Chapter20_Linear_regression.ipynb

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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.stats import bayes_mvs, linregress\n",
    "from math import factorial\n",
    "import scikits.bootstrap as bs\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from warnings import filterwarnings\n",
    "\n",
    "%matplotlib inline\n",
    "filterwarnings('ignore')"
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   "source": [
    "# Linear regression"
   ]
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   "metadata": {},
   "source": [
    "## Introduction"
   ]
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   "source": [
    "<p>In this lecture I will discuss the correlation between variables.  *Correlation* between variables refers to the existence of a relationship between them and *linear* refers to the fact that they are directly coupled.  As the value of one increases, the other either increases or decreases proportionally.  This proportionality is constant, i.e. one or both are not squared or subject to a transcedental transformation.</p>\n",
    "<p>Many mathematical steps are required to calculate the relationship between two variables.  Fortunately these can all be done with a few simple Python&#8482; functions.</p>"
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   "source": [
    "## Simple linear regeression"
   ]
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   "source": [
    "<p>With linear regression we are directly comparing two sets of numerical variables as opposed to two sets of numerical variables locked up in two categorical groups.</p>\n",
    "<p>The best way to start comparing two sets of numerical variables is to plot them on a Cartesian coordinate (*xy*) plane.  We choose one variable to appear on the *x*-axis and one on the*y*-axis.  We then take a row of data (i.e. from the same patient), find the corresponding entries for the two variables and plot them on our *xy*-plane.  For this to happen, we need to make sure that for every row, both values are available.</p>\n",
    "<p>It is necessary to discard entries when both values are not available.  This can happen frequently in clinical data collection.</p>\n",
    "<p>Let's give it a go with this data set.</p>"
   ]
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PCT</th>\n",
       "      <th>CRP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.6</td>\n",
       "      <td>32.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.8</td>\n",
       "      <td>88.2</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.9</td>\n",
       "      <td>44.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.7</td>\n",
       "      <td>84.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.3</td>\n",
       "      <td>14.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>9.7</td>\n",
       "      <td>106.8</td>\n",
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       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>97.4</td>\n",
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       "      <th>7</th>\n",
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       "      <td>91.9</td>\n",
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       "      <td>3.4</td>\n",
       "      <td>31.7</td>\n",
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       "      <td>7.0</td>\n",
       "      <td>64.1</td>\n",
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       "      <th>11</th>\n",
       "      <td>7.8</td>\n",
       "      <td>69.3</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>8.2</td>\n",
       "      <td>84.7</td>\n",
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       "      <th>13</th>\n",
       "      <td>9.4</td>\n",
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       "      <td>5.4</td>\n",
       "      <td>45.0</td>\n",
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       "      <th>15</th>\n",
       "      <td>8.1</td>\n",
       "      <td>77.9</td>\n",
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       "      <th>16</th>\n",
       "      <td>5.5</td>\n",
       "      <td>55.8</td>\n",
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       "      <th>17</th>\n",
       "      <td>4.7</td>\n",
       "      <td>51.4</td>\n",
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       "      <td>59.3</td>\n",
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       "      <th>19</th>\n",
       "      <td>8.6</td>\n",
       "      <td>92.3</td>\n",
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       "      <th>20</th>\n",
       "      <td>5.9</td>\n",
       "      <td>54.5</td>\n",
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       "      <th>21</th>\n",
       "      <td>NaN</td>\n",
       "      <td>59.0</td>\n",
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       "      <td>8.9</td>\n",
       "      <td>87.0</td>\n",
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       "      <th>24</th>\n",
       "      <td>6.4</td>\n",
       "      <td>73.5</td>\n",
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       "      <th>25</th>\n",
       "      <td>5.6</td>\n",
       "      <td>53.2</td>\n",
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       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2.5</td>\n",
       "      <td>17.3</td>\n",
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       "      <td>6.4</td>\n",
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       "      <td>9.6</td>\n",
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       "    PCT    CRP\n",
       "0   2.6   32.6\n",
       "1   9.8   88.2\n",
       "2   4.9   44.6\n",
       "3   7.7   84.2\n",
       "4   2.3   14.3\n",
       "5   9.7  106.8\n",
       "6   NaN   97.4\n",
       "7   9.8   91.9\n",
       "8   3.4   31.7\n",
       "9   3.5   25.0\n",
       "10  7.0   64.1\n",
       "11  7.8   69.3\n",
       "12  8.2   84.7\n",
       "13  9.4    NaN\n",
       "14  5.4   45.0\n",
       "15  8.1   77.9\n",
       "16  5.5   55.8\n",
       "17  4.7   51.4\n",
       "18  5.0   59.3\n",
       "19  8.6   92.3\n",
       "20  5.9   54.5\n",
       "21  NaN   59.0\n",
       "22  5.7   52.7\n",
       "23  8.9   87.0\n",
       "24  6.4   73.5\n",
       "25  5.6   53.2\n",
       "26  2.5   17.3\n",
       "27  6.4   55.7\n",
       "28  9.6   94.0"
      ]
     },
     "execution_count": 3,
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   "source": [
    "reg_data = pd.read_csv('Regression.csv') # Reading in the csv file and saving it as a computer\n",
    "# variable named reg_data, which is then a DataFrame object\n",
    "reg_data # Displaying all the data"
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    "<p>First off we note that there are two variables in our data set; procalcitonin (PCT) and C-reactive protein (CRP).  Both are ratio-type numerical data.  Lastly, we note that some of the data entries are missing.<p>\n",
    "<p>So, before we go ahead and do all of this, let's get rid of all the rows that do not contain any data (even if only one of the two are absent).</p>"
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      "text/plain": [
       "    PCT    CRP\n",
       "0   2.6   32.6\n",
       "1   9.8   88.2\n",
       "2   4.9   44.6\n",
       "3   7.7   84.2\n",
       "4   2.3   14.3\n",
       "5   9.7  106.8\n",
       "7   9.8   91.9\n",
       "8   3.4   31.7\n",
       "9   3.5   25.0\n",
       "10  7.0   64.1\n",
       "11  7.8   69.3\n",
       "12  8.2   84.7\n",
       "14  5.4   45.0\n",
       "15  8.1   77.9\n",
       "16  5.5   55.8\n",
       "17  4.7   51.4\n",
       "18  5.0   59.3\n",
       "19  8.6   92.3\n",
       "20  5.9   54.5\n",
       "22  5.7   52.7\n",
       "23  8.9   87.0\n",
       "24  6.4   73.5\n",
       "25  5.6   53.2\n",
       "26  2.5   17.3\n",
       "27  6.4   55.7\n",
       "28  9.6   94.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data_2 = reg_data.dropna(subset = ['PCT', 'CRP']) # The subset = [] argument lists all the\n",
    "# columns from which you would like empty entries to be removed\n",
    "reg_data_2"
   ]
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   "metadata": {},
   "source": [
    "<p>Note how all the rows where an entry was missing, was removed.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As per usual, we can describe our data and even get the normal violin plots (or boxplots if you prefere those) going, so that we can get a feel for our data.</p>"
   ]
  },
  {
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   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "count    26.000000\n",
       "mean      6.346154\n",
       "std       2.362749\n",
       "min       2.300000\n",
       "25%       4.925000\n",
       "50%       6.150000\n",
       "75%       8.175000\n",
       "max       9.800000\n",
       "Name: PCT, dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data_2['PCT'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     26.000000\n",
       "mean      61.807692\n",
       "std       25.329081\n",
       "min       14.300000\n",
       "25%       46.600000\n",
       "50%       57.550000\n",
       "75%       84.575000\n",
       "max      106.800000\n",
       "Name: CRP, dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data_2['CRP'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+jnvu+Rds3ryBu3/TkGNZSkBCCDz++KNwHAfu0EwoqiY7EhFRQlA0F7wl8+Ap\nngfTdvDoo7/Afffdh66uTtnRKIWxLCWgHTu24fDhg9D8xdD9xbLjEBElHCO7HL6KG6H5gti+fTu+\n9a2v4cCB/bJjUYpiWUowkUgETz31OKBo8IRmyo5DRJSwVCMD3rIlcAWnoqOzA//5n/fjmWee5OJv\nGnQsSwnmxRefQ0dHG1x5lVBdftlxiIgSmqKocOdPhK98ORQjA2vWvIj77luFhoazsqNRCmFZSiD1\n9bVYu/a/oRoZcOVNkB2HiChpaN48+EaugJ49EidPnsCqVV/HG2+8LjsWpQiWpQThOA4effSXcBwH\nrtAMKKouOxIRUVJRNAPe4rnwFM9D3HTwy1/+BD//+Y8RiYRlR6Mkx7KUINauXYOjRw9DzyyF7i+R\nHYeIKGn1Lv5eAdWbh+3bt+Kee/4Fx49z528aOJalBFBXV4vVq/8ARXPDXTgLiqLIjkRElNRUlx++\n8mVw5U1Ec3Mj7r9/Ff785xfgOI7saJSEWJYks20bv/zVT2BZFtyFc7hTNxHRIFEUFe6CqfCWLYFQ\n3fjjH5/Cgw/eh9bWFtnRKMmwLEm2Zs2LOFl9AnpWOYysEbLjEBGlHD0jhIyKG6H7S3Do0AF8656v\nYdeunbJjURJhWZKopuY0/vSnP0LRvfAUzpIdh4goZSm6G54RC+AunI1IJIof//i/8Nvf/hKxWFR2\nNEoCLEuSWJaFX/7yJ7BtG56iOVA0l+xIREQpTVEUuAJj4B15A1R3DjZtWo9Vq/4F1dXHZUejBMey\nJMkf/vA4ampOwciu4JEmRETDSHNnwzfyfTByx6Oh4SzuvfcevPjic7BtW3Y0SlAsSxJs3/4G1q17\nBao7G25OvxERDTtF1eAJzYC3bDGE6sZzzz2D737322hsbJAdjRKQIoS4mseLpqauwcqSFs6cqcG/\n//s3YVoCvpHvg+rOkh2JiCitCTuO6Nm3YHWehsvlxh133IVFi5ZyG5cUFAxmDugflWVpGEUiYXz7\n299AQ8NZeEqug5FVKjsSEREBEELA6jyFWMNfIOw4Jk2agrvv/gJyc/NkR6NBxLKU4IQQeOSRh7Fr\n104YuZXwhKbLjkRERH/DMcOI1u+E3VMPr9eLj3/8U5g/fyFHmVIEy1KCW7PmRTzzzJPQfEF4y5ZA\nUbhcjIgoEQkhYLafQLzxbQjHwtSpM/DJT36Go0wpgGUpgb355hv42c9/DEXzwFdxA1TdKzsSERFd\nghPvRrSwPXzNAAAgAElEQVR+B+xwI9weDz720b/DokXLoKr8ZTdZsSwlqKqqfXj44f+AI1R4y5dC\n8wRkRyIiosskhIDZcQLxxt0QtomxY8fj7ru/gMLCItnRaABYlhLQyZMn8MAD30EsbsJbugh6Rkh2\nJCIiGgDHjCDWsAtW1xnouo6VKz+Im266GYbBDYWTCctSgmloqMe9965Cd3cXr3wjIkoRZmdN7xVz\nVgTBYAHuuutuTJkyTXYsukwsSwmkvb0N9923Cs3NTXAXzoYrMEZ2JCIiGiTCNhFr3gez9SgAgdmz\nr8Edd3yCC8CTAMtSgmhubsKDD96HxsYGuPInwR2cIjsSERENATvahujZXXAizXC5XHj/+2/GjTd+\nAG63W3Y0eg8sSwmgtvYMHnzwfnR0tMGVNxGu4BTuzUFElMKEELA6qhFr2gthRZGTE8BHPnIH5s69\njlfNJSCWJcmqq4/joYceQE9PN9wF0+HKq5QdiYiIhomwTcRbDiLeeggQDkaOHIXbb78T48dPkB2N\n3oVlSaKDB6vwgx88iFgsDk/RHBg5o2RHIiIiCRyzB7HGPbA6TwMAJk2agttu+xgqKkZLTkYAy5IU\nQghs3rwBv//9o7AdB57iebzqjYiIYEdaEGvaC7unAQAwc+Yc3HrrR1FSMkJysvTGsjTM4vE4fve7\nX2Pr1s1QNBc8JfOhZxTKjkVERAnE6mlArGkvnEgLFEXBrFlzsHLlB1FeXiE7WlpiWRpGjY0N+PGP\n/ws1NaehegLwllwH1eWXHYuIiBKQEAJ2dx1izVVwoq0AgMmTp2Llyg9i3LhKXgg0jFiWhsnBg1X4\n0Y8eQiQSgZEzGu7QTCiqJjsWERElOCEE7HAD4s0HYIcbAQCjRo3B8uU3Yvbsa6DruuSEqY9laZg8\n8MB3cPjwQXiKruFCbiIiGhA70ox480FY3bUAgOzsHCxZshyLFi1Ddna25HSpa6BliTX2ClmWCSgq\nixIREQ2Y5s2Ht3QhnHgX4m1H0dlejeeffxYvvvg8Zs2ajQULFmPixMncqylBsCwRERFJoroy4QnN\nhMifArPjJMy2o9ixYzt27NiO3Nw8LFiwCNdddz2CwQLZUdMayxIREZFkimbAlTsWRmAMnEgLzI4T\naGuvwQsvrMYLL6zGqFGjcc018zB79rU8g04CliUiIqIEoSgKNF8+NF8+RGgmrM4amJ0nceLECZw4\ncRxPPfV7jBkzDrNnX4tp02YgFOKWNcOBZYmIiCgBKaoOI6cCRk4FHCsKq6sGVudpHDt2BMeOHcFT\nT/0OhYVFmDZtJqZOnY4xY8bBMAzZsVMSyxIREVGCU3UPXIGxcAXGwjEjsHrqYHfVoaGxAa+88me8\n8sqfYRgujBs3HpWVkzBhwkSUl1dA07i1zWBgWSIiIkoiquGFK2c0kDMawrFhhxthddfDDjegqmof\nqqr2AQA8Hg8qKkZj9Oixfbcx8PszJadPTixLRERESUpRNej+Iuj+IgCAY0Vhhxth95xFPNyMgwer\ncPBg1bn7B4MFKCsrR2lpOcrKylFWNhKBQC53Eb8EliUiIqIUoeoeqFllMLLKAADCjsGOtMKONMOO\nNKO5tR1NTTuxa9fOc49xuz0oKipGUVExiotLUFhYhGCwAMFgAbxen6xvJaGwLBEREaUoRXOfN/Ik\nhICwInCi7bBjbXCi7TDjnTh56iROnjxxweP9/kwEgwXIy8tDIJCHQCAXubm5CARykZWVjezsHHg8\nnuH+toYdyxIlFceKAI4tOwYlE1WDqntlpyBKCIqiQDF8UA0f9Mzic38vhANh9sCJdcKJd8Exu+HE\nexCOd6P6ZDWqq4+/59d0uVzIyspGZmYW/H4//P5MZGT4kZmZhQULFiEQCAzHtzakWJYoKdjRdkRq\nt0LEB3YWYWZmJhYvXgwA2LhxI7q60utMw3SnuDLhLbkOmidHdhSihKQoKhRXJlTXhQvAhRAQdgzC\nDMOxwhBmuHd0yopCWFFYdhQt7d1obmkBhHPeY6PRCD760b8brm9jyLAskVTRht2wuk5f8n7CjAAY\n+KHPixcvxhe+8IVz//vFF18c8Nei5CPiXQhXvwLF4AgT9U/PLIMnNF12jISiKAoU3QPoHmjIfc/7\nCSEAYfetk2pBtPYNmGZ8GJMOHZYlSnhCCFxNUSLqJSCE4FU/RAMkhANhRSDMSO8IU9/IkrCjvaNM\ndgzCjgN2vPcjekesUgHLEknlCU0HLuO3uO7jfx7wFBzQO/V2sT9T+lBdmcgYvVJ2DKKEdW7xd9+a\nJRHvObd2SVi9U2/9UVUNmX4/MjLy4ff3rlmaP3/hMKUfWixLlBS8JdchWrsVzgALU1dXF6fe0pjq\nyoSn5DrZMYgSQm8pisKJtcGOtsOJd8KJdULEuyAc84L7a5qGvNw8BALlfVfC5SEnJ4Ds7BxkZ2f3\nXRWXDa/Xl7IjtyxLlBQ0Tw4yRq/k1XB05Xg1HKU5x4rCibT07rUU7d0uQNjR8+6jaRoKC4tQXFyM\nUKgIBQUhBIMFKCgIIScnAFVNjem0gWJZoqTCH3pERO9NCAFhdsPqaYAdboIdaYYwe867T15+EGWl\nk/t28i5DSckI5OcX8By5frAsERERJTHHisLurocVboDd0whhhc99zufLwOjKaefOhxs5sgIZGX6J\naZMTyxIREVESEULAibbB6q6D1V0HJ9p67nN+fyYqK6/FhAmTUFk5AYWFxSm7jmg4sSwREREluN6C\n1Aqz8zSsrhoIs3f0SFU1VFZOxNSpMzBp0hSUlIxI+/VFQ4FliYiIKEHZ0XZYnSdhdtacW3vk9fow\nffYCTJs2E5MnT4HPlyE5ZepjWSIiIkogwo7D7DwNs/3EuSk2j8eDGbMXYM6cuZg0aQoMw5CcMr2w\nLBEREUnWO83WgnjrUVhdZwBhQ1EUTJs2A9ddtwjTpk2HYbhkx0xbLEtERESSCMeG1XUa8daj50aR\nCkKFWLhgMebPX4hAICA5IQEsSwOgAMKBHWmB5s2THYaIiJKQsGKItx2F2X4MwopCURTMmDEby5ev\nQGXlRF7BlmBYlq7QwoWLceLEMYRPrYM7NBNGzmi+qImI6LI4ZgTx1kOw2o9DOBa8Xh8WLV+JJUve\nh2CwQHY8eg9K74nuAyaamgZ+uGmy2rdvD3728x8h3NMDPXskPIWzoajsnUREdHFOvBvxloMwO6oB\n4SAnJ4Abb/wAFi1aArfbIzte2ggGMwc0usGyNEDNzU145JHv4+TJE1DdOfCOWADVxV1RiYjoHY4Z\nQbzlAMz244BwEAwWYOXKD2LevAW8ok0CliUJTNPEk08+ho0b10HRPfCWLobmyZEdi4iIJBNWDPHW\ngzDbjkI4NoLBAnzoQx/BNdfM4xlsErEsSfTaa6/giSd+C0VzwTviemi+fNmRiIhIAuHYMNuOIN58\nAMIxkZMTwC233IYFCxZB17lcQzaWJcm2bduCX/3qpxBQ4Sm5Drq/SHYkIiIaJkIIWF1nEG/cA8fs\nhi8jAzd/4ENYuvR93B8pgbAsJYDdu3fhkUe+D8t24CmeCyOrTHYkIiIaYnakFbHGt2GHm6CqKpYt\nW4Gbb74Vfj/XsSYalqUEcejQAXz/Bw8iFo3BUzIfRlap7EhERDQEhB1HrGkfzLZjAASmT5+Jj33s\nThQWcmYhUbEsJZDq6uP4j/+4F7F4HN7SRdAzQrIjERHRIBFCwOo8hVjjbggrisLCItx556cxadIU\n2dHoEliWEszBg1V46KEH4AgF3vKl0Dzcsp6IKNk5sU5Ez74FO9wIw3Dh5ps/hBUrVnIbgCTBspSA\nduzYjp/97IeA5oavfBlUV6bsSERENABCOIi3HES8uQoQDqZPn4WPf/yTyM8Pyo5GV2CgZYnXMQ6h\na66Zi66uDjz++G8RqdkEb/lyqDp3aiUiSiZ2pBXR+h1wYu3Izs7BXXfdjVmz5siORcOIZWmILVu2\nAh0dHXjppecRqdkEX/lyKCo3JCMiSnTCsRBr2g+z9TAAgeuvX4KPfezj8PkyZEejYcayNAxuvfWj\naGtrxdatmxE7uwue4mtkRyIion7YkRZE696EE+9Efn4B7r7785gwYZLsWCQJy9IwUBQFn/jEZ1BT\ncxqnT5+A6suDK2e07FhERPQ3hGMj3lyFeMtBAALLl6/Ahz98B9xut+xoJBEXeA+jpqZG/Nu//SvC\nkSh85cugeXNlRyIioj52tK13NCnWjry8fHz2s19CZeVE2bFoEPFquCSxd+/bePj7D0LVffBV3ABF\n428rREQyCeHAbD2MWNM+QDhYtGgpPvaxO+H1emVHo0HGspREnn/+WbzwwmpoGUXwll4PRRnQvx0R\nEV0lx+xBtG477HATsrKy8ZnPfBFTp06XHYuGCLcOSCK33HIbTpw4hv379yLechDufA7zEhENN7Pj\nJGINuyBsEzNmzManP/05ZGZmyY5FCYgjS5J0d3fhm9/8Gjo6O+AbeQM0T47sSEREaUHYcUTP7oLV\neQoulxt33vkpLFiwiKP8aWCgI0vqYAehy+P3Z+Luuz8PCAfRuu0QwpYdiYgo5dnhZoSrX4HVeQqj\nRo3Gt7/9XSxcuJhFifrFaTiJpk6djoULF+P11zci3nwA7iAPYSQiGgpCOIg3H0C8uQqKAnzgAx/C\nLbfcBl3nj0G6NL5KJLvjjruwf/8+tDUfgO4v4XYCRESDzDF7EK3dBjvSjEAgF1/4wv/A+PETZMei\nJMJpOMm8Xh8+85kvABCI1r8J4XA6johosJidNQhXvwI70ozZs6/Bt7/9XRYlumIsSwlg0qQpWLJk\nOZxYB+LN+2XHISJKesKxEK3fgWjtVhga8OlPfx5f/vI/IiPDLzsaJSFOwyWIj37049i3by+amw9B\nzyzldBwR0QDZ0TZEa7fBiXeitLQMX/rSP6CoqER2LEpiHFlKEB6Pp/fqOAhEz+7CVW7pQESUdoQQ\niLceQfjkq3DinVi+/EZ84xvfZlGiq8aRpQQyYcIkzJkzFzt3bofVUQ0jZ5TsSEREScGxoojWvQm7\npx5+fyY++9kvYdq0GbJjUYpgWUowt99+J/bseRuxpj3QM0dA0VyyIxERJTSru773AhkrikmTpuBz\nn/sysrO50S8NHk7DJZjc3DzccsutEFas91BHIiK6KOHYiDa8jUjNJqjCxO2334n/83++yqJEg44j\nSwnohhtuwuuvb0RDwzEYOaOgeQKyIxERJRQ72o5o3TY4sQ6UlJTgc5/7e5SXV8iORSmKI0sJSNd1\n3HnnpwEIxLjYm4jonN5F3Id7F3HHOrB48TI8/PDDLEo0pDiylKAmT56KWbPmYNeunbA6T8LI5hsB\nEaU3xwwjWv8m7J4G+P2Z+MxnvoDp02fB4/Ggq8uUHY9SGMtSArvjjk9g7949iDXuhZ5ZCkXlPxcR\npR8hBKzOk4g1/AXCNjF16nTcffcXkZ2dLTsapQlOwyWwvLx8rFhxE4QVQbz1iOw4RETDzrGiiJ7Z\ngmjdm3DpKj71qc/hH//xn1mUaFhxqCLB3XjjB7Bhw2sItx6EKzAaiuaWHYmIaFiYnTWINbwFYcUw\nfvwEfOYzX0QwWCA7FqUhjiwlOJ/Phw984IMQtolY80HZcYiIhpxjRhA5swXR2q3QYOOOO+7CP//z\nv7IokTQcWUoCS5e+D2vXvoy2tiNw5Y6FamTIjkRENOiEELA6qhFr3A1hxzF27HjcffcXUFhYJDsa\npTmOLCUBw3Dh1ls/AggH8ab9suMQEQ06J96FSM1GROt3wKUr+MQn7sZXv/pNFiVKCBxZShLz5y/E\nyy//GXV1J2HkVUJzc3EjESU/4ViItxxEvOUQIGxMmTINn/zkZ5GXly87GtE5HFlKEqqq4sMfvh2A\nQLxxr+w4RERXzequQ/jEy4g3VyE7Kwtf/vL/wv/+3/+PRYkSDkeWksj06TMxZsw4HDt2BHa4GZqP\nbyhElHycWCdijXtgdddCVVWsWLESt9xyG7xer+xoRBfFkaUkoigKPvKROwAAsWauXSKi5CKsGKJn\n/4Ke6jWwumsxdux4rFp1H26//U4WJUpoHFlKMuPGVaKyciIOHToAO9ICzZsnOxIRUb+EY8NsO4p4\nSxWEbSIYLMBHP/pxzJo1B4qiyI5HdEksS0no5ptvxaFDBxBrroKv9HrZcYiILko4NsyOE4g3H4Cw\nIvD5MnDLLbdj6dIboOv88UPJg6/WJFRZOfGdtUvRNmiegOxIRETnCGHDbK9GvOUAhBmGYbiw7MaV\nuOmmD8Lv98uOR3TFWJaSkKIouOWWW/HQQw8g3lwF74gFsiMREUHYZu9IUusRCLMHumFg6Q034f3v\nv5lnuVFSY1lKUpMmTUVFxWhUVx+HHW2H5smRHYmI0pRjhhFvPQKr/TiEY8IwXFi0/EbcdNPNyMnh\nyDclP5alJKUoCm6++Vb84AcPIt5yAN6S+bIjEVEaEULADjfCbD8Oq6sGEAJZWdlYtuwGLF68DJmZ\nWbIjEg0alqUkNm3aDJSVjcTp0yfh5E+G6uabExENLceKwmyvhtV+HI7ZDQAoLi7BihUrMXfufBiG\nS3JCosHHspTEekeXPoQf//hhxFoOwFs8V3YkIkpBwo7D6qqF2XkadvgsIAQMw4W58xfi+uuXYOzY\n8dwCgFIay1KSmzFjNkpKRqC29lTv6JKLV5oQ0dUTdgxWdz2szhpYPfWAcAAA5eUVWLhwMebOnQ+f\nL0NySqLhwbKU5FRVxU033YJf/OIRxFuPwFM4U3YkIkpCQgg4sQ5Y3XWwu+tgR1oACABAyYhSXDNn\nHq65Zi5CoUK5QYkkYFlKAXPmzMWzzz6F9o4TEMHJUDSuGSCi/gkhIOJdsMKNsPtuwooC6J3iHzNm\nLKZOnX5u9JoonbEspQBd1/G+970fTz/9OOJtx+DOnyg7EhElGGGbsKOtsCMtcCItsKMt58oRAGRl\nZWPixJmYMmU6pkyZBr8/U2JaosTCspQiFi1aghdeWI1Y21G4csdDUTXZkYhIEseKwom2w4m1wY62\nw4m2wYl3nnefnJwAxo+fifHjJ6CyciJCoUIu0iZ6DyxLKcLr9WHx4qV4+eU/w+o8BSNnlOxIRDTE\nhBWDHe+EE+t45xbvPG/ECADcbg/Kx1Vi1KgxfbfRyM3lIdxEl4tlKYUsX34j1q5dg3jrYejZFfwt\nkSgFCOFAxLvhxLv6bp1wYp1w4l0QduyC++flBzGiZAJKS8tRVjYSZWXlyM8PQlVVCemJUgPLUgrJ\nzc3DtdfOx7ZtW2D3nIXuL5IdiYgugxACwor2FqFzpaj3JsxuQIjz7q8oCoLBAhQVFffdSjBiRCmK\nikrg8XgkfRdEqYtlKcWsWHETtm3bgnjLIZYlogQj7PgFZciJdUGYXRCOdcH9MzIyUFg6BoWFRedu\noVARQqFCGIYh4TsgSk8sSymmrGwkJkyYhIMHq2BH26B5eIglXb3eBcOtcMweCDMMxwxDmGEIOwYB\n0bthoXAACEDRoKgGFFUHVAOKZkDRvVB1LxTd0/tnwwfF8EFRUu9CBOFYcOLdfbcuiHePEtnRC+5v\nGC6EiosRChX+TSkq5BVpRAmCZSkF3XjjB3DwYBXiLYfgLZknOw4lIccMww43wA43wQ43wYl3XXAf\nRVHg8/mgaTo0zYCmadA0DfF4HNFoFNFoB8TfTB9d8DV0X19xyoDq8kM1Ms79WdG9UJTEW2cjhADs\nOByzp+/W3VeIeguSsMIXPEZRFOTnB1FYOB6h0DtlqKioGDk5Aa4nIkpwLEspaPLkqSguLkFdfQ0c\nczpUwys7EiUB4diwus7A7DgBu6fh3N+73R6MnTwVY8aMQ0FBCLm5ecjLy0dOTgCa9t4jQ0IIxOMx\n9PT0oKOjHe3tbWhvb0dbWyva2lrR3NyE5uYmtLa2QESaL/wCinJ+mdL7RqN0D9S+ESpF8wzqNhnC\nsSHsKIQV6x01syK9o2jnPvaNqDnmRR8fCOQiFBqJgoLQeVNmwWABp82IkhjLUgpSFAXLlq3A7373\na5jtx+AOTpEdiRKYE+tEvO0orM5TEHYcADB27HjMmjUH48ZVorS0vN9S9F4URYHb7YHb7en3MnXL\nss6Vp6amRjQ1NaKrqw21tXVoaWlBR0czRLipnyfSoGguKKoBaH3Tf4rWOyr11xvQt0ha9H4UDoSw\nIGwLcMze9UJO/KLrht7N7fYgWFyI/Pxg360AwWAQBQW9hcjl4u75RKlIudQw+SWIpqYLh+dJvlgs\niq985X8gagpkjLk5JdeG0NVxrCjiTfthth8HIJCVlY3rrrseCxcuRmGh3IsDgsFM/PW9xbIstLa2\noKWlGe3tbejo6EBnZzs6OjrQ0dGOcDiMcLin72MYjmNf9vNomg6PxwOv1wuv14fMzExkZmad+5iT\nE0AgkItAIBe5ubnwen1D9S3TVXj364WoP8Fg5oD21OHIUopyuz1YuHAJ1q79b1idNTCyR8qORAlC\nOBbirYdhthyEcCwUFhbhtts+hhkzZg9oBGmo6bqOgoIQCgpCl7yvEAKWZcKyrL6bDcvqnTLTtN7R\nJk1ToaoaPB4PdJ1vgUR0aXynSGFLl74Pr766BvHWoyxLBACwuusRrd8BYUXg92fi1ls/goULl6RM\naVAUBYbhgmFwOoyIBk9qvEPSRRUUhDBt2kzs3r0LdqQFmpfHG6QrIWzEGvfBbD0ETdNx48oP4qab\nbua0EhHRZWBZSnHLlt2A3bt3Id56hNsIpCkn3o1I7Rtwoq0oKCjEl7/8v1BePlJ2LCKipMGylOIm\nTpyMoqJi1J+tgWNNh6pzG4F0YnbWIFa/A8IxMW/eAtx1193wevkaICK6EtwJLcUpioLly1cAwoHZ\ndlx2HBpG8ZZDiNZuhaGr+Oxnv4TPf/7vWZSIiAaAZSkNzJu3EF6vF2b7MQhx+ZdVU3ISQiDWuBex\nxt3Izg7gG9/4Nq677nrZsYiIkhbLUhrweDxYuHAxhBWF1VkjOw4NISEEYmd3Id5yAAUFIfzrv67C\niBGlsmMRESU1lqU0sWTJ+wAAZtsxyUloqAhhI1q3DWb7MZSWluHrX1+F/Pyg7FhEREmPZSlNhEKF\nmDRpCuxIM+xou+w4NMiEcBCt3Qar8zTGjBmHr371m8jOzpYdi4goJbAspZGlSzm6lIqEEIg1vA2r\n6wzGj5+Af/qnr8Pny5Adi4goZbAspZGpU2cgEMiF1XkSwr74qemUfOIth2C2HUVJSSn+4R/+CW63\nW3YkIqKUwrKURjRNw6JFSyEcC2bnSdlxaBCYHdWIN+1BIJCLr3zlq/D5uCM3EdFgY1lKM9dfvwSq\nqsFsOwYhhOw4dBWs7rOI1u+A1+vDV77yNQQCubIjERGlJJalNJOTE8DMmbPhxDpgR5plx6EBsqPt\niNZuga5p+Md//L8oKRkhOxIRUcpiWUpDS5YsB8CF3slK2CaitVshHAuf//zfY9y4StmRiIhSGstS\nGqqsnIjCwmJYXTVwrKjsOHQFhBCInt0JJ96FFStWYs6cubIjERGlPJalNKQoSu/oknBgtp+QHYeu\ngNl27NxeSh/+8O2y4xARpQWWpTR13XUL4XK5YLYfhxCO7Dh0GexIC2KNb8Pvz8SXvvQP0HVddiQi\norTAspSmfL4MXHvtfAizB3bPWdlx6BKEHUO09g0oEPjiF/8ncnPzZEciIkobLEtpbPHivy70Pi45\nCfVHCIFI3ZtwzB7cfPOtmDRpiuxIRERphWUpjVVUjEJ5eQWs7jo4Zlh2HHoPVkc17O46TJgwCbfc\ncpvsOEREaYdlKc0tXrwMgOBC7wTlmD2INbwNj8eLz372S1BV/idLRDTc+M6b5q69dj7cHg8Xeicg\nIQSi9TsgHBN/93ef4DolIiJJWJbSnMfjwfx5CyCsCOzuetlx6F3M9uOwexowdep0LFiwSHYcIqK0\nxbJEWLRoGQAgzh29E4YT70a8cTe8Xh8+9anPQ1EU2ZGIiNIWyxKhrKwco0aNgd1TDyfeLTtO2ntn\n+s3CXXd9GoFAQHYkIqK0xrJEAN51XhwXektnth2DHW7EjBmzMHfudbLjEBGlPZYlAgDMmTMXXq8P\nZscJLvSWyDEjiDfthdfrwyc/+VlOvxERJQCWJQIAuFwu/P/27jS2qvNA4/hzrndibIiBBAwkZHtD\nDDgUQliDTWxIIIFAWAJkIWnSTJNOm2o6/dB+qDQadSqNJjNqq+bDKFKlaT9UM5qMZlTNJDNKNEmp\nmmSykqUnpCwJJMZgYxtv957lnQ+2U0PJwcv1fa/t/09Css9dzmPp5dznnuU9a9bcJhv2Kjx30nWc\nSSvd/JZsHGjnzvtUWTnNdRwAgChLGKRvzqW+w0DIvbCrSWHHJ1qw4FqtX7/BdRwAQD/KEr4wZ061\nbrjhRkXdpxRnzrmOM6nYOFK66Q15nqcHH3yEyScBII+wRcZ5Bu4Xl+F+cTmVaf294sw5bdiwUVdd\ntcB1HADAIJQlnGfZsltUXj5VYftR2ThyHWdSiDOdCs58oIqKSm3fvst1HADABShLOE9RUZHWrauT\njdIKz33qOs6EZ61Vb9MbsjbS3r0PaMqUKa4jAQAuQFnCnxg4uZgTvcde2HlSUdfnWriwRitWrHId\nBwBwEZQl/IlZs65QTc1iRT1nFPW2uY4zYdk4Uqb5baVSKe3ff4A5lQAgT1GWcFFfTCPQxoneYyU4\ne1hxplMbNjRqzpxq13EAAF+CsoSLqq39iiorpylsPyYbh67jTDhx2KvMmfc15bLLtHXrva7jAAAS\nUJZwUYWFhbrttnrZOFDQcdx1nAknc/qQbBxo+z07VV5e7joOACABZQlf6rbb6uV5ngLmXMqqqLdN\nQdsRzZ49R+vX3+46DgDgEihL+FJVVTNUW7tUcW+rop5W13EmBGut0qfelGR1330PqLCw0HUkAMAl\nUJaQ6I/3izvsOMnEEHaeVNTdrCVLbtbixbWu4wAAhoCyhESLFtVq5sxZCjo+kY3SruOMa9b+caqA\nPbLelxIAAA4lSURBVHv2u44DABgiyhISpVIp1dc3SDZS0HbUdZxxLTj7B8WZTtXXN2j2bKYKAIDx\ngrKES1q7tk6FRUUKzn4sa63rOOOSjTLKnHlfpaVluvvuHa7jAACGgbKESyovL9fKW1crDjoVdX3u\nOs64lGn5UDZKa8uWraqoqHAdBwAwDJQlDEl9faMkKcP94oYtDrqUaf1I06ZNV0PDHa7jAACGibKE\nIVmw4BotWHCtos7PFGc6XccZV9KnD0k20o4du1VSUuI6DgBgmChLGLING/r2LgVt7F0aqqj3rML2\nY5o7d75Wr17nOg4AYAQoSxiyFStWqrx8qoK2o7Jx5DrOuJBufkeStHv3XqVS/HcDgPGIrTeGrKio\nWOvW1clGaYUdn7iOk/fCziZFXU2qqVmsRYuYgBIAxivKEoalvr5Bnucpw4zeiay1Sje/Lc/ztGvX\nXtdxAACjQFnCsMyYMVO1tV/pu19c9xnXcfJW2HFccbpNK1eu0fz5V7uOAwAYBcoShq2xse/y90yr\n7zhJfrJxpPTpd1VQUKjt23e5jgMAGCXKEobtxhtv0rx58xWeO6E46HIdJ+8EZw/LBt1qaNikGTNm\nuo4DABglyhKGzfM8bdy4WZJVpvUj13Hyio0yyrR8oLKyKdqyZZvrOACALKAsYURWrFiliopKhW1H\nZKPAdZy8kWn5QDbK6K67tqm8vNx1HABAFlCWMCJFRUXasKFRNg4UtB91HScvDNzWZPr0KjU0bHId\nBwCQJZQljFhdXYMKCwsVtH4ka2PXcZzru61JrB07dqmoqNh1HABAllCWMGIVFRVavXqd4qBTYedn\nruM4NXBbk+rqeVq1aq3rOACALKIsYVQaGvqmEQgm8TQCAxNQStLu3fu4rQkATDBs1TEqc+fOU03N\nYkXdpxX1nnUdx4moq0lR1ynV1CzW4sXc1gQAJhrKEkatsfFOSVKm5feOk+SetfEXtzXZvXu/6zgA\ngDFAWcKoLVq0RHPnzlfY8YnizDnXcXIqaDuqON2uNWvWa968+a7jAADGAGUJo5ZKpXTXXdskWWVa\nPnQdJ2dsHChz5pCKi4u1fftO13EAAGOEsoSsWL78Vl1xxZUK2o9NmlugZFp+Lxv26o477tL06Ze7\njgMAGCOUJWRFKpXqu72HjSfFuUtx0KOg1VdFRaXuuOMu13EAAGOIsoSsWblyjaqqZihoO6I47HUd\nZ0xlTr8rG4favn2XSktLXccBAIwhyhKyprCwUJs33y3ZaELPuxT1tCpoP6rq6rlat67OdRwAwBij\nLCGr1q5dr8rKaQrOHpaN0q7jZJ21Vr2n3pAk7dv3EBNQAsAkwJYeWVVUVKxNm7bIxqEyrYddx8m6\nsP2Y4p4WLV9+qxYurHEdBwCQA5QlZF1d3e267LJyBWc/ko0C13GyxkaB0qffUVFRsfbsYQJKAJgs\nKEvIutLSUm3cuFk2yijTOnGujEufeV827NWWLVtVVTXDdRwAQI5QljAmGhvvUEVFpYJWX3HQ4zrO\nqEXpDgVnfVVVzWCqAACYZChLGBOlpaW6556dfecunXnPdZxRsdYqfepNyVrt3fuAiouLXUcCAOQQ\nZQljZt26Ol155WwFbUcUpdtdxxmxsPOkoq4m3XTTIi1dutx1HABAjlGWMGYKCgq0a9deSVaZ5ndd\nxxkRG2WUbnpDBQWF2rfvIXme5zoSACDHKEsYUzffvEzXX28Udp5U2N3sOs6wpZvflg17tHXrds2Z\nU+06DgDAAcoSxpTnedq9e58kKX3qHVlrHScaurDrlIK2I5o7d77uvPNu13EAAI5QljDmrr32ei1f\nvkJxb4vCcydcxxkSG4dKN70uz/P08MNfU2FhoetIAABHKEvIiXvv3aNUQYEyzW/LxqHrOJeUPv2e\n4kynNm3arAULrnEdBwDgEGUJOXHFFbN1z7ZtioMupU8fch0nUdTToqDV18yZs7Rt207XcQAAjlGW\nkDP79u3TrFlXKmj1FfWccR3nomwcqffz1yRZHTjwmEpKSlxHAgA4RllCzpSUlOjhhx+TJPV+9pps\nHDlO9KfSzW8pTrerru52bpQLAJBEWUKOGbNQGzY0Ks50KHPmfddxzhO0H1dw9mNVV8/Tnj33u44D\nAMgTlCXk3L333qfLL69SpuVDRb1nXceRJMXpDqWbXldJSYmeeOJbHH4DAHyBsoScKysr04EDj0my\n6v3sVVkbO81j41A9Jw/KxqEeeugxzZ49x2keAEB+oSzBiUWLlmjt2vWK023KOL46Lt305hfnKa1c\nudppFgBA/qEswZn77rtfM2fOUqblQwXtx5xkCNqOKGg/ovnzr9bevQ84yQAAyG+UJTgzZcpleuqp\nv1RZWZl6P39NYffpnK4/PHdSvU2vq6ysTE888S0VFRXndP0AgPGBsgSnZs+u1hNPPKWUJ/We+I3i\nTGdO1ht2Nqnn5EEVFxXpqae+q1mzrsjJegEA4w9lCc7V1CzW/v0HZKO0ek68LBtlxnR9YXezek++\nosKClL75ze/o+uvNmK4PADC+UZaQF+rrG9TYeKfidId6Tv52zCasjHpa1PvpK/Jk9eST39ZNNy0a\nk/UAACYOyhLyxp49+7VkyVJFXU3qPv6i4qAnq+8fdjer59P/lWyoxx//hmprl2b1/QEAExNlCXkj\nlUrpySe/pVWr1irubVH3sReycg85a2OlTx9Sz/GXpDjQI488rltuWZmFxACAyaDQdQBgsKKiYj36\n6Nd11VVX61e/+qW6j7+o0iuXq2jaNSN6vzjTqZ7Pfqe454yqqmbo8ce/oeuuuyHLqQEAExllCXnH\n8zxt3LhZ1dXz9MwzP1b3568p7Dql4qobVVA6fUjvYeNIYcdxpZvfko0CrVixUg8++FVNmXLZGKcH\nAEw0nrV2NK+3p0+fy1YWTHAzZ07VcMdLc/Mp/fSnf68TJz6RJKXKZqh4+nUqrJgnzys477nWWkU9\nZxS2H1N47lPZKKPi4hLt3/+Q1q5dL8/zsva3YGyNZKxg8mK8YKhmzpw6og8CyhJyZqQbtDiOdejQ\nO3rxxRf03nvvylorr6BEXtEUSSl5XkryUoqDTtmgS5JUOW26Vq1crbq6BuZQGof48MNwMF4wVCMt\nSxyGQ95LpVKqrV2q2tqlam4+pZde+h+9+upv1dPTozAMFUWhJKm4uETLVq3V6tXrtHBhjVIprl8A\nAIwee5aQM2P17c9aqziO5XkeBWmCYE8BhoPxgqFizxImLc/zVFBQcOknAgAwAnwNBwAASEBZAgAA\nSEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZ\nAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAA\nSEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZ\nAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAASEBZAgAA\nSEBZAgAASEBZAgAASOBZa11nAAAAyFvsWQIAAEhAWQIAAEhAWQIAAEhAWQIAAEhAWQIAAEhAWQIA\nAEhAWQIAAEhQONwXGGM8SSckfdS/6Le+73/fGLNS0j9ICiW94Pv+X2UvJsYrY0xK0s8kLZGUlvSo\n7/t/cJsK+cYY86ak9v5fj0j6G0k/lxRLek/Sk77vMyncJGaMuVXSj3zfrzfGXKeLjA9jzGOSvqa+\nz6G/9n3/184Cw6kLxstSSf8h6XD/wz/zff+fhzNehl2WJF0r6Q3f97desPwZSTt83z9qjPm1MeZm\n3/ffHsH7Y2K5R1Kx7/ur+wfv3/UvAyRJxphSSfJ9v37Qsn+X9D3f9182xjwjaZukf3MUEY4ZY74r\n6X5Jnf2LntYF48MY8ztJfy5pmaQySb8xxvy37/sZJ6HhzEXGyzJJT/u+//Sg51ypYYyXkZSlZZKq\njTEvSuqR9G1JTZJKfN8/2v+c5yU1SKIsYY2k/5Ik3/dfNcYsd5wH+adW0hRjzPPq2yZ9X9JXfN9/\nuf/x/5S0UZSlyexjSTsk/VP/7xcbH5Gkg77vB5ICY8zH6tuj/X+5DgvnLhwvyyTdYIzZpr69S09J\nWqFhjJfEc5aMMV81xhwa/E/SZ5J+6Pv+Bkk/lPQLSVMldQx66TlJlSP8IzGxVOj8sRH1H5oDBnRJ\n+lvf9zdJ+jNJv7zg8U6xPZnUfN//V/UdKhngDfp54POmQn88lDt4OSaZi4yXVyV9x/f99eo7zP8D\n9fWWIY+XxD1Lvu8/K+nZwcuMMWUDIXzfP2iMmdO/kqmDnlYhqe0Sfw8mhw6dPzZSvu/HrsIgL32k\nvm+C8n3/sDGmRdLSQY9PFdsTnG/wNmTg8+bCbc1USWdzGQp56znf9weK0XOSfiLpZQ1jvIzkG/4P\n1LcLS8aYWkmf+L7fISljjLmm/wTwjf1BgIOSNktS/0UA77qNgzz0iPrOZVP/l6+pkl4wxqzvf/xO\nsT3B+d66yPh4TdI6Y0yJMaZS0kL1nfwNPG+MuaX/5wb1HWob1ngZyTlLP5L0C2PMFkmBpAP9ywd2\nnxdIet73/ddH8N6YeJ6T1GiMOdj/+8MuwyAvPSvp58aYVyRZ9Y2RFkn/aIwplvSBpH9xmA/5Y+CK\nyL/QBeOj/2q4H0t6RX07Ar7Hyd2T3sB4+bqknxhjAkmfS/qa7/udwxkvnrVcjQsAAPBlONEWAAAg\nAWUJAAAgAWUJAAAgAWUJAAAgAWUJAAAgAWUJAAAgAWUJAAAgwf8D+4vwJDQ412oAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a43d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 8))\n",
    "sns.violinplot(reg_data_2, groupby = ['PCT', 'CRP'], names = ['PCT', 'CRP'])\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now, let's do some linear regression to see if these two variables are correlated.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "slope, intercept, r_value, p_value, std_err = linregress(reg_data_2['PCT'], reg_data_2['CRP'])\n",
    "# The linregress function takes arguments for the x and y values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We use the *linregress()* function that is part of the *scipy.stats* module.  It returns five values, hence the fact that we put five computer variables names up front.  Here I have chosen descriptive names, precisely for what the five values are.</p>\n",
    "<p>The first two are to do with a line we can draw across our eventual plot.  It creates a mathematical equation that represents our data and from which we can make certain predictions.  You might remember from school algebra that a straight line comes in the form of $ {y = mx + c} $, where *y* represent the *y*-value for every *x*-value.  The *m* represents the *slope* (how steep the line is) and the *c* represents the *y*-intercept.  That is where *x* is zero (i.e. where the line crosses the *y*-axis.  In our example code above called *intercept*.</p>\n",
    "<p>The *r_value* is the correlation coefficient.  More about this below.</p>\n",
    "<p>The *p_value* is our good, old friend and the *std_err* is the standard error.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slope of the line is 10.3586483239 \n",
      "\n",
      "The y-intercept is  -3.92988359403 \n",
      "\n",
      "The correlation coefficient is  0.966276272656 \n",
      "\n",
      "The p-value is  1.20224468352e-15 \n",
      "\n",
      "The standard error is  0.563489991611 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('The slope of the line is', slope, '\\n') # The '\\n' is an empty line\n",
    "print('The y-intercept is ', intercept, '\\n')\n",
    "print('The correlation coefficient is ', r_value, '\\n')\n",
    "print('The p-value is ', p_value, '\\n')\n",
    "print('The standard error is ', std_err, '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Before we go any further, let's plot this data.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WN92/9Uv3bn3T/Vu+Uh9Ywax4UvzD3ILPuS/ucObiKLMZt1RPxsMcO9jL4We2srUryfh4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\nFk4M9PP4XAAbH09973E83yc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ODg4zei9VqgcDFkee7ebY/h6SFQYq3ysOY21JhJc9l0xE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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108a93400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 8))\n",
    "sns.regplot(reg_data_2['PCT'], reg_data_2['CRP'], ci=95, n_boot=1000)\n",
    "# regplot takes many arguments\n",
    "# Listed here are the x and y data values\n",
    "# The ci refers to calculating a confidence interval (value given)\n",
    "# The n_boot gives a value for bootstrapping to get the ci values\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>So, the slope of our line is about *10*.  That means that for every increase in the *x*-axis PCT level, the *y*-axis CRP value increases by *10*.  This value is positive, hence we can say that there is a *positive* correlation between thses variables.  If one goes up, so does the other.  In a negative correlation the *slope* value is negative, meaning that as one variable value increases the other decreases.<p>\n",
    "<p>The intercept is almost *-4*.  It is just a mathematical curiosity, so as to be able to draw the line.  Certainly if the PCT is *0*, we can't have a CRP value of *-4*.  So, you have to use some common sense.</p>\n",
    "<p>With these two values, though, we can write an equation in the form above ($ y = mx + c $).  Here we go: $ CRP = (10 * PCT) - 4 $.  So, given our model, we can predict that in any patient in the population, a certain PCT value will correlate with a calculated CRP value.  Neat!</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The *r_value* as mentioned above is the correlation coefficient, also known as the *Pearson correlation coefficient*.  It gives us a numerical value between *-1* and *1* and represents how well the two variables are correlated.  A perferct *-1* means a perfect negative correlation.  All the dots on the graph will fall on the straight line.  A perfect score of *1* is perect psoitive correlation and a value of *0* means no correlation at all.<p>\n",
    "<p>It is common to find this value squared, which is called the *coefficient of determination*.  This means we only have to deal eith values from *0* to *1*, so simply a value to tell us how well correlated the values are.</p>\n",
    "<p>In our example above we have a Pearson correlation coeffienenct of about *0.97*.  This means the variables are well correlated indeed.<p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### p-value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>A *p*-value can also be calculated.  In our data set above it is well below 0.05.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### IMPORTANT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Remember the dictum: **Correlation does not mean causation!**  Even though variables are correlated is does not infer a causal relationship.  In our example here, a PCT value does not cause a CRP value!</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using our appendix data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Let's do another example using our appendicitis data set.  I'll just run through the code.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing and verifying our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>File</th>\n",
       "      <th>Age</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Delay</th>\n",
       "      <th>Stay</th>\n",
       "      <th>ICU</th>\n",
       "      <th>RVD</th>\n",
       "      <th>CD4</th>\n",
       "      <th>HR</th>\n",
       "      <th>Temp</th>\n",
       "      <th>CRP</th>\n",
       "      <th>WCC</th>\n",
       "      <th>HB</th>\n",
       "      <th>Rupture</th>\n",
       "      <th>Histo</th>\n",
       "      <th>Comp</th>\n",
       "      <th>MASS</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>38</td>\n",
       "      <td>Female</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>NaN</td>\n",
       "      <td>97</td>\n",
       "      <td>35.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>10.49</td>\n",
       "      <td>10.4</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>32</td>\n",
       "      <td>Male</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>57</td>\n",
       "      <td>109</td>\n",
       "      <td>38.8</td>\n",
       "      <td>45.3</td>\n",
       "      <td>7.08</td>\n",
       "      <td>19.8</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>19</td>\n",
       "      <td>Female</td>\n",
       "      <td>1</td>\n",
       "      <td>16</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>NaN</td>\n",
       "      <td>120</td>\n",
       "      <td>36.3</td>\n",
       "      <td>10.7</td>\n",
       "      <td>13.00</td>\n",
       "      <td>8.7</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   File  Age  Gender  Delay  Stay ICU  RVD  CD4   HR  Temp   CRP    WCC    HB  \\\n",
       "0     1   38  Female      3     6  No   No  NaN   97  35.2   NaN  10.49  10.4   \n",
       "1     2   32    Male      6    10  No  Yes   57  109  38.8  45.3   7.08  19.8   \n",
       "2     3   19  Female      1    16  No   No  NaN  120  36.3  10.7  13.00   8.7   \n",
       "\n",
       "  Rupture Histo Comp  MASS  \n",
       "0      No   Yes  Yes     5  \n",
       "1      No    No  Yes     8  \n",
       "2      No    No   No     3  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('MOOC_Mock.csv')\n",
    "data.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting admission white cell count and temperature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x109b55be0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YhaonL28pCEItLky3w1bgh9FeiocsetpreXlOq6tbpy7PYYo6eDkMQ23ttg5d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\nRwhiAAAAjvz/vpStkFxDMrwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f450f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_2 = data.dropna(subset = ['Temp', 'WCC'])\n",
    "\n",
    "plt.figure(figsize = (10, 8))\n",
    "sns.regplot(data_2['WCC'], data_2['Temp'], x_ci=95, scatter=True, fit_reg=True, ci=95, n_boot=1000, dropna=True,\n",
    "            label='Correlating admission WCC and temperature', color=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "slope, intercept, r_value, p_value, std_err = linregress(data_2['WCC'], data_2['Temp'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.041778956836434247"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16559394522007634"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.045022859353589129"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.020662910878972714"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_err"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}