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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The basis of Data Science is Machine Learning, which involves training a machine (computer) to learn how to make predictions from data. There are two primary types of Machine Learning: supervised learning and unsupervised learning. In supervised learning we can divide the data into input values and output values, and then for new input values we require the machine to predict the output values. You can think of this as a mathematical function with multiple input values, the problem is that it in general it is very difficult to write down the function. For unsupervised learning we only have input values and we require the machine to label the data. Initially, we are only going to consider supervised learning, and in this lesson, introduce linear regression, which is the simplest example.\n",
    "\n",
    "For supervised learning the data can be divided into features and targets. The features are the input values, and the targets are the output values. Typically each data point will have $n$ features and 1 target, and we have $m$ data points. Each of the data points is also referred to as instances or measurements. Hence, the data can be represented as a $(n+1) \\times m$ table or matrix. Further, the data can be categorized into continuous and discrete variables. Discrete variables only have a distinct number of values or labels. For example, for census data the city you live in will be a discrete variable, whereas your age is a continuous variable. When we train a machine to predict continuous variables this is known as regression modelling, whereas when we train a machine to predict categorical variables this is known as classification modelling. In this lesson we will only deal with continuous variables.\n",
    "\n",
    "Linear regression involves finding the linear relationship between the features which minimizes the error in predicting the output values. For only one feature, this is calculating the line of best fit, which you probably will have seen in Excel plots, and which we have already seen with `seaborn` scatter plots.\n",
    "\n",
    "For this lesson we will use the  Diabetes dataset. This is a classical Machine Learning dataset which relates a number of physiological and blood serum features with the onset of Diabetes a year later. We will also import some standard libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "df = pd.read_csv('Diabetes_Data.csv') # read the Diabetes dataset in to a pandas dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Correlation coefficients\n",
    "* One-dimensional regression\n",
    "* Testing and training\n",
    "* Two-dimensional regression\n",
    "* Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will first investigate the Diabetes data. The first two features are self-explanatory, then `BP` is blood pressure in mm of Hg, `BMI` is body mass index (a healthy range for adults is 18.5 to 25) and `S1`-`S6` are various blood serum measurements. `Y` is the target variable, and is a measure of disease progression one year after the original measurements. The aim is to predict `Y` from the other variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AGE</th>\n",
       "      <th>SEX</th>\n",
       "      <th>BMI</th>\n",
       "      <th>BP</th>\n",
       "      <th>S1</th>\n",
       "      <th>S2</th>\n",
       "      <th>S3</th>\n",
       "      <th>S4</th>\n",
       "      <th>S5</th>\n",
       "      <th>S6</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>59</td>\n",
       "      <td>2</td>\n",
       "      <td>32.1</td>\n",
       "      <td>101.0</td>\n",
       "      <td>157</td>\n",
       "      <td>93.2</td>\n",
       "      <td>38.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.8598</td>\n",
       "      <td>87</td>\n",
       "      <td>151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>48</td>\n",
       "      <td>1</td>\n",
       "      <td>21.6</td>\n",
       "      <td>87.0</td>\n",
       "      <td>183</td>\n",
       "      <td>103.2</td>\n",
       "      <td>70.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.8918</td>\n",
       "      <td>69</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>72</td>\n",
       "      <td>2</td>\n",
       "      <td>30.5</td>\n",
       "      <td>93.0</td>\n",
       "      <td>156</td>\n",
       "      <td>93.6</td>\n",
       "      <td>41.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.6728</td>\n",
       "      <td>85</td>\n",
       "      <td>141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>24</td>\n",
       "      <td>1</td>\n",
       "      <td>25.3</td>\n",
       "      <td>84.0</td>\n",
       "      <td>198</td>\n",
       "      <td>131.4</td>\n",
       "      <td>40.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.8903</td>\n",
       "      <td>89</td>\n",
       "      <td>206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>50</td>\n",
       "      <td>1</td>\n",
       "      <td>23.0</td>\n",
       "      <td>101.0</td>\n",
       "      <td>192</td>\n",
       "      <td>125.4</td>\n",
       "      <td>52.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.2905</td>\n",
       "      <td>80</td>\n",
       "      <td>135</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   AGE  SEX   BMI     BP   S1     S2    S3   S4      S5  S6    Y\n",
       "0   59    2  32.1  101.0  157   93.2  38.0  4.0  4.8598  87  151\n",
       "1   48    1  21.6   87.0  183  103.2  70.0  3.0  3.8918  69   75\n",
       "2   72    2  30.5   93.0  156   93.6  41.0  4.0  4.6728  85  141\n",
       "3   24    1  25.3   84.0  198  131.4  40.0  5.0  4.8903  89  206\n",
       "4   50    1  23.0  101.0  192  125.4  52.0  4.0  4.2905  80  135"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at the the descriptive statistics. Everything looks fine as the count for all the variables is the same, the minimum values are all negative and the standard deviation is less than the mean. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AGE</th>\n",
       "      <th>SEX</th>\n",
       "      <th>BMI</th>\n",
       "      <th>BP</th>\n",
       "      <th>S1</th>\n",
       "      <th>S2</th>\n",
       "      <th>S3</th>\n",
       "      <th>S4</th>\n",
       "      <th>S5</th>\n",
       "      <th>S6</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "      <td>442.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>48.518100</td>\n",
       "      <td>1.468326</td>\n",
       "      <td>26.375792</td>\n",
       "      <td>94.647014</td>\n",
       "      <td>189.140271</td>\n",
       "      <td>115.439140</td>\n",
       "      <td>49.788462</td>\n",
       "      <td>4.070249</td>\n",
       "      <td>4.641411</td>\n",
       "      <td>91.260181</td>\n",
       "      <td>152.133484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>13.109028</td>\n",
       "      <td>0.499561</td>\n",
       "      <td>4.418122</td>\n",
       "      <td>13.831283</td>\n",
       "      <td>34.608052</td>\n",
       "      <td>30.413081</td>\n",
       "      <td>12.934202</td>\n",
       "      <td>1.290450</td>\n",
       "      <td>0.522391</td>\n",
       "      <td>11.496335</td>\n",
       "      <td>77.093005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>19.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>62.000000</td>\n",
       "      <td>97.000000</td>\n",
       "      <td>41.600000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.258100</td>\n",
       "      <td>58.000000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>38.250000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>23.200000</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>164.250000</td>\n",
       "      <td>96.050000</td>\n",
       "      <td>40.250000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.276700</td>\n",
       "      <td>83.250000</td>\n",
       "      <td>87.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>50.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>25.700000</td>\n",
       "      <td>93.000000</td>\n",
       "      <td>186.000000</td>\n",
       "      <td>113.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.620050</td>\n",
       "      <td>91.000000</td>\n",
       "      <td>140.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>59.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>29.275000</td>\n",
       "      <td>105.000000</td>\n",
       "      <td>209.750000</td>\n",
       "      <td>134.500000</td>\n",
       "      <td>57.750000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>4.997200</td>\n",
       "      <td>98.000000</td>\n",
       "      <td>211.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>79.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>42.200000</td>\n",
       "      <td>133.000000</td>\n",
       "      <td>301.000000</td>\n",
       "      <td>242.400000</td>\n",
       "      <td>99.000000</td>\n",
       "      <td>9.090000</td>\n",
       "      <td>6.107000</td>\n",
       "      <td>124.000000</td>\n",
       "      <td>346.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              AGE         SEX         BMI          BP          S1          S2  \\\n",
       "count  442.000000  442.000000  442.000000  442.000000  442.000000  442.000000   \n",
       "mean    48.518100    1.468326   26.375792   94.647014  189.140271  115.439140   \n",
       "std     13.109028    0.499561    4.418122   13.831283   34.608052   30.413081   \n",
       "min     19.000000    1.000000   18.000000   62.000000   97.000000   41.600000   \n",
       "25%     38.250000    1.000000   23.200000   84.000000  164.250000   96.050000   \n",
       "50%     50.000000    1.000000   25.700000   93.000000  186.000000  113.000000   \n",
       "75%     59.000000    2.000000   29.275000  105.000000  209.750000  134.500000   \n",
       "max     79.000000    2.000000   42.200000  133.000000  301.000000  242.400000   \n",
       "\n",
       "               S3          S4          S5          S6           Y  \n",
       "count  442.000000  442.000000  442.000000  442.000000  442.000000  \n",
       "mean    49.788462    4.070249    4.641411   91.260181  152.133484  \n",
       "std     12.934202    1.290450    0.522391   11.496335   77.093005  \n",
       "min     22.000000    2.000000    3.258100   58.000000   25.000000  \n",
       "25%     40.250000    3.000000    4.276700   83.250000   87.000000  \n",
       "50%     48.000000    4.000000    4.620050   91.000000  140.500000  \n",
       "75%     57.750000    5.000000    4.997200   98.000000  211.500000  \n",
       "max     99.000000    9.090000    6.107000  124.000000  346.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One last check we can make for missing values is to use `df.isna()`. This checks for NaN (not a number) and returns the answer as False (0) or True (1). If we sum this over each column, then if there are no missing values the answer will be zero, other it will be a positive integer. Since the answer is zero for each column, there are no missing values for this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AGE    0\n",
       "SEX    0\n",
       "BMI    0\n",
       "BP     0\n",
       "S1     0\n",
       "S2     0\n",
       "S3     0\n",
       "S4     0\n",
       "S5     0\n",
       "S6     0\n",
       "Y      0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the field `SEX` only has the two values 2 and 1, and corresponds to categorical data. For linear regression we need to use a technique called 'One Hot Encoding' to deal with categorical data, however we are not going to use the `SEX` field here, so we will defer that to later lessons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['SEX'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at the variable correlations to search for patterns. `SEX` doesn't seem to be important in predicting `Y`, and `AGE`, `S1` and `S2` are only marginally important. The most important variables seem to be `BMI`, `BP`, `S4` and `S5`. Note that there is a strong correlation between `S1` and `S2`, and `S3` and `S4`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "corrs = df.corr() # calculate the correlation table\n",
    "# as this is a symmetric table, set up a mask so that we only plot values below the main diagonal\n",
    "mask = np.triu(np.ones_like(corrs, dtype=np.bool)) \n",
    "f, ax = plt.subplots(figsize=(10, 8)) # initialise the plots and axes\n",
    "# plot the correlations as a seaborn heatmap, with a colourbar\n",
    "sns.heatmap(corrs, mask=mask, center=0, annot=True, square=True, linewidths=.5) \n",
    "# do some fiddling so that the top and bottom are not obscured\n",
    "bottom, top = ax.get_ylim() \n",
    "ax.set_ylim(bottom + 0.5, top - 0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will investigate the relationship between different pairs of variables to understand the correlation coefficients. Consider first the relation between `S1` and `S2`, which has a correlation coefficient of 0.9. Plotting the two variables it is apparent that there is a strong linear relationship, where as `S1` increases, so does `S2`. The line of best fit is automatically calculated by `seaborn`, and as the correlation coefficient is quite high, the confidence bands are very tight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data=df, x='S1', y='S2');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The line of best fit can be calculated using the `numpy` routines `np.polyfit()` and `np.poly1d()`. The first of these fits a polynomial through the given `x` and `y` datapoints. The order of the polynomial is specified by the third argument, which, since we require a line, is 1. The line of best fit is calculated here by minimizing the least squares error. This can be converted into an optimization problem, which can be solved using linear algebra. `np.poly1d()` converts this to a formatted polynomial.\n",
    "\n",
    "Here we can see that as the correlation coefficient is positive, the slope of the line is also positive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "0.788 x - 33.6\n"
     ]
    }
   ],
   "source": [
    "p1 = np.poly1d(np.polyfit(df['S1'], df['S2'], 1))\n",
    "print(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation coefficient can now be understood in terms of the line of best fit for the normalized variables. Normalizing the variables involves transforming the variables so that they have similar distributions. In particular we subtract the mean and divide by the standard deviation (the characteristic spread of the variables). Therefore the normalized variables will have mean=0 and standard deviation=1. Plotting the original and normalized version of `S1`, we can see that is now the case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Original distribution')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = df['S1']\n",
    "Y = df['S2']\n",
    "Xn = (X-X.mean())/X.std();\n",
    "Yn = (Y-Y.mean())/Y.std();\n",
    "\n",
    "sns.histplot(X, stat='density');\n",
    "plt.title('Original distribution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Normalized distribution')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(Xn, stat='density');\n",
    "plt.title('Normalized distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can repeat the plotting and calculation of the line of best for the normalized variables. Now it is apparent that the slope of the line is the correlation coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Line of best fit is  \n",
      "0.8967 x + 1.112e-15\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=Xn, y=Yn);\n",
    "p1 = np.poly1d(np.polyfit(Xn, Yn, 1))\n",
    "print('Line of best fit is', p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $X$ and $Y$ be our original variables. Therefore if $R$ is the correlation between $X$ and $Y$, the standard deviation of $X$ is $\\sigma_X$ and the standard deviation of $Y$ is $\\sigma_Y$, then if $X$ changes by 1, the typical change in $Y$ will be\n",
    "\n",
    "$$ \\frac{\\sigma_Y R}{\\sigma_X}. $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the relationship between `S3` and `S4`, where the correlation coefficient is negative. Now as `S3` increases, `S4` decreases and vice-versa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "-0.07368 x + 7.739\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = df['S3'] \n",
    "Y = df['S4'] \n",
    "\n",
    "sns.regplot(x=X, y=Y);\n",
    "p1 = np.poly1d(np.polyfit(X, Y, 1))\n",
    "print(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again the correlation coefficient is the slope of the line of best fit for the normalized variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "-0.07368 x + 7.739\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xn = (X-X.mean())/X.std();\n",
    "Yn = (Y-Y.mean())/Y.std();\n",
    "\n",
    "sns.regplot(x=Xn, y=Yn);\n",
    "p1 = np.poly1d(np.polyfit(X, Y, 1))\n",
    "print(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, consider when the correlation is close to zero, as for `S1` and `S3`. In this case there is no clear relationship between the two variables, so the line of best fit is almost horizontal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "0.01925 x + 46.15\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = df['S1']\n",
    "Y = df['S3']\n",
    "\n",
    "sns.regplot(x=X, y=Y);\n",
    "p1 = np.poly1d(np.polyfit(X, Y, 1))\n",
    "print(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the correlation coefficient is close to zero, then it is difficult to say there is a typical change in $Y$ for a given change in $X$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "0.05152 x - 1.267e-16\n"
     ]
    },
    {
     "data": {
      "image/png": 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PtK06T6PU095OLxq6tUjpFSpNAMIG0GI67Qfc6es9+vRZPPLMeeR0E4rEDVxPvrSId+wb7bjftdeoajHg0EwM109HsZYpYCNngMB9+k2LIVUwMbe42XGf7GbuT6X4jIxmNhS30arzNEK97e10DEq/xbx0CmEDaDGd9gPu9PUef/YCJAIUia8dJAIMy8Lfzy3jpd/8Jy2/Xi38/L15gRcG02IggAeNMWAzZ2AiGuyoT3Yz96dSfIbjgVRv3EarztMI9ba30zEo/RTz0km6ugMgoj8hogQRvdxNOVpJq1Ya9SZpq3W9Vid7y2hmWQ4difjrrbjedj7vfDaZN2BYrCzVs8Vas+prRMZmnodKniSOB1K9HiatOk8j1NveTnvL9Jt3TqfotgrofwK4u8sytJRW+AE3ojaodr12qIeiAdl3YI0G5G1fbzuf936WgC0ffc8xEm1/1deojM08D5XiBR6464aG4jZadZ5GqLe9nU7X0CvpLnqNrhuBiWg/gL9ljN1Y69h+MAK3wtug1GCVzOlYSuXBGMoqVVW73mMn51tu+HJsABJtZbS0GPDgndfjufm1uq5XyUi4HUOd97OJZB5LqULZMbGABN0CYkHZrf8LoCUG2koyDpv3iV97N3M6pmNBpApGzydHG1T61ghMRPcR0WkiOr28vNxtcWrSipWGdxvt1K+1LAbTKq9UVe167TB8PXDXDXjwzusRVmUYFj/fg3dejwfuuqGu61VbQW9HXu9nZ0ZC2BEPwtFUyRIhrPLBfzzC8wklUnl89PiL+NjxF1tioK0k47CtPEvbq0oEAo/N6IfkaMNGzxuBGWPHABwD+A6gy+LUxXYTUXkNVivpAiTw7JdBWfI1qlW6XrsMXw/cdQMeuOuGpq5XzUi4HXlLPzszEkLMLj/prQLmve4Vu2j7TjvB3HYMtLVUOoM64Pvhbe/RY6d8k+r1anK0YaPndwDDiNdgpZkWGLaSlAHFSdCqGSKrGb7aUQnMud5yKo/55TRevZbEwnoO7zk44R5TbQW9HUNdpc++5+AEjh47hecvrmFxM49kTnc/Y1o8lYNDKq/j2kYO37mwipt+8+u49T8+VdY37TAmtqsqWy8g3C97m6oTABFFiOg/ENHHiChERP+aiJ4kov9CRLFOCTlseLfREhEk2kpSBhQnQau2ra6kfgDQltiBI4dncM8te7Ce1ZE3TARkwkRUxfEzV9xzVzMSbkddUqkC1/EzV5BI5RGUCZpp4epmzp0EZIlcd9ZUXsfVjTwKhgXGUDHPf6tVOv2WP75R+i052rBR1QhMRF8CcBlAGMAbAbwK4EsA/imAnYyxD2/r4kSfB3AEwBSAJQD/D2Psjysd3w9G4FbjZ1RbWM9hPKJi2s4jDzRm3G1nVGSlcwdkCWORAM4lUkjlDYxHVEzFgi03inoNzMmcjmhQxlQs5A7wDMytxlXQLSgyYSoWwGZWh24xGOZW7IDFuKF7Jh7EeCSAsUig5dHW1e7F/XccbDjCuzRK+97bD/iq6zrFsBnBe5VKRuBaNoAbGGM/Rzwx+jUAdzHGGBF9C8CL2xWKMXZ0u+cYdGolQXNoZFvdzuRtfuc2TAsXV7PYPxnBzpEQVLmAtYwOw7RwyPbGadXg7ww2Y2EVi5t55DQTQUW2Uz8D1zZyKBgWQoqEfRNhFAwLaxkdup3PXzdN7jpqr4ssBiynC1hKFnBwOlq0Sn8I2LbcFescLCWL2lLPNb0eWk6U9iPPnAeArk0C/ZYcbdioywhsD/pfYfZ2wf67Lwyyg4BfbdntGHfbGRXpd+6lZKHI8DsVCyESUFqy4/BSamAOKhI008JyqoB4SEU8pGKR8gipVFSEPRpU3Pw4F1YysBgv8gL7p2nxnUA7DJmV7oVmMow2GEFcKUr78WcvdHUXMGxG8H6i1gRwmohijLE0Y+wXnBeJ6A0AUu0VTVCJ7VbyamfR7J0jAZy6sApmq09GQgp0y8LsWLjouNJo5WqqjnqTqZWupqdiQVzdzCFvmGCM8XZWkCUgE3TTs6axf5UlgmUy3+pgtXZM9chd6V4EFKlh42lG4/mZgC0Dt8UA3TRwYi7R1UHYry+AxmIw6j2vmGzqp5YX0GMAXGMvEf08EX0ZwK8A+Kn2iSWoxnYNke3yTX/06bN48qVFSNxrFRYDNnIGxkIKFLn4Uas3Wnk7UdEjYRWT0QCiAcVt56HpmK8sh3aM4KEPvAWxoAKZ+MpflggBWUJAJqhyeXWwajumeuWudC8OzcQbNp46UdqmxaCblhsNLRG6alj264uPHX8RH20wBqOe8w6SAb0T1DMBaABARHcA+B0AfwZgA8Bn2yqZoCrbqeTlXTX56WSbdUt0VBABWUZIlRFWZagyIWewiq6TjtomnTfwg2tJvLacweW1LD71ZZ4eqpFqY34umgGFG0JnxyO4bNf53czpvrIcOTyDRz/0duwZj+DAVBR7xkIwGYNh8cRyy6l83a6fzVRJ8+pUm3E3vff2A7AYbNfhrfNNRgNNV2jzexYafT78+iKVN5AuGNuqIteJSnSDTq0JQGaMrdm//3MAxxhjf8UY+xSA69srmqAdtHLFXUqlRHEFw6oarZzK6VhKFcAY3BTOl9dzePTpsw35kddyBR0Lq9BMCwRAlch39+OcQ5UIC3ag2N7xMKZiAaxndSxu5uraMdUrd6X+BtDwLs2J0na0VRLBLnUZbjohYStW7n59YVgWzJKkUo3KKGIMtk8tG4BMRApjzADwXgD3NfBZQQ9SK13vdtJLO2mGvZOAkyiuWrTyqflV1/USADe+gu8o3rJ7tCGDtZ/BvLQ9ADAeDeJr/97fAO30w35PBKvz2XoN1/Ua2qv1dzM1mh+46wbfnEzNGPn9ZLuyngMI2LXN6GlFkrbud5MyihTP26fWIP55AN8kohUAOQDfAgAiuh7AZptl61t62TBVywV0Oy6i995+AI88cx6GZRUlirv39gMVP3P/HQfx3Pwq/8OzIJQlvqPYrsG6mpvl0WOnKt6jevrhxFwCv/PVV3Fhlb92cCqKj999GEcOz9QtdyP9Xa8htVVGfl+XXstq2CBeKs9KugCTMZgmw7lECjviQSiy1LCM7XRmGBaqqoAYY/8JwK+Cp22+nW1FjUkA/l17RetPet0wVSsyczuRm9USxVXiyOEZhFUJBL4glIirZ4jI3Tlsx2Dt156VdAGpgln1HtXqhxNzCXz0+Is4v5wBYwyMMZxLpPGx4y+6Hjf1yF1vfzeijgEaVx/V23eKJEGWGjOIe/ticTOH9ayOqVgAe8fDAAMWNnJQJWpYxmFLtNcOup4OuhH6IRK412uP1orM7EbkZrUU09v1X68UST0RVTEVqxxJXasfjh47he9dXgezeM1hALAYjyJ++77xuu91vf3t91ydW0oBhKKYhlbX9i2VLZnTwQCMhtWmno9e/34MKs1GAg8s9appGlXntDPKthXUisw8cngG9yxslKUTaGbwr7fvHrjrBlxYSePJlxahmwyyRPjATTubGvz9runURnDau5wqYDOrYyWtISBLmI4HEQsqRfeoVj9dXs/CtBhkjzqEiEc9N3Kv642UbZU6ph68fRgPKmCMYTOnY3Y8gk+9/81AHfJWYrvfj15Wr/YjQzkBlKYMqBRmX+9xXvrBMFUtMvPEXALHz1zBdDyIffYK7/iZK7hpdqxhV9N6++7EXAIvXNrE/smIu6p84dJmw8FLFa/5gbcUrezv/9wLsBifaAyL4epGHpMxFfsni/MbVuunveMRrKQLYBZcrxvGuIqk0XtdT6RsuwyppZT2obPC/+0P3lgkY7OD7na+H818HwXVGcoJoF5Pl2Y8YtphmGpk1bPdiMtqbW7VebzVzB47OY8zl9ZBBOyIh0ABajrVwmMn56EZJlbTPI12QJYQDylF53ns5DzGIypWM5o7eFtgWMvo+M8/3ZgB8qPHX8RGVgez3RktxgvOOCmotxvZXHq933jyFayk89jM6iiYFiQihGSppc/adrzA6mE73492y9YqnPt7LpGCZlhQZXIr0PWSnMCQ1gOo13+4GT/jbqYLboXfdqU2O8nJtnseb/oH53ymZcGyWFGq5mZUGWeXkljNaDBMrpoxTIbVjIZzS8kiuaZiQeweDUORCSZjfKIIyg0bID9zz824fjoKIm60PjQTw4dvu64o7qBVcRZOqu21jA7NZAgpMiajAYRUuWJMQzO027d+O9+PfvD7d+7vxdU0NrM6t5vkDVxYSdd1nxuFMQbDtFAwTOQ0E6m8js2sjrWMhuVUAUvJPFbT5eVRHYZyB1DvNrTZ7Work181supphd92q5KT1eo7r6xBRYZhMRDjHjojtuqhUVWGk8vHMcoSAZbFoHly/DhyjYRVjNi6aMcI2Sh+99kv7qBVcRbPza9hdjxcZkCtFtPQKJ1QYTb7/egH9apzf1fTBiSJ1/KwLIZU3sDOUaXmfWaM2XmcGCz7d8sCd5u1I9JNxuwSsfyYWoRKJk0vQzkB1LsN7baf8Ym5BM5cWodpWQgqMqbjQcRDasVVTysMhc0mJ3O2vS9f2UBW5yt6EDAWVrBnLFLUd067LHv1rUiErMbTMGsmsJzKI6DIriql3q10QJGQKRjIWyaPKSC+xQ0oWxvdZu9pLdVaLCCDiHA2kUZIkTAVC7oTTKviLJr5bKPqpk4+870sW7M490gzLcgSgXtZMhQMC0FZwqW1DDazujugW3aqkUYG9FYylCqgereh3fQzdraSRIBEW8bKVF6vuOpphd92M8nJHFnnFjeRKpgwLcbHXwasZw28vpopq0bm+P0XDAubeQNEW2kg1rM63rFvFMfPXGloKz3t1EhgKMrpP+2pndDMPa2lWpMJOL+cwblEGgqhrPJYq+IsGv1sM+qmTj3zvSxbNSw70V5eN5HVjCKVSyKVx0w8iGRehyLxlT8Dtw2psoRUwcB0LITVTAEbWQ2pvI5MwUBBN6GbVscHf0DEAfQsjr+0YXLduARyq1nNjBQ/+F6jU2m1La/ftmFaWEoWoFsWDk3H8Gvve1PdxuT3HJzA8TNXoMpUdh4iXm7RyaXvRSYgqMi4ee9YUZWuoCLj6kaeZ60EH/wVmVzdvJOff3EzD8Ni7lZakQk7R0O+fuN3/943cX45A9mu+MUYoJt85+C46hyYjOAn3roLz82vFa3cUwXDdXlMa2bRirSWD/78chqGyXc8ThZUBr672Tkagm4y3HPLHjw3v7atimiNxmj0ss99I7K1y/WTMeZmT7VYscrFsCxb1QI3atm0A/6q8fz8Gh555hwM08R6Rne9tMbCKlRFxoN3HsK7PDWyO0FIlbFnPCLiAPoJZytJAf4EraQL0Ey+oigd/J1Bwa/aluO3/fDX5nBxNQtVJsyOhaFbrKpbZqm73fEzV3DPLXvw1ZcXy85zcTWD2bFQ2eAPACYDsvpW1K1TpWvPeBi7x0J4fXVLfbF7NIyRsArGGDKaiX2q7G6lAT6Ga3blLj+1R1ozsWcshJW0Bs20+PaWgILJELC1V+cSafze0+ewYySIoCLh/HIGADARUXFuMw8A2DMWKnIxrKVa00yLxwMQH0z2jIWRSOaRNyzMxENFk+d2KqLVGzPg0MsxKfXKVo/rp6M39w7YVpGeHEW6c8se+Nux+H3XwQk8iEP4wncvw7Ay0AwLAZkwOx7Fh965t+ODfy3EBNCjeA1ejsHSWSFVc1WtVG3rsZPz2D8ZKVtx1WtMzmoGnptfw1gkUHYeVSYsJSt7GjjnAIqrdB2cjiESkF2XTUdnntNNN7FcQJa4gdhe0QdkqaoKLJHK4+A09+efX06jYJogALJdJUs3uQollTeQAtyBeyWjQZUlgAEraQ0Hp2Nu/9TywQ/IEt8B2L/HQypkidx7UGoY3k5FtEYMqL1sNC2VzUl5vXs0jJxmuoP4H3zjvJ1inD8HqizBMA08+vfncHA6VteqvNO86+BEzw30lRATQI/SSDIxmfhg56xEGWO4uJrF0WOn3BVi6XEBWcJULFC/Mdm0cObSOgyLlRk5d8SDWNjIuTp8P+YWk0UVtwyTV+kaCStIpDTEQ8pW1S6T4d7bD+D4mSsYCStYSWmw7Aqk8ZAK3WS+vvalfVYwLAAoKubiSKCZ/D1nArBsdZHFgIIJnF1MwmQMr69msHMkhGvJPFRJwo4RnrgsHlLAwCdR3o85mAwwiKuH4iHF3X2dS6SQLRjQLVYx8rgdtNJoWq8ahrGtVXepWsVr+PzZd8ziM3/3Q+imhaAiIa9bMCyGn377HlzbzLnnu7yexUhIgWkxpAsG1rMadNPC1c08/uH8St8MtL3KUBqB+4F6DV7xoIIrG1xPTgDyhoWCyaBIVGRY8x7nRMBe2cgjFixfA5QaG1N5HVc28iACgjKVGTkVWcKh6RjiIaUoMNWpDAagaPAH+EB8aS2L/ZMxPHjn9TgwFStq5wN33YCHPvAW7J+MYTTCPZ9GQwoOTMXKcvxXSoIWCfBSj14vKMf4zCt9SWCMT24AilRYBZPBtADDAhaTBUxEVICAhY08ArKET99zMz5zz82YiYeQKXAjdkAm7oJKWxPNibkEUnk++Hsjj1czhbavxJsxmpb6lacLBr7y0lV88m9exrXNHGIBGVc3c/jE37yMJ15YwNWNHC6vZXFpNYsLKxlcWMng0loWC+tZXN3IYXEzj+VUoczw+bZ9Y3jgzkOYiASRyhuYjAZ99eO7RsLI6xbSBcO1iTn38JFnzuH5+TXfdgi42itv2wErIXYAPUw92313+8uKB9mCYWFxM+9GwnqP8/702z57V47JnIblNH+ATIthJKTAsCwwMKykC1DsWrofvHk3vvryIs4m0lBlclP8XlrLlg3+XhwVyAP2385K85NffrniSvPosVNFEb/cQGzh/s+9gFv2jbufOTGXwMeOv4j1rA5m7yCcZHPxkIKgIuHKRh6mxY3VpWIyAIpEkCVCKm9Clgg6LFzZ4CtU5/5UMmg60dOtiDyuF6+O22IM7z44iXcemLB14vy11XTB9k5hYLZ+/NvnVvAXz1/C1c0cdo2Ei/TVx05esCc4CRYDgrIEyzLxp8+9jpv3jdUl1/Pza/jCdy/jWrL4/LVW8B9651488sw5rGYKWzUjGGE6HoREhC9893JP7gJMi0EzLP7f3Pqpmz6vGazk7633ddP7Oys/T8kx7nFmecEdP8QE0Od4DZ+FYg9BNxLWMJMIBZQiA2lAlrAzFkRGM8vO6RgbP/k3/+gO/gAfEDfzBkZDCneF8zFyzo6FsJQsYGEjh0PTMYyGVaykNV/ZS69db66Xs0tJJPMGJHupXbBX8JJllX3m0/fcjIe/Nof5FW7sPTQTdb2AFtazuH46iteWM2BgCMkS8oblrUvD3fkYQ8FkCCpbMQvea1QzaDLw4vRBRbYN+bzvw6qEI4dnyjxRnJ8MALO21CiOZxFj3BbiHGNZ9mto3rDpeK4oEmEkpGA1U8Ajz5zDg+Ar8mvJHEZCxUNFSJWwmMxVOGNj56+GY1T91JMvw2J8lzVh13lmYGUyMNuv3n8w9RlAS44pHZCLBteiY1nx387v9t91jL09QV9NABZjyGkm9xkngECu/7izzee/8+NLA6AGEa/h85Wrm7Djr3j8gO2LrJkMh0oMpED1CNgjh2eQzBtQZeJ+/bavJmNAqmDgwFS0opFzJBxwI1THo0Gspu2CL56kaQReKcxLvVGy3ohf3R6wmX3+0s9U2kU94Pndu4KfX07D4KMtdIsXVtdt9RrfaQABGVAk4LPffA23H5riXj+pPCKq4m6wspqBnSMhMADL6QLCARl7JyJgDMjpXOVxYSXTEwbML3z3MhSJ3EA/x17grK53jYSxmikUBQLmdQs7R8JF52GMuatP74D5P7590c2cmtVMMAZohoX/duI1LKcLJatc57Os6O+wKkOzbTqraQ0r0GDazgH3fPa5olV1vxBQuBoyoEhQZfL8Lrnvub+7f5P7typLxZ+RCQFFLjomIEuIBRUcedhfhq5OAER0N4BHAMgAHmeM/U6143WTFRmI6rzG1u9l7/FJxPndfY2oeCLxTDTwTDzOOUuPrygLtj7knbj8ruWVzwkGc47ztsmrriHbVYaBF1Wx+NIQAUVqyCDoqGGSecP2oCEYjLlqI4sByZyOT73/zTWjlX/7gzfiB9c2sZkzyizE3kphpdHBjpHZrwpXTjOhWwyGZbqTiQNj3Eh9eS0DwymObq+YueysaAXNLOBfvnsf/vNX52BaOsYjKq7Z7qBjYQWbOYNn+STANC1YYJiMhCBLhIurXN/902/bY/t+6wipWwbNn7llFgDw8NfncG0zB8tikCRCNKDg3/7Y9XUP/pXUJ14sxupeyZaqIc4vp9woasYAy+7H5XQBv/n/vYK8YWIpVXD72dmRpPIGfuaP/qFohd0IqxkN/+9TZxv6jB9rGf8dZiUI3BtNtQfOoP1TNy1s5nTopoWQImN2PIwdIyF3gA0qW4N10DPQ+g7YsgRV2RrU+d9bA7YiUUcWqM/Pr+GPn70AdXr/W/3e79oEQEQygD8E8H8CWADwXSJ6kjH2g1Zex/slK3s8me+rfYEzcRyYjuKXf/wN+PzzlyETIEn8PYsxqBJhNKpidjyCN+6K49+/9xD+13dex7XNPHaNhvAv370Pb9wVx7XNnDs5PXd+BZ9+6oe8Khd47xg++1nDYvj2+RX875evAeArZN20cGU9hx2jDLIEzMRDePOeEfzWP70R/+Xrc7hqD6whhfDz79mPn3vnPixu5t1rOvoN3bBwZSMLwwxBlrm+d2E9i1OvreJ3nzoLkgCZbensGbgOP6BI0AwLOd3EVCyES2v1edm8efcI/t2PX48vfPcyFpM5XDcZBRhDVjdx3UQAV5N56IYFWSZMRbgHT0433RXwO/aP4/+64w340unLWErlMRUL4u637MR4VMX3L21w7yLbE4YxnhbgOxdWcXkjWzYglw7aiWSBq6/sBcNaWsMnvryJWJAb3B11RqODbxml+kObk2dXKn5ko4pxsRrO4keW+L31rmTLV7bkDqArKQ1zi0lkNAMjIRXv2j+BQzvj/oOtXLxqDioyVIWgyv6Dr6Om4gn2+CS+kdPxkffs70kbQz04bQrIBDDL8DummzuAdwE4zxibBwAi+gKADwJo6QQwqDB7BQsG3Lp/ArfunyjStXpXoj/3jr3IaSZu3jdWZrTLlejh//S51yET/8KMR1SsZcu/5OMRFbGggr94/hImogFMRoNIpPLuhJpI5jEZC+Jn3zGLdN7ATXtH8bl73112nqxmFF1zKh5EIlkAI55GYjlTwGQ0iJ97x15ohoXPnboEWSJM2ddTwCcBZ5U/ElKQyuvQLYbbr5/Cy1c2axrQvH/vnQxj52iobNVsMuDKRg66yVfFS8k8LABLyQLu+t1vlul7l9MaXl1MVbhxQFYz8cT3r9Zxlyuz2cTgq0hUspKV7MhuhqVUHhKRm7+GAbhx9yh2j4URsAdOr7oh6H7e/t0egFWfgfzlhU0ce3YeqkQIB2T3uexGVGwlaqnB+hGnTSG18jDfzQlgD4DLnr8XAJSPEgNGPdv57ZwTjGE5Y7gRsz/3jtmGzu81+E3ZOXS8k4BM3C00pxnIGww7RwhMljAZDWIjp8EwAYDhgzfthiITTs2vFqkbdJ8B+YeJFNSiaN8tXZNhWnj82Qv4o2++xlVBdpyDRyPFDwWwlNpSBfzBifPNdGVDOLEEjSLburzrJiK2WoBcFUEmb2BhI4ecbiIWUJAq6IgElBIVIFDQLTzw3kMIKBIuLGfwzbPLWM9qmIoF8ZNv3YV3HBgvGrBVuTwnlBfnGVpM5hBRZYAIl9ezMEy27Wf0x980g2hQcc+/s47nvh3fk2ps19Ddi/i1qZRuTgB+T2PZPpaI7gNwHwDsnt3bbpnayna8Ibx4jW3feW0V//3ZC9y90bKwanvtjEVUSER44sWryGgmZicixaoGH7cx3bCQ00xsZnU38rb0hpgMANtSC7224qNmYcBnvzXfUN9U+potpzUse72ImjCaKhJBkQmawdM3eMfB2bEIFJlwaS0LiXhMg2Wn4wVsXbHM/fcZA+560w7csDOOy6tZfOXla1AksqObubfOR27bvzX4yhIe/ML38PpqFrK8lZ/Ishium4jg8Y8Up2Zxno9YUMFULIC8bmEzr0MmYCIa2Oor3cTu0Qh+/PAMnp9fw1dfWYQiESZjAeR0E58/fRkzI6GGninHJbNVz2il89dDu2SoRr2G7n7CaVMkUDncq5sTwAIA74g+C6BsX8wYOwbgGAC89W23dF1hbzFWU2/rb2xj+OszC8gUDCgSIZ3n7ot53cSv/80/YiSkYtdoCNGgUjZIp/MG0gXDzbJZD95V+5deWGhPZ9TAz9hm2rnRDdtovHuUG1TPL6fL9NixoAyZCNGggp+9dRYLazn8/VzCVlNYSOYNGBZ3DQypsm28kzAe5QPhekZDweDumzviQegWQ1iV3YhSzeBuoztGQpiJB4u+/BdXud5958iWl9RapoCvv7KIb7+2gnTeQFiVMB7hA3MEfGD++7kE3n/zrqI+IG+ItPuz/E76qSHGwgo2cgbCAaVIrff2vaP4v7/4Il65tgkCMB0PgkDbVl00qgppx0q9G+oYJ94gp5tF/fyhd/bvotNpU173Vf8D6O4E8F0Ah4joAIArAD4E4F9U/QQD8rpZFkhRSbVQ6u1QOiDrFQdtjytbybn8DKKtYDOnN6XXrYbruQRg52ioWGfrcRsrdUMrNba9c/8Ennp1CbphwmRwV2YMwGpGhwzAsSQQgImoAlXmmQ/f/YZJVx5nZTcV2zK0pQoG7n7zDiwm81j3TFoSASMhFdGgjFTewAfftgcA8M79Ezj2rXlcXM1AghPYxZAtGG46ByJCyk4xrcr8mbm4lsWu0RAyGo8olUCQJT5oX1zNuBORg+NiqMh89ZTK69jI6bAYsG+CF5YvGCbCAQUjIR4DoEiE5XQeu0bDcKbqvGlh91gIq574i8lYEAXTwg57cnGeqEQ6j9GQWmSgnIqFYDJ+zisbWewZi+Bd+8fxNy9ehermmwcSyQJ2jRJiIRUxibCc4naYWs8H4JmLGNxiOd7teTQgu687MQcA8A/nVvD73zgPReLZLtezBfz+N87jY+oN+JHrp8qu59hq+O9bajynDc57i8kcRux+cK7VbnWMN4lbvWqqXsdp05deuAyQ5DvWd20CYIwZRPTLAL4O7gb6J4yxV6p95mwihZ949NmOyLcdvMY2Vd7yZlhKFrg/tEQoGKbrWy8BiNn5TiIBBe+7caeru33y+1d53vGCAYsxSCC3oPl4JIBkXsdYWEVIlXFtM+f6sKuK5KZ0mIwG8bv//OZtten11WzZFvniagYBhdzyi5LteprVLEzFVHzx9ELRBOCs7Lb8/CXkdQN/eWYBk9EACrpZlPp5I6shqISwbyKKXaNhEAE/dcsePPH9KwAYTxXtua5lMRARNnI6VFlyzxNSeSzDakaDTASZJPczYZWXhVxJaxiPbg2YqsyTvTmTwlpGAxEhrEhQZF4cRzMtrGU0jNm7gKxmYt9EFGFPfMN1E1EkUnm8YSbuvubEX0RL0nA4xxZHFJt4446RoqRxR4+dQlCRtqqp2amoVzMaRiMBLsdkFKMlwWn1cN2knwwGrpuMujYhhy+eXkBIldxjA4qMrGbgi6cX8FO2C2wzHJiK2XEVW/2Y1QwcmIrhwFQUAPd0cyYOJwDOmWCcyaUU7+QDoGgCYgDed9MuvO+tu8omp9KJCwxl13KPZfCcu9hW1Y2Yj3cdnMAdb5zGE7908R/93u9qHABj7CsAvtLKc1YMqFCk8kAJudztrDSoIiBTmWdD0PMZr/uZc5xUwb/Xq9u8tpmzV2CEmZGgG9mYyhv4yI/sdz/zV2cWMBnjA70ErntnAEyTu1qGFAmwC8ZMRANuVs7xCC+r6FUX1NqmV9vOu9tJw0RIkZE3+Ll3jYawlMzzHPzgK3LdtBALKu5q+I9OnMP/+PZFpAomJAJiARkmg7sizmom9k/yFd/VjTyvDyBxY7DJgH975A1Fg+qVjRzGwqqbX8fV61vMVSNphmW/x1fRAMOlNb6CZADI4hPvrtEIGGNY2MgVxUh4k705ieUcVQvsn1fWcygYVlESu3qqyiVzOlSJcPvDzxSluyg9diVdwHqW7wxLE/s5kcdTsSCubuZAjOuszy2loFsWVIlwYi7RcN78avEipQnhziVSRSoyoDXppqvJUBTXY/8uuzkiep9SBwa/CcY7T/hNMvw4+zOeHVml83qTIZbSV5HAe8fDeORfvN13IHZW2b0c/Vu8zcy7A0rUXkH5GZ0cQ45EVFTbFuBuiNdNRnHf/3HQ14d9JhrE2/eO4ms/WHLVNmvZAh595hx+Vb4BP3Joyi6eQjj1Gt/OqzJhIhLAZl7DH544j6n4m/Hjh3fg4HQMO0dDRbnoI6oM3WLuKpSvyrZSPu+biOK/n3wNf3hi3k0MZzEgWTAhE19lO540K+kCpuMh7B4DllMF5A0L0YDim7zMiX520jATwY1WdnL6MPDXpmMBjIRVLKfyUGyXRwAAA0ji8jrJ7MajQbdtTiZPp72RgIxoUEbcVvfEQyqm4iYyBRObOb1ibv7SHP6xIJ9YdIv5prtwjj23lESqYGIiqrputs5xpanCAeDaJs9GqhJq1nuoRqWaAwDK0nSk8gZUuWBPsJxWpJtutO5BP0G0Fehpv9ItUfjVeyEUvV7e+rZb2JefOtn267TKsFXtPJV89h3faOezF1fTyGimm2LXQQYAAq6bjOB/3XsbV23YictkIkgSV1/81B88i9fXsjDtgXoqFoQiE1SJMB4Nuqu59UwBuq2CcshqRtlx3i+ik7tHM0ys2tGYpq2SMSyekdTVpUuSW/3LIajwbJyxoMw9lcbDdVW68ruubjI7EI4PUE6QEjEG+EyeXoKKhF868gbcNDtWMeVxpWpcTqUvb+U079+ltYOdimjeQXM5lUdWMzESVt3PPPy1OVxYycBkWymknRoDzgrZK8vCeg4TUbXovKUVtpwV/NmlpFvn+dBMvK7B1S/h3XKK223qvW+C7kFEvhXBxARQQq2BuZXneX5+DV88fRmLmznsGgvjw7ddh9sPTePUayt4+Gs/hGJ/wdcyBSylNHetQMS32lOxACwGfOvjd/rKcGIugX/zZ9/lE4K9OrfAMBZWsJbVsX8y6n5xeVWvMEbCW+6GyZyGhY1c0XGlX3C3HOVSEhnNRF633MhcWSoeeL3OMABXX+0cDSEWVLCYzOPQTLzuFZ/3uprJc8XzPuEpJJI5HYubORTqiJDdNRqEYVdbG7XTT1RrqyOjNwmeo7JZTmuYifPguNKSnGFVxtxiCgRgz3gY8RCX8+pmDhZjeNPOEeR0vqNYy2hQJJ5e2kkAt2s06N7vUlkcdYx3B8wYw2ZOd48vnTTBgKl4AKos1xy0b3/4GV6hruT8i5s5HNoxMnAr9UGj0gTQVyqgTtCsC5oTRSnZK/C/fGEBQUVCOCCDQFBlGTndwBPfu4KfuXUWEhEOTsfwoXfvKzvXXzx/GUGPcW1mJIzNPM+lc2hHuTGxEo+dnIcqSVzn7Ww9Le65E5CloqRrqiRhKVUomgCWUgWoklQ1OZs32drRY6fwvUvrYHZ/AABMT6RxyQwgS4R4iFc6OzQTb6g6VmmSt9IV6khYxVIqD7JXuk5xGD+mYiG3xu+u0XBdbXWu6U1el8obkAhI5gy36teV9VzReb0V0eIhFStpbrMJKbw2cSSguOmmyflHfOJeShbw9n3jdbUfKFbHOIn2VtM8i6pjBE/mDOwcVXwrw3mpVF3sUImBWtBfiAmghGseFzSAr7YjthvcRDTgDvCyxFfVkr3SLbU9LNnFSogIyZzupgK+upHHt8+tVP2y+VXvigdlrGX1hqo7XV7PYsdIENc2C7Bgl1W00wbvGCn26NgxEsTCRr7s/LNj9Rv5Lq9nXTWPrXmBBB6lCxS7vssEFAwTWc1oqErVo0+fxePPXkBG42Uj7739AB6464aKhkOJaifpS+b0ohq/9bTVaa83DTSvTVAcIVx6XsdomzdMNy+Q17gMwFX3aaYFZnoK6xDcfio1yDq7kUrGWydhn2lxLzVmFz4vGMC1jVxNF+RWVhfzo12F3wXVGYoJwBmsZYncbTXXk5fozIlwYDKK5XQBoRIXtOsmo667Xz04KybDZLi6mYNkp1sjoKZxLhaQcX45Y7sscsPletbArngQM/FQ3dttR4bdYyEspwpuychIQHL92x0UWcINMzGMRQLu+QMeI61DNSNfPKhggW0NVn6RxBIB8YCMgm20dXTa9XzZH336LB55hteIVWwf/kee4SkfHrjrhjLDYUCW7JTL1c97dTPnJiert61A+arY6a+Ap2+9tYMBvjPhE5/pVi3zGpcBuDOlbNtQHNvP7EjQLXRTapA9fuaKa4/wM946GWVNYtAt7j7iem3ZwXnVvIbaaZittw6EoPX03QRAVGzkdAdyz4CueAb8avlP/PjFH3tDS1Y6zoopkcoXVTLaaQccVdtyk+2/bhJzV9LEgHg40NB222ssPDAVLTJcOqtFw7SwlCpANxlumIn5Gj7r7QvG2FZlLc+gKxEPJtItXvCkYDHEggo+c8/NFfvAb0X4uJ3yQrELvEvEV7GPP3sBD9x1w5Yc9s/33bgTj39rHskKmS4BvhoGABAhFlQaSpftFKbh3k18QDUsgGDh1WubUCQJQZV7qnnPa1gMe8bCSBUM7BkLYzldKHL9dLRVJmOuZ5tpMcRt9VylugnPza+VGXzPXFoHEZ+cN3I8aM+JC+W2Gt7+8YhaUw3USEH6RqhVB6Lfdwe9LH9f1QQOKhIOTEWxbzKC2fEIdo2GMTMSwlQsiPFoAKNhnqUypPLo1kYHf6C5OqrVzuPknlckwu6xUFGu/EokUnmQhKL0ASRxr4tWtMWpt6tKhIWNHMCA2TGeBdOpIdxMX6RtT56gIrm7naBMiAYkvqOyA3bAihbFZTgTT2nN33TBQOktlYhXFvP7zJ+der1i5DYB9uDKayeMhlW3xm+1tnqvEwsqME0ee8DsFjlXIzsMW5Ul/Pxt17nnddJsa6aFsbAKzeQqIFUiLG7msJ7VIRGg2vdfs2vg7hkLIV3gQ/fl9WxRQB5QrK7yymhaPBX1Ro4HDAY9n5PtPEa7R8OYigXbXqS+EtXaU+lZcJ7RXqfX5e+7HUAnaNVK58jhGdyyb7yqcc4PrrsmBNSt+dmwrKqujNVk8GvLkcMzeOzkPPb7uH5WM3xWw1GJ3FBiqF5OFTASVrFzNFz0eqUVZ6UVIa9zgKJJwGJ8d+H3mSsbOWiGhaDMI38B2Lp3btdxqqM5xvR62uq9zvxy2o0YdncSpgVVlorO7V2ZHz12qsjd1vnpVE9LpPJuhHNI3Yr6VmTJNfhXMsiWGnzdSGGLgRiPKj44HcO5RMrXoaDdReorUa099VaJ61V6XX4xAbSZUuPZaqaAtYyOjaxWFN3pJaBIyGkmVyvQVsRfQGnthq1aLdtmuP+Og/jo8Rdx2VMIXpb4OautWOuVK6ISsjqDYVlucXeLAe89PI2vvLxUVpXM0Z97bbsKATqDa4R1VD3vOTiBo8dOlW3TS7fvZ5eSrkePZloA40bbgsF3FYpUbAT2rmQfOzmP5y+uIaRsVTzzHsPAc+o4hmJYAIghb+e4cmQ8l0ghlTcwHuHHlqqrvP03HQ/i6kYeAC8NmtUMt5hMPdHJnaCagfmTX365pc9oK6lHtePn0DEVC/SE/ECfqYD6Ea8aZTGZx1qGlx3cNRquuB08NBPHVDzgBlIpEmEqHsAhTz6ZVuDkCvKy3UhOnlhvK2spr4Fruu6O9Vynklw37hnHg3dej7Aqw7D4QPCu68bwlZeXUDC4h0vBMHF1I49UXreN/8XeR5IkQZWAaEBxVT2OTaR0m/7o02fLtu/pwlZbJCLotjFbsnVeurWlV3fkjgZk9zxBmbg32GYOSdvzxukLp90jYRW7R8NQZIJpcVm9Mu4cCWEiqmI9y2MdStVV3v6Lh1TsHgvZHms8kOwz99yMT3vUXQFZ8o1O7pSaopqqsR3PaCuoV7UTDyq4spGHYactMSyGKxtcfdgL9IYUA46jWij11a60HXRWRDtHlba43JVep1WufY+dnEdBtxD05EOyLAYGhvWsjmiwvvZUk+vI4RnX4HtiLoH7P/eCW/6S1wkGZLKwuJlHLKRAk0xkdQvMtgVYDBiPBPBpjwG61J/fuS+PP3sB0/Fg0esTURVrGd4WZ2ZhABQ7OZkBp+7w1u7CKUsYCSiYGQnZ+Y4YVtIFKDIV9YXT7nhIcd976ANvKVMlOHEG3kjfSv0nS4SZkXKbhrf9mml1VU1RSf3WbvfTZqlXteMG2nrseUWvdxkxAXSQelUuncqFUi3vi586pBS/5GDeOABg67lXJW7orJY3p9H2P3ZyvqjwuxNnZidExWfuuRkA8MknXsKVZMHV/X/4tuuKzlXpvmQ0E/ts1VUyp2MpmefJ3wBc3chBMxkCEt9VeNU+msnw8tUkiIA9I0Espw1EA7KrBgC4nUc3TSynCrj39gOuPJXa3YgqpLT/ogEZAVnCr/7l931TQLRaFdhKejUvUL19ltZM7BkLYcWTDnxnLIiMVtkzrZOICaCD1DLeeWmXy12t69Trk+133GZOh+nx8HE9YgDIMiGrW/jtD95YV7vqaf+5RGrrep4oY4mAW/aNuzp8SZZxcGorncXxM1dw0+xYkcrE775EA7bbpslwZSPnehQR7NxDEjARCyKoyLi6mQOzGLxREzIBiykNlsWw7rivMth++NxDajoeLJKnUrsbeXa8/edNAZHMcy+inGbi4mraN7lcPefuNJ36LjRCvX3mHOc4BQC1I/g7iZgAWkw1w1Cl7WwlA2Q3qLS1ffhrc267YgEZl9ZtDxuvQdOjEvHCADCLQTPMimoFv8jW0qRqXqPsuUQKK3apSFZyUQtbEbMPf20OiWS+KKmaKhfHYdx/x0F87PiLuLKeg2FZUCQJ8ZCCe28/4OrdTYu5E5sqS+58s57VQaTzGABPe5zMp6pEMO3oa6skGR7s1A/1qFuaVYXUkwKi3jTUg04j/vr13o9eVWE5CCNwC6llGPIzdlUyQHbLT9jPJ9swLZxNpJFI5SETcH45g6xmgsDcSGcn6ZlEPF6jHMJqRsO5pWTZO6X9dmEljUeeOY+Lq2lfo+zF1TQ2s5VTFwRluJPF2UTadaU0LIarG3kYplW2VWdcRNd/nwG4aXbMjeXg+ZTgFlcn+5h4SHFjPZzR3RsJ7Ry39YanX+2dQD3qlmbjU5z7qZmW6w1FdroK57pFjgp2LMJEVMXOkVDXn8dO0ai/fr33o1VxRe1C7ABaSD2GoVoJxbrtJ+y3tV1KFop832U7pYBhASGVAIvn83fSHhyaieOVq5vcBRN2TiCJRzf7xTKU9ptfUjWvUXY1bXC/fp8gL4mAgKIUnZdZqJhUzTluNKy67p3AVpzC5++7DbfsGy9LcscYD6RyPLMc//2so9t1Bn+PiCFFdivBcbsFf7NedUszqhC/2gmM8bQV3us26qgwaDTjr1/v/ehFFZaD2AG0kFoRmq36TDu5/46D0G1/ccb4T92ysMNOVuasJFWJbIMrA4gnNYuHFDedgpMAzRk08/bWN5k3cPfvfbNoZVXaB35J1RyjbOlq1sH5UyZy4yUur2exIx6EBV4uktneObplFW3Ba92D++84iKDKM4rmdBN53YRhWQhIhPVMAWeXklhYzyGg8BQlTiYMiXg6B9i/53XTNVA7ndNoMjw/TswlcPTYKdz+8DM4euxUUd869zMeUmAwLn/Brn2dzOll123H81hNvl6h176HnUJMAC2kGZ/lXvNz9tuyHpqOucnjArJkqzYIIUWCYqtWIgEZn77nZjedgiKRXU6T3DKWAB+ozy9n8NHjL7oDQWkfBGQJlr1KdfAaZR0ZvBHBzoDrjZfYOx6BIktbPvWMF6s5NB0rWpHVcw+cMqFeA7fjO79rNIzxiIqsZiGiyoioMlSJIEsSrp+OYnY0WGSjcCcru8DLdlQC9aodxyMBWBbc7LWSPYGX0urnsddTITj02vewUwgVUBNUMhY1Y/Bp9DPtTCxVem7HY8ebFI5HMfLyg7zUqISJEr9672cSyTx0z1DjJOpLF7a216V9EA8pWE5rGAkrRf70jlF2JKxgxVMgRyK+8o+FZCynClhJa3jjJ7+KmXgQm1kNmsm2jLtBBb/2vjc1dA/8VES89u5WSodpu8i7n1/++/7rSUgpDbJE9g6EuSqijayGT375Zew9Wb+7rfe4Tz7xEq4mC26KjMkoL4FZqnZ87OQ8Dk5Hq6b9ODGXwHqmgIurGaiShB0jQSiyVPY8VpOn9L2NrFakWjFMhkQqj/s/9wJu2Tfe0PPbzme/G8baXkgSJ3YADVJtRdOMwaeRz7RzNVVvuzIFA0RAQOarSMdgWqldznuSrTZSZMmt4etsr0v74MBUDA/eeT32T8Z8k9jtn4xhNKIiGlQQD0p2AkAJqbyxFQ/AGK5u5JAqmDCdnPw1ZK10D3wN45YFs8QGUUllwLN+huwkcHzwl+zfzyXSkAkV72W1+/Lo02exsFlwTSEWA5bTGq/kViJHvQnkdIthdiwMELCwwW0HpVXRKsnj997ZRBqGrcpzq59ZDKZlNfT8tnsn0Wljba/sjMQOoEFqGYuaMfjU+5l2Jpaqt11+lacqyXDk8ExVA6p3e+3XBw/4yFmpr44eO4XvXV4Hs+AmftNNEwxAQClO/FZJ1kp96GcYL83zD1RWGTifd7JvOjYRpwbBSlrDwemYr2zV7ssrVzcBeOIgwPt2NaPj3QdGarahUgI5ABgJB5DVDIxFAnXLA6DsPVUmLCV5pbmVdAES+EQctCvS1fv8diKpWieNtb2SJE5MAA3SzajJdl671rlPzCXw8Nfm8OpiCsBWPd9q6a1PzCWwkeURkF6dvcUAsrj6w9lhbKdguSO/aatWdMMqKkaTNyzML6ftfEEMF1YyZf7tjcZvxEMK8rrJg9HsPC+xoIJPvf/NZbK95+AE/vDEa7z6l13bwZGtYFgogCcL80sSVu2+ZDRzq+KaNw6CoW5/dCcG5fmLawjKPGWEU5zG775Wk8dJZueQzOlgjLfxXCIFzbB4fiuTgSBhbjGJgCxhM6v53tN6r9uP9Ep7hAqoQbppLGrntaud+8RcAh87/iLOJdLuojdvWFhYzyGV131lcCNQTQt7x8NQZYLJeLEYVSbsHQ+79Qcc//4LK2kk8wYvjJ7V3WjVerbFe8cjPELXTs7mXZ1z91M++DtpIy6spKuqLmrFb3z4tuvqqnFwYi6B42euYCKq2qopwK86ccGwcGUjj2igWE1T7b4EZPI9lx+1YlBCigTdjpNI5YuT1NUrj/c9b7H7oMx1bxaD7YrKC93LxBPjpQpmzXs8aEbaXmkPdSMpERH9LIDfBPAmAO9ijJ2u53O33norO326rkPbhjcFgncl1YngjnZeu9q5Hzs576pxLIu5qQwAvhPwSzTmpypyCq/viIewki4gb1i2a+ZW8BhjcKNVFYlXUHMMqyfmEvidr76KC6t8lXRwKoqP333Y3UH8wp9+1y80AEBxPXqFgKAqu+cG4KvW8jPoVmpfKq9jcTMPBuDAZAREhFTBQNIu+zgdDyGV1/H6atbXDkG2IfvQTAxf/ZU76rovn/ryy7i8nis7lyLx84xFAlUNjN42OAM2wG01u8bCSOZ0TEYDSGumew4A+NjxF5HKG0VR05+28y45si5u5u1iN1uFkFbSeSwmC1DsSn2M8fs9GVOxfzJWtdpdN7937aDT7SGiFxhjt5a+3q0dwMsA/hmAk126ftN0M7Kvndeudu7L61m7uDmvHazaaZYBPqj6yVDJcKoZPBWyo45x/OJ100LesHhcAcqjVU/MJfDR4y/i/HLG9ec/l0jjYx530kprGWfw9xqivefebvxGKq/j6kYeFmPQTQvnlzOucTejGVjNaEjmdMRDKiSJinYK7u+suOpXPfelZKMDgHtmMcCN3K5mYPS2wUlBHZAlFOwMpo6bq/ccLy1s+EZNl8qaNyyonip4ADAZDbrVz5w057vHQpiM1q5G1usRtY3SK+3pig2AMfYqADdYqN/oZmRfO69dLRHZSqrgpjZQZAmSxUAS8Pa943UnL1PsrJkSCDqzinzqncIthsWgyOXRqo+dnEe6YLi1nwGAGC9m7hggg6pUZAS2GOP5ilQJMvF4BMmut1waCdtoMjRv+5ZTBR6YxvhUI9sD40paQ0jhgWsraV4VLaRIrjpKlaSi3Y636ldD9wUoSr+tWxYCilTTwFh6j0bCKhSZXBn8UkQ70dh+UdO1nAVyuolYUClKse18vl2R0L1ML7RH2AAENbn/joMIyATNEwmrmxZiQaVqTv/SiOJ4iH/pGVhxkRbYK3T7p2HXsR0JK64vtmPk9a4Z+IRhuat4v6hfJ2pZNy0UDIvLbvGoZefcvtHPdcRvOJ8p2NXFLHD9NtHWDmY6HoRlMWQ0E3OLSeimBcNkGA0rsMB829rIfYmHFJi2W6VpWTBtlZoTue3gt6Op1u5KuyInGrvZc997+4GG+1rQPto2ARDR00T0ss//DzZ4nvuI6DQRnV5eXm6XuIIaBFUZqryV3kGWCT9fklffi98W99P33Iw37oi7q1WAR9iqsoSgTFAVCYpdQnI0wvXC3spQjt7YgTG+q3AMkH5Rv7tHggipMiQiO3CNMxZW3XNvN35Dtlfyu0fDCCmSq9v2RjLzymR8BzISVrAjHsJoSPFta70cOTyDT99zMw7NxOyJh3D9dBRv3LEVue3gt6Op1u5KRkonGrvZczuxHN1WfQg4XTECuxcnOgHgo/1kBB5GKvn+VzOSVsINODJNrKQ0V4k9GQ0goMhVg+A+evxFbGT1InfS8YhaZoD0GtWiAblIlbEd2Wu1SZUJhsm9eQCu019KFmBYDHvGwm4N4FZfv5o8zRoYK53D8RwaFGPssFDJCNxXcQBzi6mhyk9eD50IJ2+lz/KRw1sVnnST+4YHZMKBqVjNKmGfuefmIi+gQ9NbXkAAfKtg/XAp5QaeBRVeDyAWVMpkf/Tps3j82QvIaHyVe+/tB3DT7Fhdfett08J6FtdPR0F2ugsGPhGMePrPr+9adR+d82Q1w+3bQztGGj6f06bf+eqrOJdIA+BeVzfNjrn90ksVugTN0S030J8G8PsApgFsAPg+Y+yf1Prc2L7D7B0PflasOGw65UrWyh1AJ/BWwVpKFlxvGUUmEKjM7fDRp8/ikWfOQyKuqrEYT1URDciYGQltq2/r6btW3cdWPw+D5no5zPTUDoAx9gSAJ5r57LDkJ6+HdoWT+1XnOn7mSk9UNfJWBNMMC6pMuMFe4QK8T85cWud57y0GmQDDdjU1TO5htJLWMBoq4PaHn8He8QheXNiA5JRsBJ8EdNNERjO33beVqo15I4ZbdR9b/TzwXZqJ1bSBgsdF94EvfA+PfujtQ//9GwT6SgXk0M8h4K2kHeHkfrV+j5+5gntu2YPn5te6uu332g82szpAQE7nUb0fPf4iCNyV0bQsSETQTMaL0RM3CvOMmdybyevfntVMqD7uEKVBZc32bSW/eYdW3cdWPw/nEim3n53EdwxAumD41okW9B99OQH0cwh4K2lHMe9Kq8jn5te6ru4pqm9rp5W2LB4LYNrpGHaOhhFUZBgW4yUrLSCkSpBsX3vTYgiqxT7yEgG6BSjF3o1F9QaA5vq2WrUxZ/Bs1X1s9fOgGVbR4O8Npy6tqyzoT/puAhB+w1s4Cb6WU3mk8nybLkuED968u+i4RgyMvZKkyg9HNs3k7QS2/O2BrRKL0/Egrm7k7YpcPFYADAgEJKxnTcgS2cnXeDH7yaiK5bQOw7JcG4BEQDQgb7tOQ2l/JnM6VtIFXFzNug4NrcpF3+qc9qpMyOmenZBn69LtZ6IXcun3MqX9IwVjI37H9VUgmGkx4Tfs4cjhGdxzyx6sZ3XkDRMBmTARVXH8zBU37L/RvOO9kqTKD0c2pyIYsOVvL0vk6vDjIRW7x0I8xkDiBsyQKiGrca8YmVBUzH4kHMDsaBBhVYZh8cHtV957CL9/9JZt12nwS5CmmRaCMrnHAWiJb3yr0wvcsGMEk9GAuxOSiOdRciaXbj0TvZJLv1fx6x95ZGqf37FdjQNoFBEHUE4tL5NGPXhKPT9W0gWsZ3XEQ0pD6ZlbiTdVdLrA3TRTeaMohoCrfLgNIKzKWM0UsJbReRlHImQ1E4pEGA2rWM1obsSsRMBENIDPeCqaNUq1PnZW5ZUSpG3Xm6rdFeKaidloN/3mldZp/Prn6w/9q7y2fDFcemxf7QAE5dRKZNZoojPvKnJxM4f1rI6JqIqdI6GurLS8qxmn9m5GMxEOyDyKNqTgwFQMn7nnZnzarke8mMxjLaMjEpCQ13n6CsPiidpWM5qbvhmwcxBtU8ZqfVwrQdp2VCmdqpLlVGDz9nc3d+HDWsC9Xvz6B2C+mcP7zgYgKKaW4a8Zw2ClhF7dcMEtNUpXq73ryO7IvbiZd43Fhmnaumw++IdUGZbFoMhUVkO3UWr1ca0Eac2qUgatSla9tMP5YZDw6x+AfBf7Ygfg4cRcAkePncLtDz+Do8dO9YVOsVYis2YSnTnUs9JqZ5+dmEvgzKV1vL6awfxy2i1UUm+qZs203ORxigS3GIxT18ACw1QsWPV81drnvHcukcLCeg7LqXzVPt7OvajUTsPk1c7mFpOYX+b1dxtZCQ/iMz/s+PVPpdTLYgKw6VfDUi3D33YMg7UMwp0oUk/EffcNT7WqelI1lxqLJeIJ5xyDpiLz5G0jYbXi+eotgL5zJISJqIr1rI7FzVzFPm61kTYWkHFlIw/D5CmoDZP5VhWrxKA+88OOX/+YyZVLfscKFZBNrxRpbga/bfp2jYMn5hJYzxRwcTUDVZKwYyQIRZaKVlrtLlKvmyaYxaCZ3KdfloDFzTxmRkJFq71KkcsjYQUrKQ0W8VnAz1hcbfXYSAH0qVgIkUBl1ZRDq1QqJ+YSuLSeg2ExmMSgECBJfJtTb52NQXvmBVuU9s8X7k8n/Y4TOwCbQTIsbXdl53p/WAyzY2GAgIWNPAKyVLTSamefnUukbM8T4lG6BBgWYLLiXDR+bXUil/2Ml15jca3VY7X2dfN5cdpcMOwIZsYD2cCYb1WxSgzSMy9oDrEDsBkkw9J2V3alnx8JB5DVDIxFAlUrSgGt6zMnClUigiTLUMADusKqXCRDs5HL9arAqrWvW8+L0+aQHfEcksk1aFeqKubHID3zguYQOwCbQTIsNbuycwyCz19cw+JmHsmcXvXzlfrsPQcntm1YdIrPONW9LCcXDWNF5z6XSLVtFVvtmbj/joNI5nScW0rh1WubOLeUQjKnd+R5ce7vdDwIxnjpSxBDwbAaema97UvmNJxLpHBxNYuNrNbzdgBBaxATgM0gGZaaieb1qlKCMkEzLTdSttLn/frMKRiyXcOiE4XqVPdSZEIsKEMzWdG5U3kDq5lCQ22tl1rPRK0kb+3Cub9OxLMicSN5JNBYcJbTPlUiLGzkAAbMjoWgmVZfGIMF20dEAg8gzeRx9/qop/I6rm7kwcCLp+8cDdWdB75VUZp+bVhYz2E8omLao+JYTuWxntUxOx7uaM76bkajtjpPv4isHXx6qh6AoL2UVqiqJ32zN2kZX1kCiWQeecNyUxoAfLCo5lnUqmRyfm3YyGqYihUXO5+KBWGYXMZOpqruZNI8P4+uhz7wlpZV5erlBICC9iImgAGlUTe5UoNgPKRClshdBfrVCfDLCd9Kw2JpGypF0h7aMdLxlWqnDKgV+/0Db2lZm4UxeHgRNgABgNpGcK+3DRH/6eSEb+Q87ZSxk3RKlnr7fTv0Ur8KOouYAAQAahs86/UsaqcxvZcM9Z2SpRO++r3Ur4LOIlRAApdqaqNG1ATtjNLspQjQTsjSKfVML/WroHOIHYCgLoSaoDuIfhe0EzEBCOpCqAm6g+h3QTsRcQACQYcR9WwFnaZSHIDYAQgEHaRfUzALBpOuTABE9GkimiOil4joCSIa64YcAkGn6YRbp0BQL93aATwF4EbG2E0AzgL49S7JIRB0FJGCWdBLdGUCYIz9HWPMSVp+CsBsN+QQCDpNM4n6BIJ20Qs2gF8A8NVuC9EI/VhHVdAbCLdOQS/RtgmAiJ4mopd9/n/Qc8wnABgA/rzKee4jotNEdHp5ebld4taNMOIJtoNw6xT0El1zAyWijwD4RQDvZYzVpQDtBTdQkTpXIBD0Gz2VDpqI7gbwcQA/Vu/g3ysMWupc4ZMuEAwv3bIB/AGAOICniOj7RPTZLsnRMINkxBPqLIFguOmWF9D1jLG9jLG32f9/sRtyNMMgGfGET7pAMNz0ghdQXzFIRjzhky4QDDciHXQTDErqXFEJSiAYbsQOYIgZJHWWQCBoHDEBDDGDpM4SCASNI1RAQ86gqLMEAkHjiB2AQCAQDCliAhAIBIIhRUwAAoFAMKSICUAgEAiGFDEBCAQCwZDSV0XhiWgZwOvdlsOHKQAr3RaijQx6+wDRxkFBtNGf6xhj06Uv9tUE0KsQ0Wm/VKuDwqC3DxBtHBREGxtDqIAEAoFgSBETgEAgEAwpYgJoDce6LUCbGfT2AaKNg4JoYwMIG4BAIBAMKWIHIBAIBEOKmABaABF9mojmiOglInqCiMa6LVOrIaKfJaJXiMgiooHysiCiu4noh0R0noh+rdvytBoi+hMiShDRy92WpR0Q0V4i+gYRvWo/ow92W6ZWQ0QhInqeiF602/hbrTivmABaw1MAbmSM3QTgLIBf77I87eBlAP8MwMluC9JKiEgG8IcA3gfgzQCOEtGbuytVy/mfAO7uthBtxADwq4yxNwG4DcAvDeA9LAC4kzF2M4C3AbibiG7b7knFBNACGGN/xxgz7D9PAZjtpjztgDH2KmPsh92Wow28C8B5xtg8Y0wD8AUAH+yyTC2FMXYSwFq35WgXjLFrjLEz9u8pAK8C2NNdqVoL46TtP1X7/7YNuGICaD2/AOCr3RZCUDd7AFz2/L2AARs8hgki2g/g7QC+02VRWg4RyUT0fQAJAE8xxrbdRlEQpk6I6GkAO33e+gRj7Mv2MZ8A347+eSdlaxX1tHEAIZ/XhGtcH0JEMQB/BeBXGGPJbsvTahhjJoC32TbGJ4joRsbYtuw6YgKoE8bYXdXeJ6KPAPhJAO9lfepbW6uNA8oCgL2ev2cBXO2SLIImISIVfPD/c8bYX3dbnnbCGNsgohPgdp1tTQBCBdQCiOhuAB8H8AHGWLbb8gga4rsADhHRASIKAPgQgCe7LJOgAYiIAPwxgFcZY7/bbXnaARFNO96FRBQGcBeAue2eV0wAreEPAMQBPEVE3yeiz3ZboFZDRD9NRAsA3gPgfxPR17stUyuwjfe/DODr4MbDLzHGXumuVK2FiD4P4DkAbySiBSL6N92WqcX8KIAPA7jT/v59n4h+ottCtZhdAL5BRC+BL1qeYoz97XZPKiKBBQKBYEgROwCBQCAYUsQEIBAIBEOKmAAEAoFgSBETgEAgEAwpYgIQCASCIUVMAAJBExDRJ+ysjC/ZbofvJqJftjOKMiKa6raMAkEtRCSwQNAgRPQe8KjvWxhjBXuwDwDQAPwtgBNdFE8gqBsxAQgEjbMLwApjrAAAjLEV+/WrAMADUwWC3keogASCxvk7AHuJ6CwR/Tci+rFuCyQQNIOYAASCBrHzsr8DwH0AlgF8kYj+dVeFEgiaQKiABIImsFPzngBwgoj+EcBHwCtvCQR9g9gBCAQNQkRvJKJDnpfeBuD1LokjEDSNmAAEgsaJAfhTIvqBnZ3xzQB+k4gesDOmzgJ4iYge76qUAkENRDZQgUAgGFLEDkAgEAiGFDEBCAQCwZAiJgCBQCAYUsQEIBAIBEOKmAAEAoFgSBETgEAgEAwpYgIQCASCIUVMAAKBQDCk/P9ijw6ycYgjlgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xn = (X-X.mean())/X.std();\n",
    "Yn = (Y-Y.mean())/Y.std();\n",
    "\n",
    "sns.regplot(x=Xn, y=Yn);\n",
    "p1 = np.poly1d(np.polyfit(Xn, Yn, 1))\n",
    "print(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One-dimensional regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most of the required machine learning algorithms are implemented in a Python package called `sklearn` (SciKit Learn). Here we will show how this can be used to perform linear regression and create our first machine learning model. For this there are three routines we need to import, `LinearRegression()` which creates the model, `train_test_split()` which splits the data into training and testing sets, and `r2_score()` which is used to calculate the correlation coefficient between the data target values and the predicted target values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression # linear regression model\n",
    "from sklearn.model_selection import train_test_split # for splitting the data into training and testing sets\n",
    "from sklearn.metrics import r2_score # for comparing the predicted and test values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To understand linear regression we need to introduce some notation. To commence, assume we have one feature and one target for each data point, we can then label the data points as $(X_j, Y_j)$ where $j$ ranges from $1$ to $n$, or we can introduce the shorthand $j=1,\\dots,m$. Then the objective of linear regression is to find the line of best fit, such that\n",
    "\n",
    "$$ Y(X_j) = \\beta X_j + c, \\quad j=1,\\dots,m, $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\sum_{j=1}^m (Y_j-Y(X_j))^2 = (Y_1-Y(X_1))^2+(Y_2+Y(X_2))^2+\\cdots+(Y_m-Y(X_m))^2, $$\n",
    "\n",
    "is a minimum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For `sklearn` the models generally have the same interface, and the steps are:\n",
    "\n",
    "1. Instantatiate (setup) the model.\n",
    "2. Fit the data to the model.\n",
    "3. Score the model to test how effective it is.\n",
    "\n",
    "Fitting the data to the model is done with the method `model.fit(X, Y)`, while calculating the score of the model is done with the method `model.score(X, Y)`. For Linear Regression the default score is the 'R2 score', which calculates the square of the correlation coefficient (R squared) for the predicted model labels $Y(X_j)$ and the actual labels $Y_j$. This will be a value between 0 and 1: for values close to 1 the model is very good, and for values close to 0 the model is very poor. If this score is calculated with the values used to fit the model, this is known as the 'training score'. \n",
    "\n",
    "The model also has a number of objects associated with it. The two that we are particularly interested in are `model.coef_`, which returns the coefficients of the X values for the model (the $\\beta$ value above), and `model.intercept_`, which returns the linear intercept for the model (the $c$ value above). Note that to calculate the intercept we need to use `fit_intercept=True` when we setup the model, otherwise this is not calculated.\n",
    "\n",
    "Our first calculation is to create a model which attempts to predict the onset of Diabetes (`Y`) using `BMI`. Note that the square root of the training score is approximately equal to the correlation coefficient between these two values which we calculated earlier. The difference is due to the fact that the Linear Regression model takes a random sample of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training score is 0.344\n",
      "Correlation score is 0.586\n",
      "Coefficients are [10.233]\n",
      "Intercept is -117.773\n"
     ]
    }
   ],
   "source": [
    "X = df[['BMI']] # create a dataframe with just the BMI values\n",
    "Y = df['Y'] # create a dataframe with just the Y values\n",
    "\n",
    "linear = LinearRegression(fit_intercept=True) # instantatiate the linear regression model\n",
    "linear.fit(X, Y) # fit the data to the model\n",
    "training_score = linear.score(X, Y) # calculate rsq for the training set\n",
    "\n",
    "print(\"Training score is\",np.round(training_score, 3))\n",
    "print(\"Correlation score is\",np.round(np.sqrt(training_score), 3))\n",
    "print(\"Coefficients are\",np.round(linear.coef_, 3))\n",
    "print(\"Intercept is\",np.round(linear.intercept_,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best fit line is then:\n",
    "\n",
    "\n",
    "$ \\hat{y} = \\beta x + c = 10.233x -117.773 $\n",
    "\n",
    "The $\\beta$ coefficient is interpretted as the change in $\\hat{y}$ (the outcome variable) for a one unit increase in $x$.In other words, if we increase the value of $x$ (the BMI) from say 19 to 20, we would expect $\\hat{y}$ to increase by 10.233, on average. The standard way for writing up a interpetation like this is:\n",
    "\n",
    "\"For a one-unit increase in BMI, the measure of disease progression increases by 10.233, on average.\" \n",
    "\n",
    "The value for $c$ is the $y$-intercept. So, if we set $x$ (the BMI) to 0, then we would expect $\\hat{y}$ to be -117.773, on average.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing and training"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One significant problem with the model is that the score that has been calculated is based on the data that has been used to fit the model, rather than data that the model has not seen. In practice we want to know how effective the model will be on unseen data, as this is how a Machine Learning model would be implemented. Hence, what we can do is split the data into training and testing sets, and calculate model scores for each of these sets. Then the score of particular interest is the testing score, as this gives a more accurate measure of how well the model will be on unseen data. Note that typically we would expect the training score to be slightly better than the testing score, as this is biased towards the noise in the training set. \n",
    "\n",
    "To split the data into training and testing sets we can use the `sklearn` function `train_test_split()`. This returns training and testing sets for the features and labels, and by default creates a random split for which the training set is approximately 80% of the data and the testing set is approximately 20% of the data. To change this we can use the argument `test_size`. We can also specify a random seed for `random_state`, which ensures that that random split is the same each time we run the cell.\n",
    "\n",
    "To calculate the the testing score we calculate the predictions of the model for the testing set using `model.predict()`, and then calculate the 'R squared' score for the predicted and actual labels for the testing set using the function `r2_score()`. As is apparent the training score is slightly higher than the testing score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training score is 0.328\n",
      "Testing score is 0.321\n"
     ]
    }
   ],
   "source": [
    "# split into a training set with 80% of the data, and a testing set as the remainder\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.8, random_state=42) \n",
    "linear = LinearRegression(fit_intercept=True) # instantatiate the linear regression model\n",
    "linear.fit(X_train,Y_train) # fit the data to the model\n",
    "training_score = linear.score(X_train,Y_train) # calculate rsq for the training set\n",
    "# use the independent variables for the testing set to predict the target variable\n",
    "preds_linear = linear.predict(X_test) \n",
    "# calculate the correlation of the predicted and actual target variables\n",
    "rsquared_linear = r2_score(Y_test,preds_linear) \n",
    "# print the training and testing scores\n",
    "print(\"Training score is\",np.round(training_score, 3))\n",
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