegression object? \n",
    "***\n",
    "Check out the scikit-learn [docs here](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html). We have listed the main functions here. Most machine learning models in scikit-learn follow this same API of fitting a model with `fit`, making predictions with `predict` and the appropriate scoring function `score` for each model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Main functions | Description\n",
    "--- | --- \n",
    "`lm.fit()` | Fit a linear model\n",
    "`lm.predit()` | Predict Y using the linear model with estimated coefficients\n",
    "`lm.score()` | Returns the coefficient of determination (R^2). *A measure of how well observed outcomes are replicated by the model, as the proportion of total variation of outcomes explained by the model*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### What output can you get?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'LinearRegression' object has no attribute 'coef_'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-24-93b47343658a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# Look inside lm object\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"regression estiamted coefficients: \"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcoef_\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"regression estimated intercept: \"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mintercept_\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'LinearRegression' object has no attribute 'coef_'"
     ]
    }
   ],
   "source": [
    "# Look inside lm object\n",
    "print(\"regression estiamted coefficients: \", lm.coef_)\n",
    "print(\"regression estimated intercept: \",lm.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Output | Description\n",
    "--- | --- \n",
    "`lm.coef_` | Estimated coefficients\n",
    "`lm.intercept_` | Estimated intercept "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit a linear model\n",
    "***\n",
    "\n",
    "The `lm.fit()` function estimates the coefficients the linear regression using least squares. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use all 13 predictors to fit linear regression model\n",
    "lm.fit(X, bos.PRICE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 3 Checkup Exercise Set II</h3>\n",
    "\n",
    "<p><b>Exercise 1:</b> How would you change the model to not fit an intercept term? Would you recommend not having an intercept? Why or why not? For more information on why to include or exclude an intercept, look [here](https://online.stat.psu.edu/~ajw13/stat501/SpecialTopics/Reg_thru_origin.pdf).</p>\n",
    "\n",
    "<p><b>Exercise 2:</b> One of the assumptions of the linear model is that the residuals must be i.i.d. (independently and identically distributed). To satisfy this, is it enough that the residuals are normally distributed? Explain your answer.</p>\n",
    "\n",
    "<p><b>Exercise 3:</b> True or false. To use linear regression, $Y$ must be normally distributed. Explain your answer.</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1:\n",
    "In order to not fit an intercept value we simply need to tune the Linear Regression model parameters to include fit_intercept = False like so:\n",
    "\n",
    "lm = LinearRegression(copy_X=True, **fit_intercept=False**, n_jobs=1, normalize=False)\n",
    "\n",
    "Under null hypothesis, the intercept equals 0 and the alternative hypothesis states that the intercept does not equal 0. The t stat and p-value of less than 0.05 indicates that having an intercept is statistically significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2:\n",
    " The conditionals of the linear model includes that when plotting residuals, the graph must not show a trend."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Excercise 3: \n",
    "In order to us the linear regression model, the spread of Y must be normally distributed such that the standard deviation for all the values of the Y must be the sale of all values of the predictor variables and show homoscedasticity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  PRICE   R-squared:                       0.741\n",
      "Model:                            OLS   Adj. R-squared:                  0.734\n",
      "Method:                 Least Squares   F-statistic:                     108.1\n",
      "Date:                Mon, 26 Feb 2018   Prob (F-statistic):          6.95e-135\n",
      "Time:                        18:20:02   Log-Likelihood:                -1498.8\n",
      "No. Observations:                 506   AIC:                             3026.\n",
      "Df Residuals:                     492   BIC:                             3085.\n",
      "Df Model:                          13                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     36.4911      5.104      7.149      0.000      26.462      46.520\n",
      "CRIM          -0.1072      0.033     -3.276      0.001      -0.171      -0.043\n",
      "ZN             0.0464      0.014      3.380      0.001       0.019       0.073\n",
      "INDUS          0.0209      0.061      0.339      0.735      -0.100       0.142\n",
      "CHAS           2.6886      0.862      3.120      0.002       0.996       4.381\n",
      "NOX          -17.7958      3.821     -4.658      0.000     -25.302     -10.289\n",
      "RM             3.8048      0.418      9.102      0.000       2.983       4.626\n",
      "AGE            0.0008      0.013      0.057      0.955      -0.025       0.027\n",
      "DIS           -1.4758      0.199     -7.398      0.000      -1.868      -1.084\n",
      "RAD            0.3057      0.066      4.608      0.000       0.175       0.436\n",
      "TAX           -0.0123      0.004     -3.278      0.001      -0.020      -0.005\n",
      "PTRATIO       -0.9535      0.131     -7.287      0.000      -1.211      -0.696\n",
      "B              0.0094      0.003      3.500      0.001       0.004       0.015\n",
      "LSTAT         -0.5255      0.051    -10.366      0.000      -0.625      -0.426\n",
      "==============================================================================\n",
      "Omnibus:                      178.029   Durbin-Watson:                   1.078\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              782.015\n",
      "Skew:                           1.521   Prob(JB):                    1.54e-170\n",
      "Kurtosis:                       8.276   Cond. No.                     1.51e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.51e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "m1 = ols('PRICE ~ CRIM + ZN + INDUS + CHAS + NOX + RM + AGE + DIS + RAD +TAX +PTRATIO + B + LSTAT',bos).fit()\n",
    "print(m1.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated intercept coefficient: 36.491103280363404\n"
     ]
    }
   ],
   "source": [
    "print('Estimated intercept coefficient: {}'.format(lm.intercept_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of coefficients: 13\n"
     ]
    }
   ],
   "source": [
    "print('Number of coefficients: {}'.format(len(lm.coef_)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>estimatedCoefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>CRIM</td>\n",
       "      <td>-0.107171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ZN</td>\n",
       "      <td>0.046395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>INDUS</td>\n",
       "      <td>0.020860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>CHAS</td>\n",
       "      <td>2.688561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NOX</td>\n",
       "      <td>-17.795759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RM</td>\n",
       "      <td>3.804752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>AGE</td>\n",
       "      <td>0.000751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>DIS</td>\n",
       "      <td>-1.475759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>RAD</td>\n",
       "      <td>0.305655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>TAX</td>\n",
       "      <td>-0.012329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PTRATIO</td>\n",
       "      <td>-0.953464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>B</td>\n",
       "      <td>0.009393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>LSTAT</td>\n",
       "      <td>-0.525467</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   features  estimatedCoefficients\n",
       "0      CRIM              -0.107171\n",
       "1        ZN               0.046395\n",
       "2     INDUS               0.020860\n",
       "3      CHAS               2.688561\n",
       "4       NOX             -17.795759\n",
       "5        RM               3.804752\n",
       "6       AGE               0.000751\n",
       "7       DIS              -1.475759\n",
       "8       RAD               0.305655\n",
       "9       TAX              -0.012329\n",
       "10  PTRATIO              -0.953464\n",
       "11        B               0.009393\n",
       "12    LSTAT              -0.525467"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The coefficients\n",
    "pd.DataFrame({'features': X.columns, 'estimatedCoefficients': lm.coef_})[['features', 'estimatedCoefficients']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predict Prices \n",
    "\n",
    "We can calculate the predicted prices ($\\hat{Y}_i$) using `lm.predict`. \n",
    "\n",
    "$$ \\hat{Y}_i = \\hat{\\beta}_0 + \\hat{\\beta}_1 X_1 + \\ldots \\hat{\\beta}_{13} X_{13} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 30.00821269,  25.0298606 ,  30.5702317 ,  28.60814055,  27.94288232])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first five predicted prices\n",
    "lm.predict(X)[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 3 Checkup Exercise Set III</h3>\n",
    "\n",
    "<p><b>Exercise:</b> Histogram: Plot a histogram of all the predicted prices. Write a story about what you see. Describe the shape, center and spread of the distribution. Are there any outliers? What might be the reason for them? Should we do anything special with them?</p>\n",
    "\n",
    "<p><b>Exercise:</b> Scatterplot: Let's plot the true prices compared to the predicted prices to see they disagree (we did this with `statsmodels` before).</p>\n",
    "\n",
    "<p><b>Exercise:</b> We have looked at fitting a linear model in both `statsmodels` and `scikit-learn`. What are the advantages and disadvantages of each based on your exploration? Based on the information provided by both packages, what advantage does `statsmodels` provide?</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  1.,   0.,   0.,   0.,   0.,   1.,   1.,   1.,   2.,   1.,   5.,\n",
       "          3.,   4.,   5.,   4.,   3.,   9.,  13.,  17.,  14.,  14.,  24.,\n",
       "         22.,  23.,  33.,  32.,  23.,  33.,  23.,  25.,  24.,  11.,  17.,\n",
       "         15.,   9.,  15.,  11.,  13.,   9.,  10.,   9.,   5.,   7.,   3.,\n",
       "          1.,   3.,   3.,   2.,   2.,   1.]),\n",
       " array([ -4.28300934,  -3.30388117,  -2.324753  ,  -1.34562483,\n",
       "         -0.36649666,   0.61263152,   1.59175969,   2.57088786,\n",
       "          3.55001603,   4.5291442 ,   5.50827237,   6.48740054,\n",
       "          7.46652871,   8.44565689,   9.42478506,  10.40391323,\n",
       "         11.3830414 ,  12.36216957,  13.34129774,  14.32042591,\n",
       "         15.29955409,  16.27868226,  17.25781043,  18.2369386 ,\n",
       "         19.21606677,  20.19519494,  21.17432311,  22.15345129,\n",
       "         23.13257946,  24.11170763,  25.0908358 ,  26.06996397,\n",
       "         27.04909214,  28.02822031,  29.00734849,  29.98647666,\n",
       "         30.96560483,  31.944733  ,  32.92386117,  33.90298934,\n",
       "         34.88211751,  35.86124569,  36.84037386,  37.81950203,\n",
       "         38.7986302 ,  39.77775837,  40.75688654,  41.73601471,\n",
       "         42.71514288,  43.69427106,  44.67339923]),\n",
       " <a list of 50 Patch objects>)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AGEfQA4BxBP0MLbWHq5w/f37SyinHcRQKhbRp0yZt2LBBO3bs0OXLlxeoQvfcuXNHx48f\nV11dnSoqKvTkk0/q1KlTyS0+rI47Ho/r8OHDqq6uVkVFhQKBgC5dupTstzrur4rH46qrq9Pzzz+f\nbLM0boJ+Bpbaw1U++eQT7du3b1J7Z2enQqGQdu7cqfb2doXDYTU3NyscDi9Ale7p6upSe3u7Ghoa\nFAqFVFdXp4MHD+rVV1+VZHfcL730kk6ePKndu3ers7NT+fn5CgQCunbtmiS74/6qo0eP6sqVKylt\npsbtIC0TExNOdXW1s3///mRbPB53Nm/e7Lz44osLWJn7vvzyS6enp8cpLy93Hn/8caeioiLZFw6H\nnYqKCufYsWPJtn/961+O3+93+vr6FqJcV4yPjzt+v985fPhwSvuvf/1r53vf+57Zcd++fdspLy9P\nGcPY2Jjz6KOPOp2dnWbH/VWXLl1yKioqnO9+97vOc8895ziOva9zZvRpWkoPV3n33XfV09OjZ599\nVk1NTSl9Q0NDisViqqmpSbb5fD5VVlZm9XmIRCJ6+umntWXLlpT20tJS3bhxQx999JHJcefn5+v0\n6dPatm1bsi0nJ0cej0fxeNzs9b5rfHxcra2t2rVrl1asWJFstzZugj5NS+nhKuvXr9f58+cVCAQm\nbTF99zwUFxentK9atSrZl418Pp/279+vdevWpbS/8847WrlypT7//HNJ9sadk5OjdevWyefzaWJi\nQlevXlVra6s8Ho8aGhrMXu+7XnnlFSUSCf3sZz9Labc2boI+Tek8XMWKFStW6Otf//o9+yKRiPLy\n8pSXl5fSXlBQkDxHVpw5c0YffPCBnnnmmSUx7q6uLtXW1urcuXN65plntGbNGtPjvnz5srq7u/Xb\n3/520visjduVTc2WAsflh6tkK8dxlsQ5eOONN3TgwAFt3bpVTU1NOnbsmPlx19bWqrKyUh9//LG6\nurqUSCS0fPlyk+OemJjQr371K/3whz+8535c1r7OCfo0uflwlWxWVFSkeDyuRCKh3NzcZHs0Gk2e\no2x3/PhxtbW1afPmzTp06JA8Hs+SGPfDDz8sSaqsrFQ0GlVvb69aWlpMjvvkyZP6xz/+oZ6eHo2P\njyfbHcfR+Pi4uevNrZs08XCVf1u9erUcx9Ho6GhK++joqEpLSxeoKve0t7crGAzqqaee0ssvv5z8\n1d3quL/44gudPXt20u2IsrIyxeNx+Xw+k+MeGBjQP//5Tz3++OMqLy9XeXm5/vrXv+r1119XeXm5\ncnJyTI2boE8TD1f5N7/fr2XLlqWch1u3bunixYtZfx5OnDihY8eOKRAIKBgMKifnv7/wWh337du3\n1draqrfeeiul/f3339cDDzyg2tpak+P+zW9+o/7+/pT/SkpKVF1drf7+ftXX15saN7du0sTDVf6t\noKBATU1N6ujokNfrVUlJibq7u1VYWKjGxsaFLi9j169f16FDh/TQQw+pvr5eQ0NDKf2PPPKIyXGv\nXbtWW7duVVtbmxKJhIqLi/X222/r3LlzOnjwoAoLC02Oe82aNZPali9frm984xtav369JJkaN0E/\nAz/96U/15Zdf6rXXXtPvfvc7lZWVqbe3d9ISLOv27t0rr9ervr4+xWIx+f1+BYPBrLx3edd7772n\neDyuzz77TNu3b5/U/+GHH5octyS1tbXp6NGj6unp0fXr1/Xggw+qo6NDTzzxhCSb1zsdlsbNg0cA\nwDju0QOAcQQ9ABhH0AOAcQQ9ABhH0AOAcQQ9ABhH0AOAcQQ9ABhH0AOAcf8PLBYhkOI1nqEAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5330bfb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn\n",
    "predictions = lm.predict(X)\n",
    "plt.hist(predictions, bins =50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2d532e64780>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAAECCAYAAABdUASVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5320af4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.boxplot(predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are most definitely outliers that we can see from the histogram that are also confirmed in the boxplot that we can see above. The five dots that appear on the outside fall outside of the boxplot range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2d53303f358>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WbQVKv7LFYjFmzZrFGBXo6OjI6jl37hzjGDZ9TM+mbNmyBW/evAEAmJqa4uLFi0rlW7p0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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d532b463c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: scatter plot between *RM* and *PRICE*dd\n",
    "plt.scatter(predictions, bos.PRICE)\n",
    "plt.xlabel(\"Predicted Prices\")\n",
    "plt.ylabel(\"Housing Prices\")\n",
    "plt.title(\"Relationship between predictions and housing price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1:\n",
    "The distribution follows a right skew and is not entirely symmetrical. From the boxplot one can see that outliers are present perhaps due to the fact that the features in the data are not all on the same scale. Some of the data come in ratios, while others do not. Also, there are two coefficients (INDUS and AGE) that are not statistically significant and can be the cause of these outliers.\n",
    "\n",
    "#### Exercise 2:\n",
    "The scatter plot show a strong positive trend between the original prices and the predicted prices\n",
    "\n",
    "#### Exercise 3:\n",
    "    \n",
    "Statsmodels provides a table with all the necessary statistical information as well as p-values to determine statistical significance whereas scikit-learn does not. Statsmodels gives a nice streamlined overview of the data's information; and while scikit-learn also provides the same information, it would takes several more lines of code to accomplish.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the Model: Sum-of-Squares\n",
    "\n",
    "The partitioning of the sum-of-squares shows the variance in the predictions explained by the model and the variance that is attributed to error.\n",
    "\n",
    "$$TSS = ESS + RSS$$\n",
    "\n",
    "#### Residual Sum-of-Squares (aka $RSS$)\n",
    "\n",
    "The residual sum-of-squares is one of the basic ways of quantifying how much error exists in the fitted model. We will revisit this in a bit.\n",
    "\n",
    "$$ RSS = \\sum_{i=1}^N r_i^2 = \\sum_{i=1}^N \\left(y_i - \\left(\\beta_0 + \\beta_1 x_i\\right)\\right)^2 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11080.2762841\n"
     ]
    }
   ],
   "source": [
    "print(np.sum((bos.PRICE - lm.predict(X)) ** 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Explained Sum-of-Squares (aka $ESS$)\n",
    "\n",
    "The explained sum-of-squares measures the variance explained by the regression model.\n",
    "\n",
    "$$ESS = \\sum_{i=1}^N \\left( \\hat{y}_i - \\bar{y} \\right)^2 = \\sum_{i=1}^N \\left( \\left( \\hat{\\beta}_0 + \\hat{\\beta}_1 x_i \\right) - \\bar{y} \\right)^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.70929118766e-24\n"
     ]
    }
   ],
   "source": [
    "print(np.sum(lm.predict(X) - np.mean(bos.PRICE)) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the Model: The Coefficient of Determination ($R^2$)\n",
    "\n",
    "The coefficient of determination, $R^2$, tells us the percentage of the variance in the response variable $Y$ that can be explained by the linear regression model.\n",
    "\n",
    "$$ R^2 = \\frac{ESS}{TSS} $$\n",
    "\n",
    "The $R^2$ value is one of the most common metrics that people use in describing the quality of a model, but it is important to note that *$R^2$ increases artificially as a side-effect of increasing the number of independent variables.* While $R^2$ is reported in almost all statistical packages, another metric called the *adjusted $R^2$* is also provided as it takes into account the number of variables in the model, and can sometimes even be used for non-linear regression models!\n",
    "\n",
    "$$R_{adj}^2 = 1 - \\left( 1 - R^2 \\right) \\frac{N - 1}{N - K - 1} = R^2 - \\left( 1 - R^2 \\right) \\frac{K}{N - K - 1} = 1 - \\frac{\\frac{RSS}{DF_R}}{\\frac{TSS}{DF_T}}$$\n",
    "\n",
    "where $N$ is the number of observations, $K$ is the number of variables, $DF_R = N - K - 1$ is the degrees of freedom associated with the residual error and $DF_T = N - 1$ is the degrees of the freedom of the total error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the Model: Mean Squared Error and the $F$-Statistic\n",
    "***\n",
    "The mean squared errors are just the *averages* of the sum-of-squares errors over their respective degrees of freedom.\n",
    "\n",
    "$$MSE = \\frac{ESS}{K}$$\n",
    "$$MSR = \\frac{RSS}{N-K-1}$$\n",
    "\n",
    "**Remember: ** Notation may vary across resources particularly the use of *R* and *E* in *RSS/ESS* and *MSR/MSE*. In some resources, E = explained and R = residual. In other resources, E = error and R = regression (explained). **This is a very important distinction that requires looking at the formula to determine which naming scheme is being used.**\n",
    "\n",
    "Given the MSR and MSE, we can now determine whether or not the entire model we just fit is even statistically significant. We use an $F$-test for this. The null hypothesis is that all of the $\\beta$ coefficients are zero, that is, none of them have any effect on $Y$. The alternative is that *at least one* $\\beta$ coefficient is nonzero, but it doesn't tell us which one in a multiple regression:\n",
    "\n",
    "$$H_0: \\beta_i = 0, \\mbox{for all $i$} \\\\\n",
    "H_A: \\beta_i > 0, \\mbox{for some $i$}$$ \n",
    "\n",
    "$$F = \\frac{MSR}{MSE} = \\left( \\frac{R^2}{1 - R^2} \\right) \\left( \\frac{N - K - 1}{K} \\right)$$\n",
    " \n",
    "Once we compute the $F$-statistic, we can use the $F$-distribution with $N-K$ and $K-1$ degrees of degrees of freedom to get a p-value.\n",
    "\n",
    "**Warning!** The $F$-statistic mentioned in this section is NOT the same as the F1-measure or F1-value discused in Unit 7."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 3 Checkup Exercise Set IV</h3>\n",
    "\n",
    "<p>Let's look at the relationship between `PTRATIO` and housing price.</p>\n",
    "\n",
    "<p><b>Exercise 1:</b> Try fitting a linear regression model using only the 'PTRATIO' (pupil-teacher ratio by town) and interpret the intercept and the coefficients.</p>\n",
    "\n",
    "<p><b>Exercise 2:</b> Calculate (or extract) the $R^2$ value. What does it tell you?</p>\n",
    "\n",
    "<p><b>Exercise 3:</b> Compute the $F$-statistic. What does it tell you?</p>\n",
    "\n",
    "<p><b>Exercise 4:</b> Take a close look at the $F$-statistic and the $t$-statistic for the regression coefficient. What relationship do you notice? Note that this relationship only applies in *simple* linear regression models.</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  PRICE   R-squared:                       0.258\n",
      "Model:                            OLS   Adj. R-squared:                  0.256\n",
      "Method:                 Least Squares   F-statistic:                     175.1\n",
      "Date:                Mon, 26 Feb 2018   Prob (F-statistic):           1.61e-34\n",
      "Time:                        18:10:25   Log-Likelihood:                -1764.8\n",
      "No. Observations:                 506   AIC:                             3534.\n",
      "Df Residuals:                     504   BIC:                             3542.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     62.3446      3.029     20.581      0.000      56.393      68.296\n",
      "PTRATIO       -2.1572      0.163    -13.233      0.000      -2.477      -1.837\n",
      "==============================================================================\n",
      "Omnibus:                       92.924   Durbin-Watson:                   0.725\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              191.444\n",
      "Skew:                           1.001   Prob(JB):                     2.68e-42\n",
      "Kurtosis:                       5.252   Cond. No.                         160.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# your turn\n",
    "m = ols('PRICE ~ PTRATIO',bos).fit()\n",
    "print(m.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1:\n",
    "\n",
    "Fitting the linear regression with only the pupil to teacher ratio (PTRATIO) to predict the housing prices results in a formula of **y = -2.1572x + 62.3446**\n",
    "\n",
    "The negative slope indicates that the pupil teacher ratio increasing by one unit would decrease the housing price by a factor of 2.1572, while the intercept would show that if there were no pupil teacher ratio,the housing price would be 62.3446."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2: \n",
    "The R-Squared value if .258 which means that there is pupil teacher ratio accounts for a 25.8% relationship towards determining housing price.\n",
    "\n",
    "Adjusted R Squared adjusts for when more data is added to the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3:\n",
    "The F-Stat falls at 175.1 with a p-value of 1.61e-34 shows that the overall model with PTRatio is statistically significant, and thus cuold be used as a factor in determining housing price."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Excercise 4:\n",
    "\n",
    "The F-stat shows whether or not the regression model with all of its chosen coefficients is statistically significant while T-stat shows the statistical significance of each coefficient (predictor variable) in the model. The T-stat for the intercept is 20.581 and the slope with PTRATIO is -13.233 with both their p-values being less than 0.05. This shows that the coefficients do not equal to zero and that there is an relationship between the pupil-teacher ratio and the housing price. So if the T-stat shows significance for each coefficient then the R-stat would also be significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 3 Checkup Exercise Set V</h3>\n",
    "\n",
    "<p>Fit a linear regression model using three independent variables</p>\n",
    "\n",
    "<ol>\n",
    "<li> 'CRIM' (per capita crime rate by town)\n",
    "<li> 'RM' (average number of rooms per dwelling)\n",
    "<li> 'PTRATIO' (pupil-teacher ratio by town)\n",
    "</ol>\n",
    "\n",
    "<p><b>Exercise:</b> Compute or extract the $F$-statistic. What does it tell you about the model?</p>\n",
    "\n",
    "<p><b>Exercise:</b> Compute or extract the $R^2$ statistic. What does it tell you about the model?</p>\n",
    "\n",
    "<p><b>Exercise:</b> Which variables in the model are significant in predicting house price? Write a story that interprets the coefficients.</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.593414155114\n"
     ]
    }
   ],
   "source": [
    "# your turn\n",
    "fit_score = lm.fit(X[['CRIM', 'RM', 'PTRATIO']], bos.PRICE).score(X[['CRIM', 'RM', 'PTRATIO']], bos.PRICE)\n",
    "print(fit_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  PRICE   R-squared:                       0.593\n",
      "Model:                            OLS   Adj. R-squared:                  0.591\n",
      "Method:                 Least Squares   F-statistic:                     244.2\n",
      "Date:                Mon, 26 Feb 2018   Prob (F-statistic):           1.09e-97\n",
      "Time:                        18:42:45   Log-Likelihood:                -1612.6\n",
      "No. Observations:                 506   AIC:                             3233.\n",
      "Df Residuals:                     502   BIC:                             3250.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -3.3066      4.038     -0.819      0.413     -11.240       4.627\n",
      "PTRATIO       -1.0742      0.133     -8.081      0.000      -1.335      -0.813\n",
      "CRIM          -0.2021      0.032     -6.301      0.000      -0.265      -0.139\n",
      "RM             7.3816      0.402     18.360      0.000       6.592       8.171\n",
      "==============================================================================\n",
      "Omnibus:                      233.249   Durbin-Watson:                   0.828\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             2002.374\n",
      "Skew:                           1.802   Prob(JB):                         0.00\n",
      "Kurtosis:                      12.054   Cond. No.                         311.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "m = ols('PRICE ~ PTRATIO + CRIM + RM',bos).fit()\n",
    "print(m.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Excercise 2 & 3:\n",
    "\n",
    "The F-stat shows that crime per capita rate, average number of rooms, and pupil-teacher ratio are statistically significant in the model and validates the $R^2$ value in that there is a correlation between the three independent variables and their relationship to house prices.\n",
    "\n",
    "The adjusted $R^2$ (.591) shows that 59.1% of the housing prices can be interpreted by the three features through the regression model. The can explain for the 59.1% variability in housing prices.\n",
    "\n",
    "\n",
    "#### Exercise 4:\n",
    "\n",
    "All three features are statistically significant in prediciting housing price due to their p-values being lower than 0.05. The only variable that is not significant is the intercept.\n",
    "\n",
    "    1. RM (# of Rooms): Increase in one unit or room leads to an increase of housing \n",
    "    price by 7.3816\n",
    "    2. CRIM (Crime Rate): Increase in one unit of Crime Rate leads to a decrease in \n",
    "    housing prices by 0.2021\n",
    "    3. PTRATIO (Pupil to Teacher Ratio): increase in one unit of pupil to teacher ratio leads \n",
    "    to a decrease in housing price by 1.0742\n",
    "    \n",
    "The only positive factor in this model is the number of rooms a home may have (the more the better)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4: Comparing Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During modeling, there will be times when we want to compare models to see which one is more predictive or fits the data better. There are many ways to compare models, but we will focus on two."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The $F$-Statistic Revisited\n",
    "\n",
    "The $F$-statistic can also be used to compare two *nested* models, that is, two models trained on the same dataset where one of the models contains a *subset* of the variables of the other model. The *full* model contains $K$ variables and the *reduced* model contains a subset of these $K$ variables. This allows us to add additional variables to a base model and then test if adding the variables helped the model fit.\n",
    "\n",
    "$$F = \\frac{\\left( \\frac{RSS_{reduced} - RSS_{full}}{DF_{reduced} - DF_{full}} \\right)}{\\left( \\frac{RSS_{full}}{DF_{full}} \\right)}$$\n",
    "\n",
    "where $DF_x = N - K_x - 1$ where $K_x$ is the number of variables in model $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Akaike Information Criterion (AIC)\n",
    "\n",
    "Another statistic for comparing two models is AIC, which is based on the likelihood function and takes into account the number of variables in the model.\n",
    "\n",
    "$$AIC = 2 K - 2 \\log_e{L}$$\n",
    "\n",
    "where $L$ is the likelihood of the model. AIC is meaningless in the absolute sense, and is only meaningful when compared to AIC values from other models. Lower values of AIC indicate better fitting models.\n",
    "\n",
    "`statsmodels` provides the AIC in its output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 4 Checkup Exercises</h3>\n",
    "\n",
    "<p><b>Exercise:</b> Find another variable (or two) to add to the model we built in Part 3. Compute the $F$-test comparing the two models as well as the AIC. Which model is better?</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\kj.park\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:879: RuntimeWarning: invalid value encountered in greater\n",
      "  return (self.a < x) & (x < self.b)\n",
      "c:\\users\\kj.park\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:879: RuntimeWarning: invalid value encountered in less\n",
      "  return (self.a < x) & (x < self.b)\n",
      "c:\\users\\kj.park\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:1818: RuntimeWarning: invalid value encountered in less_equal\n",
      "  cond2 = cond0 & (x <= self.a)\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>df_resid</th>\n",
       "      <th>ssr</th>\n",
       "      <th>df_diff</th>\n",
       "      <th>ss_diff</th>\n",
       "      <th>F</th>\n",
       "      <th>Pr(&gt;F)</th>\n",
       "    </tr>\n",
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       "   df_resid           ssr  df_diff    ss_diff       F    Pr(>F)\n",
       "0     502.0  17367.841062      0.0        NaN     NaN       NaN\n",
       "1     500.0  16842.757972      2.0  525.08309  7.7939  0.000464"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.anova import anova_lm\n",
    "from statsmodels.regression.linear_model import RegressionResults\n",
    "\n",
    "extra_coef_model = ols('PRICE ~ CRIM + RM + PTRATIO + DIS + TAX', bos).fit()\n",
    "prev_model = ols('PRICE ~ CRIM + RM + PTRATIO', bos).fit()\n",
    "anova_results = anova_lm(prev_model, extra_coef_model)\n",
    "anova_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F-statistic:  7.79390006866\n",
      "The AIC of the model with extra features is:  3221.56632195\n",
      "While the AIC of the previous model is:  3233.10027446\n"
     ]
    }
   ],
   "source": [
    "F_stat = ((prev_model.ssr - extra_coef_model.ssr) / (502-500)) / (extra_coef_model.ssr/500)\n",
    "print('F-statistic: ',F_stat)\n",
    "\n",
    "extra_AIC = RegressionResults.aic(extra_coef_model)\n",
    "prev_AIC = RegressionResults.aic(prev_model)\n",
    "print('The AIC of the model with extra features is: ', extra_AIC)\n",
    "print('While the AIC of the previous model is: ', prev_AIC)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise:\n",
    "In adding the two extra variables DIS (the distance to a Boston Employment Center) and TAX (tax rate) makes the model with the extra features a better model (according to the \n",
    "Akaike Information Criterion). Since the AIC of the model with the extra features is smaller (3221.566..) than the model with less features (3233.10027446), the extra feature model is a better fitting model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Part 5: Evaluating the Model via Model Assumptions and Other Issues\n",
    "***\n",
    "Linear regression makes several assumptions. It is always best to check that these assumptions are valid after fitting a linear regression model.\n",
    "\n",
    "<div class=\"span5 alert alert-danger\">\n",
    "<ul>\n",
    "  <li>**Linearity**. The dependent variable $Y$ is a linear combination of the regression coefficients and the independent variables $X$. This can be verified with a scatterplot of each $X$ vs. $Y$ and plotting correlations among $X$. Nonlinearity can sometimes be resolved by [transforming](https://onlinecourses.science.psu.edu/stat501/node/318) one or more independent variables, the dependent variable, or both. In other cases, a [generalized linear model](https://en.wikipedia.org/wiki/Generalized_linear_model) or a [nonlinear model](https://en.wikipedia.org/wiki/Nonlinear_regression) may be warranted.</li>\n",
    "  <li>**Constant standard deviation**. The SD of the dependent variable $Y$ should be constant for different values of X. We can check this by plotting each $X$ against $Y$ and verifying that there is no \"funnel\" shape showing data points fanning out as $X$ increases or decreases. Some techniques for dealing with non-constant variance include weighted least squares (WLS), [robust standard errors](https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors), or variance stabilizing transformations.\n",
    "    </li>\n",
    "  <li> **Normal distribution for errors**.  The $\\epsilon$ term we discussed at the beginning are assumed to be normally distributed. This can be verified with a fitted values vs. residuals plot and verifying that there is no pattern, and with a quantile plot.\n",
    "  $$ \\epsilon_i \\sim N(0, \\sigma^2)$$\n",
    "Sometimes the distributions of responses $Y$ may not be normally distributed at any given value of $X$.  e.g. skewed positively or negatively. </li>\n",
    "<li> **Independent errors**.  The observations are assumed to be obtained independently.\n",
    "    <ul>\n",
    "        <li>e.g. Observations across time may be correlated\n",
    "    </ul>\n",
    "</li>\n",
    "</ul>  \n",
    "\n",
    "</div>\n",
    "\n",
    "There are some other issues that are important investigate with linear regression models.\n",
    "\n",
    "<div class=\"span5 alert alert-danger\">\n",
    "<ul>\n",
    "  <li>**Correlated Predictors:** Care should be taken to make sure that the independent variables in a regression model are not too highly correlated. Correlated predictors typically do not majorly affect prediction, but do inflate standard errors of coefficients making interpretation unreliable. Common solutions are dropping the least important variables involved in the correlations, using regularlization, or, when many predictors are highly correlated, considering a dimension reduction technique such as principal component analysis (PCA).\n",
    "  <li>**Influential Points:** Data points that have undue influence on the regression model. These points can be high leverage points or outliers. Such points are typically removed and the regression model rerun.\n",
    "</ul>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"span5 alert alert-info\">\n",
    "<h3>Part 5 Checkup Exercises</h3>\n",
    "\n",
    "<p>Take the reduced model from Part 3 to answer the following exercises. Take a look at [this blog post](http://mpastell.com/2013/04/19/python_regression/) for more information on using statsmodels to construct these plots.</p>\n",
    "    \n",
    "<p><b>Exercise:</b> Construct a fitted values versus residuals plot. What does the plot tell you? Are there any violations of the model assumptions?</p>\n",
    "\n",
    "<p><b>Exercise:</b> Construct a quantile plot of the residuals. What does the plot tell you?</p>\n",
    "\n",
    "<p><b>Exercise:</b> What are some advantages and disadvantages of the fitted vs. residual and quantile plot compared to each other?</p>\n",
    "\n",
    "<p><b>Exercise:</b> Identify any outliers (if any) in your model and write a story describing what these outliers might represent.</p>\n",
    "\n",
    "<p><b>Exercise:</b> Construct a leverage plot and identify high leverage points in the model. Write a story explaining possible reasons for the high leverage points.</p>\n",
    "\n",
    "<p><b>Exercise:</b> Remove the outliers and high leverage points from your model and run the regression again. How do the results change?</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2d533b81278>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cWbH8p59+QmxsLG7cuAEAaNOmjWJ969atcfXqVb/IEAi0ahZRoRqqYCgUSr3H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\nQRAtBhkZgiAIosUgI0MQBEG0GP8f+F1jBQwxLXgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5330e24a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=prev_model.fittedvalues, y=prev_model.resid)\n",
    "plt.xlabel('Fitted Values')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Fitted Values vs. Residuals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Excercise 1:\n",
    "\n",
    "Plotting the fitted values against the residuals shows does not show a linear relationship, but isntead a more quadratic type. We can assume that this is not in line with the linearity assumption of the model. Residual plots provides more information on the linearity and homoscedasticity of the data as opposed to scatter plots that are used for exploring predictor variables. If there is no shape in the residual plot, then both linearity and homoscedasticity are followed. Outliers can also be detected in the residual plot such that when comparing to the scatter plot of the least square line, one can tell which outliers have the most influence on the least square line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QtmzBCygGuYbMTz/9hLe3N71796ZHjx5UKsbRCUIIURzi4pThxuvXF37tyC5d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\nkiRJmjCykZEkSZImjGxkJEmSpAnzH8EDnb9PHvrhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5331a0160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(prev_model.resid, plot=plt)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 2:\n",
    "\n",
    "This quantile plot of the residuals tells us that the residuals follow a normal distribution with heavy tails. This may potentially be due outliers in the data. QQ plots can only determine whether data follows a Normal vs Exponential distrbution, but only for assumptive purposes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 3:\n",
    "\n",
    "Residual plots need a QQ plot to assume normality of residuals. A residual plot can assume linearity and homoscedasticity, but cannot determine the normality of said residuals. A QQ plot (quanitle plot), can only assume whether a set of data follows a normal or exponential distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2d5332437f0>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OuAWH5D6+2F5Hpo+KcR0fd7sfIcTVqZQBslXWsWPHuOGGG3p1DemQ83TnlsOu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\nIYTwIsFBCCGEl/8fBIHQmhzXcpUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5332a27f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(prev_model.resid, norm_hist=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 4:\n",
    "\n",
    "From the pairing of both the QQ and histogram plots, we can considers residuals above 20 are outliers. \n",
    "\n",
    "From the histogram and qqplot, the residuals that are considered outliers are the ones that are above 20. The outliers present in the data indicate that these homes are located in the same town and county by having several features that share the same metrics. Massachusetts State assesses property taxes by the cost, market, and income method, so when the property tax rate is the same across all these homes, this shows that the homes are in the same town. \n",
    "\n",
    "Additionally, all homes are located on the Charles River and are within the same school district when the pupil-teacher ratio is a shared metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GRmlhUQBK6xopzqGYaCwjI0Oa0dnCwgLAP8tK6OnpSfXDwsKkY6xcuTLfRGX/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\nQCSEEEKIKe8/MovEGla43sIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5331a3908>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.graphics.regressionplots import *\n",
    "\n",
    "\n",
    "plot_leverage_resid2(prev_model, alpha=0.05, ax = ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 5:\n",
    "\n",
    "The higher leverage points show homes that are in the same neighborhood from the outliers. However, the crime rate per capita for these houses are extremely high and the value of the home the is low relative to the homes in the outlier set of data.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GWloaFy9eJCQk/4rXmqZx/PhxwFkLExISQp8+fRg3bhyaphXaBGSxWDh8+LDx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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5331a3908>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.graphics.influence_plot(prev_model, criterion=\"cooks\",ax= ax)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>PRICE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>380</th>\n",
       "      <td>88.9762</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.671</td>\n",
       "      <td>6.968</td>\n",
       "      <td>91.9</td>\n",
       "      <td>1.4165</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>17.21</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>405</th>\n",
       "      <td>67.9208</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.693</td>\n",
       "      <td>5.683</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1.4254</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>384.97</td>\n",
       "      <td>22.98</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>418</th>\n",
       "      <td>73.5341</td>\n",
       "      <td>0.0</td>\n",
       "      <td>18.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.679</td>\n",
       "      <td>5.957</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1.8026</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>16.45</td>\n",
       "      <td>20.62</td>\n",
       "      <td>8.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        CRIM   ZN  INDUS  CHAS    NOX     RM    AGE     DIS   RAD    TAX  \\\n",
       "380  88.9762  0.0   18.1   0.0  0.671  6.968   91.9  1.4165  24.0  666.0   \n",
       "405  67.9208  0.0   18.1   0.0  0.693  5.683  100.0  1.4254  24.0  666.0   \n",
       "418  73.5341  0.0   18.1   0.0  0.679  5.957  100.0  1.8026  24.0  666.0   \n",
       "\n",
       "     PTRATIO       B  LSTAT  PRICE  \n",
       "380     20.2  396.90  17.21   10.4  \n",
       "405     20.2  384.97  22.98    5.0  \n",
       "418     20.2   16.45  20.62    8.8  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "high_lev  = bos.iloc[[380, 405, 418,]]\n",
    "high_lev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "fixed_boston =bos.drop([365, 367, 368, 369,370,371,372,380, 405, 418], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  PRICE   R-squared:                       0.715\n",
      "Model:                            OLS   Adj. R-squared:                  0.714\n",
      "Method:                 Least Squares   F-statistic:                     412.0\n",
      "Date:                Mon, 26 Feb 2018   Prob (F-statistic):          9.12e-134\n",
      "Time:                        19:29:12   Log-Likelihood:                -1469.9\n",
      "No. Observations:                 496   AIC:                             2948.\n",
      "Df Residuals:                     492   BIC:                             2965.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -5.9837      3.301     -1.813      0.070     -12.469       0.501\n",
      "CRIM          -0.2507      0.035     -7.106      0.000      -0.320      -0.181\n",
      "RM             7.9214      0.337     23.514      0.000       7.260       8.583\n",
      "PTRATIO       -1.1285      0.108    -10.491      0.000      -1.340      -0.917\n",
      "==============================================================================\n",
      "Omnibus:                       14.891   Durbin-Watson:                   1.096\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               28.604\n",
      "Skew:                           0.125   Prob(JB):                     6.15e-07\n",
      "Kurtosis:                       4.150   Cond. No.                         312.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = ols('PRICE~CRIM + RM + PTRATIO', data=fixed_boston).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2d5351a3ef0>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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r1YJZ3pamxRXXt0uXLrhx4wZ2796NZs2aCeantm3b4sKFC4iPj0fHjh3tmrSK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\nPl0wL24AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d5351f1940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.residplot(x=model.fittedvalues, y=model.resid)\n",
    "plt.xlabel('Fitted Values')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Fitted Values vs. Residuals without Outliers and High Leverage Points')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZuozIB4xOMp6enqxatQo/Pz8cHR2pWrUqc+fO5d69exw8eJBmzZoRGhpqyViF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\nIUJGQkYIIUTISMgIIYQImV/lEk6jnSqgnwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d53342dac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats.probplot(model.resid, plot=plt)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 6:\n",
    "\n",
    "The $R^2$ value increases from its previous 59.3% to a greater 71.5 percent (an increase of 12.2%)\n",
    "\n",
    "Much better look at the QQ plot after removing high leverage points from the dataset which shows the reduction of the high tail after residuals > 20. Reducing the leverage points indeed helped the data follow a more normal distribution."
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