03-IntroLinearRegression_REMOTE_50727.ipynb 291 KB
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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": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.7/site-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
      "  import pandas.util.testing as tm\n"
     ]
    }
   ],
   "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": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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": 2,
     "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": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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": 3,
     "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": 4,
   "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": 4,
     "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1])"
      ]
     },
     "execution_count": 5,
     "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": 6,
   "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": 7,
   "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 or RMS 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": 8,
   "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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3M3j28eCCX8AL98UP91O7/9vA09b62L0V+HKGuqx/rAGSNwGPAO9rQ/uBM6rqbOD1wLVJnjrBSH8H/BRwVsvy1vmoS2w76deSXsbjj5Imuq+SHAd8CHhdVX1npU2XGBvLvlou07Tn1RK5pj6vVvj3m8q8qqpHq+osBs+SzgWeudRm8/FXuO+w9VbgB+afwrbbg218qpf1J9kKvBx4dbWTW+2p5Dfa8m0Mfiv/9KQyVdWBNrF+APwDjz2dnfa+Ohr4VeC6BVkntq+SHMPgP//7qurDbXiq82qZTFOfV0vlmva8WmFfTXVetcd4ELiVwTnw41smePy++OF+avf/BMOf/jxEbwV+E7C1LW8Fblww/hsZOB/49vxT4nHL4EMt3gC8oqq+t2B8JoP3TCfJ04EtwH2TyNQec+G52l8B5l8NchNwaftr+Jkt16cnlQt4IXBPVe2bH5jUvmrnGq8B9lTV2xbcNbV5tVymac+rFXJNbV6t8O8HU5pX7THmXyH05JZjD3ALcEnbbPGcmp9rlwCfmP/lvCbr+QvoOL8YPBXaD/wfg99aVzA4V7QT2NtuT6zH/hL8Tga/YT8PzE4w070Mzmnd0b7m/8L8a8DdDP4y/1nglye8r/657Ys726TZtGD7N7V99UXgpZPK1MbfC/zOom0nsq+An2PwdPXOBf9eL5vmvFoh01Tn1Qq5pjavlss0zXkF/Cxwe8t0F4+9AubpDH6B3Qt8EHhiG39SW7+33f/09Ty+l9JLUqd6O4UiSWoscEnqlAUuSZ2ywCWpUxa4JHXKAtcRKcmb2rvH3ZnBO9Wdl+Q17V3iKslJ084orWY9n0ovdSnJcxlc4XhOVT3cyvpY4PvARxlcTSdteBa4jkSbgK9X1cMAVfX1Nv4AwDreHE6aKE+h6Ej0ceD0JF9K8rdJfn7agaS1sMB1xKnB+zc/B9gGzAHXJfnNqYaS1sBTKDoiVdWjDM5135rk8wzeYOi908wkHS6PwHXESfKMJFsWDJ0FfHVaeaS1ssB1JDoO2JHkC0nupH3WY5I/TLKPwfs335nk3VNNKa3CdyOUpE55BC5JnbLAJalTFrgkdcoCl6ROWeCS1CkLXJI6ZYFLUqf+H634j3kTsJ+yAAAAAElFTkSuQmCC\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.distplot(X, hist=True, kde=False);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7GVaSiyedUerFKzG17iR5E/NX0b6hql7qyvp84CfAg8CBCcaT+maBaz3aADxbVS8BVNWz3fanAeYvHpRWP6dQtB59Ebg8ybeT/EOS35p0IGkQFrjWne5+zm8EdgNzwD1J/nCioaQBOIWidam7JegB4ECSbwI7mX8SjtQMR+Bad5JckWTLaZu2At+bVB5pUBa41qNXATNJHuvuKncl8JdJ/rS7K+NG4JEkd0w0pdSDdyOUpEY5ApekRlngktQoC1ySGmWBS1KjLHBJapQFLkmNssAlqVH/B6DQrP8ckizpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(Xn, hist=True, kde=False);"
   ]
  },
  {
   "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": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Line of best fit is  \n",
      "0.8967 x + 1.096e-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": 17,
   "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": 18,
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "0.01925 x + 46.15\n"
     ]
    },
    {
     "data": {
      "image/png": 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l4touUirVTsIy8aTyPrJMg/F0ElBGzanFAki1KBgIDEPgSclywWHXUH330mAsB1MxBv2FNth1dcp42ms1oNt1n5vZ/5vBsK0XBU3TtKOAeye23vV2MOenMzx4/HkuL+RJJyyklGTLbs12o9cYTye4OKd2P1KCJ2W4QLhVvqquJ5FS4kqBKVa8iMqu13AX1WgsP/LUSz27I2snvbzzrMdW7HOrdDtOQbOF2KhhuFM+5bWMjXO5Epmiw3SmiCng/HSWV2dymIKa7UavkU7GSEY8gCxDcMtwkphphAFuAaYhsAyDuGkQmOekhLhpNNxFNRrLm8V4uhXvcyv2uVX0oqBpiSCR3N88+jaefOjelqT8TiVxq+XyOZ+zGemL0Re3mM2WMQ0lyc9myzXbrb7GcF8M0xDsGkpwcKwf0xCkkxYDCauinYGERTqp/nlIHM/D8ySDKWvNXVS9sWx3PepeZSve51bsc6to9ZFm0+jU1ruWsXExX2ZsQCW6K7teKOGXXa9mu9XXODg2wD+7Z5TnJufDa370Xa+Dqnaixxx3mbLvfXRgx8C6VWPRvpyfzlB2vIpFrJXUFL2W2qK63Qfu3lMxxr1ej2OzDdvdoCsuqe1Cu6RuLTbTpTXa1uRMFseTIMEyBYfGB3rClXYtNupG2mtuqJvhPtoNF9WtSCOXVL0o9CCbIcVtRhuf/vIrPPHsBXJlFST19iPjvHBpaVO+sNHJwXE9phaLAOwZVjr8pYKDRBmF9wwl+fc/9vd6zi+/3iI6kylVpKYIjlcvcht9f7vvbTOEgl6Npek1Gi0K2qbQY2xGgq/NaOPTX36FTz3zKgXbxTKUMe7pF6/zpv1DG45gboaoIdeTcHhigNvG+5nPlVj0FwRQRuEri0UefvJMx5OotTruG01NsZmpLZq5t81ISaHTXmwcbVPoMTbDD3oz2nji2QsYAixDyR2GAMfz+Mq5GV781X/cljbWopb/+ut/9S8ADwHgOxJJCdmy23Ff81bHvV5cSJCaYq14kY2+v933thlxLr0aS7OV0DuFHmOjkk4zCesatdGuhHe5srsqh5Ah1PGNtLHe9wbvC6KOq5WmnmTd0mSzfWr1s63n6fL++w425QGz0fe3QjP3thmeOzeDd1Cn0YtCj7ERP+hm1RONkqO1S63UHzdX1STwJCRMY91trFftFX1fdJ2KmtMMwbqkyVb61OpnWy+W4eH7b28qXmSj72+FZu6tXQkQG7EZbWx3tKG5x9iI90S1kW25YHMjU0RKKiqG1WujP25Sdr22GOkCm4IhVrKAehJ2DyZIxMw126hltHz81OS6jIjRcZleLnIjU1p1jiFgpC+2KsndWgbhVgyb29kzpvreZrMlFvJ2mPV1u7ltbnW0oXkLsRFJJ7qFD+oNe57E9SorhtVrI1Ny2make/j+23nkbbeRipk4nrrOI2+7DYRYs4160vf56cy6+hcdl4nBJDvTiXDHIFALwkQ6we6hVJjk7kMnzq6rklujPm1nKTZ6b9eXCizkbUb7Y+waTOpqaFsMbWjuQdab4CtqZJvNljBQGUMTprHK8FerjX2n2muke/j+23n4/tsrjj03Ob9mG/WMlmXHW5eBtNr4ODGYZMAv+QlU/C2a5G6Xn2Cv1Upua6mEtsMiUIvg3qp3T9sxadx2Ru8UthFRI1vZ9ZCoRG7jaRXZ67geZy4t1DWINjLStcsAHW1juVDm/HSGi3N5FvPl8Jr1pO+4KdZlRKx1X8sFm4Vcia9fnOf6UpHlgh2e73oqXUVApmhzZT7Pc5Nz3PGRP+edv3kq7Gs7DZvtrGrXTbRb6Nam4aIghOgTQvwbIcSHhBBJIcS/FEI8LYT4P4QQA5vVSU1zRLfwhhAYQiVySydjZIo2U4tFhKCuSqSeegNomwE6aCNmCK74Evne4SRl1wuvWc9oeXjn4LrUL9X3FTcNJGB7koQpKLseV5cK4cIQJLkDf0FYKFByJQKQUnJ+OsuHTpxtqIprVSLeTgXob4akcduZhoZmIcQfoSqkpYA7gG+jqqP9KLBLSvlT62pUiGHgCeBOlHfgzwDfAT4PHAAuAj8ppVxodJ3taGhuF9WGv1enVaqHPcOpVfn71zIidyJKtNY1Z7NFciWXuGWQKTqM9MUYG0i0zSAbGK/PXFpAALuGlPro6mIRiap6JgSUbA/LFIwNxFnK2+RttWsIPZcEWAJum0gz3BdvS1R4ozEOjOzNtlMdSf7++w6uUuN1ku1sUN8ubMTQfLuU8peBXwC+D/hFKeUp4N8Ad22gT58CviSlPOJf59vAh4GvSCkPA1/xf9esk2oJVqJSPAxGEtI1u6XvhDqg+pqZos1spky+7LJrMMlof4yFvM31pUJbDLJRSdyTEk9KrvqpL24ZTmIAJccDCftHU+zojzOfsyk6K2okGfyTYHtw7nqmbZJ9vTE+f2O5pR1ErUjyTz3zKp/+8ivr6td62M4G9ZuBpgzNUkophPgz6W8r/N/X5csqhBgE3gr8S/9aZaAshHgPcMw/7TPASeDR9bShUUSNmoEkGqXZLX0nokSrrzmTKYVGcSEEYwNJ+uJW23LWRI3XcdPAcSUI1e6h8QGuiyLJmODwRDp8T3/CYiZTIlty8KTKkwSAyq2HELTNmFpvjMuuZKiFKOh6keRPPHthU3cL29mgvt1Za1E4LYQYkFJmpZQ/ExwUQnwPkFlnm4eAGeB3hRB3AS8AjwA7pZTXAKSU14QQNZ8oIcRDwEMA+/fvX2cXbj42UjWtHRXXonz6y69w9soieT/qeUd/jKLjYggRpruGyijrRuqTZpLMRdN2jw0kuLpUQEi1O8iXHWzPY+9wquI9gXE7RFa8qHrQVefX2z2t1cd6Yxy3jJZ2abmy2iHAisHck2C7TmgD2Sxq3TM0F//R7PX0wtN+1lIfPQ6EBmUhxE8LIZ4C/hXwY+ts0wLuBn5bSvlGIEcLqiIp5XEp5VEp5dHx8fF1duHmYyNb+naqAwL1hu16xAwV0DaTtTGAHf3xCvVWM1HW64niHkzFuGUohWEITMNgIp3k8PgAlln5dQiM23fsTFcsDknLIG4KYqZYdX6t3VMzfaw3xocn0i0ZbYNIcteT2K4XRm0bgk01XNe65w+dOMsHm4z/aOZ6W9UQ3+ustVN4HLgfQAjxVuATwC8CbwD+K/DAOtq8AlyRUn7N//0EalG4IYTY7e8SdgP6024z693SN5LQWpXeqtUblqnUGzHTIG6ZqyVl0wjVPtPLRWayJTwJP/v7p3nkbbfx3OR8U0nmqiVxyxRMpJNhkZfZXLmmcTuQbqNpuG9kSjiuxARmMsWa50dpNRFeVC/b6i7t/fcd5FPPvIobcakFteAGhXo2IpkH97PW513rnqcWCiBgdxPxH81cT8c+dIa1dgqmlHLe//mfAsellH8spfwocNt6GpRSXgcuCyHu8A+9HfgW8DTwPv/Y+4Cn1nN9TXtpJKGtR3qrlyiv5HgNo6yD9BSB5Ot6kk898yovTS02pV6pJYkHxWamM8WGxu1abrT7RlKMDcSbMoY3Y6ivN5ZAS7u0IJI80GwZAsYH4uwaSrWcWHEjkn6te3Y8D7cqIVY3nR00tVlrp2AKISwppYOavB9q4b2N+EXgD4UQcWAS+J9RC9QfCSF+FrgE/MQGrq9pE40kNKBl6S1I2xxdGDypjjeKsp7JllbSXUvCnEp5u/ko5+rrP3j8+Yr+NzJuHzsyweOnJjngyYq2mjGGN2OobzTOrdbCfvj+25uKHG/ERiX9WvdsGQZUCQTddHbQ1Gatif1J4KtCiFmgAPwNgBDiNmBpvY1KKf8HUMtH9u3rveZ2opcMao3qKktoueZyoN5wPK8iUd777ztY8/xAfRIKmP6rKQSGCHTncl1G8Fr3Fo36rh77tWpMnzw3zSf+/NtcmFO/Hxrr59F3HGlKBdRs/epmVTobdQ6oOTae17Rxvbr92WwJV0pcV3J+OsPOdALLNLrm7KCpT0P1kZTyfwN+Gfg94L7AJdV/3y92tms3J71mUGsUnbqeyNV6ifLquUsGqhvT31oYAmKGwDINPAkDCWvdRvDq/i8X/Khvakd9N7rfk+em+eCJs7w6k0NKWRH5DGurgJoZy1ZUOs202crYgJL0TaM543qtBHljA3H2jaRAwpXFAjFDdMXZQdMYnTq7x+i1GrONolOBun/rRL3nWqm4Gy0oa7Eq6nsmi+NK9o6kSCdXR303GovHT03yd5cXkB4Y/sTpSZUa4437R9b87JqJAq71bJy/kQFBRXxFu+otV/dn2Q+CHErFWvq8e+2Z1jSOaNZZUjdIM6qeVtRBzaoRNotjRyb4OEo9cWUhz96q/j9wZXFVSoVWFoRmx+bh+2/nwmyWp1+8ju1KTEPw7tfvamlBqNVWMKFfWcjjuhJTwNRigbipitsPJKxw7BuNxUeeegnXk5gR9YoQSh3VzGe31jjDxlU6rY5ROmEhpWSpYLN3pI+Pvut1sEYfa7GRZ7qXVKk3C3pR2ABRaSq6df84VLhsrnVOlF40qNVzZT15bpoTZ6YYTyfY70uOJ85M8fq9w019cVsZm5Pnpnnh0hIHdvSFUuoLl5aaDsiq29a7vy/cBXzgsy/gSbXgOJ5Kg7FjIMaBHSu5H+uNxb6RPmazJaS3EvkspVK5NPvZreUy3G7jbTXVYxTsBH7tPXdW9KvVSXm9z3Sr352bmSBQ0fVk5T8p8Tz8V5XexagSIqrRi8IGaMZ3ulX/6nYa1JqVstbrj76WZ9JG3l8dB3Hm0gJCwM50EhEXLfupP35qkrLjMpdVacXjpkE6aYXvf/zUJCN9MeZy5XBi95DM52z+9x9vzhD6wRNnWczbSN8q7klVze0th0Z58PjzG47ziD4bjutxY7lE2VUG+2biJZoZo07EAqz3me7V2ITgMzs/naHseMRMEVbsa2e/HNfD8Sdyx5N+wayVid7xvPC1FQxTLwodo5ltcatb52bUCM3QrJRV67wPnTgb6o4bvbfevQVJ3NZquxlvnuA6rudhCMHVpQKgopJbUZO8cmOZ5aKDgcAUAseVzOXKOO5y2JexgQQJS3nKBAtHKmY0bQj9jQfuqvA+Ojzezzvv3MWJM1M1xwJoSRIOno3HvnSOi3N5YqZg30iKsusxn7NxXI/DG5icOqW6XO8z3WuqVFh5Jm3XZSlvg4CCDRdms03vYhzXU55YnprsXdd/DdKSrGOibyd6UdgAzWyL17N1bkcysWalrI34o280idtaYxPtW8IycTyJkDCbLTHoqzeaVZPYrpLeAyOwEOB5krJ/POjLYCq2KrV4s9T63KpjITYa5xHGS+zoazleYi06qbpczzPdi6rU4JmcyzoYhqpZ4nmS5YLNriGT3z75Xe45NLpqsg/ccV3fM62X0YvCBmhmW9wN/+qT56Y5c2kB1/NIWCbj6QTpZG3JeiPGy/UkcTt5bpqPfPGbTC0VkSpRKcN9FnuG+yrGJrgHTyrjret5+GUNcKQgX3bCgjlH//1frbmNj1sGuZJD0XP9FKfKrzruZ49bz+dUrfp5y6FRnpuc5/JCnoG4iRCCV6azJC2DsYFEuNhsJM4DWpOg16ue6tSz2mv9qYX0pXjl4RZV2UguzuUYTFqUHBfTEHgSJEq4MA3Ba/M5ri8V126kh9GLwgZoZlvcLnVQswTbWyHAECsG01uGVUWxailrI8bLevf2+KnJmhLeQMLi4SfPsFxa8X+XwELewXFz3LlnuCLXUFDprOhL86YA10/2Vio7CGCxUG5qGz8+kGAhV15Je+0vDON+VtZWP6dqtdvFuSxfvzjP+ECchGXw6kxOjaUgrOwGrNrhrEcSblaCbtVQ2+lntRv9kXK1wdUN9PN+XY2oIdb1dfj12JlOMpcrETMNHE9iCOVQEDMNirbHrsFU3fduFXScwjYj8Al3XMnVpQIGIqwqNjG4EvATNZZVJ4IL/NFjpmApb1NyPSzD4BeOfU9NF9BaEvOJM1Oh3jV4//hAnKtLxZXo5Ah9MZO79g1zeSHPcsGmP2GSsExe8/Xz/hyOZQp29MfJl13G0wmuLxX9L6faxlumYNdQcpUq5R2f/CqvzuQw/epqSq+rYh76ExYxP0GelJJs2Q0l/UzJCV0zs2U3lNjxlO0AACAASURBVG6rF77JmWxohwDCeg0CQmkybhrsGlLBV+MDCWaypXVVmGu2slmvxQc025+1dhPBhO7WUM2s+luth20DfH1ynk89cx7HdVnI2aHwNJyKEbNMHnnbYe45NNrWNttNzDTYv6NfxyncLASqBRFXT6symkokVCwIwaSyazBJzCxVGCo/+q7X8eKVRf7zye/iepKkZZJOWjXdTWtJfyfOTPGm/UP82Us3Kt5/bblUc0EAyNtuGJV7falIoeyyZ0Slt1YRwuq8W4ZSpJMW376eYX/MpOx6YZSt8KXyWqqUbNllz3CS2WyZgu0i/QXBlUrKzpUlCzkbwxCM9FmhCmC0L8Z5/+c9w8lQus2XHXYNrtgbAi+gsqt0XKZQK4Lrl0CdXi5SdDxihkD459ca+2Yk4WYl6F4z1K7VH8+TPPPtG/zq//ctYoZgIGFxdanAv/3iN/nl+2/nnkM71pTkO809h0Z5hMN87huXcbwcZccjbgr2jvTz3jfv6/kFoRn0orDNiKoWAqNpII3Vc5OtlQju8VOT7B1JrZLqmjFU58sOXzk3s+r9iwW7oeQWnJuwDMqux0ymRNJS23Sk2iUE9xMk1ov723jhb+PjplFTlRKMy6HxASb9yOWy56ndh2FQtF0QajKfy9nEfBXabK5MzDRAwmy2zKHxAfJlh7JTmYgvbhqrdwr+8XQyhmmI0GhtR5LqrbfCXDOG214w1Eq5Ymy9ZSjFdKYY2pskUCg7jA0kuDCr0oP81l9/F4GSZj1PkvBf/+D5S7zx1pFN63cj7jk0ui0m/3roRWGb0WzyNVOsqDxMoaTxi3N5Hjz+PB9466FV58RNg7GB+JqG6kzRZnq5SN5WgTRRA+vOdILX5gt1+37u+nLoJQTguC77R1NM+bWUdw0kVJU0V/L++w5y4swUgymL2UwZz68Om07GWC7YxAxRkdQuOi5l1/PtFYTFc6T/P+Gn0BACXL9qWclR55dc1UchJY6EXNkhZhjsHEwwmLKYzpRJJy0SlsGVhQKuBEeoVBTppMVH3/U6PnjiLPmSg+0pdVJ11HQ7aZehtpY65x/dMV5hjF3xtlG+9dHfA/7JG/fwqWfOq91jTOngHU/yT4/uCz1yri0XGExaZEsOC/myKsZkGmSLdlvHRlMfvShsM5pRLaQTFuens5i+KiMoTp+wjJWEalIytVTCNEQY4Tu1WOTwxEBFe1FpNFO0ubpY9G0Yqw2slmnQFzMpOS7B3B8Y6iRULAgQGKFtDk8MIKUkV3aZSCfD+3n93mEePzWJ7WbCbfxIX5yZbAnbk6sil1dSWhQQQNISK6U1/f8FaiXH9XBkZV8AXFcSTHPj/TEyJZcri0VunxjgwTfv57nJec7fWEYIiBv+9YV6/4tXFskUnTWjpttFs2qmaj2840llc/Ekf3t+ll//y+9gmYK+mMnUYp5f+cI316U7j6peri8X2DWYWqVy2T2Y4spCjsWCjUC5fNp+ENfXJ+e3tYTeCClVNuCy61F21L+S4/qv/jHXW/W7+jlynuuFu9h66EVhG7KWaiF0LpCVE3HJ8bi+VCSdtFguOOE50ddqx4SoNHplPh9OpAI1gZqmYDZbwjIFtiv5x983wZ+9dAPhSRKWiiqey5VXLQhR/vxfvTX8OZBaP/LUSzWNkA8ef56FfJnrS0Vfzy/wPI8PfPYF7t4/UuHdZLtuuMswDJC+F8qO/hizWSWZWv7kHRAsCJYhyBSVW6KNx9RigdfvHebh+2+va1B94tkLG4qaXgspZViK0/M9a950YIT/euub8PzJ3pOSq4uFyDnwte/O8blvXObacoHdVRP1Z557DdMQJC2l8klaJlK6fO4bl9ecoL8+OV/zuo3e99437+OjT78EgDDw3ZYFwymrqTY7TTA5RyfkkuNhux4lO5iIXcpOMIFXTtylyOS9ekJ3655XdjwaT+XtQy8KNyFRo2upMjtyJNJXsn80xWy2HKqPdg0kyJUr3xBIox/54jdXSdYSMDxJUXpMpJOhV9Jof4ylvE3RcXHyklTMxHadmn2NtteMS2M0chkJJd/wa3hezV1DdJcx7nsf5couluGobKx+235tH0Cl7hZC7bASloFlCPJlN+xLPYNqruyyf7SvbtR01H1S+mqZ4DVMaxD87k/onqfOWW9QVOBNYxmCwaTFXK7Ep545zyOonUCgzomSjBlcX66vBmzmuvW459AoAwmLQtnB8SQx02C0P05f3Kxo05OyclKtkJRXJmLbrZqQV0nR0Ym89nnVk3SvkrAMEpZBzH+NmwYJyyRuCeJ+udsghujxBtfZ0ouC40nmsiWAMNhKoCQw4fsD+k4gq/4eRSDCY8F7o+8Lr7lGIqmtQtTo+vLVJaVDR92jYSjXTsOvWXBofEWtUS/C99iRCZaLalIPq6OhpDwP+P4Dozz50L1hdO9QKsnYQDK85kymtBIWEXmvQFVkC2gmSjsauWz7toBAhdNKNbOotD85kw2N3bafbqPs68oF4HnKNmEZ8F9OfpdbhlLMZIqk/H5KKcnbLqmYQaZok4xZobG3YDvs6E9wcTbXFa+az33jMpYhQuNvYHsIpPLdgynmcqWKYMSoP77ryUp1hj/Z/s7fXsBxPQwMciUXT0pKjsdv/fWr/Oj87spJuWqidj2JRGD5wWEzmRK+hy8/+lvPUna8hjvLbmII/Ak4mJBXJuqV4/6kba38Hkzgjc5T51ReOzg3Zoqm56eYafTeoiCEuAhkABdwpJRHhRCjwOeBA8BF4CellAuNruN5Kq3vZhJdXNTvdc6rjv6quEbt44YhKhatisUq2mjk+sHiFfSt0aJo+Mf/5d+/lV/702/jyZWxk6hAK9fzkJ6kL242VdEsUOcEi4IM/6fwJBURyrWirOOmYDBlsVRwqN4jRyuyvXJjmaK/RVeG7wTppMXl+ZySmFnZ3ttu1RYIJV0mLIPL8zmKtlshiav3rqhgHnzzPh77i+/guGWG+2Khi+qw308pg/GSSCTDfQlMQ3BpPse/evvtypfdsysMqj9x916+ePYq15aL4cLbH7f4+X90W1MLQj11DCgbSDCpBpOtHZFwQ5VGlX75/EyGuGmQLTp4BPcvmc6U+PAfv8hS0eb68kqErueP0XSmxA9+8lTLcQALeZvf/upkS++J4lRvbetgCEhYZuWk6k+iJdsLd2qpmMn3jA+wZySlJm9TrEy4kYk5FpmUE5a5cl4selwVIeqk8NjoGWgX3dwp/ICUcjby+4eBr0gpPyGE+LD/+6Pd6Vp9gi16+FWo+51YhyTT3PO+YQ7vTPO/HruNz33jMqZRwJQSIQSelFiGYChlsWdY+V2HRsGhFA++eR8Hxvq5OKuidb82OcdvfuW8klKof8d/++oMf/rSdUAVnbFdj6mFAjsHPQxDsH+0n3/2/fv5P//yO1xbVju/hCX4Z/fs50ffsIcLszm+NjkXGmkNoXYBU4tKTbN3pJ+Lczm+PjlP0fEqjNeg0lkkLAPbdyMdG0hydbGx+uPOvUP84g/cFt7/rTv6wZf4bx2Nc3W5iO2n1hjpUx5EwU7qdXsG+Zm/f4Av/N1VpjMFRvsTvP3IBLYnsV3Pj5z1o7Vtl1PnZ/jOjUzF5B1VZ5Rdj9lMmSuLKx5Ks5kyL04tYhlGqFZaL7k6D97XL9aXyUotqFGMiJBiGYK9/gSsJl4zIimvTL5z2RLfupYhV7IZSsW599Aod+waVJNvbEVCjkrVUQm6ukJceE++Wmu4LxYu2FeXCvzEm/Z23V6xFutVybVKVyKa/Z3C0eiiIIT4DnBMSnlNCLEbOCmlvKPRdV7/hrvlF//qVGc7u82JPmhRqbYZ75Jf+vzZULUwmy0xn1+9a0snTDwJo/1xXE8ynSkSLCFCCHYMJJpua2oxx2LeCXdAnqeu8WvvvpN7Do3yS58/y5WFHAt5O3Q5Daa78YEYhlAxDT/+hj0cHO+vMua5FSqMUlTSrmH4WyyUmc2WIbrLWNcnsDlUSMCRCbjsOxcYBqG6Rkp4475h9o6mViTjqDrDXC19J6xKlcY3ryzxX776KjHTaPm56iTRZzagYLvs6E/wH//pXV3rVzO0q++9GtEsgb8UQkjgcSnlcWCnlPIagL8w1FT4CiEeAh4C2LN332b1tydo59Yxei2kZCbnhNvpn2xSaooaIccGEqsWBQPIl5X76UDCJRWzGOmLs1ywUYKm5Ae/dyd52+EvXr6+Minbqz00zt1YxlIiZ4U+WQjJp545T/kvPeZzZdRVVzOTXenbE397odXh6ggCQon2yK70iqRsGWQKDpfm8+Rtl3TcYqlYZiBhYQilnjD8CxRtl3/7w9/L5HSOZ74zzVyuxEQ6yY+/YQ/f/z2jxE11zUaFVYJn4fpygb6YCULw3dks+bK77mfsvtvHiFtGQ/fTWn3opFoEWLfhvBfYrL53a1H4B1LKq/7E/1dCiHPNvtFfQI6D2il0qoO9xka2jq5X6d/8jQvz/N5zFzH87KMLOTVhDqUshBD88d9NMZ0ts3soSSniJlfhIud65Eoq/4uKJparVEj+vA/AjUwZKFd2TMLvP//ahsZFSri2jqyUgY0mFTMpOR4GK2m1JSrQbiZbwhCBwVOG+YwCadnxg7fe9fd2EzMEf/LNq1iGUKoqPxfPz913iHsP7SBuGfwvn32BS/N5ZTvyVVyeJ7l1Rz+ffvCNYd+Cz7ovbjLaH6Noe3gqmzkjffHwvILtsmswhefBUy+qtkf742RLDr/73EUGU7GmJtbATbTd6olmI383Sy0CrGk472U2q+9dWRSklFf912khxBeAe4AbQojdEfXRdDf61kmixsBqr4vavswrE/KfvniNfNnFMARLBaWbLjoev/KFb9KfsBjpixG3jBUjo+uRL7st6X4XCituoX/6zWudGIJVBC5ycdPXFfu6//mcimZNxkwOjvVjGQZnLi2s2gX0xw1G+xP81Ftu5bXZPH/20jU8z/PrOqhzUjFDBavFDHb0J8iVHRbyNiXHo2i7jPbFGO1PhFG0ZUfFHezojzHSlwjbujinbCk7Ix5Y87kST/2PKRUlLWCsP0EqZpGKqUn7z755nftftxOI+AnI6tfKu6rlETScslgsOKTiVqiOyZYcYobgo0+/hADG0wkEYpUHUbOs5YlUTbuk+1bb3QjvffM+PvXMeQq2W6HWeu+be1/rsFl93/RFQQjRDxhSyoz/8w8BHweeBt4HfMJ/faoT7Qe5WKr9kaPudKuk4jpBJ9XGwEbBKSXH3ZAxsBHZkkO2VNvPv1WsiBR7eOdAKBXHfJ1xtU55JlPipaklMiWH4VSMgzv6+dvJWaSnchUNpWIIATOZcsWELoCxgRiWWZlZMpAaR/vj4YM/nSnxjtft5MylSsOnIVR1ONv1uP971cQbNwWf/folHH9BMADbUYZYld5CsFx0EAIsA8quyskkJSwVbVWZzT++kFPuo+mkijlw/RxLMT+/0XLRZrFghy69hlCpsE0jxWAyhmUIZrLFsFhR0fW4ZTjJXCT2Y8dAgpLrccvwirQ3ky3647ai8hlPJ/FkkVuGU0wt5EPDNmLF+WF6ucTuYUE6sdL2xGCyIn4h+hnIqsVpOqPajXq59RsW05kio/1xojx7fpb/9Nev+ob2OIuFMv/pr1/l0fgdvOW2Mf+yNR54ufrXG5kig0mr4n5TcZMbmUJY7yK6bir7jaw4Xnlf9b9ozURV9yqb1fdu7BR2Al/wHwAL+L+llF8SQnwD+CMhxM8Cl4CfWOtC05kSn/zyK2rStWtI4VVBKcGxTk3OGyVmiojhrtIP+dJ8Hsf1sExBoeyG+XkMAYPJGK4n6U9Y/OSb9xE3DT7/jctMLapCLoE+WXoSYagEcCN9KiDoykJepZyQahLfN9K3YcNbtUHs8kIe0wDXU4uO4atjsiWXsYHKSNVQaoybCAR9cYOi7fD/nLlC3BQV9+N5KtDurr0j7BpKIhC8fC3D3pEUN5ZU+vCgrcAovVCwiZlGmGrbEN7KccMIzzeEhzAE87kyw77KJmaqJHmBmmk+V0YIQcqfuIJYhuA9+bLL/tF+Un6sxa2j/UxninzPRDocq8BjKRlRCez3z6uIiLZdbt85GCbNe/D482FivYRlhqqtuWyZodRK2wOJ5r/it+6o0W7Z4dYd/eEYBPzh1y6RjBnhuTHTIF92ePIbl3n3G/c03SbAgbDdlTHIlx0O7BhoS/K+ikVRqvZ+wpeuZcRRIHALDhadwP02fC+VC6lktUuz+pP03Zujf1s5Fv69Rv/WYjOS8W36oiClnARWzTZSyjng7a1cayFf5k/Otl/NUR0oUvP3yOSdsCrd4ypd5AxitYJOIp4cgRtePTc6qNS7Fu0Clq8UnxhM0B+3kEgyRYd333ULAJ957mIkj8+KzGZ4MBA3kCi3wtH+ODd8N9CRvjgF28XxJG/cN8Qvff5sXdVAI9VBsM0tOi5Jy9fZi5VFLJCqbddjIGExky3yxTNX+N3/fpFMycUQMBA3cX3pPm4a/iSX4tpSSdVWEIAAx4OfP/Y94eR0danAcCqG7cnQZ9wQgCdDA3XZ8fy/wVh/nNlsGQ8V/Sw8tbsY64+zUFBR11JKCrZLOmkhIYzdCBLljaeViunqYhH8KlxB4r61qvCtlbwv8OxayNssFeyKhIVB1PTYQIKrSwWEVDrm8zcy2J5K033y3HTTRWkaJdCrTop3fjpTkToc1p+Wu9MV1qI7kNX29t4JSJWRRQlqLxrVi0/F+VULTtR9XvqCn/S9/hqxpYvs7DjwvfJHP/aZVRN1ZTSgWTEBRyfsWlGCrUQGbjbBRPzytaVwMur3J8Nq6f6XPn+Wl68uhiUsoxwa6+ehf3hoxeMkboU++LsGU7xx3xBf+taN0E215KgkWr/8Q7dz3+Fxnnt1jl//y++ERV6KtovtST72rtdx7MgEpiH4m1dmwkRsSwWbvrhJpuhUSO+WoQrilB2Pq0vFVQuY6atqXN/Iu3MwQTJmMpMphdldD471V+RGCiKRr0d2Co6n+h/UTwA1FYwPxEnFrZXdEiseQXuGU5Qcl3zZZSgVC5PJARX31Z8ww+jsTNHm+lIRCWGepeoJOZhcr/gqoJlsiaFUbFWxnKCd8zeWyZRcRvtj7OhfKcTTFzMqUnAvF2yuLRUouyoD6c50Ass0miraU69/0XuuLupzZaHAaH8svHfYWAGfWu12qjqhBoQQdV1St/Si0MtxChs1wjV6f6PYAlAqmItzWRYLq+0MAjg41scfvP9eTCF8/3Qj/Pm/n59V6Z3LLgnLYDydZDAVYyZTJF92GUyp1NR9cZPxdOWEEDMEI/2JVRWzgpxFZcdlLldWUcC++iuQYoLdg1fl75+wDKSEgYTKHbR3JNWw2lh1W6BcWE1f7TOcilXUdWikSkxYqtpckI213n1FJ8vlgs2O/viq6m37qhaVaIW5YGJdLtjcyKja1cGi8tiXznFhNocrV1Jtm4bKZZMruy1N1MHE+8qN5bCW9uGJ9JoTcK0EfzOZIgt5e83PQ9Ob6EVhk9lIQFiz74/6lu8aSvHP79mPYcB//KvzWP5E8Z3rmYoJNm7A7uEUnoS/efRtq9oNJrmpxbyKCZACDxlOpJ6UfO+uQb59fRlDCG4ZSoW1EpYLZa4sFjiwo7/mJBFMSC9NLZAtqe2LZKXucj2SliphOZCwuL5c5PBEek1pMiw1emOZsivJlpRaIqjtcH2pwGy20vBdi91DiXDnUkuaj95XteTvuF5YB2LPcBLLNMIyp8G1zl3PIIA9IymkVKovpelSbqpLBZv5XDm0wwQ66d1DCTwJv/aeOyuk60ClE93pSqlSwfzae+5ctVgiYSwdJ2aaDSfz+x57RlXzq7ru9aUCh3cOaul+C9JoUdjSCfF6lY262H3uG5d9CVB9PP0JVU3sxJkrvPP1uzENwY/dvYf/6eheX8JXX9YHjz9fYfzri5uhTj5IbFcvqR2sJJxLWqaqe+ynCZ3LlcP0yUKo17Kr8scEi8KNTImYYdRNVhf8q1Dv+LWVC3b9/B6mIUgnVbW1wxPpplQT1anDqyXdfNnFMkVYJKYeYwNJzt/IgCD0IKp3X0E7ZdcLk+gFJTmDim1TC4WKa0UrzAEqs6uAhKnGccpPxSGC/4RKtX1jucQb94+seZ+wUmkt+GznsiqDbKDCWy447BqyVlXUi1KvgtvhiOFbs33Qi0IHqBd5eGO5QCJmKslPqOI1gdrG9I8FroQjfXGEECwX7DB51/WlIn/32kLdL291tTQDJXVGjaWNDHiB8XI8neDqYhEPCUJNnKZcMaiOpxNMLRQoOV7FdfcOr214DPqYL7u+J5Ey7NaKpjAFvl5/tdG2Hp/+8is88ewFcmWX/rjJ++87uMqQGRiIDT/fUz1U5LW3ysZUz6AaNf4GNg/ESt3m6msFBuKi46pIZQApwnEOFq2y6yHdFSM9gprG3yA1eS2DbVDxLW+rezel8DOXwrXFQsPEkp0yBNeq6KZ3Gt3H6HYHtjJCCOVZFDPpi1sMJC2GUjH2j/ThuCoXfJC2wJNwYGyAPcMpdg4mGU8nGO2PM9QXI52M0Re3SMZMLNNg/2h/qJ++ulTAcVW0sEAZ/E6eqx3XNxA3mVpUBlbTd8+RHiRMk6WCzUQ62VBNELijppMxbhlOhgVmTEMwlo6H/vrpZIyxtHJpDa57+8QAlln5ONWqB5xOWEqt4k9wQXrtKIaAoYTKt2Maxpr9Dvj0l1/hU8+8SsF2sQzV/qeeeZUXryzy8Xd/HxPpZGj0HkvHSViNH/9AnVPtFVavznEwfqDSJwfqnqBus2VUepgNpmLs6I/TH1fpKwwhuGU4GY5z4FYSVMjzpFK17fYXjY89/TLTmWJYW+LEmSkeuHtPeJ/BuAFkiqoEqOHbcYJobEOomtGZolP3uTp2ZKJi/Jr9PBoRqCqj/W/0bGs2D71TqIFlGCsGWL8cZfDPMqISfm0vpV/4gdv42NMvU3TcdUlWgWSmksfhz57KU8c0RN2tvvB9712xYsgVwK07+io8dNZqN192GEhYqqqYK3ng7j2hBOq4HjcyJWxXcvvEAI++40iF0XUtaTKwYZlC4ESkdFOs2BgQgpInGUhY/MYDdzW0G0SlzCeevYAh1OcGvjuu5/HEsxf49HtVGgkJ3DKksqTabv1obyv4bIUIA8Xq3VfUgLtcdBAoL6rg6kGd5kTMCP35g2s5nmTPcIqZbIlM0aFouwwkLGazJYJgdFfK0CvO9STpVLxubYnnJudDlU7QrzOXFvA8Dw+xalcWxHyM9MUaqpDWqubXKo1qYwR/3wo7iO2429n2i4IQagI3Tf/Vn9QN3xslOCbEakluvTRbG3et93/gsy+oGgC+10k6GUNKWdcXfDpTVCUMg2+9VCUNZzLN5QZq1O/X7x3mE3/+bS7OFYgZBnuHk5Rdr6LyWTP3HK36Jn31E6jJKRUzKAfF3mX9ihT1KrBlSw4xs/JdhlAR39HzZ7MlsmW37vWDqO6YIejzF6Z69xXty0DCYiFnrzZg+6tzzDT46Xtv5bnJea4s5OmPmwiUemjXYJKYWWI+Z5Mr2ZR9dZHhx2KUXUnSEuwZTpItOWEEeZSoWivaL9cvDCQ9iWUaOJHUJwlrpS7FemIM1ku96nTnpzNrVtfrFZqpBLgV2dKLghAolcsqab5S0u8GG5Wsjh2Z4O79I3UNh7WwXWW4jcdW1CKO51FuoUpVvX4fOzLB46cmORDxjQfqGl3rEa36Fr3GTKbEeDpR99pR6kmZqiaEmkgDVOS3qDg/U3QwDSV1J0wVxVx0XJAqcNEyBIfGB0KjfKP7ivZlciYbRj3brkfcMMIaAsH1opJ8NCoZlGG7L24xkymxdyQRxlokY0r/bxqqGl7gKNDo2Yj2K+E7DsT8na5VxwGhHdHDzVLPeF12PIZSjavr9QrNVALcimxpm0LMNLhlOMXEYJIdAwmG+5TeOxU3SVhm1xaEdvGBtx4Kq59JKZnNFrmyUOCVG8s8ePz5VfrXuGVAGFqvKmgFE107uLyQr8jQCK1HsX7grYdYKticn87wrWvLvHx1icmZnFKlVKlzGhl0a/WjL6YWBVV0xsPx/NKOnuS1uRyTM1kyRVsZ4UWwYKj3W2IlCjQwbi8XbBZyJe577JmK8T55bpoHjz/PfY89w5lLC2G/VQoVv5BOYCCWMjQ0B/cTvP/rF+e5vlRkOWLkDWo5By60HipFByiHgaWCzWK+zPnpDFcWCsxkiqrcZ5UxPjpG4+lEGO1adj3SSQtPwmDKauq56gTVz3bQ/yDuIsp6I6U3SvRzrjUulxdU6pnJmSznri+rsq2u15W+tpMtvShsd6IGvuvLReZzNiN9MXYPpWoa5g5PpBlLx7F8KdjyDcSHI7l2NkLUkBrQaOdSDwF+9THf2GkAUjK1WDlBNmPQjZ57554RHnnbbaRiJo7n68t9Q7brKU+mq4tFzMiOIjBrGIZBwlR2ItNQke4SZYSNqgY+/eVXKgykAsJ+G0Jg+4F5oBaZcmj0V33sj5vh+xOmoOyqyl/BfQfnFGwVKHjLUMp3n1UG66i6abQ/xkLe5vpSYZXxNzpGgeNAYMw+ODbAI2+7jQM7Bpp6rjpBPeP17TsH2/KMbZRmDOGB00TgjOF46hluJd9UL7K1e38TUO3f32irGhiKdw1ZHckhU8s1calgEzeNitw99VI7BFG8gVcTqAXC9dTELZFcWyqQTloN+97IRfLYkQkevv92Tp6b5uf+4DQR8wqOB6bwkAI8VNnRpYKDVJoj4qYgHbEhBDEH0fF+4tkLoZpruWCrFBye5LX5FemwWllXdDxemloClNSbiAlVctOVYW3pS/N5EjGDgYTF++87GBr200kLy1QG/35f7VOtbqqVWqJ6jIq2G7rEnrm0wGK+zKPvOMLjpybXfK46RT21XCfzIDVLM6ohGV39I69bOSAY9E5hy9CM6qYTqrACJQAAIABJREFUroNRqq8f810ly65XV5qqlrhyJYf5/Eq66ej3SaWyljUl30b9qHXuY186hx248ka0iK5Uu4JH3nZbRV0EU7ASK0D98Q5UO8sFm6nFQkUVuIBaX6ogiV/edlnIO2Fhn4r5xB+T1+8drnl/GT8yu7pPtdQVFbvMpQKz2VKYTkRKyfnpLB86cZZXbiz3jLqmut+deIabpZnvW+A0YZkCV0osUzkC5MqbVGy9Q+idwhahnmGuelvdbtfBaqojeKOG0lrSVLXEFZ1Cq6dTUxhYMZqKlF3rPidncxW/i4iq6O79Izx8/+08NznPwbHahvN64x2odmazJVVfocb1ESCqcjgFMRkBQdBcsDAaAg7vTIftP/nQvavub9+p5p6B6jF68Pjz/N3lBaS3kvZbSBWbELdUtHyz19wMOv0MN0Mz37d6ThP1MgZsFfSi0EM08nler+qmk9RyK3RcjzOXFrjvsWcYiJt815+c46ZyfWxE2fUYS8XqSqnR8amVbC6Il3jsS+fCinMy/N8KQTTwmUsLuJ5HwjJDl99AGvy199zJh06cZWqhgON5WIZBOrmi2ik5npL+/WtahoGUssKmEBDEmlQuClXn+NuZRlL6eiOLLy/kcb0V24ZqT31WA5YVGnzrpenu9gTdbpqJLWhmrDud8rtbaPVRj7CWYWs9qptOU23wzRRtphaLCKHUMa/O5LBdqarduZKrSwViQYxIDccwU8BC3qE/bq76W3R8gmufn85iCiqMwB86cZbz09m6fd7Rp+Sgjz39sl/fQdk3ri4WyRTtCmlQgpL6/TgDyYpqJywI48cfBGlK4qYIvd6CKPTgYkEm2FrEjBVjdCPJfz2qlX0jfZh+Qr2wO1ItZIcn0hVqpoW8zWh/jF2DyW0ZZdxsJHUzY90rqq5207UsqUIIEzgNTEkpf0QIcRD4HDAKnAF+SkpZbnSNo0ePytOnT3e+s5tArWRmjfLTt3p+J6hOHf3qdDaM0J3NlnD84vWup9I0B8+aK1Utg6BOMigjbxCxe3hiYFUEdvR+leufXBUDMJMpUfYl+OA1igHcsSvNcF+c6UwxXKgMBBIV4zExqL7Y1QZYWJ2G+kMnzrKQt8OJ3pMw3Bfjp++9ld9//jUW8zYgw8hk0w8s9PAD5FDeTaAy2O7b0d+R9NMnz03zwRNnWazq60hfjF+PRIz3wjPVaW6Ge2yGRllSu7lTeAT4duT3x4BPSikPAwvAz3alV12i1RiAdsQMbJRqSUmi0kQPpmJhIXvLXEkP4klV9emRt93GwbEBHE+SMAVJPzeU7aoU4d++nuEdn/xqhfQWvd/g2iKSbC4wAisPG/WeqFAugH2jKbIlJ7xW1OXTL0wVTshrje+xIxP81L23EjdVFLZyXbUY64/zRy9cYaw/zq7BBKZhqMjouMlIKkbMMhhMGCqewbdJWAa4iA1Jmo186o8dmeA3HriLXYMJbE9VhoubBj91760VbbXzmVrLx79b9ML3ptfpyqIghNgLvAt4wv9dAG8DTvinfAb4sW70rVu0GgPQrpiBjXLsyARPPnQvf/Po27h7/0iYFC+aEC5hqcjZW3f0h0beJx+6l3sOjLJ3tI9dQ8owF+jZBUo99METZ8PJZK1kc4ERWOn2Kz2OhFBpxC3TYO9IX8W1BlMxDo0PsH+0j7v9dNTV7QVEx/fkuWlOnJli93CSO28ZZNdggoWCw2LBDsuBGobB4//iTZz/Dz/Mtz7+Dk5/9Ic4uKOPvC2JGQZJv/IfCA6P99c0LjdDsyoRwzA4NNbPnbcMsns4yYkzUxXntOuZ6uVkd73yvellumVo/k3g3wBBVNUOYFFKGZQKuwK0Vv17C1HL0NWq0arV89uduGutexgbiHNloYArVxLCpZMWH33X61bdw/RyMYxbAMLU4tnSiidT9bWnFosgYddgIoyGff99B/mD519jIW+rADn/ekJC3BK8Npfj0nw+DGgz/Cq3gRG5Vt/qjW+1V9VywcEQKoXGeDpZ199fRLYxXsQwPTmb452/eWqV4byZz/AjX3iRq8ulMCBvR3+cwVSsoRdYrf695dAo//nkd3E8j4RpMNQXI2aaNZP/1apCV11RbiilFnvHlUxninzgsy/ULVPazPPVDpXaZhmHt3KivE3fKQghfgSYllK+ED1c49Saxg4hxENCiNNCiNMzMzMd6WMnqSdFAS0ZrVoxcrVbcmvmHnIlByGUrcAwVgy1te4hOG74Segs00AIVU8gqq4Jru1JuG28n8MTA3iS8N4fvv92fv2Buzjsp/GOGSrJXn9C1YcO/fRRdg7b83cnDfpWb3yr1RBB6oxyJFVHLbVEpuSwZzjpOwkov1XD/7nacN4o3iM4519/7gxXlkrhLsuTMJMtq0p4kbbXUpsEO5+RvphfREkyn7N54O49q5L/VfehOso7X3aZzZTJFO0w/buKYPeaevY6udPYDONwL++UmqEbO4V/ALxbCPHDQBIYRO0choUQlr9b2AtcrfVmKeVx4DgoQ/PmdLl9NJLYWlUfNOvP3e7EXc3cQz2DXnWbQeK/v7u04PvrK/lASlVHILqtb+Z+a51T7afvOCsZUlMxMzRU1+pbo9oT0ftTtgUvVGdBbbVE8D7TECQsA0MIirYb1m0IqrStFe8RjPnTL14HVtxeg7Gby9l8/8HBuv2t7l9w/aFUknF//x4k8HvYP79eH6JR3rB2Rbm1nr1OJ5rrdBzEVk+Ut+k7BSnlr0gp90opDwDvBZ6RUv5z4K+BB/zT3gc8tdl92wy6Yehqd5uNrhcYGL92YY7JmRzfurYcJqKr1ebJc9Ms5suUXY+y41F2XPXP/30xX65IRPeOT36VOz7y59zxkT/nnb95qinpK/DT9/xkd54fWCZRKSjO38jw3Zkcz03OVRi4GxlLqxO6DaYsHFclwzt3fZnz0xmWCvYqtcRbDo1yZaFArqzusWS7YV9Kjkeu7NZMrFZvzF1PhpHRgZ0F1I6h2qe+VgK6txwaDZPzXVsskClWJudrpg9BlHdAX9zEcSW5skveN/47rkpOeO76MteXipy/sdzw89rKxuCt3v9eilN4FPglIcSrKBvD73S5Px2hG4audrdZ73pBsreLc1k/K6dKfFdyPK4uFpnLlSraDLbZZddj30hK5f73q4vFTMG+kVRYs+HTX36FD544y6szOaSUFaka1loY9o30he6f1R7Yricp+j6jUQN3tUpkrbiRoWSMwZSqoCb9m6/WiQYqmtH+WN2qc6AWh6nFYkW8Rr0xj9pOGlFLbRIUT5rOFElaBnYkXiO4fnUEb73PPTi+XLBZLNhh6VCJ+jyDBcsUKglgpuTW/dy2ujF4q/e/a3EK7WArxilU+/YHhq5OBr20u8161wsStl1fKlJy3NA/X6BcUw0hePxfvKmhX/z5GxkQsDOdZDZbougX4gk8igy/BCooQ60A3ugbL4PqZ7ar4iIOT6RDaflnPvONVVHE1cR8A7cwlDqoVn2HZuNGMkWb60tFJHBwRx9CCCZncwj/3oSA1+byNQ1nKvhPVMRr1BvzfNlhNrs6nMcy1PuH++J1jZ3RPge6/2AchvpizOdsBhImt+8cDMfxQyfOkik6FVHeP3XvrZw4M0XMFFxfKiqXYVRpUYCLc3kEkIiteI3tGIhxYMdAzbHsxneknWyF/vdqnMJNSTeiINvdZr3rBQnbyq4XGnqDmsBx0yCdMNf0i3c8pTa6ulSg5Hhhem0Jfq0EZSQGP1WD54XVui7MZlkuOioFSN7m4lyWjz39Mi9eWVy1Q4hSy8BdrRKB5uNGMkWbq4vFsLZCEH3tuB6epwLmpFT2jepYCgAkYYW1tcY8GTNX7UiC0qavTGcbGjujfQ5iNuKmQdHxaqbTfvHKYsMo74l0kqLjETNWak2nkzGCYnhBOvdbhpPs6E/UHcutHim81fuvcx91gW4k/Gp3m7WuFyRsi5sGjl/60fBU9shdQ8lVicJqGT8tQxkpDQS29MIJLzqnO56HaZhhqoagWtdc1sFAeTt5UrJccNg1ZPHEsxeUlBpJCOdJSdlRgW4x01hl4E6ZrSWKi97LTKak4iSkUqCY/gRquyp4T0iYzZZI+gZZ11NxC0G/raoKa2uN+WymVGGk9zyJ7XnELaOhsbN6/AdTMSxTrKqCV21Q3j2UCttvxsEgqEYXreuxVqW3XkiKtxG2cv/1TkHTNoKqarbrUXI8iraL7alKX7V8wWsZP9PJIJtqpf4/+qB6Ely/qlo6aYXb9CDSGVainQND6M70ShWzwCYhBKrQjeNRsF3VX9cLaxrUMsw2ihsJzi85LlJKPPxFQKyovlxPUnKVQdl2vf+/vXOPkeusDvjvzGN31vv0Y+0YbyB2MRCEkmCs1FHDQ2nUQtSWPkxFWkHagqAPSt8iLVVKUf8gTWlVqhaSAiKtKEnqtiJCooICrqmUB46TmASb2CzBWcf2ru19ep8zc/rH/e7d6/Hc3bs7M/fOeM5PWnn23jsz5zv38577nfOdcyiWlP6uHGW83tTlshe0jrt3/oNv2UVvIUfJbfkslcuUnLttW+/lBQgrVzpr7X4WZ/UUdU97OnOxdWmkixkFo654Rd8kcBkADHTlqy6fqy2z79t/I6/d1hs89YL3pJnPep3R8hncH1nPZ37f/huDbl1+pjMsZzsHmc7ZzHIXM1UyGeEVfZ30FPLknbAKZLPCe/e9ig/f/pp1541k3VP/K/q7KOSW/ei5UDU8X099XTm29RboL3iNkfo3eL72uO6Gt71ua5Cb4Rkg4dWD3bx2W0+QXe5TudKJcnNEdT8LB5TX8pn37b+Rv9l/Y8u6U9qNtnQftXK2YT1o1PjvPzRMX1eeayrcCxu7O1f8Y1rt3D2PPs9SyUuCUpd5vLm7g45ctuoflHsefZ7eQo4Llxa9nsYKfd35INPZD4Tu3NLN+ZkFzs8scHrSc7sUchmu29xFbyF/2d78oyMTPP/yJJcWvTLlR0cmgnFW050/Fj/QmMvKZdnXWbdiyGc9g9HXlQ/0899/8NZgLP79+fMvPxfr/lTq0C8f/uKFS+SzwrbeTnLZTNWn85X0PzY9z/S81xAomxHueMM2njo1uWo2cNRnttP/sVam7XYftcLOgEbSyPHfeu83vb7Foad8VWVybolvf+S2Nct5/6FhToxOs1gs05EVdrtdMFFZ2/cfGubEuSmv4Fto91G4DMOJc1NMzC2hbuurTy4jDG3soqczx+TcEu960xB//82TQZlvz2Xl7bDa2ldYVXf+942Mz9Ltej+8MDpDIef1lehzfSgq9VPr/Qm/v1gqc25qgaVymd2DPdz9jutj3+NP/c8LVUte7N+zg8eGLzIyPstQGz5QXS2stPuo7VYKrZ5tWCuNHH/c7nBxWGugbrXr/fPh7GYtl4O2oKWyMja9EGRRf/b/fkhGvEA2eIZhqVTi0mIplu6iMqtX00+t96fy/X1dHauu1qrx2PBFhjZ2XbEl97Hhi21VYrodaTujUK1bWCtlG9ZKvcdf2Q1tam4p+Mw0OlH5rhO/HefOzRu4+x3XA94fzCdfvEi5rOQyXi5AWTXY2TS/VGJkfI6J2UWm5ovkq0TcKnMd1qK7D75lV9VubuFCfLXen3rd35fGZ8kKDI/NsFAsB+1DR8bnOHh8tC0eoNqVtgs0t3q2Ya3Uc/yVhb+WyhrkJKQRUPQb35wYnQl2GJ0cu8TvfukIf3LgWUan5+l0vROWXGJdPiPBjqUyBHvzM+JdU6qwApWd09aqu2r7/MPUen/qdX97O3OcnpgPtsyqegZRVVuquJuxdtrOKERtw2uX7XH1HH/YVSHi/dvflWdgQwff/sht6+4PsF7uPzTM9HyRbEbIZjLejwiXFktMzxfZ0JFja18h2AVULGuQPewHZAd7C4gIm7s7AG9ba1nLFMteFdTujuy6dXf/oWH6u/Ls3trL667pY/fWXvpdiWufWu9Pve6vH2ssljSozQSeqy2flctkNq4u2s599LbXbeXjEAQB2y1Y5o//E189FvQy3rWl+4rr4uxQajZX3Evjs55bJrQVU8TPhPaWBr2FPEMb4czEHAsumeya3g7OTi1w4dIi0/NFtvR0uh1UyvlLSxTLnjF4/607uWFoINbcqaa/Sn1NzS1xfmaBFy/McucDjwefVcv8rNf8nlkssWOgwKmLXumLjOu7XSb5e9zuuwV9ktJD2xkFaO1sw3oxu1RmaGNX4Pu/59Hn+ThctqUyn5XLSiT4533qGViuB9dudNm9oc5r6hrP+AFj8AxDdpPX/tJvuuK3C/X7NoMXpH311r4rAqurzZ0o/fW4ff6VtYY6s3KFjmuZn/WY38v3Nkux7PWvLrvs9CTvcdy5eLWTpB7azn1kVHf7hF0Cq533qXRVjE3PMzI+x4nR6UT78volrl84N0VJ1ZVpXs7u7e7I0ltYzqg9PzPPqYuzfOfFC/z6g9/h7OQc/V15ygqL5TJLJeWl8dmqpa/jEKU/EQkVsfN6DQjC1r5CpI7XMv569kP2721fV45y2WVbo5HZ6Y0i7ly82klSD2YU2pDV6r3HrQcfzl49OznH+OwSm7rzXNNXSKzbVDjYvb2/i83dHWQy4lYLXnbvP9y5h/tcRu3ZqXnOzyxSKqkrc+11PRubWQhKXgPBVtX1EKW/mYViZOE4/5q1umUa1eXLv7fXbe6hf0Pey7Yu5Ni5JX62dT1o9d4E9SJJPbSl+6jdWc3tsxa3UHj/f/g9SeV/VO7LH+wt0N2Zq1riOshTODVOJueVyc6UvaY7vhEo5LOBm6Syz3FcVtJflL7C19Qy/nrqvRncrM3mokyLJPVgK4U604ilfL1ZbYfKenawxOkBXG+9HDw+ypFT4/zowqWgu1vl91aTs1heLpyXDWdf41UYLaNs6emM/JyosfjHT4xOMzI+x9j0fKT+6rVL6KXxWYqlMsNjMxw/O1W1a9tKNPt8bffdgj5J6sGMQh1plYbdq9V7X089+JX2xzdCL/5n+tVHi6GuYauVuM5llgvn5bIZciE/US5Ul6ja58RpXn9NX4FN3XnGZ5c4OzlXVX/1qrnf05Hl9MQ8xZJXortY0iu6tq2mw2aer63em6BeJKmHxN1HIlIADgGd7vsPqOpfiMhO4CFgE3AEeI+qXtlSqolppRIa1VwD693ydvD4KOOXFrwCbJkM2/ouL8DWCL3cf2iYpVIJLSuLJUVQshk4OznP1r5C8ARVOaZbdm3i5Og047NLqDjLIEJvR4ZCPktfl+c/j3oSi9u8fkuPFzyO6tQGtbtnDh4f5dT4nNd4SJScQCaT8VqByuoRkVaZr83gxmoGktJDGiuFBeA2Vb0RuAl4u4jsA+4F/k5VdwPjwPtSkK0mWjkott6nRv99S2VlaKALBEYmvEY7/pNMI/RyYnSa89OLIF45bQSKZSjpcvG4amM6cOQ079n3qitKTYeD0Ss9icVtXl+PMa6EP7aFYskbv7osbdUrurZF0crz1Wgcia8U1EuVnHG/5t2PArcBv+KOPwh8DPh00vLVQisHxdb71BhVgG1gQ0dkhy+oXS+LxTI411EmmyWHl6DWlV9u+Rk1pseGLwa9jytZ7UksaizdoRyEeo1xJfyxFXJeHkEhu5xHUK1r21rG0grz1WgcqcQURCQrIs8Ao8DXgR8AE6rqP96MADsi3vsBETksIofHxsaSETgmrRwUW+tTox+gfPLFi5ydnA8K4VV7X5Rebtm1ad1BTr8xjt9JrexqFKlq8JlHTo1TLJVjjykOUWN5/607mZpb4sS5aY6dmeTEuWmm1pnnEAf/fg32drq6RAqiLBTLa+ratlTy8kuGx2Y4dmaKkfE5btm1qSEyG61BKkZBVUuqehMwBNwMXF/tsoj3PqCqe1V17+DgYCPFXDOtHBRbSyG1sFumMysslsq8PDkXGIY43bj279nBgSOn1x3kfM22PjZ3dwSd1HJZoaczy2JJg88UgdMu+LzamOISdY9vGBpYtdhdPfHvV28hzysGvHpOxbKyoaN6E6Kosezfs4Px2SXmiyU6ssKm7jwHjpxuqmCzkSyp5imo6oSIHAT2AQMiknOrhSHg5TRlWy+tGhTzyz2s1lULLnfLbO0r8PLEPIpyfmaBXFYuWwWEg9bhgOudDzxeU5DTl/ea/lwg78j4HBs35IPP3NZb4PTEHGcn5+npzNWtlHdUr4T+rnzVpvb1mg9RZcp7OnNkM7KuZklRfROaLdhsJEfiKwURGRSRAfe6C7gdOAZ8C9jvLrsL+HLSsrUza1nlhF1N/pNqPiPMF8uxVwG1BjmrydvTmWVLz3Kz+r6uPDsGCig0fOXW6KBto8qUW7DZqCSNlcJ24EERyeIZpUdU9Ssi8j3gIRH5K+Bp4HMpyNbWxF3lVAYoewt5shkJtl/GWQXUI8hZKW+1LOFcNsOeV25seLewRgdtqwXNAQY2dEQGzeNgwWajksRXCqp6VFXfqKo3qOobVPXj7viwqt6sqq9W1Xep6kLSshnxWC2gHufpsxFB+TQD/Y3+7kY90bfy5gijMVhGs7FmVnM1xQlaNyIon2agv9Hf3aiOga28OcJoDOJ3WGpF9u7dq4cPH05bDKOCcO33cNDa/tisH9OpUU9E5ClV3VvtnK0UjLpjT5/1x3RqJIWtFAzDMNqMlVYK1k/BMFLE+g8bzYa5jwwjJVqhdLXRfphRMIyUsP7DRjNiRsEwUsKyiY1mxIyCYaREo3IPDKMWzCikQLP3xTWSwbKJjWbEjELCWHDR8LHcA6MZsS2pCdMqfXGNZGjVUuvG1YsZhYR5aXyWga78ZcdaKbho++oN4+rG3EcJ08rBRXN9GcbVjxmFhGnl4KLtqzeMqx8zCgnTysFF21dvGFc/FlNIgVYNLlqXLsO4+kmjR/O1IvItETkmIs+LyO+545tE5OsicsL9uzFp2YyVaWXXl2EY8UjDfVQE/khVrwf2Ab8jIq8H7ga+oaq7gW+4340mopVdX4ZhxCNx95GqngHOuNfTInIM2AG8E3ibu+xB4CDwkaTlM1amVV1fhmHEI9VAs4hcB7wReALY5gyGbziq/uURkQ+IyGEROTw2NpaUqIZhGG1BakZBRHqA/wB+X1Wn4r5PVR9Q1b2qundwcLBxAhqGYbQhqRgFEcnjGYQvqup/usPnRGS7O78dsIwowzCMhElj95EAnwOOqerfhk49CtzlXt8FfDlp2QzDMNqdNPIUfgJ4D/BdEXnGHfsz4BPAIyLyPuAU8K4UZDMMw2hrRFXTlmHdiMgY8KM6fuQW4HwdP68eNKNM0JxymUzxMJni04xy1UOmV6lq1aBsSxuFeiMih1V1b9pyhGlGmaA55TKZ4mEyxacZ5Wq0TFb7yDAMwwgwo2AYhmEEmFG4nAfSFqAKzSgTNKdcJlM8TKb4NKNcDZXJYgqGYRhGgK0UDMMwjAAzCoZhGEZAWxkFEfm8iIyKyHOhY1X7OIjHp0TkpIgcFZE9Ccp0n4gcd9/7XyIy4I5fJyJzIvKM+/lMgjJ9TEROh777jtC5P3V6+r6I/HSCMj0ckudFPxkyQT2tqTdIEnNqBZnSnlNRcqU2r1aQKbV5JSIFEXlSRJ51Mv2lO75TRJ5wc+phEelwxzvd7yfd+etqFkJV2+YHeAuwB3gudOyvgbvd67uBe93rO4CvAoLX9+GJBGX6KSDnXt8bkum68HUJ6+ljwB9Xufb1wLNAJ7AT+AGQTUKmivOfBO5JWE/bgT3udS/wgtNHanNqBZnSnlNRcqU2r6JkSnNeubnR417n8SpI7wMeAd7tjn8G+C33+reBz7jX7wYerlWGtlopqOoh4GLF4Xfi9W/A/fvzoeP/oh6PAwPiCvY1WiZV/ZqqFt2vjwND9f7etcq0Au8EHlLVBVX9IXASuDlJmUREgF8GvlTv711FpjOqesS9ngbCvUFSmVNRMjXBnIrSVRQNn1eryZTGvHJzY8b9mnc/CtwGHHDHK+eUP9cOAD/p5F43bWUUIojq47ADeCl03QgrT+JG8Rt4T5c+O0XkaRH5XxF5c8KyfMi5Hz4vy+1Sm0FPbwbOqeqJ0LFE9STxeoMkqqsKmcKkOqeqyJX6vIrQVSrzSkSyzmU1Cnwdb5U0ETLqYV0EenLnJ4HNtXy/GYVoqlnbRPfvishH8dqXftEdOgO8UlXfCPwh8G8i0peQOJ8Gfgy4ycnxSV/MKtcmvc/5Ti5/mktUTxK/N0hiuoqSKe05VUWu1OfVCvcvlXmlqiVVvQlvNXczcH21y3zxVzi3LswoRPdxGAGuDV03BLyclFAichfwM8CvqnMYuqX0Bff6KbwniNckIY+qnnOTtQz8M8tL+bT1lAN+EXg4JGtiepK19QZJRFcRMqU+p6rJlfa8WkFXqc4r9x0TeG2J9+G5Gv2q1mFdBHpy5/uJ7/qtihmF6D4OjwLvFY99wKTvEmg0IvJ2vP7UP6eqs6HjgyKSda93AbuB4YRkCvu+fwHwdwE9Crzb7YLY6WR6MgmZHLcDx1V1xD+QlJ6c73YtvUEaPqeiZEp7Tq0gV2rzaoX7BynNK/cd/s6wLifHMeBbwH53WeWc8ufafuCbvsFfN7VGqlvpB28peAZYwrOw78Pzv30DOOH+3aTLuwD+Ee9p4LvA3gRlOonnJ3zG/fi7C34JeB5vV8YR4GcTlOlfnR6Ouom4PXT9R52evg+8IymZ3PEvAL9ZcW1SeroVb6l+NHSv7khzTq0gU9pzKkqu1OZVlExpzivgBuBpJ9NzLO982oVnFE8C/w50uuMF9/tJd35XrTJYmQvDMAwjwNxHhmEYRoAZBcMwDCPAjIJhGIYRYEbBMAzDCDCjYBiGYQSYUTCMOiAiH3VVLY+KV0Hzx0XkQ656pYrIlrRlNIw45Fa/xDCMlRCRW/Ayhfeo6oIzAB3AIvAVvKxUw2gJzCgYRu1sB86r6gKAqp53x18GqLFopWEkirmPDKPefX4YAAAAuklEQVR2vgZcKyIviMg/ichb0xbIMNaLGQXDqBH16t+/CfgAMAY8LCK/lqpQhrFOzH1kGHVAVUt4sYODIvJdvCJlX0hTJsNYD7ZSMIwaEZHXisju0KGbgB+lJY9h1IIZBcOonR7gQRH5nogcxfUeFpEPi8gIXv37oyLy2VSlNIwYWJVUwzAMI8BWCoZhGEaAGQXDMAwjwIyCYRiGEWBGwTAMwwgwo2AYhmEEmFEwDMMwAswoGIZhGAH/D3RgwsRniIx1AAAAAElFTkSuQmCC\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": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "0.05152 x - 1.164e-16\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(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": 21,
   "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 $m$, 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",
    "$$ \\left( \\sum_{j=1}^m (Y_j-Y(X_j))^2 \\right)^\\frac12 = \\left( (Y_1-Y(X_1))^2+(Y_2+Y(X_2))^2+\\cdots+(Y_m-Y(X_m))^2\\right)^\\frac12, $$\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": 22,
   "metadata": {},
   "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": [
    "## 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 better idea 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": 23,
   "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",
    "print(\"Testing score is\",np.round(rsquared_linear, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also evaluate the model by plotting the predicted test values against the actual test values, and plotting the line of best fit for this data. This is compared against the line $x=y$, which is shown in orange, and will alway have a greater slope that the line of best fit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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=Y_test, y=preds_linear);\n",
    "sns.lineplot(x=preds_linear, y=preds_linear);\n",
    "# add a title including the correlation coefficient\n",
    "plt.title(\"Linear Regression, Rsq=%f\" % rsquared_linear)\n",
    "plt.ylabel(\"Predicted\") # xlabel\n",
    "plt.xlabel(\"Actual\"); # ylabel"
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