Mini_Project_Linear_Regression.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": 60,
   "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",
    "*Image from http://www.learner.org/courses/againstallodds/about/glossary.html. Note this image uses $\\alpha$ and $\\beta$ instead of $\\beta_0$ and $\\beta_1$.*\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",
    "$$ \\mathscr{L} = \\sum_{i=1}^N \\epsilon_i^2 = \\sum_{i=1}^N \\left( y_i - \\hat{y}_i \\right)^2  = \\sum_{i=1}^N \\left(y_i - \\left(\\beta_0 + \\beta_1 x_i\\right)\\right)^2 $$\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}\\sum_{i=1}^N x_i - \\hat{\\beta}_1 \\sum_{i=1}^N 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": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "import pandas as pd\n",
    "\n",
    "boston = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _boston_dataset:\n",
      "\n",
      "Boston house prices dataset\n",
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. 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",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/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",
      ".. topic:: 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",
      "\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": 66,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.00632</td>\n",
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       "      <td>0.538</td>\n",
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       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
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       "      <td>394.63</td>\n",
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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": 66,
     "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": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 67,
     "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": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506,)\n"
     ]
    }
   ],
   "source": [
    "print(boston.target.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 69,
     "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": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>3.613524</td>\n",
       "      <td>11.363636</td>\n",
       "      <td>11.136779</td>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.554695</td>\n",
       "      <td>6.284634</td>\n",
       "      <td>68.574901</td>\n",
       "      <td>3.795043</td>\n",
       "      <td>9.549407</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>356.674032</td>\n",
       "      <td>12.653063</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.601545</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>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>3.677083</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     3.613524   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.601545   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%      3.677083   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": 70,
     "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": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between CRIM and Price')"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between RM and Price')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(bos.RM, bos.PRICE)\n",
    "plt.xlabel(\"Per capita crime rate by town (RM)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between RM and Price\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between PTRATIO and Price')"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(bos.PTRATIO, bos.PRICE)\n",
    "\n",
    "plt.xlabel(\"Per capita crime rate by town (PTRATIO)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between PTRATIO 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": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12e958b90>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: describe relationship\n",
    "## Outliers\n",
    "bos.CRIM.plot ( kind='box')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12e827090>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bos.RM.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12ed37450>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.AGE.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12edd7610>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lZGVlqXXr1nrnnXd0/vx55eXlKS8vT5IUGxurvn37Kj09Xe3atXN0ZqAmHCkADXThwgVJtZ8rqBQdHa309HTl5uZq0aJFGjx4sFq3bi1J+uuvv7RlyxYNGDBAO3fudHRmoCYcKQANVFxcLEm68cYbg/6ZuLg4DRw4UAMHDpR06QtvX3zxhd59910VFRVp6tSp2rlzp5o2berIzEBNOFIAGqigoEDS3yeSa3Lo0CF9/fXXunjxYpVtbdq00VNPPaXNmzfr9ttvV0lJiT777DNH5gVqQxSABigtLdW3334rSZf98lp6errGjBlT7aUvKl1//fXq16+fpL+PQIAriSgADbBq1SoVFxerc+fOSk5OrnXfu+++W5K0evXqWver/BRTfHx8aIYE6oAoAPUQCAS0ceNGLVmyRNHR0UF9r2D8+PFyuVzauHGjsrOzde7cuX9sLysr09tvv61PP/1UCQkJ9v0H4EriRDNQi9OnT2vq1Kn270AgoOLiYhUUFOjkyZNq0qSJ5s+fr7S0tMs+V3x8vHJycjR16lS9//77Wrt2rbp27armzZvL5/Ppxx9/1JkzZ9S2bVstW7aMC+IhLIgCUIuSkhJt3brV/h0ZGamYmBi1bdtWgwYN0siRI9WmTZugn+++++7Tjh079OGHHyovL0+HDx/W3r17FRsbq/bt26tfv34aMWKE3G63E78OcFkRFZe7ihcA4JrB8SkAwBAFAIAhCgAAQxQAAIYoAAAMUQAAGKIAADBEAQBgiAIAwBAFAID5f6iuHHkyNpY3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.DIS.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12eed50d0>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.RAD.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12efb1250>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.TAX.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12f050990>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.PTRATIO.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12f15ea10>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.B.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12f234990>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.LSTAT.plot ( kind='box')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12f319350>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bos.PRICE.plot ( kind='box')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between RM and Price')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: scatter plot between *RM* and *PRICE*\n",
    "plt.scatter(bos.RM, bos.PRICE)\n",
    "plt.xlabel(\"Average number of rooms per dwelling (RM)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between RM and Price\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between PTRATIO and Price')"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: scatter plot between *PTRATIO* and *PRICE*\n",
    "plt.scatter(bos.PTRATIO, bos.PRICE)\n",
    "plt.xlabel(\"Pupil-to-Teacher Ratio (PTRATIO)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between PTRATIO and Price\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between PTRATIO and Price')"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn: create some other scatter plots\n",
    "plt.scatter(bos.TAX, bos.PRICE)\n",
    "plt.xlabel(\"Pupil-to-Teacher Ratio (PTRATIO)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between PTRATIO and Price\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship between PTRATIO and Price')"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dMnGWjo6O2Lp1K5ycnPD48WMcP3681fE2NjbYtGkT7O3tpdveeecd6X3fu3dPup34ACdMmCDjgNS5c2epCbx9+/Zy2/nFF19IBw4A0KVLF7z77rsAgLt375K+X4FAgK1bt8oIkfHjx+P9998HAIUftrLzhYSEyPTb6NGj8eGHHwIAdu/eLd1+/vx5JCYmQiQSYePGjTJ95uHhgY0bN8LAwAAHDx5EUVGR0usaGhpi8ODBAGQVanFxMZKSktCnTx8YGBjIVbDAqzXJmpoa6frZL7/8gkGDBkn3NTc3x7fffgtfX1/k5+fLPP8///wT5eXlCAoKwpIlS2RmPMOHD5c6FSmaxU6ZMgUzZ86UChYLCwupxSM9PV1GmdOltrYWKSkp+PHHH6VtX7BgAenZGVnoygqC5ORkqSxormAdHR3Rv39/AOoxExNLNFQiIoyMjKT7k5kVERaVPn36YO7cudJBHtAkBwhlqUimeXh44Mcff5SaYA0NDfHJJ5/A1NQUDQ0NMpaWP//8Ew0NDQgKCsLMmTOlAwE7Ozts3rwZVlZWpO9TFRKJBC9fvkRUVBTee+89FBcXw9LSEvPmzWu1r1AoxJIlS6TtsbW1VXjeO3fuIDY2Fubm5ti2bZuMA9SAAQOwaNEiAK/W79nUPwCHYTqKzB1CoRCjR49GYGAgJkyY0OpjjYyMBAAMGjRIbsfZ2dlh0KBBiIyMRFRUFLp166awDXPnzsWcOXMUmofMzMwAAFVVVaTuSR6XL18G0DTSkue9ZmFhgeDgYGzbtg2XL1/G9OnTZX4fMGCAXLdykUiE7OxsGUFJPOxff/0VQqEQAwcOlAqcUaNGYdSoUQrbKS9o28PDAwCUrt22pH///lITXHOmTp2KrVu34v79+yguLlb60jenb9++8Pb2brV98uTJ2LRpExISElBUVAQ7OzvpuzFixAi5gtbLywteXl5ISkrCzZs3ZYStPN544w2cOnUK169flyYniYmJgUQiwdChQ1FZWYmUlBTk5eXB2dkZjY2NiI6OhlAolCrnO3fu4MWLF7C3t8fAgQPlXmfs2LG4f/8+oqKipIMaYqavqI3jxo3D6tWr8ejRIzx//hwODg4yv8sb2Xfp0kX6//LycqkQJcOWLVuUmqQFAgHmzp0rTeLAJnRlBQExe+3WrVurRCLjx49HTEwMrl27hqdPn3Jq3ibWUKkOQIiwPzKluYkEFYrWAVXJtMGDB0sVE4GxsTFcXFyQlpYmI2+IweR//vOfVuexsbHBiBEjaCd0UJVkpH379ti8ebNcE7GXlxfatWtH6jpXrlwB0OQ0RSz9NWfatGkIDAyUylY29Q/AoYKNjIyUxjnV1tYiOjoaa9asQXZ2NioqKjBs2DC5LyIx8rp9+zbefvttuefOzc0FAFLegcTLdOPGDaSlpSE7OxvZ2dlITEyUmkMULe6T4fHjxwAgV+kQ9OzZU2bf5rQMeCcglG7zts2dOxf//PMPMjMz8f7778PMzAz9+vXD4MGDMXz4cIWxhObm5nKFLTELprJo36tXL7nbnZycYGlpibKyMuTm5pJWsIr6zdHRUXq+zMxM2NnZSd+NM2fOKFz/efr0KQBy78bgwYNhYGCA2NhYaUIAYh1NLBbjyZMnSElJwa1bt+Ds7IyHDx+ipKQEYrFY6vSTlpYGoMlsq+h9JdbFiTaVl5cjPz8fALBhwwZs375d7nGGhoaor69HZmZmKwUr771pPuig4jADtE40IRAIYGJiAmtra3Tr1g2jR4+WyWrGJnRlBdB0n6dOnQIgf7AyatQorF69GnV1dTh27Jh0xsIFjo6OyM7OlusHoQiJRCLdX5H1SR5CoRBxcXFITk5GTk4OsrOzkZSUJJWNimSaInlDvDvEcZWVlXj+/DkAKMx+Jm9gTJaWiSYMDAxgbm4OR0dH+Pn54c0331QYJtjyW1AGsZbr6ekp93cLCwvpRANgX/+oJWOCsbExhg4dih49emDy5Mm4du0aPvjgA/zvf/9rNXsjRlDPnj1TGW9XVlam8tqHDh3Ctm3bUFBQIN0mFArRvXt3eHt7S0dpdCG83JSNqIgXRZ73pVAoVHr+5qPazp074+TJk9i2bRvOnTuHkpISXL16FVevXsWaNWsQGBiI77//vtVHxKZJT5lZqF27digrKyP1XAiUxdqam5ujrKwM1dXVAF69Gzk5OSods8i0wdbWFr6+vrh79y7i4+PRp08f3Lx5E+bm5ujduzeePHmCw4cPIzY2FkFBQYiKigIAmcB3ok2VlZW4c+eO0usR+zZ/DxITE1W2U969UHlvyKAs0YQ6oSIrgKZlIEJOrF+/HuvXr1d47tDQUCxcuLDVDI4t3N3dkZ2dLV2LJUN6errUwqZICbTk3LlzWL9+vcyA3cDAAJ6enhg1apRSJzey703zd07RN8rERKwsuYgq5FmvFEFY58jG9LOtf9SaksjR0RHr1q3D3Llzcf/+ffz0009YtWqVzD6EiWPZsmVy7e9UOHLkiDTV1sSJExEYGAhPT0+4u7vD2NgYhw8fZqxgiQenbM2LeBBsJG5wcnLC6tWr8d133yE+Ph43btxAVFQU7ty5gytXrmD+/PkIDQ3lTIgQyk4eRB9QGYkrC7AnFBHxIRPvxqZNmzBmzBjS11BGYGAg7t69ixs3bkjXyl9//XUYGRlhwIABAF6texHvypAhQ6THE20aMmSINAZSFcQxQJNlhexsvy1BRlYAr8zDZmZmCgV+Q0MDCgsLkZeXh+joaLz++uuctHnUqFGIiopCdHQ0amtrSQ1siaUCa2trUrmWr127JnX6Gjp0KEaPHg1vb2+IRCKYmZnh2rVrrHiRN19HrqyslAnTIlAmC7QFYlBGdhmQTf0DaMCL+LXXXsPUqVMBNM0uW4ZJEFmSlAWUJyYm4tGjRyodOQgHmcWLF2PdunUYN24cvLy8pC8+YU5kAmE2e/TokcJ9iLi05gvmdMjPz8f169chkUhgYGAAX19fzJ8/HwcOHMCePXsANPUNYbbkAkXnzs3NRXl5OYRCIaX7lGc2B5pmqeXl5TAwMJCuLZJ5N+7evYuUlBTSH3/zcB1CkRJxzg4ODujatStycnLw6NEjPHjwACKRSCZsi/i/sjbl5ubi3r17UscrKysrqVJVdFxDQwOuX7+OrKwsyuZefUGVrKioqJCumS1btgxRUVFy/12+fFm6/sals9OoUaPQrl07FBUV4dChQyr3Ly8vl3r9T548mVQK1j///BMSiQTBwcHYsWMHJk2ahB49ekgVAxsyDWhSTMSSgSLZpgsJgojvU5HcIkIfP/30U9TX17OqfwANheksXbpU6gG6atUqmbhFYnZw7tw5FBcXtzq2rKwMs2fPRlBQEP7991+l1yEqZshb56uurpaGgLQUYKqC2ptDtPfKlStyK3SUl5dLR9lMRs61tbUYP3485syZI9c9vl+/flLzD5cCOTo6Wro20xxCcA0aNIiSc01MTIx0PbI5RD7Yfv36Sc9H9HVYWJjcdeOcnBzMnDkTEyZMkPGMVvY8e/TogQ4dOuDu3bvSRAXNnZUIZfvbb7+hsbGxVXWhfv36wdzcHNnZ2bh+/brce/zqq68wbdo0mYojhGJXJIgjIiIwZ84cBAUFtek0espkxdmzZ1FVVQWhUKjUoU0oFEoTP0RGRsqVK2xgbW0tTVyyfv36VolImlNbW4vly5ejoKAA7du3l3rhq0KZTJNIJFKnIzZkAOGIJG9QUllZySi5jLognBEvX74sd238/PnziI+PR3p6OoyMjFjVP4CGFKylpSWWLVsGoGmh+Pfff5f+JhaL0b9/f7x8+VKaYJygoKAACxYsQGlpKRwcHDBhwgSl1yFGL/v375cZbWRnZ2P+/PnSc7cU1sR66pMnT1TeS79+/SAWi1FbW4v58+fLuMcXFBRg4cKFKCgoQOfOnTFlyhSV51OEsbGx1Ev466+/lllgr62txW+//Ya6ujo4OzvLLNqzTVVVFRYvXiyzPnHixAns3r0bBgYGlNfxamtrsWjRIpk18qNHj+Kvv/6CQCDAwoULpdvHjx8Pd3d3ZGVlYfHixTKK/vHjx1iwYAHq6+vRvXt3mXAZVc8zMDAQtbW1OH36NCwsLKROacArZUusv7ZUsBYWFpg9ezYA4PPPP5dRstXV1VizZg1u3rwJQ0NDqQcxALz33nswMTFBREQENmzYIPMOXr16FatXrwbQFI4jzzzXVlAmK4iB67Bhw1SGxhDfXl1dnTQkgwumTZuGiRMnorq6GnPnzsWOHTtkBLtEIkFcXBxmzZqFCxcuwMTEBJs2bSK9rELItKNHj6KwsFC6/dmzZ/jss8+kzn9Us93JY968eTA3N5fGptfX1wMAXr58iU8//VTuQFvbGDRoEHx9fVFWVtZKZsTGxkrX7OfMmQOAXf0DqHkNtjkTJ07EsWPHEBsbi507d2LChAlS0+L69eul6bhGjx4NDw8PGBgYICMjA3V1dbCwsMDvv/+usmrCRx99hI8++gjXr1/H4MGDIRKJUFFRgaysLEgkEgwcOBA3b95EYWEhJBKJdKZDeMedPXsWEyZMwIABA7By5UqF11m/fj3mzp2LlJQUjBs3Dh4eHjAyMkJqairq6+vh7OyMLVu2UJrZyWP58uWIi4tDamoqxo0bh86dO6Ndu3bIycnBy5cvYWJigjVr1nBa7cfV1RUJCQkYNmwYvLy8UFJSgidPnsDAwEBl/lV5DB48GLdu3cLw4cPh6emJkpIS6Yx22bJlMrNJY2NjbN26FfPmzcOVK1cwZMgQeHh4oK6uDo8fP0ZDQwOcnJywbds2mWsQz/Phw4fSNavmFVWGDBmCo0ePoq6uDgEBATKxhf3794dAIIBEIoG1tbXcUmYLFy5ERkYGzpw5gzlz5sDZ2Rk2NjbIysqSDuxWrVol44Ht4eGBtWvXYtmyZdixYwf27dsHkUiEkpIS6Szltddew+eff06pP/URebJCKBRKTfotq+XIo0uXLujbty/i4uJw7NgxqUDlgnXr1sHd3R1bt27Fhg0bsGXLFri5ucHU1BT5+fnSpQI3NzesW7eOUiWdDz/8ENHR0UhJScGwYcMgEolQX1+Px48fo76+HgMGDEBcXBxqa2vx4sWLVoUGqNCpUyesXbsWn332GbZu3YpDhw6hY8eOyMjIQFVVFYYMGSINU9RWBAIBNmzYgNmzZyMmJgZDhw6Fp6cnysrKpI6Sb731lsw7xJb+ATSci/ibb76BUChETU2NjAODo6Mjjh49iqVLl6Jnz57Iy8tDRkYGOnTogGnTpuHkyZNKw2IIRo0ahQMHDuD1119Hu3btkJycjLKyMgQEBCAkJAR79+6VZjNqnlBg0qRJmD17Nuzs7PD48WOVAcUODg44cuQIli5dih49eiAvLw9ZWVno2rUrlixZghMnTqiMlyKDjY0NDh06hLlz50IkEuHp06dITU2FlZUVpk6dioiICIWxmGzRvXt3HDhwAGKxGJmZmaiursbQoUOxb98+WjGSPXv2xMGDByEWi/H48WO8fPkSr732Gvbs2SPXycDDwwMnT57Ehx9+iC5duuDx48fIzs6Gq6sr5s6dixMnTqBTp04yx7z22mv49NNP4eTkhLy8PCQkJMiEMQwaNEhqXiccmwhsbW2lSTUGDx4sd/BiZGSEjRs3YsOGDQgICEBFRQWSk5NhYmKCkSNH4u+//5ZrvXjzzTcRFhaGt956CzY2NkhOTkZJSQl69+6NL7/8Ert27WI9qYOu0lJWhIeHQyKRwNbWViaBijKI9dy0tDSVHt9MWbBgAU6fPo25c+eia9euePLkCZKSkmBgYIChQ4di7dq1OH36NOUydX369MGJEycwatQo2NnZIS0tDYWFhfDz88OPP/6IvXv3Sp2l2MheNWrUKBw+fBijR4+GQCBAeno6vL298fvvv8s4+2kzzs7OUg9yNzc3pKeno6ioCP7+/vj111+l2aoI2NI/ACCQUPXn52mTEHU+R48ezRct5+Hh4SGBRmewPDw8PDw8+gqvYHl4eHh4eDiAV7A8PDw8PDwcwCtYHh4eHh4eDuCdnEiQmJiImpoaGBoaUsqDycPDw9OWqampQUNDA0xMTNCjRw9NN0ftaCwOVpeoqY7Z8LwAACAASURBVKlBY2MjGhsbFZa+4+Hh4eGRDxuJL3QRXsGSwNDQEI2NjdKSSgREEgGmCSTaInzf0YPvN3rw/UYfJn1XWVmJxsZGmeQtbQlewZLAxMQEdXV1MDc3l6mBSKQlY1IXsa3C9x09+H6jB99v9GHSd8nJySgvL2+zS2u8guVRKykFZYhOK0RKRjnMhAJYupTBy5F5rt2UgjKcuJuHpPyXAIBuHS0xyc+FlXPrIkQ/l1fXw8LUCAEe9lrZF7rSTlXQuQ9Vx7T83dnGDHkvqlReQ9l5id8eF1ag4GU1jIUGqK1rhImRIWrqG+BoZQp3+3bSY84lPMXu6yWorJPAOfE2gv1dMKqnE7udp8fwCpZHLUSnFWJTZCpiM2UrVPx5LwoDRLZYMtwTAR72tM77/alEJD2VLX58Kfk5tl/OgLeTJb4Z34PWuXURRf0MgFE/s42utFMVdO5D1THDu3VAZNIzub8ru4ay83o7WUIAtPpOlGEoABqaucDGPyvAmYQCWJoaYdFQD3wQ2JX0udoqvBcxCQgzh4WFhVwTcd++fTXVNJ3g8K1sfBEaj0Ylb5qBAPg52AdT+3emdN4Vx+Oh6gUWAFg7mdq5tRVl7xxX/cw2mmgnF98qnfsgcwxVDARAsJ8LQu/msnpeVUzp64Jfpvgq3UeR7Gwr8HGwPJwSnVZISqA0SoAVoQ8QnVaofMdm510Rqlq5AoAEwPLj5M+ti3DVz2yjK+1UBZ37IHsMVRolwLE76lWuAHA0Lhc7r6Sr3rENwytYHk7ZFJlK+sNvlACbI1NJn5eK7UUC8ufWRbjqZ7bRlXaqgs59UDlGV9hyKU3TTdBqeAXLwxkpBWWk1pGaE5NZjJQC5etEdM5L9ty6CFf9zDa60k5V0L0POu+stlNWXY9zCU813QythVewPJxB17yn6jgmZkNtNTkygat+ZhtdaacqtK09mib0Tq6mm6C18F7EPJxRXl3PyXF0zwsACXkvaR+rrXDVz2zDtJ3aEtKj7n7Tdsr4/lAIr2B5OMPClN7rpeo4uucFgON3cjFAZKsXHsUEXPUz29C93rOyGkzdeUNrQnrU3W/ajiXfHwrhTcQ8nEFX6Kk6jokwlUC7vVPpwFU/sw3d6+2/maVw/TI2sxizdsfgyK0cJk2jhC7E56qTYH8XTTdBa+EVLA9neDlaYoDIltIxYpGtSrMfnfM2R5u9U+nAVT+zDd3npsrxVt0hPXT7m8k7q61YmhrxmZ2UwCtYHk5ZMtwTBgJy+xoIgI+Ge5I+r4DkeeWhjd6pTOCqn9mGSjupoO5BE53+5ureNcmioR6aboJWwytYHk4J8LDHT8G9VQoWIuMNWfNbgIc9fg7uDSbySt/MxFz0M9uQbSedwZM6B010+pvsMbrClL4ufLpEFfAKlodzpvV3xb55YogVmMjEIlvsmyem7Hg0rb8r9r8nhr2FMa126Zs3KFf9zDZk2jlT7Err3OocNNHpbzLHfPFmN4W/06WbkyW6O1FbEjBUMBCwNDXCF292U5kmkYf3IuZpBpdhEMQI/lU1nWyYCQX4v6F+jK4R4GGPhUM9sCoikfKx+ugN2rKfNR3SoghV7Qyhae5V96CJTn+TOeaDwK7SClHbL1NPR/jhkC4wFxqxU03n4sOmajoO7flqOhTRPwnDQxl1VjbxcrSEl6Ml4kyLpX8zRVe8aNUJ0c/ajqJ26kroEQGd/lZ1jJejJZaP6Ya4rBJKWaDEIlssH9OdlXaO6ukEu+o8AHxREzrwJuI2zuFb2Zi1O0arwiCooitetDzk4QdNr9AVBzae1vAKtg2jL5VNAP0XQikFZdgTnYljieU4nVqhVx7Q8uAHTa/QFQc2ntbwJuI2DJ2KINr68RJCiGx9Tm29j5ZwVaheF1gy3BOzdseQekd1cdBEhWn9XeHS3hybI1MRI8faJBbZ4iM9fhd0FV7BtlGYVDbR1lmCvgkhVcW5CfO9pguoc4W+DprooisObDyv4BVsG4VJZRNt/pj1RQhRNd87tzfTSgXD9Dno26CJDXTFgY2HV7BtFl2pwEIXXRdCum6+Z9MzXV8GTTxtD17BtlF0LQyiLaHr5nuuTNu6PmjiaXvw0rKNwodBaC+6bL7XddM2P0vmYRNewbZRiDAIqgHsvLDhHl023+uqaVudyVZ42g58HGwbRt9jR3UVXTXfMzFtaxJ9SLbCo53wCrYN01YC2IkkDSGRqdgTnalxga4KXTXfMzFtawp9SrbCo33wJuI2jj6HQVAx+2nT2puumu910bStqyZtHt2AV7A8ehkGQdaTdd7rItzPLdW6tTc6WYw0/fx0zbSt697aPNoPr2B5pOhLGAQVs9/vVzMV/q7JTElUshjNe12kFQ46umba1mVvbR7dgFewPHoHFbOfKjQZTkLGfO/jYo3d1zK1Ip2irpm2tdmkrWlrBA878ApWB+A/NvLQMfupQpNrb8oK1T8vqyFlRlbnIEGXEvRro0mbDxfSL3gFq8XwHxt1uPLy1PTam7xC9V+HPdQ6Bx1dStCvbSbttl7cQR9hFKZTVFSE27dv49KlSwCAxsZGlJeXs9Kwtg4fm0cPLs132hSioc0xp9P6u2LfPDHECuq5ikW22DdPrHEloU01Z/lwIf2E1gw2MjISW7duxaNHjwAAAoEAiYmJyM3NRVBQEKZNm4bPPvsMRkb8BJkO6ko3p4+mZy7Nd9qQKYlA2x10dMUzXVtM2ny4kH5CWRpt2bIFW7duhUQigUAggKGhIRoaGgAAeXl5qKysxF9//YWUlBTs2rULhoaGrDda3+H6Y9Nn0zOX7dZ0pqTmaLODTnO03TNdG0zafLiQ/kLJRHzjxg1s2bIF7dq1w3fffYeYmBj4+PhIfxeLxfj5559hbm6O69ev4+DBg6w3WN/h2vSn76ZnOmY/smjToEMbHXS0ATpZuzRt0tbFDFg85KD0te3duxcCgQC//PILhg4d2up3AwMDBAUFwc7ODv/9738RHh6OmTNnstbYtgCXpj9dr3RCFipmP7JoQ6ak5mibg46mUWWVebOzBD6OJgqP16RJW1esETzUoaRg7927BycnJ7nKtTmDBw9Gp06dkJaWxqhxbREuP7a2ss5D1uxHFk2Hk8hD12JOuYSM9+2tTODDflbo21f5uTRh0takNULb18h1HUpPqKKiAp06dSK1r62tLQoLeRMGVbj62NraOg8bSRoA7QgnUYS2OOhoErJWGQmA7bdfIqBPodY9S01YI/TZD0OboCTNO3TogMzMTNTX1yv1EK6trUVmZiYcHBwYN7CtwdXHpu1ep1xAxuw3xLuDzhY60AYHHU1DxSojgXZaZdRtjeDjbdUHJQUbEBCAo0ePYseOHVi0aJHC/bZu3YqKigqMHTuWcQPbGlx9bG15nUeZ2U9XwkkUoc/VkFShT1YZdVkj6PhhmNK6Eg9AUcG+//77iIiIwNatW5GXl4dx48ahuroaAFBaWor09HQcOnQIERERMDExwdy5czlptL7DxcfGe50qR9vDSZSh64MEuuiTVUZd1gg6fhjL+hnTuhYPRQXr4uKCzZs345NPPsGJEycQFhYm/W3gwIEAAIlEAhMTE6xduxYikYhxA1+8eIEJEybg2bNnSE5ObvV7ZmYmQkJCEBcXhxcvXsDV1RVTp07FjBkzYGCgm/XkufjYeK9T/UeXBwl00DerDNfWCLoz/mxPO7haC2lds61DeXoyePBgnDx5Ert378alS5eQn58v/c3W1haBgYF477330LVrV1YauGrVKjx79kzub0lJSZgxYwbKy8vh7++P3r17IyYmBj/88APu37+PX3/9lZU2aAK2Pzbe65RH39BHqwyX1gi6M/74Z7W8gqUJrTfN2dkZ33zzDb755htUVFSgvLwc5ubmsLRkVxifOnUK//zzj9zfJBIJli1bhvLycqxbtw4TJ04EABQXF2P27NmIiIjAyJEjMXr0aFbbpE7Y/th4r1MefULbrDJsKkUurBF0Z+5VdSwGlLcxaCnY6upqXLx4EWPHjkW7du3Qrl07AMDhw4dRU1ODoKAgWFlZMWpYQUEBVq9eDT8/Pzx48ECajpEgOjoaycnJGDBggFS5Ak2z6O+++w5vv/029u3bp9MKloCtj433OuXRJ7TFKqMrIS90Z+5mQgHLLWk7UF6kvH79OgIDA/HZZ5+hoKBA5rd///0XP/30E8aMGYMbN24wathXX32F2tparF27Vu7vV69eBQCMGDGi1W/+/v6ws7NDXFwcX92nBZpOC8fDwyZLhnvCgKT8F4B9q4wupR6lq+R7d+CdnOhCaUjz4MEDvP/++6ivr4eXlxfq6upkfh87diyqq6tx7949LFiwAMePH0eXLl0oN+rAgQO4evUqVq5cCTc3N7n7EFmivLy85P4uEolQVFSE9PR0+Pr6Um6DPtNWvU559A+yVhkBmjI5sTmT1LXUo3Rn/Pz6K30ozWB///131NfXY86cOQgPD4eLi4vM71OnTsWhQ4fw3nvvoaqqCjt37qTcoKysLPzyyy8YNGgQZsyYoXA/wvFJUTILYjufTUoxXo6WmBMgwuLhnpgTIOKVK49OQsYq880b7TFcZE6rGIAi6IS8aBoqM37eD4M5lGawcXFxsLW1xeeff650v48//hhHjx7F9evXKTWmoaEBy5cvh4GBAdasWQOBQPGbUFVVBQAwNZUfBk1sr6yspNQGZZSXlyMuLq7VdnnbeMjB9x09+H6TxRTAsn7GyPa0Q/yzWlTVSWAmFKB3B2O4WgvxoKAGKy8VIbEwqtWxPeyFmNLDQmkxgJZkl9bRCnk5cfGmRmeEpgA+6GuFHbdfQtnYQABgfl8rmJZmSbfx7xx1KCnYsrIyeHt7q6zxamRkhM6dO8uNW1XGH3/8gbt37+KHH35QmfOYaIMyJQwAjY2NlNrAw8Oju7haC1spsAuZlUoVSmJhHVZHleDDflYYLjIndZ34Z7W02qcNIS8jROboYG6IY4/KkfC8rtXvPR2EeKs7tQEHj3wo5yLOyclBQ0ODUiXb2NiIvLw82NjYkD53UlISQkJCMGTIEEyZMkXl/mZmZgAgzSTVEmI74eHMBhYWFvD29pb+TYzo+qoq0cHTCr7v6MH3GzWi0wqxMy5G6WwNaMpTvCPuJQL6dCe1Tnr9RSoA6ubl9g4d0bev5s2ufQHMGUsutIjJO5ecnNymHU0pKVixWIwTJ05g+/btSnMR79mzByUlJRg3bhzpc2/YsAF1dXWoq6trZYImZqHE9i+//BIdOnTAo0ePUFhYKDepxfPnzwEoXqPl4eHRf7gq0agNSS7YcFJsa9m/1A2lpz179mycOnUKW7duRWZmJoKDg+Hp6Qlzc3NUVVUhLS0NJ0+eRHh4OIyMjPDee++RPjexVhodHa1wn4iICABNa7yenp64cuUK0tLSIBaLZfaTSCTIyMiAoaEhaxmleHh4dAsuiwEwSXLBVDHqStwtD0UF6+XlhdWrV+Obb77B6dOn5WZZkkgkMDIywvfff4/u3buTPve+ffsU/tajRw80NDTIrOkOHjwYf/zxByIjI1t5G9+5cwfFxcUYMGAALCwsSLeBh4dHf+CyGACdkJduTpb4OuwhI8XIl5rTLSgnmggKCsLJkycxZcoUODg4QCKRSP/Z2NhgwoQJOHbsGCZNmsRFe6UMGDAAnp6eiI6OxpEjR6Tbi4uLsWrVKgDAnDlzOG0DDzewGUrBQx196X+uiwFQTXKRrGRGTSYhBdW4W7oDDB72oLUgIBKJ8P333wNoKq5eUlICMzMzxukRqUCE8rz77rtYuXIljh07hg4dOiA2NhalpaWYOnUqhg0bprb2tHXYWA/iTV+aRd/6n+t1UipJLgBAwjAhBVfryTzcwXjF3djYGI6Ojmy0hTI+Pj44evQoNm/ejJiYGKSmpsLNzQ2ffvopKU9kHuawJZR505dm0cf+V0cxADJVr0qr6pD0lJwVQJFi1Kfi8m0JhQr277//BgBMnDhRuo5JbKOCsmxMZElMTFT4m4eHBzZv3sz4GjzUYUsoH76VjRXH41WGUmhLyjl9Q9dS/pFFXcUAlKUeBYBRG1ont1CGPMWoT8Xl2xIKFez3338PgUCA1157TapgiW1UYEPB8mgfbAjlBwU1WLvzBiUByJu+qEHGdM/U9KjNOa3VWaJRXsjLnuhMWudqqRj1rbh8W0Ghgu3fvz+AVwkdmm/j4WEqlFVl11GGtpi+tFmxkDXdMzE9Pi+r0fo1W2KdVJWFhKsSjWwpxpRn9BzNmMbdphSU4XRqBarqJHhQnalV77guoLD35YXNKAul4Wk7MF0Pik4rpK1cCTRp+tJ2ZyAqpvuKWnoKIORiKk4/yNeJNdtp/V1R+TxXYWpAscgWH3H0zNhwtIpOK8SpB/m0zkP3nuS+4wlNS3Xa8I7rCpSe/ooVK+Ds7Iy5c+eymoKQR7dguh60KTKVkXIFNGf60nZnIKqm+2B/F+U7KuDU/XydWjP3cTSBj6MJLF281Gp1YMPRalNkqkoPZHnQLS6v7e+4LkFJwV68eBFGRkZYsGABV+3h0QGYmL3ozH7lwWbKOQJVJl9dcAaiarq/RfNZkJX32rZmru7UgEwdreh+L3SLy+vCO65LUJJSdXV1cHFxUVlNh0e/YWL2Yiv4Xd5HTXdNlKzJV1vjEIn7flxUQVkYZxWzV85REdqyZq4pmDha0f1eJvh2ovXuaes7rqtQkpRDhgzB+fPn8eDBA/j4+HDVJh410FwoF5RWw9HKFO727UgpJSZmr7MPn9I6tjktTV9M1kTJmMNm/hGDQV3stC4OUdl9U8HN1pxzRduWw0XIJqSQ52hF11rk2YF6ilg+1pZ9KCnYTz/9FPn5+Zg1axZGjhwJPz8/ODg4wMREcd3AwMBAxo3kYQ8yQlmVUqJj9gKA52U1jE27LUf4TNaLyJrDJACuZxTRai9XikXVfVOhv7stckoqSZ1LAPLm4ea09XARMgkp5DlaqbNqDx9ryz6UnsKoUaMANCX0P336NE6fPq10f4FAoDRJBI96ISuUyTgxLBnuiRl/xFC6/ubIVHwf1IvSMc1pOcJnul5ExRxGFy4Uy4OCGnx/lR3lCgA9na3QX0RuhiUW2eJGBvUZMxdr5rqGsoQUihSUOrJREfCxtuxD6a3v2LEjV+3g4RiyyohAlRODg6Viq4UiiJE7ndmvvBE+k/UitpytVMGFYjmaWM7qwIAQ8KpmWD4u1vjjKr3ECfw63SuoOFqpKxsVoB01bvUNyl7EPLoJndmaMicGJuakJcM9MfOPGFKmRgGAnyf3xrT+rjLb2YjFVQdsK5bs0jokFraO5aRLc2GsbIb1vKwGs3aTe2bKrsFDHXVlo1LnbLmtwA892gBMZmuKnBiYmJMCPOwxv5+VymQThElYnpma6XqROsxaXCiW+Ge1rJ1LkTCWN8P6OuwhrVkz0/SD2oy6MnkxcZKigjpny20FlQq2trYWkZGRiI+PR0VFBTp27IjAwEBKxdR5NAvT2Zo8Jwam5qQRInN0MDfEmRwBJacPAqbrRVybtbhSLFV17NiGqQhj2rGYHKUf1DSayORF10mKKurM3dwWUCplbt26hWXLluHpU9nQik2bNmHkyJFYs2aNtBAAj/bCdLYm73g2zEk+jiaYM7YvrZkAXQWZ8KQUKQVlnAp9MsqL7uzHTEit2IY8qApjugO0mWJXzjP9qDsftCazHNFxkqJzDXXMltsKCqVUbm4u3n//fVRVVUEgEMDNzQ2WlpbIzs5GaWkpzp8/j4qKCuzevVud7eWhAdPZGqGUmn/EbJqTWpokUwrKsCc6U6kAofthn0kowJmEAgwQ2aKbkyXpOp1kUaW8qM5+WgpTe3MDWu16d5Ab6TjnljwurKB1zQ6WprSOI4MmZpHakuWI62xU6pottwUUSt49e/agqqoKvXr1wrp169ClSxfpbydPnsTq1atx/fp13L59G/369VNLY3nowfRDaK6Umgsuts1JVIQm3VhcgtjMYghAP66zOe++5gZ3O9XKi8rsx7m9mcK+MDcSoLKefKvFIlusmkg9PIppIotjcbnwd2vPuiDW1CyyLWU5aj5bPnTpLqrqJPDq4spX06GIwuHwjRs3IBQKsXXrVhnlCjQVYV+yZAkkEgmuXr3KeSN56BOdVoivwx6yci5CcB25lQPglTnJQIXVkow56fCtbMzaHaNQmLe8NtCk4FVdWxmErGRidBWLbLHqP70wJ0CkVPBQmf0sP/4AM5X0BRXlSnedTNXzIENWcWWrZ8YUqrNItrzFmXit6zJejpYY59kOb/WwUPmO87RGoYJ9+vQp3Nzc4OjoKPf3ESNGAAAyMjK4aRkPY9gQki1pKbim9XfFvnliiEW2cvcXi2yxb55Y6UyCrtAkq+CVIQHg7WQJSxpmdCrKi8rsRwLQqp7SErrrZFRjppXBtqKjM4tkAyZe69oAsewSEpmKPdGZOq/4dQWFUqWmpkapAxOheF++fMl+q3gYw6aQbAkhuBwsTaTrg2N6OWHe6yLkvaii7HzBxPSmar2IDElPy7B2suqi3M0RgHsvXDKYGhmgur6x1XYm62RsZ7hiy1yqyVmkrmY50vbaxfqOQgXb0NCgtGoO8Vt9PZ8mSxvhOg1gTGYxRm2IarWd6kfLRoLxAA975JZUIjazmPZ6amVtA36erNp7EgBE9u3wQ1AvOFiatHLGAtDKw5PLWUx1fSM+GeEJKzMhK16lXA0G2EgKz2QW6cPQ30oXsxzxdV01D59oQg9RVxpAeVD9aNlIME7M1pmMJ8qr6zEnQKR0NuxmZ44FQ7rCpb05JecfFxszBi1TTejdPFxZOpSVc3E5GGCaFJ7RLFKOgtXWnMBsoC0ez20dXsHqIZpe96Hy0bJhemNjtk7MNFTFGh6+lY2Zu2MorZHmvqhi1jgVZBVVslYyjEuTJtNzszWLpBsq5WJjRulZajLLUVvyeNZmeAWrh2h63Qdo+mh/OJWIfz9+Q+l+TIUmW7P1lsJFXqzhzivp+OnfJMbX4gK2SoZxadJkem4ms8iy3KZ3hK1QKVVoMssRX9dVe1D6xqekpOCdd95RegJl+wgEAuzdu5d+63jkosq0pS3VLR49LcPmyFSlgoap6Y2N2TqZmcbhW9laq1wB9gZVXM5imJ7by9ESIvt2yKSQ+IJ4tnG55Mv8EaFSAL0YaU1nOeLrumoPSiVxWVkZYmNjlZ5A2T4CAfO0bjyvIGva0iZTz4bzKeirJNkAnYQRIvt2UkHAVLGQTYCx4ng8o+twDVuDKqYJPBTBhrk0Oq2QUlYpQYtnS6XMH90VB01nOYpOK8RumiUFtcHypW8o/CoXLVqkznbwqICqRyBVIdnNyRIpBWWsex5LoNpUTKV8HQA8LqpAdFohHCxNkPCklHbbyM40NkWmMs72xDVsCnQqGbrIwJa5lOpzILJrAeyX+WuOi40Z5g0WtbIkaVueZFVoi+VLn+AVrA5AxyOQahrDleN7ILekkpPYWVWm4gAPe7hTMP1JJMD8/XEoYzDi7u1shRVvdleZPJ0Lj2xFzjLE7OfrsIe0zKBsQTbhO2GfIlNyUBMxsJmFFdJ1RTbL/LUk90WVzDujzXmSlaFNli99gR+y6AB0PAIPfzCIVlUMpkkbFKHMVJxSUEZJoQBgpFx9XKwRvuh1HL6VjTfWXUJ2cWWrfQhByEXGG2K2o0ip/xDUi7SnMlfONGQTvgNQS1J4puuKbJX5U3UdXciTLA9Fg7SUgjKcTq1AVZ0ED6oz+VzEFOEVrJbDxCOQTlUMZWEqX4c9pD2bk0BxKIA6w4oMBMC43h0x9NfLSpU6IQhHdJefKpQJhJBSFnP5sxaUDCNbHo2NEmqqjqe7PhiV8hzl1fXIeMGNeZigvLpeY7GnTK0s8gZpcmfhCYkA+AxQVOAVrJbRUtA8K6umdR5iRE23hqQ8BUB1rbQlikIB1OVcYSAAgv1c8POZJFKzw0YJcD6xgNU2kDXnalPJMDLl0eiWUFNmTnWzNUd/d1v0dLZCZV0D5XMDwKXk57iU/JzWsVRIfVaOq2mFGok9ZTJAlTdI4zNAsQevYLUEpqXBWtJSabFRQzLAwx4fj/TEhvP0E6jLCwVQh3OFj4s1xvXuiLUklSsBm4ZFquZceYOjkuf56N3BGJOGDWSxZZpBlSDPKq5EVnEljt1Rb7voEH7/CeVj2Io9pTtAdbExw9q3ZJUrnwGKXXgFqwUw9f6TB1dKa8lwL/wT/xTJNAuVyxMG6vhAH+SWIrOwgtP8zMpgYs5tPjiKi9OP4hpcFqPQJdiIPaX7rRO+AM3hM0CxC69gNQxXgobNl76leXlugDulyjPNkScMuIq9bAkTxygmhdk1HRupjXBdjIIJAgE75QLJwMbyCFt5kvkMUOzDK1gNw4WgYStsQ5nZ2tnGDHk0cuwqEgZsx16yzcgejrjwqEBl2MonI71gaWqktthHrqDrtETmuMO3sjVWjEIVxGDo0K1sRNzP5/x6bFia6AxQ5ckIPgMU+/AKVoNwVfXGx8Wa8TlUma3pKFdlip+IvaQ7M+aaQV3t8O5r7lrhdMQldGM4yR53+Fa2VmXFGtPTET07WbcaDNzJKgHAvYJl632hGvcuzxdAV2veajOUFGxYWBjpfQ0NDWFqagp7e3t4eXmhXbt2lBun73AVnrL7WiaGeHeg/fFyYbYm4+Azrb8rTt3Px1UNVwOSByF82QhJ0VY2RaYodWBT5D1K1ut03usi7L6WydoA6sMhXdDB0hTl1fW4k11Cy1u4ZydrLJbzXqorq9G97BesvDtkk4Mo8wXQxZq32g6lnlmxYgWt/MKGhoaYMGECvvzyS1ha6r4gYguuRn5MnQ/YNluTdfA5fCsb17RQubacebPhka1NNOVafoCcEtVWiZbeo1S8Tn+nmSNXEZU1DZgzRgQA2BOdSUvBKlIOdL8dquu3bHriMg3t0rWah6zuPwAAIABJREFUt7oAJQUbFBSErKws3L17FwDQqVMndOvWDe3atUNFRQVSU1ORk5MDALC3t4eFhQXKyspQVFSEsLAwpKen4++//4ZQKGT/TnQQLkd+dJ0P6JqteztbIT6vtYdrb2cr9OncHgUvq7EnWnEmGDaKpnOBJsuOqQPCZEul35sP4DTprLT3RhYePS1jlPSAzSIUYpEtgv2dsZyCCZxtT1y6ce8Ae2u5PK+gJOE//vhjBAcHw9bWFmvWrMGQIUNa7RMTE4Ply5dDIBBg//79sLe3R2JiIpYuXYr4+HgcPnwYM2fOZKv9Og3XIz86zgd0zdbB/i5YP/VV+r9nZdW4l1OK+LzSVop3gMgWb3aWwMfRRLpNG71KBdBs2TGuIaoE0en2mMxinEt4qnFnpeZma7aVA511TQdLE9U7t4ALT1y6VhY21nJ5XmFAZeeNGzeipKQEISEhcpUrAIjFYmzduhX5+fnYvHkzAKBHjx4ICQkBAJw6dYpZi/UIYsTIFXRM0EwcHbwcLTEnQIQOVib4OyYb8XnyK93EZhZjdVQJIjObcgBz5ezFBJF9O+x/T6zXmWqYVgkKvZPLWluYQJith3frAAOSK1gtlUNKQRn2RGciJDIVe6IzkVJQJl3XVLUq1nwJhO4A9cTd3FbX1wQBHvaY5OdMat/J/i56O/hkC0oz2KioKLi7u6Nv375K9+vZsyc8PDxw8eJFrF69GgDQpUsXuLq6Iisri35r9RAuw1PomKCZOjqQXZOTANh++yUC+hRqTJjIw83OHAuGdMW0/q6abopS2Mj9y3RQwySumG0aJcDFpGeUHX2UeT93c7KEBMrXVFuua9IdoG6/nNFqG9s5f8m8M9FphThxN4/U+Y7fyUWQnzOvZJVASZpWVVWhQ4cOpPY1NDREWZms4LS0tMSzZ8+oXFLvIev9R/fc6jim+XFUTL1EAYDXNfiBfjikK8yFhjrjDfygoAZHE8uRWBjV6jcqApkND3ZLLfMejcksxvdBvbBvnpiUo48q7+ckFdnKBGg9i2PTr4JMzl+ySpNs6BWfyYldKL0NnTt3RmpqKjIyMtClSxeF+2VmZiI1NRXu7u7SbY2NjcjLy4OTkxPtxuorZLz/SqvqVH7wLY+hoyyYODrQzQTj72ZDtZms0cHSBHMCRBq7PhUO38rG6qgShWZdKknY2fBgD/Z3wZkEdoshMCU6rRBzAkQqczizEYomQWsvYLaVjaKcv1Tijskm7u/jasNncmIZyl7E69atw4cffoiQkBB4eXm12ictLQ0fffQRJBIJxo4dK92+d+9elJSUIDAwkHmrdQQqZjxV3n/RaYVqcz6g6+hAf1ZEPfSLLXQlSJ6slzXZJOx0q9MQiEW2GNXTSS0pLqnQ/Hkqy+HMllNdy1kcF2k/GyXAkkN3sXCoBwI87HE3u4RS3DHZxP0zxG602sdnclIMJQU7Y8YMXLhwAXfu3EFQUBB8fHzg5eUFc3NzVFRUICUlBfHx8WhsbESvXr3w3//+FwCwePFiXLhwAQYGBpgzZw4nN6JN0M2GAyj2/mMjkJwsDpYmEItscSNDuZBoeS26yspcaKgxQU23HKC6Yct0x0bVJgFeDaqoDsbICH0DATDepxOtCjXPympU7sO2U13LWRwXfhWF5bVYFZFIen+qcceNEuBcwlM6TcNjJXWV2zqUvIhNTEywa9cuTJ8+HQKBAPfu3cORI0ewd+9eHD16FPfv34eBgQGmTZuGvXv3wsSkyWU9ISEBVlZWWLNmDby9vTm5EW3h8K1szNodo/ADJkaXR27lUD73tP6u2DdPDLECz2OxyBb75tH3fI1OK8TUnTcwakOUSuUKNAnL5tdi4iC1ZLgnaQ9QNtkfk03rWagTJknYm6Pq3STL2sk+MibRn4J7q3x2xGDsq3E9SL3Di4Z50Grb/ptZKp8nFxnUmp+TbJ9oGwUkBidyj3upG4NUTUBZIlpYWOCbb77BokWLEBUVhYyMDLx48QJmZmbw8PBAYGBgK0eoXbt2wc3NTe8TTKijliKTQHJl0CmZ1zIlIxMHKS9HS9Iz9GA/F4TezWVlhiDRgbqWbCRhZyv95Rdvdms1gKOaQYjsO0zHqiFvXbQlXCwLtDynqj7RJxytTTXdBK2Ftsubra0tgoKCSO3r4UFvNKprqNMDj810fXSFLxvrT82dsagI6kn+zvjhVCIe0axLq+w+tA02krAzXXMUoGnmqsg6Qmfgp+odpmtqVfU8ucigJu+civrkWVkNtl9OZ70NmsLdjs8zrwjt8rPXYdiopaipJPJMhC+T9afma3kEZAV1gIc9/v34DWyKTMHG88wSJsi7D22CaWwy0zXH7k6W+Hp8D1IDEDYHftIKS6HxlOuzKnueXAyklJ2zZZ+kFJTplYLV1oGpNkD5y33w4AG2bt2Ke/fuoaKiAg0Nir0RBQIBEhPJL8zrMkzMeM/Lamg7RTGFDYeP5qZIss5YAgAf9rOi7OzVkiXDvdDPzZYVU5y2ekMyjU2m+24GeNjh2wk9Ndon0/q74mFeKfbdzKZ8rKLn6eVoiV7OVngoJ3c2HaiGxHHhacwWvZ2tFWZgkwefi1g5lBTsw4cPMWvWLNTW1kJCYkhJZh99ga4Z70Z6Eb4/lajS5f7jEewX8o5OK8SXocxrc0alPJdpF5EFadvldGQVVbbaXyyyxZgWuYiVQWY2G+Bhj3MJTxF6JxeJ+S+RXUy9Xi2ZZ6isLc1/awqDkcBcaET6eSk6N1PTO913c6DITiuEZwdLemt88u6b8KJmS7nSDYlbMtwTM/+I0ariFsQSDJ+LmD0oKdjt27ejpqYGHh4eeP/99yESiWBqyi9wA/TNeOcTC0jFNv52PqXVdjqzW0KI30gvInVtMlxKfi5TKszS1EhuGj1XW3MsHNqUhjAuLk7leZWFlLjZmqO/uy16OlvB3NgQx+/kMZ4RKHuGZFLqJatYD1b0vMiEdTFJwq7rdT7ptiPhSamMmfhCZiV2xrEXPsMkJC7Awx4fj/RUWn9XnRDvjDrDAdsClN7c27dvw8TEBH/99Rfs7fmObQ7dF43Jt64qc0/zGVHz6jZcoyhHbXZxJb4IjYcAAnRVESCmyqs5q7gSWcWVOHaHYWObcfxOrrSoOpW2kM2wJe95kcm0M/OPGIzs4YhxPh1x6n6+0ndGAGBEd0ekFJTBwdJE7v2QJSm/DHP2xAIAunW0xCQ/F43MaOm2/0xCAc4kFGCAyBbeFrXYH19O6XvraGUKa3Oh3OerqrYqGZysuJ+cEJFCyu67pbJkWleW5xUCCQU7rq+vL7p27YrQ0FAu26R1JCcno7y8HBYWFjJxvMQsjCh+MHXnDY2sqxgIgH3zxDJrbkyTCXCJgQBYObg9fBxN5BaOoJK1iou2NVeAXLSFeF4AaJ3b3EiAynpyBxEzYLbeB28nS3xD0uGJDorM5Jr4tojn5GBpwrrzoTrfcYEA8Ha0pDVQOJfwFLsvPkRlnQTODu0R7O+CUT3Jp7tVJDvbCpRmsK6urnyyfiVQ9aBl69tqHpZAJ55V3TRKgGOPyhWuwWqyNmzzGGUHSxN8yUFfEs9L8v//T5XKegkEACb4dkJ1XYNSU3/ztHm3Hxczvpfkp2WY+UcM1k5uyl1LRfEoW79WZSYf3q0Dbj0upuxNzATiOR3+YBDrM3d1vuMSCWBtJsS5T94g/bzkPY/4Z68sAlw6XuoTlBTsf/7zH6xfvx5nzpzBmDFjuGqTzkJl/WJkd0ecTWQvUXpMZrFOKFeChOd1yC6tQ8v5qzbUhm2UAPP3x3Fajo2px7MEQMSDJ4BE9UCtUdKUFIRsbloy1152/IHc3+QJX1XK09fFWmm7YjOLNfZOxGQWY+2ZR6yaxzXxjsdkFpNOaUilQIA+10tmA8PvvvvuO7I79+nTBw8ePMD+/fthZGQES0tLCIVCNDY2or6+Xu4/fcjeVFRUhNraWhgbG8usPefn5wMAOnXqJN3Wy9ka/dxtkVdShbwXrT1ZxSJbrJ3sg9jHRXgsx8OWCQ9yS1FewyyJuzpxtjRCYC/ZBOPh95/gSspzBUeoj9r6Rk03gVUkAISGBnizlxPuZL/g7Dp5L6oQdjcPHa3N0NPZGodvZWPhgTvILZHv1Z33ogp3sl9olTdtS24/LsG+m1m4nl6ETjZmcLU1V3lMSkEZwu8/wbXUQiTmv0Q7EyPYWTRZbP64lonbj0u4bnYrIh7k40rKc9zIKMKVlOdy7yk6rRALD9whVc85MqkA/dxtlfaHItnZVqBcTaehoQGVlZX49ddf8euvvyrdvy3FwTaHTGWcK8ns50Mlk+hcm6iqa/0V60p1G10kJrMYsY+5nzkRZvaSylqsPZOkExYVMiiauck6E9bgbk6J3DAgst7m6qTlPfH1YNmFkoJNTX3lUs7HwapGUbKETZHMMw/pA2bC1tnQtSU0RF9R1yfZKAG2XErTG+VK0HyNHgAl5zEq9ZzVSaMEWH78AS48esrXg2UZStIsMjKSq3a0GbRhjVFb6N3BWObv6LRChN7J01BreNiGyzVsTUIopLySKr0ZKEsAnEuk58CqrRnQtAFKCtbZ2ZmrdrQZuCiVpYv0dBDC1frV+rwuOWixgZnQEFUMi57zaA5Fa8ptEX5ZRzGU6sHyMId/GZu8qN/qbiH9m61SaroEr1x59AV+WUcxCntmyZIlEAgE+Oqrr+Dg4CDdRgWBQICNGzcya6Ge0dZfRiKRQ1eDV+YoTca98vDwMMPZxkzTTdBaFEr7s2fPQiAQYMmSJVIFe/bsWUonFwhaO7G0ddq6x93yMU0Fu+PimhQsvybNw6Pb3M0poZTdqS2hUMEuXLgQAoEA7du3l25btGiRWhqlz3g5WsLFxgy5cmJk2wIXk57hg8Cu0r/5NWkeHt0mKV87vaO1AYUKdvHixa228QqWHYZ2c6BV35Is3ZwsYW0mlJstqLezFfp0bo8OliaorKvH9ssZnLVDHoRbP4G61qTZTE2padysjWBmZqa1YR+6iKutObKL2U38wsPTthcENcSsQe6cKVgDAbDy/ydjV1VHdU90JidtUEV0WiF8/n8hEXWtSUvQNPDQdaX0fz3bYUoPS1Rbu6klWby1mRD+rjbSajp3s0v00iFt4dCuWHE8Xm8GYeqkW0crTTdBa6El3eLi4lBfXw+xuKkiSH19PX799VeEh4ejoaEBgYGBWLp0qXTtlkcWOgW0ydCy7JSiRBcEmvJoLq+uB/6/glXnmnRVbQPefc0NiXmlyC6pQsFL3cl8ZWJkgD9n94dpaRaApn4b3q0Dzj/itvhGaVUdXO3MpUXPiVJmX4bGI0tPZnxikS1c2qtOf8gjn0l+fPimIiiF6TQ0NOCjjz7CzJkzceTIEen2tWvXYu/evSguLkZpaSnCw8Mxffp0VFSQSy7dFlky3BMGLPqAiUW22DdPTCn5tqY8mptflxhsqIOs4krsvZ6FW1kvUPCyBr2crTBroBuGemv/QHD1xJ4yg5HDt7I5V64Ee69nYVVEIkZtiMLUnTcAAL+/208t1+YaotA4n12NHt2dlA/i2zqUFOzx48dx7tw5GBsbQyQSAQDKyspw+PBhAMCCBQuwf/9+DBw4ELm5udizZw/7LdYTiMo7TJSsi40Zvp3QA+c+eQOHPxhEeTaoKY/mltdle7BBlod5L/F3TBaEhtodDi6yb4dp/V2lfz8oqMEXofEaaUtsZjFm7o7BB/viNHJ9thnv0wlHbuXwnuw0EAD4enwPTTdDq6EkWSIiIiAQCLBjxw6pw9OlS5dQW1sLkUiEjz76CP369cNvv/0GY2NjXLhwgZNG6wvT+rti3zwxxDRmcAYCYO1bPpgTIKI9gvRytIQbicogbCIW2bZqLxuDDbo0SoBzLJYNZBsBgB+CegFoCmk6nVqBbbdLNboGKpEAmSRLn2k74fef4OT9J2q7nqOl/BrIuoZAAKyd7NPmww5VQclGmJKSgs6dO2PQoEHSbVFRURAIBBg6dKh0m62tLVxdXZGTk0OrUf+vvTsPi6ps/wD+HUa2AZEdUSRRHBAVAwU0xSW3SElxzdzodc3KNLXUV8vUTHrVFDXNjRINUcM9V1AxTAQ1QFB23Nn3RQZmzu8PfufEwMwwZ5gNeD7X1XXlWWaeGc6c+zzb/QiFQoSEhOD06dPIyMiAUChEly5d8P7772PevHnQ1xe/SBMSErBnzx4kJCSgsrISjo6OmD17Nnx9fRV6f3VquPLO3+kFMhfQBhr3tTaHR1dztfWl0c1xktB9e4Hhqc1eK7W1oP/OADD1l79JLasVyGlhK15J4uVgjiVkwXW5sAqwFRUVsLe3F9t2584dABALukBdkomamhrWBRIKhVi8eDFu3rwJHo+Hvn37ol27doiLi0NgYCBu3bqF3377DYaGddlDoqKisHDhQohEInh4eMDQ0BB///03VqxYgbS0NCxbtox1GTSBHpD08SAHRKXlSw00yr64e3U2wakHSnkpmThyPBRIWuavsqYWheU1yMyvQFFlNcx4enCwMkJozAvVF1qD9NvpwLdvJ/yVlofzca9J/yChER/0tUVOfiEqayh0tjLDRHc7klSCBVYB1tzcnFlkHAAePXqEwsJCGBgYwMPDg9leWlqKZ8+eKbTA7smTJ3Hz5k04OTnhwIEDsLGxAQAUFhZi8eLFePjwIX7++WcsX74cb968wcqVKwEAhw8fxoABAwAAz549w6xZs7Bv3z6MGjUKvXv3Zl0OTWpqPVllv5eqtTdoh30z+8n9Xk2NfgaAe5lFraaZUpLqWhFO3W/dDxGE9jsX9+/9PiE3B5cTc+DpYI4vSA1WLqz6YD08PFBQUIBff/0V5eXl2L17NzgcDgYPHsw02woEAqxfvx7V1dViQVdep0+fBgCsWbOGCa5AXXBfv349AODixYsAgLNnz6KgoAC+vr5McAUAe3t7rFixAgAQHBzMugzagq7Rfj6iR7P6Wpt6D1WP4h3TqyNScsrEEkw0R1RaPrIKWm9wJQhtRg90OxGjWBdgW8KqBjt//nxcu3YNAQEBCAgIAEVR4HK5WLBgAQAgLi4OCxYsQGlpKfT19TF37lzWBTIzM0O3bt3g6uraaF/Xrl0BALm5ddMTbt++DQAYMWJEo2OHDx8OLpeLyMhI1mVoa74Y0UOlSQtO3X+BU/8/6JR++jUA8KykBvFRmaxr6DvDU9W2cDhBEI1R/78mbmczQ1KTlYFVgHV2dsbBgwcREBCA1NRU2NvbY+nSpUwwNDExQUlJCbp06YJt27aBz+ezLtC+ffuk7ktIqJua0LFjXR9AamoqAEh8H2NjY1hbW+P169fIz89XqLm6raBH8aojQw/99NvRiIvX5UIABWL7m2p+IosDtF52poZwe8sU5+s1S2ozWxMDvC59o+liaAwFYNOFJFxaOkTTRdFarDMNeHp64o8//pC4z97eHqGhoejbt2+zC9YQRVHYuXMnAGD06NEAgLy8PACQmjHKysqKBFg5qXMUL0Xh/4NrY/cyCzHrUDS2THSVmDQj+O+nKi0boTkCoajFBFcAbTq40h5n13X9kGQTkik1lQ+Xy1VJcAWA7du3IyYmBpaWlpg3bx4AoKqqbkUaAwMDiefQ2ysrlTMNpby8HPfvN55gL2lbS2QA4Kv+enjWwwKbbhehoEqkkXKI/r/5qSLvOVxtxKdkXY5XT/YiQv1yW8EUlrZo75+xmOlK8hFLwirAvnrFfkJ2p06dWJ/T0M6dO7F//37o6elhx44dMDevG5TD5XJBUVST686KRJoJFC2VfQddvO/IQ3BCucbKQAE49bhcLMA+K6lBXiX5WxKENnlaopmc5i0BqwAraTCRLBwOB0lJSazOqa+2thYbNmxAaGgo9PX1sWvXLrGRyYaGhigtLUV1dXWj5BMA8OZNXROOkZGRwmWoz9jYGE5OTsy/6Zprv379lPL62iI05hmOPcrWdDGQmFeD9nZ8pvkpPioTDftsNYEDwNHaGKm5mnsAIQht0aFDB6n3wOTkZJSXt93fCatpOhRFyfUfAPTo0UOhQU60iooKLFq0CKGhoTAxMcGhQ4cwdOhQsWOsra0B/NsX21BTfbREY1Fp+Vq1HFn9Bdk1tfpPfV4O5jg6zwvXvhyKgEl90ETjCdSV/ZEDNFkWglAFZ1vS/yoNqxrsgwfSU/68efMGubm5CA8Px4EDB+Dg4MAMSmKrpKQEH3/8MRITE2Fra4v9+/dLDNY9evRAWloa0tPTYWdnJ7avvLwcubm5MDc3JwOcWNgZnqo1wRUQD6qaWv3Hu4cl3nW2bjSNqKmBYV4O5rA20Vf5wB06pWJnM0OZZSmuqkFyC18Pl9A+fm52TR/URrG6Y/F40hPD83g8mJubw9nZGV27dsWKFStw7NgxzJgxg1WBBAIBFixYgMTERDg6OuLQoUPMtJyGvL29cenSJVy/fr1R7TYiIoJZm5aQjzZOgakfVDUx3+7HSZJHM9Oayrq1KzwVgOoCbMPUmbLKEpWWr5ZF2om2w1CXS0YQy6CSKsHYsWPx448/4sSJE6wDbGBgIP755x/Y2toiODiYGdAkyZgxY7Bt2zacPn0aI0eOZILp8+fPsW3bNnA4HPj7+zfno7Qp9ZtjtUVuWTV2hacygUIVC9VL49yxPTqbGcp1rLT0jsqudXc04mJ4V0Pwu9mL1ajlSaupzvnORNtQVSMk03RkUFmbm4WFBTIyMlidU1RUxKQ2NDc3x+bNm6Ueu3XrVhgbG2Pjxo1YsmQJFi5cCA8PDxgZGeHu3buoqqrCsmXL4Ozs3KzP0ZZoQx9nQ3tvpov927lje3AAtSS/f5JdJnNOrjyUXevOqRDCzFAHHw+qW485Ki0fO8NTJT50SEraQVYtIpQtKi2fBFgpVBJg8/LykJ6eLrNJWZKYmBhm5G9iYiISExOlHrt161YAdSObg4ODsWfPHsTFxYGiKDg5OcHf3x8+Pj6Kf4g2SFN9nGw8yS6rG9AD9QRZEQWsClM8JRyd61lZtW4KwN7YUgx6Ox8viipl1kalJe1o2KydlV+B31SQwIMec0Uqy60byQsuHas7alpamtR9FEVBIBAgMzMTe/fuhUAgwLBhw1gVZvTo0UhOTmZ1DgC4u7vj0KFDrM8jxKmjj9PCSA+FFYJm3XQp1I2YdbZpjycSBu10szRCZn6F0m7sIgoIDE9V+PtRdq5nCsDGC0lIySlr8jVlPSDUb9Z+nK3c/ne6b7iphwCi5cspIRmtpGEVYOVdwJyiKBgaGmLx4sUKFYrQDGXXtiQJWTAAeWXV2Hz2ARLz2K8XTKMooIOhLq4uGyJ1QI+0ZtA+nU2Q8LKU1ftFZxYq3Nekir5PSQ8W0sjzgNCchwBXuw7wc+sstf/XzoyHTReS8JiMYG6VbEwkZ9IjWAZYqoklTLhcLkxMTODm5oZFixaJJWUgWgZVrqzj5WDO1Jo2DLPAs5IaFOvbMAur773Jrs+eDp50f2R9skb3RqXlI+El+wQozelr0nTfZ1MPCIo+BHAAfP2es8zgPcjREpeWDsHO8BTsuJZKmoxbGZ6+9nctaQqrb+bJkyeqKgehJeS90epwgLmDHXDor0y5bsg6HGDJiB5i2+w76MKvX11wDIrKVKi8TQU9SaN7ryiYpSqRZa23IWlBP6ugAr/dUf0iBk19V/RDwMYLSaxqyPL6YgQf/d8ylzlX19WuAw7eziRBuEUhfy1pyKMH0Yg8CRTouZeO1sZyBeMtE11l1nIUHcGsyHmKDub648ELeDqYKzyimNYw6Cv6cMGWPN/VIEdLmBjqyv2aFNj1Tzc1bxiAXNcUoT0qqyWvjEU0I8Cmp6fj1q1byMrKQkVFBXg8Huzt7TF48GD07NlTmWUkNECeGyHALhjLomjQU+Q8RQcrUWjeiGJll4cteb4rRZKNKNI/LW3eMKD55nSCnbS8tptruCms705VVVVYv349zp8/L5Z7GKhL7r99+3b4+Phgw4YNMDY2VmphCfWTdSOkyRuMm3oNRah76kxzRxQruzxsyFNmRZONKHsupLRrqrOpIV4WV4ldY2vPPNK6DGRtSUmV4oMVWztWAVYoFOKTTz5BdHQ0gLpVZFxcXMDj8VBeXo5Hjx4hLi4Oly5dQlFREYKCglRSaEI7yROMZZ3LNsjQg6YU0ZzBXM0ZUayM8nAAOHWUPEVJGnm/K3U21ctDnmtKlQPziKZV15AmYmlYraYTFhaGu3fvwtbWFmFhYTh69CjWrFmDpUuXYu3atTh+/DhOnjyJjh074u7duzhz5oyqyk20Ql+M6AEdOVeEkTRoig16MJeiC9AoO60kXZ6mPj8HwCf9TbBunItKvit1NtUri7zfHaEaZjw9TRdBa7EKsKdPnwaHw0FgYKDUftbevXtj586doCgKYWFhSikk0TbIe6OUZ9CUPKZ52GNSP8VWAlFFjW2ahz2C53rBy0Fy/m0vB3N8M8QMIxx4Kvuu1NlUr0z0d2cnZ+5oQnnMjUiAlYbVY2dKSgq6du2K3r17yzzO1dUVXbt2RWpqarMKR7Q9yho0Ja9enUxw6j7781RVY2uqP/v+/X8Lq4rvSt1N9co0yNEScwc74Lvz7Oc4E4rLKSWZnKRhdZcQCARy5xc2MjLC69eqXQeTaJ2UMWiKzXup8zx5ydufrYrvik2fZnOb6pVN0zXptii3rFrTRdBarAJsp06dkJaWhtLSUpiYmEg9rqSkBKmpqbC1tW12AYm2qzmDpti8R0utsdWnzO+KTbIRZTTVK5O6RmQT/6quFWm6CFqLVR/ssGHDUF1djfXr10MkkvylikQirF+/HjU1NayT/ROEJqhzcFVLIU9/cPBcr2Yn3VAFNn/PpnAAfNC3E+a88xbe62WDD94mlYaGOpJcxFKxqsHOnTsXp0+fxqVLl5CRkYEpU6agZ8+eMDIyQnl5OR4/foyTJ08iJSUFJiYmmDt3rqrKTRBK05Ix1GaRAAAgAElEQVRrbKqkzqZ6ZWKb7jP+RYnUPux3na0R/iQX5+JeqbDELVsHFpm/2hpWAdbKygr79u3DokWL8OTJE2zatKnRMRRFwdzcHLt374a1tbXSCkoQqqTuwVUtiTqa6pWN7d9T0kPEw2dFJGWjHF4VV2m6CFqL9VBINzc3XL16FUePHkVkZKRYqkQHBwcMHToU06dPh5mZmSrKSxAq01JrbIRk9f+ex288RFUNBX43e4l/z4YPEVFp+SS4yknYxCprbZlCcw06dOiATz/9FJ9++qmyy0MQGtcSa2yEdHyb9hjbwwgA0K9f46UNJdkZnkqCq5zeCEgmJ2lYDXIiCIJo7RRZ8KBN45AUWtJIrcEqK83hhAkTlPI6BEEQ6qDsNJitHUlRKZ3UALtq1SpwmvlkwuFwSIAlCKJFUdXCBc1hqKuDXp06IPZpkaaL0ghpSpdOaoDt1KmTzBNfvXoFPT09WFq2vVGVBEFohjoGoGly4QJpuloYoVdnE60MsC6dyHgFaaReSRERETJPdHZ2Rp8+fXDs2DGlF4ogCKK+qLR87AxPldg36ulgji+UOIVKG6diPc4uwzBnK00XQ6KhfDIdUxoyyIkgCK0WGvMMsw5FSx14dC+zELMOReNEzHOlvB+dblH7aGdnZ2dTsoKRNCTAEgShteSdjyqigFVh8c0aoJSSU4agqEx8e+4RKCmpYDWJp8vVysD/8Ln2NVtrC+3rbCAIgvh/bOajiiggMDyVdROvrOZnbWJs0I7VSkfqcj+LBFhpSA2WIAitpMh81OjMQqTklMl9fFPNz4rQ4QCT3e2UPn2Fzkz1w8Q+WjU1pqhSoOkiaC0SYAmC0EqKNvfKe54q0iHamRoieK4Xtk7tK3M1ovYsRyrXXyJxmoc95g52gH477bh9m/H0NV0ErUWaiAmCkElTuZkVnY8q73mqSIc419uBaaKWlds6r6yaVVNvcVUN8+Cw9swjZOZXKLfgzeBgaaTpImgtEmAJgpBInVNjJFF0Pqo856kqHaKk70NSbmu+TXu5ltSjJWeXYebBaGhR1yvD3JgsVyeN1Cvx1aum1z8UCARNHtdUwgqCILRPaMwzmTd/emrMlomuKlt0XdHgLc95qkiHWL8ZVx70knqbLiThcXbT/cbaGFwBgKdL6mnSSP1mRowYIfNEDoeDR48eyTyOw+EgKSlJ8dIRBKF2bKfGdDYzVElNlp6PyqamKW+QU3Y6RB0OsGRED9bnDXK0RPsWvmB5ZY32pZbUFlJ7ySmKavZ/Ii2cS0YQhGyKTI1RlS9G9JB7xCybIKfMdIg6HGDLRFeFHjJax8o9WjSkWctIvcrCw8PVWQ6CILRAc6bGqGLgEz0tpakaNdsgp6wat5eDOZY0oy+6Nazc87K4UtNF0FpSA2znzp3VWQ6CILRAc6bGqGpkMd1XGRieimgJwV+RIKdI8zPNztSQGS3c3M+sjSv3sJWSXa7pImgt0jtNEARD1VNjFCVryosiQS4lpwxONsaIySxkNXhIhwMETGbfHCyt3Nq4cg9bBrraMR9XG7X8vy5BEEqjyqkxyiBpygsbzUmLqEhfa1NTnfradWBdDm3T0cRA00XQWiTAEgTBUOXUGE27nlmJX+4rlsdXkWZoeaY6tfwBTsBEdztNF0FrkQBLEARDlVNjNCk+pxr7Ykvlbg7u/5YZenUyQVdLI4WaoVWRhlFbje7VUdNF0Fqk8ZwgCDGqmhqjSSeTyln1tXJ1OPhufG98PMhBoYcHVaRh1FZXE7M1XQStRQIsQRBi5F2xpTnzP9UpJacMSfk1rM5huypPw/drDU2/8gp78ELTRdBaJMASBNHINA97mavBeDmYI3iul8rSJCqTqlflUdZ5LVVZK5hqpCqkD5YgCImUPTVGU9Q99ag1zG1lg+3Se20J+WYIgpCpuVNjNE3dU49aw9xWNsgoYulIEzFBEK2auqceabJP2sSAq9b302+nQ0YRy0ACLEEQrRrfpj1cLNmtWONq10HhWjs91UkThvKt1fp+wrYyVFpBJMASBNHqTXExZrXmS/yLEkz95W+FByyxmeqkTOoO7rUiikzTkYEEWIIgWj1XG30s6m/CKujRi8qfiHnO+v3kneqkbMYG7dQe3H/7O0t9b9bCkABLEESbMNKBJ3PqkST0ovKK1GTlmeq02seZVXmaQo/8Vmdwf1VcpZ43aoHa1nA3giDaNDoAjdt1G49elsp1Dr2ovCKDl+SZ6rRwaHdcTczGguD7rF+/vvopK5ta4k+Z2mmiLbyFIAGWIIg2JSWnTO7gSmvuovJNTXUa3aujwuvTApJTVjYM7lkFFcgpeYMXxVWsP78s7m9pZkBXS0ACLEEQbYo2LioP1A2MmnWI/Wo/TaWsbBjcU3LKMPqnyOYUVczcwQ5Ke63WhvTBEgTRpmhrhiZF+k4VSVnJt2kP547KeVDQ4+q06CQkqkZqsARBtCnanKGpqb7Tt8x58HAwR69OJs1KWblunAtmHoxmtcKQJAKhqFlN560dCbAEQbQp2p6hSR05oAc5WmLLpD5YFZYAqplRVtVN5y0ZCbAEQbQpLWVReVXngFbWSOOHz4vwMUg/rCSkD5YgiDanNS4qr4hBjpYIXTgQV5cNgXV7fYVeIyW7XMmlaj1IgCUIos1pbYvKNxffpj06mRoodK6BLgkj0pAmYoIg2qSmmki9HMyxZESPVh9caR1NDACUKHgeIQkJsARBtFmtZVF5ZZjobofLiTkKnUdIRgIsQRBtXktfVF4ZRvfqiPYG7VDGYr5ve4N2ZD1YGUjjOUEQBAEA+Gy4o0qPb2tIgCUIgiAA1C08MMm9s1zHTulnh4VDu6u4RC0baSImCIIgGNumvg2+TXvsvpEmsbm4vUE7fDbckQRXOZAASxAEQYhZOLQ7s4zeoYhHqKyh0NnKDBPd7UifKwskwBIEQRASje7VERZvXgIA+vXrp+HStDwcimpuJsrWLz4+HjU1NdDR0QGPx2O2l5fXZTAxNjbWVNFaLPLdKYZ8b4oh35vimvPdVVZWQiQSQVdXF66ursoumtYjNVg5CIVCAIBIJGIutvokbSPkQ747xZDvTTHke1Ncc747+h7a1pAAKwd9fX1UV1eDy+VCX1+xfJ0EQRBtTXV1NYRCYZu9b5ImYoIgCIJQATIPliAIgiBUgARYgiAIglABEmAJgiAIQgVIgCUIgiAIFSABliAIgiBUgARYgiAIglABEmAJgiAIQgVIgCUIgiAIFSABliAIgiBUgARYgiAIglABEmAJgiAIQgVIgCUIgiAIFSABliAIgiBUgCxXp6A7d+5g3759SE5ORk1NDXr16oX58+djyJAhmi6axgmFQoSEhOD06dPIyMiAUChEly5d8P7772PevHliS1fFxsZixowZUl/L19cXW7duVUextcKZM2fw9ddfS92/aNEiLFu2jPl3QkIC9uzZg4SEBFRWVsLR0RGzZ8+Gr6+vOoqrcU5OTnIdd+TIEXh5eQEAXr9+jWHDhkk91t3dHSEhIcoontYKCwvD6tWrcezYMfTv37/R/szMTOzatQv3799HcXEx7O3tMXXqVMyYMQM6Oo3rZTk5OdizZw+ioqKQl5cHW1tbfPDBB5g/fz709PTU8ZG0EgmwCqAvTj09PQwYMAAikQjR0dGYP38+NmzYgGnTpmm6iBojFAqxePFi3Lx5EzweD3379kW7du0QFxeHwMBA3Lp1C7/99hsMDQ0BAElJSQAANzc32NnZNXo9d3d3tZZf0x4/fgwAGDRoEMzNzRvt79mzJ/P/UVFRWLhwIUQiETw8PGBoaIi///4bK1asQFpamlggbq1kPUg8e/YMcXFxaN++Pbp06cJsp685Jycn8Pn8Ruc5ODgov6Ba5OHDh9i4caPU/U+ePMGMGTNQXl4Od3d39OnTB9HR0di0aRPi4uIaPfBmZ2dj2rRpyM7OhouLC3r16oUHDx4gMDAQd+/exeHDh6Grq6vqj6WdKIKV7Oxsqnfv3lS/fv2o5ORkZntcXBzl7u5O9enTh8rOztZgCTUrJCSE4vP5lK+vr9j3UFBQQE2bNo3i8/nU1q1bme2rVq2i+Hw+FRsbq4niap2ZM2dSfD6/yWuoqqqKGjhwINWrVy/q77//ZrY/ffqUGjJkCMXn86mEhARVF1drVVRUUGPGjKGcnJyomzdviu3btWsXxefzqbNnz2qodJpz+fJlys3NjeLz+RSfz6diYmLE9otEIsrX15fi8/nUmTNnmO0FBQXM9suXL4uds3DhQorP51N79uxhtlVUVFD+/v4Un8+nDh06pNoPpcVIHyxLx44dg0AggL+/v9jTr6urK+bPn4/q6mqEhoZqsISadfr0aQDAmjVrYGNjw2w3NzfH+vXrAQAXL15kticlJUFHR0esZtaWPXnyBJaWlmLfnSRnz55FQUEBfH19MWDAAGa7vb09VqxYAQAIDg5WaVm12ebNm5GZmYmZM2di6NChYvvoGmyvXr00UTSNyM7OxldffYUlS5ZAJBLB0tJS4nFRUVFITk6Gp6cnxo8fz2yv//utf11lZGTg5s2bsLe3x6JFi5jtPB4P33//PbhcLo4ePaqaD9UCkADL0u3btwEAI0eObLSP3hYZGanWMmkTMzMzdOvWDa6uro32de3aFQCQm5sLABAIBEhPT0e3bt3A4/HUWUyt9Pz5c5SWlsp146evwxEjRjTaN3z4cHC53DZ7HcbHx+PUqVOwtbXFl19+2Wj/48ePwePxWn1TcH07duzA2bNn0bt3b4SGhqJbt24Sj5N1f3N3d4eFhQXu37+P8vJyAMBff/0FiqIwfPjwRn2znTp1gouLC16+fIm0tDQlf6KWgQRYFiiKQlpaGnR0dCReoF27doWOjg7S0tJAUZQGSqh5+/btw6VLlyQGzISEBABAx44dAQCpqamoqalB586d8dNPP8HHxweurq549913ERAQgNLSUrWWXdPo/lcLCwts3LgRo0aNQp8+fTBmzBjs2bMH1dXVzLGpqakAILEP0djYGNbW1igsLER+fr56Cq9FNm/eDIqisGLFikbXYXFxMV69egUHBwcEBQXhgw8+QN++fTF48GCsW7cOOTk5Giq1anXr1g0BAQE4efKkzIFhdCCUdF0Bdf3TIpEI6enpYsf36NFD6vsCQEpKisJlb8lIgGWhpKQEAoEApqamEkfGtWvXDmZmZqiqqkJFRYUGSqi9KIrCzp07AQCjR48G8G9T3a1bt3DkyBF06dIF/fr1Q2lpKQ4fPowpU6agsLBQY2VWN/r7CAsLw4ULF+Do6Ii+ffsiJycHgYGBmDNnDt68eQMAyMvLAwBYWVlJfC16e1sLsJGRkXj48CEcHR0xduzYRvvph5jExET89NNPsLCwgJeXF4RCIU6cOIFJkyYhIyND3cVWuQULFmDChAkSRwDXR7cuyXtd0cdbW1vLdXxbQwIsC1VVVQDAjICVxMDAAABIgG1g+/btiImJgaWlJebNmwfg35udp6cnwsPDsX//fgQFBeHq1asYOHAgsrKy8O2332qy2GpFfx8+Pj64ceMG9u7di6NHj+LChQtwdnbGw4cPsWPHDgD/Xov09dYQvb2yslINJdcev/32G4C6gMLhcBrtpx9i+Hw+Ll26hKCgIOzfvx/h4eEYN24c8vLymD7stojtdUWuQ9lIgGWhqae/+tpqE7EkO3fuxP79+6Gnp4cdO3Yw009Wr16Ny5cvY+/evWJTUszNzREQEAAej4dr164xT8mtXWBgIC5evIgff/xRrGnTzs4OW7ZsAYfDQWhoKGpqasDlcsHhcCQGkfpEIpGqi601MjIyEBUVhU6dOmHcuHESj/H398f169fx22+/iU3d4fF42LRpE2xsbJCYmIh//vlHXcXWKlwuFwDkvq7YHt/WkADLAn3Tq98X1hDdhEcG7QC1tbX45ptv8PPPP0NfXx+7d++Gh4cHs19XVxcODg4wNjZudK6NjQ1cXFxAURRT62jt9PX14ejoKLH7oWfPnujYsSMqKyuRlZUFQ0NDUBQl9Vqkr0MjIyOVllmbXL58GRRFwdfXl7nxN8TlctGlSxeJc4wNDQ2ZEdmJiYkqLau2olvn6OunoYbXlbzHt9X7IQmwLBgbG4PH46GoqAi1tbWN9tfW1qKoqAj6+vowMTHRQAm1R0VFBRYtWoTQ0FCYmJjg0KFDjaZLNIWeSkA3Q7V19b8Pus+L7ottqKk+2tbo+vXrACCx71Vebf2ao68raX2mDa8reY+X1kfb2pEAywKHw4GjoyOEQiGysrIa7c/MzIRIJJI6Aq+tKCkpwaxZs3D79m3Y2tri2LFjYjVX2saNG/Hpp5+ioKBA4uu8ePECwL+jjluz8vJyrFu3DkuWLJH48AaIfx/0qE16NGfD18rNzYW5ubnU+Y6tTUFBARITE9G1a1eZo2R3796NJUuWIDk5WeL+tnTNSUJfV5Km1VAUhYyMDHC5XHTv3r3J44F/r8+2ek8kAZYlb29vAP8+LddHb2NbU2tNBAIBFixYgMTERDg6OuL48eNSf1wPHz7E9evXERER0WhfSkoKHj9+DFNT0zaREMDIyAjXrl3DlStXEBMT02j/rVu3UFRUBD6fD2tra5nXYUREBIRCYZu6DuPj4wHUpdyUJTk5GVeuXMGlS5ca7SsoKEBUVBR0dXWZvMVtDX1dhYeHN9r34MEDFBYWol+/fky3Dn38jRs3GvWzvnr1Co8fP0bnzp3h6Oio4pJrJxJgWZo4cSL09fVx4MABPHr0iNmekJCAgwcPwsDAAB999JEGS6hZgYGB+Oeff2Bra4vg4GCZNQE6Z/NPP/0kVhMrLCzE6tWrIRQKMW/evDaRLJzD4WDq1KkA6mr29edjPnv2DBs2bAAAfPLJJwCAMWPGwMLCAqdPn8atW7eYY58/f45t27aBw+HA399ffR9Aw+jfYu/evWUeR19zQUFBuH//PrO9oqICa9asQXl5OSZPntymmtbr8/T0RI8ePRAVFYUTJ04w2wsLC/Hdd98BAD7++GNme5cuXeDt7Y2MjAxmGh5QN2p47dq1EAqFYse3NRyKDHdl7dixY9iwYYPYk250dDRqa2sREBAglmKsLSkqKsKwYcPw5s0b9OrVS2q2GADYunUrRCIRli5diitXrkBXVxf9+/eHoaEhoqOjUVFRAR8fH2zbtk3qgJXW5s2bN/jPf/6D+/fvg8fjoV+/fgDqri2BQID//Oc/YivthIeHY8mSJRAKhfDw8ICRkRHu3r2LqqoqLFu2TCx1XWv39ddf48yZM9i5cyfee+89mcdu2bIFQUFB0NHRgbu7O8zMzBAbG4uioiL0798fBw8elDkVrzWYNWsW7t27J3E1nfj4eMyZMweVlZXo27cvrK2tce/ePZSUlGDq1KmNFgp4/vw5pk+fjry8PPD5fDg4OODBgwfIy8vDkCFDsHfvXrRr1zbXlSEBVkE3btzAwYMHkZSUBD09PTg5OeGTTz7BwIEDNV00jbl69So+//xzuY6l+8AoikJoaChOnjzJZMlydHTE1KlTMXny5CaH/7c2AoEAv/76K86fP4+srCzo6enBxcUFs2bNYhJ01PfgwQPs2bMHcXFxoCgKjo6O8Pf3h4+PjwZKrznz589HZGQkgoKC8M477zR5/KVLl3D06FEkJSVBJBLB3t4e48ePx5w5c9rEyi+yAixQ16caGBjIPNy99dZb+PDDDzFlyhSJD7yvX79GYGAgIiMjUVZWhi5dujDfZ/3lKdsaEmAJgiAIQgVIHyxBEARBqAAJsARBEAShAiTAEgRBEIQKkABLEARBECpAAixBEARBqAAJsARBEAShAiTAEgRBEIQKtMn0Gi9evMCIESMk7uNwONDT02Ny4E6aNAkjR45Ucwn/tWrVKpw+fVosi09YWBhWr16NXr16ISwsjNXriUQiPH36FA4ODqooLgDZ368sn332mdyJKtQpOjoas2fPhqmpKaKjozVdHKnoa0UaLpeL9u3bw97eHqNGjYK/v79S01CWl5ejoqICNjY2zLZdu3Zh9+7dGDNmDAIDA5X2XrJ8//33OH36NK5evcosSydtAQAOh4N27dqhQ4cOcHJygq+vL8aPH8+s/Uz/1tg6cuQIvLy8mjxfR0cHhoaG6NSpEzw9PbFo0SK5Vp7ZvXs3du3aBaAu1ej7778vtl8Zv0E6GUVTv8s7d+7g/PnzuH//PvLy8iAUCmFjYwN3d3dMmjQJnp6eEs8TCoX44IMP0LFjRxw6dIh1WVuCNhlg6+vdu7fYTYaiKAgEArx48QIRERGIiIjARx99hG+//VaDpVSOhIQEfPvtt/Dy8hJLuads+vr6cHd3b7T99evXeP36NYyNjSUuAGBra6uyMrUlFhYWeOuttxptFwgEePbsGeLj4xEfH48rV67g2LFjMDAwaPZ7XrhwAVu2bMHGjRvFAqy6xcbGIjg4GMuXL5e45iufz2+0/nB1dTWys7MRFRWFqKgoXL16Fbt37waXy4WFhYXEazklJQXl5eWwtbWVeN22b99e7N96enoS8yQLhULk5OQgNTUVqampuHDhAkJDQ5t8AD579izz/6dOnWoUYNXxGywsLMTKlSvx119/Aahb87VLly4QiUR49uwZzpw5gzNnzmD06NHYsmVLo7WJuVwuVqxYwSxrSeeJblWoNuj58+cUn8+n+Hw+9fz5c4nHCAQCavv27cxx4eHhai5lnZycHCotLY0qKChgtv3xxx8Un8+n/Pz8WL3W119/TfH5fGrLli3KLqZcAgMDKT6fT82cOVMj76+ou3fvUnw+n/L09NR0UWSi/75ff/211GNqa2up33//nXJycqL4fD61fft2pbz38OHDKT6fT0VERIhtLygooNLS0qjs7GylvI8stbW1lK+vLzVo0CCqqqpKbB/9O757967Ec0UiEXXs2DHmezly5IjM95o5cybF5/OpwMBAmcfRv9Xhw4fLPC46Opry8vKi+Hw+NW3aNJnHxsbGUnw+n/rwww+pt99+m3J2dqZevHgh8xwam9+grM+Yn59PjRo1iuLz+dSQIUOos2fPUtXV1cz+6upq6sSJE9SgQYMoPp9PjR07liosLJT4Ph9++CHl6elJFRUVyfUZWhLSByuFrq4uli1bxix/9fvvv2ukHNbW1ujevbvEp3GCYIvL5WL69OmYOHEigLrajyqZm5uje/fuaqnVnjt3DsnJyfD392ddK+dwOPjoo4+YmqC6f++enp5YtWoVgLplHCWt80uja6+enp545513IBKJVP53bGjlypV4+vQp+Hw+wsLC8MEHH4i1BOrp6WHKlCkICQmBnZ0dUlNTmRWhGlq0aBGKi4uxf/9+dRVfbUiAbcLw4cMB1DWvEkRrMWTIEABAfn4+iouLNVya5qMoCvv27YOuri7z8KCId999FwCQkZGBiooKZRVPLvTfBIDUACsQCJi1bL29vTFq1CgAdX3FDddjVZXIyEhERUWBy+Vix44dsLCwkHpsly5dsGnTJgDAn3/+yTQn1+ft7Q0bGxuEhISgpKREZeXWBBJgm0D319T/se3atQtOTk5YsmSJxHMCAgLg5OTEPJHSnJyc0KdPH4hEIhw+fBhjxoxBnz59MGLEiEZrgNJWrVoFJycnBAQEKPwZXrx4AScnJ2YAzOHDhyWWLysrC9988w3effdd9O7dG56envj4448lLk6tKvRqMpMmTYKbmxvefvtt+Pn54dChQ6iurpZ4TnV1NY4dO4Y5c+Zg4MCB6N27N/r3748pU6bg8OHDEAgEEs97/vw5vv/+e4wePRqurq7w9PTE3LlzJd4EaBUVFdi5cyfztxs8eDBWrlyJZ8+eSTxeJBIhLCwMM2bMQP/+/eHq6or3338fO3bsQFlZWaPj6b/3pUuXsGvXLnh5eeHtt9/GxIkTUV5eLsc3KB96EA9QF5zqEwqFOHv2LBYsWIDBgwejd+/ecHd3x/jx4xEYGChW7rCwMDg5OeHly5cA6mojTk5OzOA7Wb+V3NxcbNmyhfku+/Xrh+nTp+PEiROora1l9Xnu3r2LrKwsDBw4sFmtPfX7TtUdYGX9TWgREREoLS2Fqakp3NzcMGLECOjp6SE7Oxu3b99WSzlDQkIA1FU+unfv3uTxAwcOhIeHBwDg+PHjjfbr6Ojg/fffR2VlJc6dO6fcwmoYCbBNoG+cyhyAs27dOgQEBKC0tBQ9evRAXl4ejh49ismTJ8tsGlIUPeCBftKkR/h17dqVOeb69esYP348QkNDUVRUBCcnJxgbG+POnTtYunQpli9fDqFQqPSy1VdcXIwZM2bghx9+QFJSEqysrGBvb4/k5GT8+OOPmD59OoqKisTOKSsrw/Tp07FhwwbExMSgQ4cO4PP54HK5iI+PR0BAABYvXtzovaKiouDn54cjR44gLy8Pjo6O0NfXx19//YW5c+dKbHITCAT46KOP8PPPP6OmpgZdu3ZFcXExzp07h4kTJ+L58+eNjv/kk0+wevVqxMbGwsTEBN27d8ezZ8+wd+9e+Pn5NTqH9uuvv2L37t0wNTWFhYUFDAwMGg3OaY4rV64AAOzs7GBmZsZsr6mpwcKFC/HVV1/h1q1bMDQ0hJOTEwwNDfHkyRPs2bMHM2bMYB5a6EFAdPOgo6Oj2LUmzcOHD+Hr64ugoCC8evUKPXr0gKWlJR48eIB169Zh7ty5rAIc/XkGDx7M6nto6OnTpwDqfjPq7pa5evUqgLrmamkLx585cwYAMHr0aGZUuLe3NwDg5MmTKi+jSCRCTEwMAGDQoEFyn0ePaI6KipJ4H6Ff6/Lly0oopfYgAVaGkpIS5olq6NChSnlNgUCAU6dOYcGCBbh9+zbCwsJw8+ZNeHl5ITc3F1999ZXUp1dFWVlZISQkhGmCGjt2LEJCQpgFuTMzM/Hll1/izZs3mDVrFu7cuYM//vgDEREROHDgAExMTHDhwgVmWoCqrHmwkAIAABFOSURBVFq1CvHx8XBzc8OVK1dw9epVnDt3DuHh4ejfvz8SExPx3//+V+ycPXv2IDExEd27d8e1a9dw+fJlhIWF4c6dO1izZg0A4Pbt24iPj2fOKSwsxPLly1FWVoapU6fir7/+QlhYGCIjI5kpFevXr8eLFy/E3quyshLZ2dk4cOAAIiIicP78eZw7dw5WVlYoKyvDwYMHxY7/8ccfcfPmTXTv3h2nT59GREQETp8+jdu3b2P06NF4/vw5vvjiC4lNe//88w9Wr16NK1euIDw8HLt371bKd/zmzRv8/PPPuHDhAgBgwYIFYvuPHz+O27dvw9LSEmfPnsW1a9fwxx9/ICoqCjt27ICOjg6Sk5Nx/fp1AHW/i5CQEFhZWQEAVqxYgZCQEJm/l+LiYqbf7b333mN+B1euXMHJkydha2uLu3fvYv369XJ/rrt37wIAM2ZCETU1NUwN65133lHbIuEikQjXr19nWqnGjh2Lzp07NzqusLCQaV0ZO3Yss33cuHEAgJs3byI/P1+lZX358iXTgiFpFLI0zs7OAOp+Q3RrR3303y0uLg5v3rxRQkm1AwmwDVAUhdLSUkRGRmLevHkoLCxE+/btMXfuXKW9x6hRo7B8+XLmB2xubo7AwEB06NABjx49QlRUlNLeSx4HDhxAdXU1vL29sXbtWhgaGjL7hgwZgh9++AEAEBQU1KgGqSwJCQm4ceMGzMzM8PPPP8Pe3p7ZZ2tri8DAQPB4PISHh+PJkyfMvnv37oHD4WD16tViNyUul4s5c+Ywr5OWlsbsO3HiBIqKivD2229jw4YNzPQBDocDf39/DBs2DDU1Nfjzzz8blXP16tVifWXdunXDnDlzANTVymg5OTk4fvw4dHV1sWvXLri4uDD7zMzMsHXrVnTq1AmJiYmIiIho9D42NjbM6wJgVZuKjIzE9OnTxf778MMPMW7cOHh4eGDnzp3Q0dHB/PnzG02NuHv3LrhcLj7//HPmpkjz8fGBl5cXAOl9hPI4duwYiouLwefzsW3bNpiamjL7XF1d8fPPP4PD4eD8+fNifzdp8vPzkZmZCQ6HI1eTZUPl5eWIiYnBokWLkJ6eDl1dXXz22WesX0eWvLy8Rn+T6dOnY8KECfDy8sKnn36K8vJyDB48GN99953E17h48SJqampgZWUlNrd0+PDh4PF4qKmpkTkPWhnq99fX/7s1pX6LRmFhYaP9xsbG6NSpE2pqasR+Ry1dm58H29RkbDMzMwQGBiq1iXjWrFmNtpmammLUqFE4deoUbt682eymLjYiIyMBAB999JHE/SNHjkSnTp3w6tUr3L17Fz4+PkovQ3h4OABI7UOzsLDAwIEDER4ejsjISObmHxYWBoFAAF1d3UbnCAQCmJiYAACqqqqY7Tdv3gQA+Pn5gcPhNDrvu+++Q01NjcRahKSkI46OjgDEbz6RkZGoqalB3759Jd709fX1MXLkSBw5cgSRkZGNXrdv374SyyaPgoICFBQUSNzXvXt3DB06FH5+fhJrIHv27EFNTY3E9xYKhczDSP3vk61bt24BAKZOnSqxluji4oJ+/fohNjYWN2/eZL5faegakbm5eaO5lg3Nnj1b5n4ej4fvv/9eahOtogQCAR48eCBxn7m5OSZNmgQfHx+muVcSunnYx8dHrL/W0NAQ7777Li5cuIBTp05h/vz5Si17ffVbWyT95qThcrnM/0trobO3t8erV68k1nBbqjYfYBsmmtDR0QGPx4ONjQ3c3Nzg4+MDHo+n9PeUpEePHgD+7QdSh/LycuTl5QGAWC2roZ49e+LVq1fIyspSSTnoGlFsbCymT58u8Ri6yTYzM1Nsu56eHvLy8nD//n1kZmbixYsXSE9Px5MnT5hAUP9HTfd70t93Qx07dpS4ncfjSewHpa+P+oOw6M/z9OlTqZ+H/t4bfh4ATJOrIvz8/LBlyxYAdZ87Ozsbhw4dQnBwMHJzc9GzZ0+ZzXu6urooKSlBbGwsMjIy8Pz5c2RmZiIpKYkZaNWcbgz6GurZs6fUY1xcXBAbGyvX9UbXiBomd5CkYaIJDocDQ0NDWFlZoU+fPhg7diyrmpm8OnfuLNZSUV5ejjNnzmDbtm0oKSmBiYmJzD7N9PR0PHr0CIB48zBt3LhxuHDhArKyshATE8MMKlK2+tOt2Iz4rf/wWb/Pvz767yKphttStfkAu3PnTtjZ2ant/dq1ayf1KZveLml0aVM2btyIpKSkRttdXFywbt06qefVH0gi6+mfDiL08UuWLGECRH1Dhw5l+nbZoG/cubm5yM3NlXls/e+npKQEW7Zswfnz51FTU8NsNzU1xaBBg/DkyZNGfan0j72p2k5DbNIK0p+nuLhYas2l4bH16evrsyqbNBwOB7a2tli7di1MTEywZ88efP3119DT08N7773X6Pjq6mps374doaGhYrVUIyMjuLm5IT8/X6yJXhH0NSRr0FbD602W0tJSAJBr7uvatWuZZm5NMjY2xsyZM9GtWzfMmzcPQUFBqK2txdq1ayUeT9deATSZ8ejkyZMqC7BWVlbg8XiorKxEcnIyXF1d5TqPvmYMDQ3RpUsXicfQXVOK3P+0VZsPsM0h7SleVvNZbW0tampqJDav0DcTaU94sqSkpEi8kTc1UKN+7by8vFxqLYAOAvTxjx49ktiUIylFnzzoH9dXX30ld383RVFYtGgRHjx4AHNzc8ycOROurq5wdHRkmvQ//PDDRgHWwMAA5eXlqKysVKis8qA/z4wZM/DNN9+o7H3Y+Oyzz3Dv3j3ExMRg9erVcHFxEevrBoA1a9bgwoUL4PF4WLhwIdzc3NC9e3fY2dlBR0cHy5cvb3aA5fF4KC0tlTntqOH1Jgv9MNISb8zvvPMOFixYgL179yI4OBju7u6N0h6KRCKcP38eANChQwepDxJVVVUoLS3FlStXsG7dOrlq9GxxuVyMGDEC58+fx40bNzBlyhS5zrtx4wYAYMCAAWLNxfXRfz9lPVxqAxJgFUBfINLmV0qq2dWXnp7eaAAJ8O9TXlN9TpIEBwezPgeoa1azsrJCXl4ekpKSJPY1UxTF1I7pACppYE5z0K+bkZEh9ZikpCRwOBx06dIFxsbGePjwIR48eIB27drh+PHjEoN7dnZ2o21du3bFo0ePkJ6eLjFf640bN3Dw4EEMHDhQ4cEu9BQoWZ8nPT0dlZWVsLe3R4cOHRR6HzZ0dHSwefNm+Pr6orKyEmvWrMHRo0eZ/Tk5Obh48SIA4JdffpGYpF3S98mWg4MD4uLikJSUhP79+0s8JjExEYB8D2z0AJqWmjDj008/RXh4OFJSUvDdd99hwIABYuMQoqOj8fr1awB1c1ClDeR68uQJxo8fjzdv3uDcuXOYMWOGSso7adIkJsAmJSXJ7FoCgPj4eGb084cffij1OPrv19QUr5aEjCJWAH0zlNR3VlZWxswTk0bSSL/CwkJm6gOdnUXZ6IErDWve9KhYegJ5Q9evX0dOTg50dXVV1rw2bNgwAHVzASX1wZSVlcHf3x8TJkxgEl/QNWhjY2OJN+KoqCjmxlQ/cQE9gKx+wvT6zp8/j9jY2GZllfH29oaOjg7u3bsnMcjW1tZi8eLFmDx5MoKCghR+H7bs7e3x6aefAgBiYmLEVmN6+fIlc21Iummmp6fjn3/+AYBGiSCkXVuS0FN4Tp48KTGhxKNHj5j3kWeuJZ0Yv6KiQqnJONRFV1cXGzZsAIfDQXFxMX788Uex/fR12rt3b5mjpJ2dnZnxHapMnThw4ECMGzcOIpEIy5Ytk5ggh5aTk4OVK1eCoigMGDCA+Z1LOxaA2Pz8lo4EWAXQc7aePn2KX3/9ldmen5+PpUuXNnljPnr0qNgPIC8vD59//jnKysowbNgwufs12KL7HF+9eiW2fe7cuTAwMMDt27exadMmsSbuyMhIZu7p7NmzYWlpqZKyeXl5wcPDA6WlpVi4cKHYQK+cnBwsXrwYJSUlsLKygq+vL4B/f4jFxcViuWNFIhGuXbuGL7/8ktlWv7VhxowZMDExQUxMDDZv3swMTqIoCsHBwbh48SJ0dXWbVQOwt7eHr68vhEIhFi1axNTIgLp+45UrVyIrKws8Hk/qIChV+fjjj5kb9f/+9z+m5vDWW28xo1N/+eUXsYQA0dHRmD9/PhMQG2bVoptyG15bkkyfPh3m5uZISUnBihUrxGqe8fHx+Pzzz0FRFN577z306tWrydeztLRkRnzHxcU1ebw2cnNzw6RJkwDUPYDTD+lVVVVMEg0/P78mX4dusk1KShK75pRt3bp1cHZ2RlZWFqZOnYqLFy+K/cYEAgEuXryIKVOmICsrC507d8bWrVulvl5ubi5ev36Ndu3aqez+pwkkwCrAxcUFo0ePBgD88MMPGD58OCZMmIBhw4bh/v37TfYhOjg44L///S+GDh2KiRMnYvjw4YiNjYWTkxM2btyosnLTa2JeuXIFvr6+zHt1794d//vf/6Cvr4/g4GC88847mDx5Mt59913Mnz8fJSUl8PHxwbJly1RWNgDYtm0bevTogfj4eIwZMwbjxo3DBx98gBEjRuDevXswNjbGgQMHmD4oOs0kUDe1ZujQoZg0aRIGDRqEzz77DNXV1ejbty8AiA2csra2xvbt22FoaIjffvsNgwYNYs7btGkTuFwuNmzY0Own6W+++QYeHh54+vQpJk6ciDFjxsDPzw9Dhw7Fn3/+CV1dXQQGBqp9eTddXV1m4FthYSFz47OwsGAeKvbv3w9vb29MmjQJ3t7emD17NnJycpjBMw0HotHX1pYtWzBx4kSZ6xSbm5tj9+7d6NChAy5dugRvb2/m+5kyZQpevXoFLy8vVr8FulWiJc+hXL58OTOCef369aipqcHVq1dRWVkJXV1diaOHGxo3bhzzsKPKzE6mpqb4/fffMXr0aGRnZ+PLL7/EgAEDMGHCBIwfPx5eXl748ssvkZOTg0GDBuH48eMyR8bT40fc3NxYDz7UZiTAKmj79u346quvwOfzkZ+fj5ycHIwcORJhYWES+/XqCwgIwOeffw4ul4u0tDTY29tj6dKl+P333+VabFlRfn5+8Pf3h4WFBbKyssQGq4wePRpnzpzB5MmTYWpqiidPnjDJJ3bt2oUdO3awmvemCBsbG5w8eRIrV65Er1698PLlS2RkZMDa2hrTpk3D2bNnG03t2LlzJ1avXo2ePXuirKwMqampaN++PaZNm4YzZ84wC0XfunVLbA6ft7c3zp49i8mTJ8PY2BjJyckQCoUYOXIkQkJCmpUwnmZsbIygoCBs2LAB/fr1Q0FBAVJSUmBiYgJfX1+cOnVK5rxHVaKb+YC65kT6Bvff//4XAQEBcHV1RW1tLZKTk6GrqwtfX1+cOHGCWRElJiZGrDl21apVTF7czMxMid0n9fXr1w/nz5/H7NmzYWtri9TUVBQXF8PDwwObN2/Gr7/+ysxhlgf9WWTlkdZ25ubmTKtLWloaDh8+LJZJTp7Bj8bGxszo8AsXLqg0K5KRkRF27dqFI0eOYMKECbCwsEB6ejoyMjJgaWkJPz8//Prrrzh8+HCT9zU6uQ79d2wtOJSy8/IRUtFP+efPn2eVZowgiKb5+fkhKSkJV65caVX9eK3dmzdvMHjwYLRr1w43btwQyyTX0pEaLEEQrQKdV1lW8zShfa5evYqysjLMmjWrVQVXgARYgiBaiTFjxoDP5+PkyZNqX2qOUNyRI0fQoUMHzJw5U9NFUToSYAmCaBV0dHSwadMmFBcXq3XqE6G4y5cvIyEhAatXr1bLXHB1IwGWIIhWo2/fvvD398fhw4dbVU7b1kgoFGLHjh3w9vaWawpSS0QGOREEQRCECpAaLEEQBEGoAAmwBEEQBKECJMASBEEQhAqQAEsQBEEQKkACLEEQBEGoAAmwBEEQBKEC/weNaKMxLjmG7gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(bos.AGE, bos.PRICE)\n",
    "plt.xlabel(\"Pupil-to-Teacher Ratio (PTRATIO)\")\n",
    "plt.ylabel(\"Housing Price\")\n",
    "plt.title(\"Relationship between PTRATIO and Price\")"
   ]
  },
  {
   "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": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12f7a1810>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(y=\"PRICE\", x=\"RM\", data=bos, fit_reg = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histograms\n",
    "***\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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>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": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#your turn\n",
    "\n",
    "plt.hist( bos.CRIM )\n",
    "plt.title(\"CRIM\")\n",
    "plt.xlabel(\"Crime rate per capita\")\n",
    "plt.ylabel(\"Frequencey\")\n",
    "plt.show()\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": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import regression modules\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  PRICE   R-squared:                       0.484\n",
      "Model:                            OLS   Adj. R-squared:                  0.483\n",
      "Method:                 Least Squares   F-statistic:                     471.8\n",
      "Date:                Sun, 22 Mar 2020   Prob (F-statistic):           2.49e-74\n",
      "Time:                        13:49:28   Log-Likelihood:                -1673.1\n",
      "No. Observations:                 506   AIC:                             3350.\n",
      "Df Residuals:                     504   BIC:                             3359.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept    -34.6706      2.650    -13.084      0.000     -39.877     -29.465\n",
      "RM             9.1021      0.419     21.722      0.000       8.279       9.925\n",
      "==============================================================================\n",
      "Omnibus:                      102.585   Durbin-Watson:                   0.684\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              612.449\n",
      "Skew:                           0.726   Prob(JB):                    1.02e-133\n",
      "Kurtosis:                       8.190   Cond. No.                         58.4\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\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 ~ RM',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 statisticall 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": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Prices vs Predicted Prices: $Y_i$ vs $\\\\hat{Y}_i$')"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your turn\n",
    "\n",
    "plt.scatter(bos['PRICE'], m.fittedvalues)\n",
    "plt.xlabel(\"Prices: $Y_i$\")\n",
    "plt.ylabel(\"Predicted prices: $\\hat{Y}_i$\")\n",
    "plt.title(\"Prices vs Predicted Prices: $Y_i$ vs $\\hat{Y}_i$\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting Linear Regression using `sklearn`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 94,
     "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": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Look inside lm object\n",
    "# lm.<tab>\n",
    "\n",
    "# lm.fit\n",
    "# lm.fit_intercept\n",
    "# lm.get_params\n",
    "# lm.n_jobs\n",
    "# lm.normalize\n",
    "# lm.predict\n",
    "# lm.score\n",
    "# lm.set_params\n",
    "\n",
    "#coef_\n",
    "#intercept_\n",
    "#score \n"
   ]
  },
  {
   "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": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use all 13 predictors to fit linear regression model\n",
    "lm.fit(X, bos.PRICE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated intercept coefficient: 36.45948838508978\n"
     ]
    }
   ],
   "source": [
    "print('Estimated intercept coefficient: {}'.format(lm.intercept_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "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": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>estimatedCoefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>CRIM</td>\n",
       "      <td>-0.108011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ZN</td>\n",
       "      <td>0.046420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>INDUS</td>\n",
       "      <td>0.020559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>CHAS</td>\n",
       "      <td>2.686734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NOX</td>\n",
       "      <td>-17.766611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RM</td>\n",
       "      <td>3.809865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>AGE</td>\n",
       "      <td>0.000692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>DIS</td>\n",
       "      <td>-1.475567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>RAD</td>\n",
       "      <td>0.306049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>TAX</td>\n",
       "      <td>-0.012335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PTRATIO</td>\n",
       "      <td>-0.952747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>B</td>\n",
       "      <td>0.009312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>LSTAT</td>\n",
       "      <td>-0.524758</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   features  estimatedCoefficients\n",
       "0      CRIM              -0.108011\n",
       "1        ZN               0.046420\n",
       "2     INDUS               0.020559\n",
       "3      CHAS               2.686734\n",
       "4       NOX             -17.766611\n",
       "5        RM               3.809865\n",
       "6       AGE               0.000692\n",
       "7       DIS              -1.475567\n",
       "8       RAD               0.306049\n",
       "9       TAX              -0.012335\n",
       "10  PTRATIO              -0.952747\n",
       "11        B               0.009312\n",
       "12    LSTAT              -0.524758"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame({'features': X.columns, 'estimatedCoefficients': lm.coef_})[['features', 'estimatedCoefficients']]"
   ]
  },
  {
   "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:</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://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-is-regression-through-the-origin/).</p>\n",
    "\n",
    "<p><b>Exercise:</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:</b> True or false. To use linear regression, $Y$ must be normally distributed. Explain your answer.</p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=False, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# your turn\n",
    "lm = LinearRegression ( fit_intercept = False )\n",
    "lm\n",
    "lm.fit( X, bos.PRICE  )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimated intercept and coefficients\n",
    "\n",
    "Let's look at the estimated coefficients from the linear model using `1m.intercept_` and `lm.coef_`.  \n",
    "\n",
    "After we have fit our linear regression model using the least squares method, we want to see what are the estimates of our coefficients $\\beta_0$, $\\beta_1$, ..., $\\beta_{13}$: \n",
    "\n",
    "$$ \\hat{\\beta}_0, \\hat{\\beta}_1, \\ldots, \\hat{\\beta}_{13} $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated intercept coefficient: 0.0\n"
     ]
    }
   ],
   "source": [
    "print('Estimated intercept coefficient: {}'.format(lm.intercept_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "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": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>features</th>\n",
       "      <th>estimatedCoefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>CRIM</td>\n",
       "      <td>-0.092897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ZN</td>\n",
       "      <td>0.048715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>INDUS</td>\n",
       "      <td>-0.004060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>CHAS</td>\n",
       "      <td>2.853999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NOX</td>\n",
       "      <td>-2.868436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RM</td>\n",
       "      <td>5.928148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>AGE</td>\n",
       "      <td>-0.007269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>DIS</td>\n",
       "      <td>-0.968514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>RAD</td>\n",
       "      <td>0.171151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>TAX</td>\n",
       "      <td>-0.009396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PTRATIO</td>\n",
       "      <td>-0.392191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>B</td>\n",
       "      <td>0.014906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>LSTAT</td>\n",
       "      <td>-0.416304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   features  estimatedCoefficients\n",
       "0      CRIM              -0.092897\n",
       "1        ZN               0.048715\n",
       "2     INDUS              -0.004060\n",
       "3      CHAS               2.853999\n",
       "4       NOX              -2.868436\n",
       "5        RM               5.928148\n",
       "6       AGE              -0.007269\n",
       "7       DIS              -0.968514\n",
       "8       RAD               0.171151\n",
       "9       TAX              -0.009396\n",
       "10  PTRATIO              -0.392191\n",
       "11        B               0.014906\n",
       "12    LSTAT              -0.416304"
      ]
     },
     "execution_count": 103,
     "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": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([30.00384338, 25.02556238, 30.56759672, 28.60703649, 27.94352423])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first five predicted prices\n",
    "lm = LinearRegression ()\n",
    "lm.fit ( X , bos.PRICE )\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": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# your turn\n",
    "\n",
    "Exercise: Histogram: Plot a histogram of all the predicted prices. \n",
    "        \n",
    "Write a story about what you see. Describe the shape, center and spread of the distribution. \n",
    "\n",
    "Are there any outliers? What might be the reason for them? Should we do anything special with them?\n",
    "\n",
    "Exercise: Scatterplot: \n",
    "\n",
    "Let's plot the true prices compared to the predicted prices to see they disagree (we did this with `statsmodels` before).\n",
    "\n",
    "Exercise: \n",
    "We have looked at fitting a linear model in both `statsmodels` and `scikit-learn`. \n",
    "\n",
    "What are the advantages and disadvantages of each based on your exploration? Based on the information \n",
    "\n",
    "provided by both packages, what advantage does `statsmodels` provide?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12efb1fd0>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame ( lm.predict(X) ).plot ( kind='hist')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12efb8f90>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame ( lm.predict(X) ).plot ( kind='box')\n",
    "\n",
    "## As per below plot there seem to be outliers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Prices vs Predicted Prices: $Y_i$ vs $\\\\hat{Y}_i$')"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(bos.PRICE, lm.predict(X))\n",
    "plt.xlabel(\"Prices: $Y_i$\")\n",
    "plt.ylabel(\"Predicted prices: $\\hat{Y}_i$\")\n",
    "plt.title(\"Prices vs Predicted Prices: $Y_i$ vs $\\hat{Y}_i$\")"
   ]
  },
  {
   "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": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11078.784577954977\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": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "31637.510837064252\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",
    "$$MSE = \\frac{RSS}{N-K-1}$$\n",
    "\n",
    "$$MSR = \\frac{ESS}{K}$$\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:</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:</b> Calculate (or extract) the $R^2$ value. What does it tell you?</p>\n",
    "\n",
    "<p><b>Exercise:</b> Compute the $F$-statistic. What does it tell you?</p>\n",
    "\n",
    "<p><b>Exercise:</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": "markdown",
   "metadata": {},
   "source": [
    "The F-test can be used in regression analysis to determine whether a complex model is better than a simpler version of the same model in explaining the variance in the dependent variable.\n",
    "\n",
    "The test statistic of the F-test is a random variable whose Probability Density Function is the F-distribution under the assumption that the null hypothesis is true.\n",
    "\n",
    "The testing procedure for the F-test for regression is identical in its structure to that of other parametric tests of significance such as the t-test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# your turn\n",
    "lm = LinearRegression()\n",
    "lm.fit(X[['PTRATIO']], bos.PRICE)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "62.652200013769274\n"
     ]
    }
   ],
   "source": [
    "# RSS\n",
    "\n",
    "msePTRATIO = np.mean((bos.PRICE - lm.predict(X[['PTRATIO']])) ** 2)\n",
    "print ( msePTRATIO )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11014.282208052498\n"
     ]
    }
   ],
   "source": [
    "# ESS\n",
    "\n",
    "print(np.sum((lm.predict(X[['PTRATIO']]) - np.mean(bos.PRICE)) ** 2) )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=array([[180.41083565]]), p=2.2403356869359164e-35, df_denom=504, df_num=1>\n"
     ]
    }
   ],
   "source": [
    "m = ols('PRICE ~ RM',bos).fit()\n",
    "\n",
    "A = np.identity(len(m.params))\n",
    "A = A[1:,:]\n",
    "\n",
    "print ( m.f_test ( m.params ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "471.84673987638644 2.4872288710081537e-74\n"
     ]
    }
   ],
   "source": [
    "print ( m.fvalue, m.f_pvalue ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                             Test for Constraints                             \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "c0          1284.9003     95.662     13.432      0.000    1096.955    1472.845\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print ( m.t_test ( m.params ))\n",
    "\n"
   ]
  },
  {
   "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": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual sum of squares: 71.69073588196659\n",
      "explained sum of squares: 6440.783058744663\n",
      "f-test: <F test: F=array([[3447.5132023]]), p=1.6148110841516367e-227, df_denom=504, df_num=1>\n",
      "t-test:                              Test for Constraints                             \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "c0           577.7626      9.840     58.716      0.000     558.430     597.095\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# your turn\n",
    "lm = LinearRegression()\n",
    "lm.fit(X[['CRIM']], bos.PRICE)\n",
    "\n",
    "# RSS \n",
    "msePTRATIO = np.mean((bos.PRICE - lm.predict(X[['CRIM']])) ** 2)\n",
    "print ( 'Residual sum of squares:' , msePTRATIO ) , \n",
    "\n",
    "# ESS\n",
    "\n",
    "print('explained sum of squares:', np.sum((lm.predict(X[['CRIM']]) - np.mean(bos.PRICE)) ** 2) )\n",
    "\n",
    "m = ols('PRICE ~ CRIM',bos).fit()\n",
    "\n",
    "\n",
    "print ( 'f-test:', m.f_test ( m.params ))\n",
    "print ( 't-test:' , m.t_test ( m.params ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual sum of squares: 62.652200013769274\n",
      "explained sum of squares: 11014.282208052498\n",
      "f-test: <F test: F=array([[423.04290249]]), p=1.0548426099399517e-68, df_denom=504, df_num=1>\n",
      "t-test:                              Test for Constraints                             \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "c0          3891.5060    189.202     20.568      0.000    3519.784    4263.228\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "# your turn\n",
    "lm = LinearRegression()\n",
    "lm.fit(X[['PTRATIO']], bos.PRICE)\n",
    "\n",
    "# RSS \n",
    "msePTRATIO = np.mean((bos.PRICE - lm.predict(X[['PTRATIO']])) ** 2)\n",
    "print ( 'Residual sum of squares:' , msePTRATIO ) , \n",
    "\n",
    "# ESS\n",
    "\n",
    "print('explained sum of squares:', np.sum((lm.predict(X[['PTRATIO']]) - np.mean(bos.PRICE)) ** 2) )\n",
    "\n",
    "m = ols('PRICE ~ PTRATIO',bos).fit()\n",
    "\n",
    "\n",
    "print ( 'f-test:', m.f_test ( m.params ))\n",
    "print ( 't-test:' , m.t_test ( m.params ))"
   ]
  },
  {
   "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": 152,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual sum of squares: 21.894831181729202\n",
      "explained sum of squares: 31637.510837064252\n",
      "f-test: <F test: F=array([[17.52042383]]), p=3.35637033474462e-05, df_denom=502, df_num=1>\n",
      "t-test:                              Test for Constraints                             \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "c0            67.0181     16.011      4.186      0.000      35.561      98.475\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "# your turn\n",
    "lm = LinearRegression()\n",
    "lm.fit(X, bos.PRICE)\n",
    "\n",
    "# RSS \n",
    "msePTRATIO = np.mean((bos.PRICE - lm.predict(X)) ** 2)\n",
    "print ( 'Residual sum of squares:' , msePTRATIO ) , \n",
    "\n",
    "# ESS\n",
    "\n",
    "print('explained sum of squares:', np.sum((lm.predict(X) - np.mean(bos.PRICE)) ** 2) )\n",
    "\n",
    "m = ols('PRICE ~ PTRATIO + CRIM + RM  ',bos).fit()\n",
    "\n",
    "\n",
    "print ( 'f-test:', m.f_test ( m.params ))\n",
    "print ( 't-test:' , m.t_test ( m.params ))"
   ]
  },
  {
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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