{ "cells": [ { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# HIDDEN\n", "from datascience import *\n", "%matplotlib inline\n", "import matplotlib.pyplot as plots\n", "plots.style.use('fivethirtyeight')\n", "import math\n", "import numpy as np\n", "from scipy import stats" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# HIDDEN\n", "def r_scatter(r):\n", " plots.figure(figsize=(5,5))\n", " \"Generate a scatter plot with a correlation approximately r\"\n", " x = np.random.normal(0, 1, 1000)\n", " z = np.random.normal(0, 1, 1000)\n", " y = r*x + (np.sqrt(1-r**2))*z\n", " plots.scatter(x, y)\n", " plots.xlim(-4, 4)\n", " plots.ylim(-4, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Correlation ###\n", "\n", "In this section we will develop a measure of how tightly clustered a scatter diagram is about a straight line. Formally, this is called measuring *linear association*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The table `hybrid` contains data on hybrid passenger cars sold in the United States from 1997 to 2013. The data were adapted from the online data archive of [Prof. Larry Winner](http://www.stat.ufl.edu/%7Ewinner/) of the University of Florida. The columns:\n", "\n", "- `vehicle`: model of the car\n", "- `year`: year of manufacture\n", "- `msrp`: manufacturer's suggested retail price in 2013 dollars\n", "- `acceleration`: acceleration rate in km per hour per second\n", "- `mpg`: fuel econonmy in miles per gallon\n", "- `class`: the model's class." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "hybrid = Table.read_table('hybrid.csv')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
vehicle year msrp acceleration mpg class
Prius (1st Gen) 1997 24509.7 7.46 41.26 Compact
Tino 2000 35355 8.2 54.1 Compact
Prius (2nd Gen) 2000 26832.2 7.97 45.23 Compact
Insight 2000 18936.4 9.52 53 Two Seater
Civic (1st Gen) 2001 25833.4 7.04 47.04 Compact
Insight 2001 19036.7 9.52 53 Two Seater
Insight 2002 19137 9.71 53 Two Seater
Alphard 2003 38084.8 8.33 40.46 Minivan
Insight 2003 19137 9.52 53 Two Seater
Civic 2003 14071.9 8.62 41 Compact
\n", "

... (143 rows omitted)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hybrid.scatter('acceleration', 'msrp')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the positive association. The scatter of points is sloping upwards, indicating that cars with greater acceleration tended to cost more, on average; conversely, the cars that cost more tended to have greater acceleration on average. \n", "\n", "The scatter diagram of MSRP versus mileage shows a negative association. Hybrid cars with higher mileage tended to cost less, on average. This seems surprising till you consider that cars that accelerate fast tend to be less fuel efficient and have lower mileage. As the previous scatter plot showed, those were also the cars that tended to cost more. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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25+5b/AjhClpVdE6ePMlbb73FU089Za98hADsUyBk3zUhnK9Vs9e6d++Ot7e3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\nx86jxnyvlF1jy47/o6Kyhs7+nUj8+WM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hybrid.scatter('mpg', 'msrp')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Along with the negative association, the scatter diagram of price versus efficiency shows a non-linear relation between the two variables. The points appear to be clustered around a curve, not around a straight line. \n", "\n", "If we restrict the data just to the SUV class, however, the association between price and efficiency is still negative but the relation appears to be more linear. The relation between the price and acceleration of SUV's also shows a linear trend, but with a positive slope." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "suv = hybrid.where('class', 'SUV')\n", "suv.scatter('mpg', 'msrp')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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qq+8UOiIijYCrrL7TQgIRkUbAVVbfaaQjIiKmUeiIiIhpFDoiImKaOofOiRMnSE5OJioq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\nXb16ldmzZxMfH09wcLCj27m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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "suv.scatter('acceleration', 'msrp')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You will have noticed that we can derive useful information from the general orientation and shape of a scatter diagram even without paying attention to the units in which the variables were measured.\n", "\n", "Indeed, we could plot all the variables in standard units and the plots would look the same. This gives us a way to compare the degree of linearity in two scatter diagrams.\n", "\n", "Recall that in an earlier section we defined the function `standard_units` to convert an array of numbers to standard units." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def standard_units(any_numbers):\n", " \"Convert any array of numbers to standard units.\"\n", " return (any_numbers - np.mean(any_numbers))/np.std(any_numbers) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use this function to re-draw the two scatter diagrams for SUVs, with all the variables measured in standard units." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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eno5WrVoBAO7fv48TJ05g9uzZGDduHGJiYnDo0CFRiySSmvLBxdJHj3lTD0mW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\nrgIYblpJAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Table().with_columns(\n", " 'mpg (standard units)', standard_units(suv.column('mpg')), \n", " 'msrp (standard units)', standard_units(suv.column('msrp'))\n", ").scatter(0, 1)\n", "plots.xlim(-3, 3)\n", "plots.ylim(-3, 3);" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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F+/btw969e3VdJ1G5ONpb4/33/EQ3U1Vfnb9EgMA2+HPnzmH8+PFwdnZ++SAjI9SpUwcz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\nuLm5IT8/Hzt37kTPnj1x4sQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Table().with_columns(\n", " 'acceleration (standard units)', standard_units(suv.column('acceleration')), \n", " 'msrp (standard units)', standard_units(suv.column('msrp'))\n", ").scatter(0, 1)\n", "plots.xlim(-3, 3)\n", "plots.ylim(-3, 3);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The associations that we see in these figures are the same as those we saw before. Also, because the two scatter diagrams are now drawn on exactly the same scale, we can see that the linear relation in the second diagram is a little more fuzzy than in the first.\n", "\n", "We will now define a measure that uses standard units to quantify the kinds of association that we have seen." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The correlation coefficient ###\n", "\n", "The *correlation coefficient* measures the strength of the linear relationship between two variables. Graphically, it measures how clustered the scatter diagram is around a straight line.\n", "\n", "The term *correlation coefficient* isn't easy to say, so it is usually shortened to *correlation* and denoted by $r$.\n", "\n", "Here are some mathematical facts about $r$ that we will just observe by simulation.\n", "\n", "- The correlation coefficient $r$ is a number between $-1$ and 1.\n", "- $r$ measures the extent to which the scatter plot clusters around a straight line.\n", "- $r = 1$ if the scatter diagram is a perfect straight line sloping upwards, and $r = -1$ if the scatter diagram is a perfect straight line sloping downwards." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function ``r_scatter`` takes a value of $r$ as its argument and simulates a scatter plot with a correlation very close to $r$. Because of randomness in the simulation, the correlation is not expected to be exactly equal to $r$.\n", "\n", "Call ``r_scatter`` a few times, with different values of $r$ as the argument, and see how the scatter plot changes. \n", "\n", "When $r=1$ the scatter plot is perfectly linear and slopes upward. When $r=-1$, the scatter plot is perfectly linear and slopes downward. When $r=0$, the scatter plot is a formless cloud around the horizontal axis, and the variables are said to be *uncorrelated*." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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//Suff/zxxxJKS+M8/Y6XLnWjp4ftf926ODQ0iB5B1zT+MG/KFPVWxgeQmqpi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\nzWYztm3bBkVREBsbi7KyMgQFBYmO5cFms2HPnj3IzMxEQIA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_scatter(0.9)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TgKi58arbTfSWk41UCNBd7znNKeNDFkgMhvul4gnI55MZ8R3azolaiFQgx/zi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\nTk6kA/Nrr6Vjx44A7r03bDk3nR/x2bqM4ODatUG4XDpmztQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_scatter(0.25)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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K26G1NSnsh2/nBzX6iKdNU/HmmwOYPl3Ftm0khjoQEEyaEBqs1OG0nxsbJWze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\nb79NogDeeIO0mZqq4t57FZw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xulwq8vNlrFnjBwBMnqzixAmSqNHQIOmbYdpS3M46M7af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\nXLgQra2tqtYFAGazGZMmTcLWrVsRERGhdjl96urqsHz5chw/fhw1NTU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/fO+9Eq5f5ynjn02b3Ni82Y3MTAl2O3l/S0sbJClPfe/27XHYt8+Jnh6j/0V+\nvoxbt2T09vLYuNFN+VbU1HjUz6T30OjtBa5dM1pzKudXP6BU37ARaGiqcnMMZKWpdV4rLxfR3MyF\n5KCnoL+x9PdzOH1aYAt0DABMkEeFkSzQaC/o7dvjsHmz29BFN3s2iYbPn6cjXLN874MPinjwQXMx\nyMig888pKTL++7/9ZV6LFw/g2WeNOVSfzwOnky5FczqBBQt8kCRgxw63ehMYGCAlZqLIYdkyD3W8\nVisRb2X6yP33i+jtFXDhAo/sbBlXrvgjX615kddLn9+WFv+iX1aWCzNnxqG+njSIXL/OYdmyRIgi\nR5nKK9Os9Vaa2nZongfS02X89Ke030WwJ6DychF79jhx5owFNpuMrVvj8cYbbhb5MgAwQR4VRrJA\no0SKFy/6cN99loDizvNASYlxQGk4N4LSUgmDgyI6O0k03tgooLTUv039TLorVzg4nQKamkqQmytT\npWhHj5LIUpYBlwvUjaG62gOO84uw8v8cB3X6SHk58Oc/0wt7Bw70qwtkpaUiVqwgbdH6+ub775fU\nxcHGxhbU1xdTTyjV1R7Ex8tq2Z0irB9+6DTkzPXt0GYOesGegIiIAxs2xLMFOoYBJsijwEgWaJRc\nos126XYhvGAq7mYlWVZreDcCZV9aX+O8PBG//a0LPT0c0tPp7U2aJFPpDCVNof2MdXUCzp3jqcd8\nWSYpi92749SoesYMEYmJMqqqiI/F11/zuHKFjvg9HnqBTDGg37o1Hvv3998WSB5JSWQKx8WLPLKy\nctHRQYtofLys/lv5/8ZGHq++mhTwcyjY7fqhq/KQT0Bm3792sbavL/B4Lcb4hgnyKBDJBZpA4m4W\npZWW6jv/ws9biyJZ2IqPB+LjiZFPZydRDu0iYHOzgJYWHosWDaKuTsDBgxbVU1jvW7x3rxMDAxK6\nuuKxenWimvfV5pP37HEiP5+O+NvbaYHu6yPH29XFQZZpe06/s1ySwUZTuYHohVX7OX7yk0HTc9Pb\nS6dmenuHfgIy+/6Dmfkz7h6YII9xAol7oChtODcCva/xokV+4fjgA5faZrxuHUkV+CsTSLXD0qW0\nw9rp07SQ1tcL2LGDlMEp+2lpoY+/v5/DxIkSdu50obubA88DWVm0QJeWSti82YWMDBlnz9LOci4X\n1H/39sKQx92yxUnly71e8nl6e4G8PAmSBNVyVJsbzsoCXniBTs0M5wmINX4wACbIY55AC0iRbCTQ\nCozXS9ct5bEPAAAgAElEQVTexsUR/+TmZgHbt8fdjnZBibaSSlByrDNn0tHo9OmSWga3dasLGRmi\noVSOOMOlUGVoogh8+qkTX31lQUmJiKqqBGzY4Mbp0xaUltL7mDFDVAU2OZnkxLV53G+/FSDLACCj\nqEjEwADw0ktDD1edOZOMbVLKAGfOFIf1BBTpxg9mYj82YYI8xgm0gBTJRgK9z4O+nO63v3Xh668F\n2GykO66vz2eaSsjLE2G3y2huJq3ULS1kbFJLi983wunkUFwMxMXR+W+lfldfhrZunRsbNsTj44+d\n+OADN+LiyEJkSwtHpRL6+znKHP9f/7Xf1EyostKL5mYe6ekyNdHEzHK0vp6H0wksXeqv0mhrI1Ua\noQigVjQVIyllsXakjR/M+2JswgR5FIhk9BKsyiIajQRm5XRff81j7doE9ZHd4xmkor05c0R89FE/\nkpNh8D9+/fUEfPKJE1VVHjV9sGqVx1Cepyye6cvQBAFqmoDnibtdVVXC7U5B/zZ276a78y5cEPCT\nnwxSZkI1NZ6AE02UiFX7uTweDs88k6xWiQRqEAn0fZuJ5oMPXoqIaxlLgYxNmCCPApGMXu60x4FZ\nOd1DDxHBVVqLr1xpx5EjiVR0fuaMgOPH6bxuQoKMN9/0oKODp9IH2dmiabNFdbUH995L7/uBB/xm\nSQUF5LWiyOHaNQ47d7pw6xaHGTNIvTN9nvzla+XlIg4fJib12uNLSpLx3nsuzJjhNw0yM7MnTwCB\nBTDQ920mmmVloX8XwW7szPtibMIEeRSIZPQSTmpiqMg81Mi9vFyk/JKXLUvEpk1unD/PQ5aBCROM\n0XlTE2fIC8+cSUSxsxOUW5vXC9w2CgTHkVFM8fEcXnghQTW5t9lI56DXK6G+3opbtzj09MiYOdOH\nJUu8ePVVf3R84EA/ZJnDO++4MXWqhLQ0CeXlJAd97hwPh4PD1as8pkyR1Hy41UpM6l9/PYEyDZo9\nWzTkkufMEQ1mSVoB1H/fyoTr/PyRiWawGzvzvhibMEEeBSIZvehTE6II1dlML6pmF3B5uUiZ6AQy\nK9Lv0+HgsHZtovqzL78khkFLlniRkjIN7e2A10uE1OEg237zzTjV/3jOHDGgh8OxY4KhXfnhh2mB\nkWXgL/8yGR984KJeu3u309AA43Jx+Pu/93+u2lonLBZSX/311zxcLg63bnFwOjn86lduXL3KYeJE\nUsZXU+MxtENrxU4R1dZWLuC4J/337fFweOqpZBw/3m8QzVCmjGhd+ALd2Jn3xdiECfIoEK3oRTHV\nCSSqZpE5x4VmVqRlYIBErRs2uJCdLWPLljjVdP611xLUSojERDJ8dOvWeAiCjC1b3HA4ONx/P6nX\nPXNGoCZYK3Pprl41Tm/meZFycFPao/Wdch0dPPLy6LRGdze9veZmHo8/TlIGEybIWL7cH03v2uVE\nZqZM1UDv2+fEsWMCHA6ywFhRIZp6RSvne9Ys+vtUvm99qqOxkceCBb6wRVO5sWrLBFlaYnzABHkU\niFb0cuaMcbKzVlTNInO9WVEoF/iJE3QL8+7dpDnkxg3zSgil7O3yZR7Tpon45hsLbt3i0N4uQxBk\niCJHRe67d9ONG0q7sn4it9JerW/oGBwk5XCtrWSySGIi/bkVk/6CAhlnztBi3dnJ49YturTP6wW6\nu3m8804Curo4ypRf75thdhNTvm99qmO4Aqp8Z9u2xaO62oPERJL+CWakz0rgxgZMkMcRDQ08JapK\nmZniZDZzpllk7m+93r49LuiUZeXCvnyZFrGzZy3YsCEen37qNK2E6OsjAuT1crh5k6fE+tNPnbh2\nTS9qglqyVlHhQ0WFMcLfujUee/aQmue9e51obibHtHp1IgSB+DF3d/MYGJBx//2DBqMjMgkbyMmh\no2mOA5KSYCjtq6nx4Gc/82L16kScP8+rUbXeNyOYyAZrmVbEMi1t6EtSubG2tfFYsyYBR48ao3It\nrARu7MAEeRxht0vYsCFRzdM+9JBomr4YylchUPQU6FHZZiP/drtJFcKNG3TUWl7uQ00N8Td+5RXa\n0e2rr4j1pGISNGWKBLtdQl2dBWlpMjIyZNPKga4uDunpwKxZInw+oKODiCRAOuwUc3wScYsGo6O6\nOmK+rywSJieTRbzNmxMgCDJefdWry0MTc3nSpCIZbgy9vUOnn0JpmT50KBuFhcG/Z+U7U0yfmpo4\nAIH9L1gJ3NiBCXKMMpzHzIwMGYsXD0CSiFNbc7N/9FJbG6+6pum3G2r6RP+onJAgY2CA5IitVhlZ\nWUQgT54cQE2NoLYhp6bKan2v3j3NZgPcbr9J0Pr1bvzoR36BOnzYqS5S5ufLOHasH19/LcBul2Cx\nEK9ki4UuxdO70PX08OpNJyvLjbi4OHz7LU8Z4f/sZ15wHPDKK6S0DjC6vCUkSNi924fubh7r17ux\ndWu8emN48knfsL4/vVi2tlpvT5MOjJnpU7DIl5XAjR2YIMcow3nMVOwyb9wAFi6kGzDWrElAQYE8\nosdX/aOyYgj/xhtuKjq8dMmKVav8FRg7djhx+LATDQ08srNF7N3rxJdfkpK57dvj8PLL/mh0qJl9\ntbVOQ9NIebmIgQFZ9bnQ1ypPnaosxAF/+pOMP/7RakhHAMCqVYmoqnIjPx+4cEGg0hwuFyAIHNUS\nvmePE+npwAMPiIbKllDPs3JOlYVQUbTi88/JoqfNBtPRUQqhRr6sBG7swAQ5RhnOY6YSOe3ZY6Xe\nm5DgN705eNAS9nYVAqU39CV3oggqgiwokDFrlt8IX5KAtDQyzmjLFjcGBvzRqH6slDY9MDjIUTMB\ntZUif/u3fvHbuNFNif5bb8WjqsoLh4NDaippd9ZuIy5OhsUCVFURI3yPh5xLRbTz8kSsXetBayv9\nxNHby+HJJ32mkap+VNNQYnn9Oih3OuUmWl3twQsvJJgKeqiRLyuBGzswQY5RRvKYaTZ6SVn0CWW7\ngR63h7qw9UNRP/6YRNBKakGJ8PTbkSSoIpadTaYyX7vGY/JkCUlJMjWmKjeXbt7QV4oMDnK4cYND\nRgYAcABk/OAHg0FHOuXn01Oxa2udmDPHhw8/dKpldNoyOEUslfFSZjfPcMXywAH6RtnXx1H/bybo\n+rFWHR1AsFwyI/ZhghyjjOQxUz96yW6XqTzs8eP9aGzkA253uGkN/VDU1lZi8q59vDcTC61AHzhg\noew8X345iZpgrdQFOxwccnIkyDIxqtdG5DNnipTArltH11cDxIO5pYVHYaEEr1emfu9wcHj8cRGi\nKGD16ngsX04v8Fks5Pwq46XMxDfY92d2w9Nvo7RURFWVG6Wl5AZkJuj+cjpWRTFeYIIco4zkMVPJ\nJStiYGYbuWCBL+D7h7sqr4/MFZP3wUEOZ86Q0ji9WOjFSZllpyzONTcLOHeOrq0+eVJAaioMJXQ7\nd7rQ0cEbmkX0OeWUFFCTTTZvdqOqyq3mtBXxKy8XsWWLG+fP01NZRJHDqlWJyMmRcOMG0NXF46OP\nnIiLk3HPPcADD0hBvz+zG15FBRHwxkYRGRkCli2jPaSD3ZBZFcX4gQnyOEQvBvrH4aEu2OGmS/SR\n+c2bfltNpTROv28zcVIiy0mTZPW9+soMQSDlcNrP1dAgYMOGeMNEkClTZE2VhQsdHUnq+xYvHjCk\nK2SZnLOMDBk+H0lL7NrlQkMDj/vvF7FyJRHj9evd1OJpTY0HM2b4nwACpX6CDQ+w2RpRV1eC5mYB\nOTkSKiu9aGrikZJCFg/r66Prfc0YXZgg3wVMny6pdb5paSQKDUZ5uYhjx/rR3U1m0skyqBxwIJTI\n/OJFH4qKLLBYZGzb5kJ/v780rqBApoTKrNNNaSdWcsstLRw++cSJs2cFFBdLaGnhkJ0to6eHo4So\npETEm296cM899Kiq0lISsZaXA198AWrhUF8i19ZGV3XU1HjUsVI1NR6kpwM7d7px/Tpw+jQduff2\nkkXHuXNJlUVPD71Qpzwd6E2F8vP9AspxFtjtspqu0KZqamudeOaZZLUiQ5mQbd7wwxiLMEG+C/D5\nOINXbzB4HpAkzlRMtJhFgPQAVvL4fvq0gLffdqlNDP39/rFOwTrdiIiSbsKWFg4VFcbc8J49ZOHN\n4+FQVZWItjYeO3ZIph4RdXUC5s1LV5tBrFYZ2dnBJ3P39vr/bbORY1NM7fVDXtPSZBQWSmrUv2KF\n1zQSVsRdeZKwWPyf2eHIVtMpem8RpcJE35pu1vDDGJtETZB37NiB9957D1evXkVxcTHefvttPPLI\nI9HaHSMIoZZgaQklLxnK4l+gJgbthOjdu53o6vKPQFLQmyXpBaqnh0NFBZCeLgX1iNC7o7W1cbdr\njj2wWkGJY1KSUWQBqNUq2ioSUl7XD6+XPElkZkqYOFFCQ4OgCrjZzebiRd5Qp11WRp5aWlr8JYtG\nbxFy89C3prOc8fghKoJ88OBBrF69Gps2bcKcOXPwm9/8Bn/3d3+HL774AtnZ2dHYJSMIw8kxhvIe\nvWh3dpI65AsXpqG3lyxIXbzIm5amaSdEt7QIWLky0SDqdXV+s6ScHAmlpXQ0+53viOB5Gd98I2Dv\nXidu3uSQmytTjRp2u4xr14i1ZmYm/f7Zs33wejmcO8er00pee01SG0LS0yVkZ0tYs8aNigoRnZ0c\nVYcsCMDAAG3tuWePf7rJtm1kcGtKikyZ3Ac7t7m5/mkr27fH4ZNPSDUIz0NNxVy/HpoJFGPsERVB\nfv/99/GjH/0IixYtAgC88847+I//+A988MEHeP3116OxS0YQhiqhM0s9hOKXoBcWm42u5tCOQPrs\ns34qjz1zpg/btrkwZYqIwUEOa9a4kZQEyntYa2pfWelFVVUCdu1y3RZQ4JVXErF48YC6j5oaD3Jz\nycKXPhrnedKJp31/ayuPX/6SzhdPmSJjyRJ/OuDjj52GVMnGjW643eTmcu2a0So0Lc0v6gAwYYJE\nmf8E+z4yMsi0lYYGHv39HJYtS0JXF5kP2NAgYMECH1W3zXLG44uIC/Lg4CDOnDmDl19+mfr5X/zF\nX+CLL76I9O4YITBUCV2g1IM21aBfSNKKtiIM+ihYm391ueg89sGDpAVaP8du3z4nDhywYPp0CXa7\njO5u0sjR1cVBFDmIIqA0fIgivQ+rVUZ9PQ+rFbponENKCvH5aG/3G+tXVdFGR6mpMh591CiWH35I\ndz5mZEiq34Y+B15cLIHjgBde8H+m48f7Da3VyvchiqShxu/2Rr6rzk6gr0/AokUDsNlkyLI/Emad\nd+OXiAtyT08PRFGE3W6nfj558mT813/9V6R3N24YTc/aYPli5XeBF5JE1bDI66UbNLT5V73pvGLh\nqc+Hnj4toLo6EevXu6n97dvnxJIlXrz4YhIV0SqjnqxWGT4fh1dfTTSIpM1G/Cx+/OMkbNzoViP1\n0lKR6vorKZFgsRjFTsndKttrb/d/lgMHrNi7l3gvFxQQA6Lz5wUcPOiEJMn49lsBt25xAYcG6G+G\nitubzQbDjYpFwuOfmKmyaGxsHO1DMOVOHVd3dy7mzUvXXJjXYLe33JFjy8rKhdXqF7qsLBcaG1uo\n3+mF8+JFH2y2S6bH/tFH/UhN9cJikfHP/+xFbu4gAA5Wqz89MHWqpIqltjV65kwRW7a4cO0abRIv\nCBKSkzldRCshJ0fE5s1ke+vWJQAglpgffdSPGzck5OQAHg+P1lYBNTUexMXJ6ry9vDwRmza50dJC\n2qMnTmxGY6OHOjccZ4HFkoNNmzhMniwjPl7GlSv+RpEFCwbx7LPGNI3if9HeTvLTmZky2to4w7m7\ncGEa9ZlaW62w2xvR0TGd+vnVqyIuXx79ayRWr1MgNo8t3AniERfkSZMmQRAEOBwO6ufd3d2GqFlL\nJEafR5rGxsY7dlx1dXTzRmdnEubODbzvSB5bYaE+JxkHnp9O/U6/kHTffRZ1//pjv3FDwlNPWQEA\n3/kOAMSpeU8lN/r22wmoqfHAbpewebObytHW1HhQXCzpTOKNDR85OTKeeSaVet/JkxZ0dXFITOTQ\n12eBKNLjmHbudKnHunjxACWmhw/nqY0b+fky4uMlOBw89Zq9e53Yt8+qek4nJdFt10oKZfHiAaqG\nWJtP1567vj6/uOflicjK4lFXV4KsLJmK3rOyBBQWTg/7qSmST1538noIl1g+tnCIuCBbrVaUl5fj\nD3/4A+bNm6f+/D//8z/x9NNPR3p344bR7LYKlpNUfme2kKRc7HovicxMkuPVIstkgvTgIPl3Vxcp\n/Xr3XRfcbjrytVplADJSUmRdlMhh/34n2tp42O0S+vv9JWs2G6kh3rGDVDkodc5r1tClcrdu+ZtJ\n9E0hDQ08fvWreFUElQVA7Wu+/FLA0qUDOHdOQFqabGjLVtI0+m2npMjYscNpWITTGwRpbzD79jlx\n8iRxrFN8M8L1qBitaSFsbNTwiErKorKyEosXL0ZFRQXmzJmDnTt34urVq/jJT34Sjd2NC2LdszaU\naReKl8TNmxLIwpsfvTAojmkeD5lZpxU1n49DSgoMZWrJycSnWImaP/7Yaciz/u//TZzTlNbjsjJR\nF4FK2LjRjXvukZGWRm/f6eTw058OYPVqktLo6OAMtcA2G3D9OvHH6OvjsHZtgtpkMm2ahJYWHlVV\nHkOJXkmJFLCxJtCiaEsLT032Hk698Wj5XLCxUcMjKoL8/e9/Hzdu3MDGjRtx9epVlJSUYP/+/bj3\n3nujsbtxwVhcOddf7IqXxGef9QOIC/rahARZrekFgD17lMhXxo0bJHp97DF6WnNLC6/aUQJGd7n2\ndh6SJKqt4haLjI4OHuvWucFxMJkm3Y99+5y4fJlHVpaMzZvj8b3vDQLA7ZZmCa++6h+JVVoqoaoq\nAS+9NID77vOhocGC732PmDQNDJDjW7qUONXl5EhDjnbSi9bevU7dU5I04qem0XryYoZHwyNqi3ov\nvvgiXnzxxWhtnhEGkXx81G5LaYBQLvaKCh9qa31wOKw4dcpfsyyKMLy2sFCiKg+sVlInrI12RRG3\np0oDXi/J16akyGqVRHGxRC0I3nMPKXvTtor7F9c4dHbSItHfzxuqNqZOlVBV5cHkyRLcbuCnPx2A\n203EuK+PGO//6lcJ+MUvRCo637XLhcREkvddutQLgKRmiooklJRIVGlbIJOhCxfIwmNqqhySR0Uo\n3+sDD4iorXWiqcnYCRnu30w4MMOj4REzVRaM6BGpx0d9K3NenkhNqbZYZDzxRAq1n/JyEX/8o4Cv\nv+axezfxncjOlpCWRvsy68Xp9GkBsgzDghrPA3/3d/79b9rkpl6jRKXahTtlcU1fDqe36UxOJl19\nAOD1ckhIAH796zgsXjyAc+d4lJZKWLmSNKN0dtLReU8Ph/R02eDdXFPjwc2b9LBZxRtabzLEceSm\ntGOHf4r0cOrHtdTXCwFL7sL9m7HZQv9bifUUXKzCBPkuIFKPj9pWZoB4FTscnOqtfOCAhSpVu36d\nND0oDmVkEgiHgQEBK1fGYedOt/peWaY9hydMkNHcTIteRwePjg6O2n9LC/0ah4MPOPB069Z4fPih\nE9eu8XC5uNvRt3+f2dlkMGxJiYibN8kE7C1b3JSgVVeTfLE+v61sTx+FKw5w2p8p3tDHj/dTlSda\nRzw9ZhFrKN9rUxNn+E5Cce4z23ZZWeh/K2MxBRcLMEG+C4jU46O2ldlsWwUFsq5UTca775Iqh2XL\n3FTkWF3tQX09D44j0ZQSTfod0GCoYJg8WUJ/Py3chYXG11y4wGPfPiJ0ubn+z97VxaG1VcDcuYPo\n7ubR0MCrPsdlZSKWL/ebwtfUkBri7m5aTPv6gLQ0Dlev8vjkEyeuXOGRna3kn40zAdPS/DXX/oVB\n8u/GRh4LFvhQUSHi9GkBb7zhRlaWC+XlcYZzbxaxhvK9mn0noUTJLOUwOjBBvguI1ONjQYGMN9+M\nUxe55swRDSVc58/TAqZMEZFlfTszwHEcnnoqWT02rQPapk0u9PaCmvwcFydj+3Z6/48+KmLPHifO\nnLFg5kwfVq70i2p1tQebN8eprde5uaR5ZNIkCfPn+yDLQHs7EeO2Nh7NzYJ6fL29JJLVC+yDD4qI\nj5fh9XJ49ll/S/kPfziAKVOIMP/2t8S9zm4n7nFKzXVKCqnk0EfC2miysbFFrQHXYhaxzp/vM/1e\ntdF0fj65SYX7hGT2N3P58nD+ahjhwAT5LiDUx8ehFonKy0Xs3OnGlSscHn7Y+HueB5UusFplZGSQ\niKy7m46sZ80SsWxZkioQ+ohs2jQJHg+wZk2CKnrt7QLee8+ttiQnJ5N9pqcDGzbEY906iRJVtxtY\ntsxryOkWFJBpIxMmAB4PqbxQSte0ka0skzTH/v3EYrO9nUdzM499+6z40Y8GMThobCmvqfGgrU1Q\nby5VVaRZ5eRJC3bscKK0VERBgQiHg4ckAWfP8qojXnm5CI6zGHwvtFNBlHPh9XI4c0ZARYXxe9VH\n0/qGmlBTIizlcOdhgsxQGWqRKBRhLy8XcejQNXR2JlHTOs6e5amURGcnj7Y2XhUIs4js3DmSUhBF\nGKohlK437Tw6vehXVIg4eZKe6jFxImkoOXDAgvx8GV4v+fm2bfGorvYgPl7GlCkSBAHYsCFBFT/F\nTEipqFCOXd9SnpQk4+OPrVi3zo3eXlKdkZMjoauLfC698b/+s3i92Zg3z7gAqFRcXL9uPoVEiz6a\ndji4IZ+Q9N/9sWP9kCRu2FUWjOHBBJmhEonFP54H7PYWzJ07nXIyy8+X8cgjPjQ28sjPJxUZ2s41\nM7EvLZVQXy9QZj5KOkF7jBxHmiuys6XbC4c8SktFNDTwhpx3aiqoRTolemxr47FmDbH37OzkkZ8v\n4bXX3FiwIMUw+aO9naQdqqs9hjx3VpaE558fRFycjPvvl9DYKGDLFmIzWlQEHDxoMf0smZkyrl8H\n2tuTKM9lZQFwzx4nMjJkABxWrPDCZiN+y2bfkVn+d9as4DdS/Xff3W2cGBNOlQVjeDBBZqhEeiFH\nH3UdPuxUS9wKCoD5831qnXJdHZkW7XDwKC6WUFEhqimQ/n7OkE4AiNDa7TJefJGUojU18XjoIRF2\nu4QbN3hwHIdDhyzYtcuF9nYO990noqlJMESPn3xC3Npyc0kjiJKD3r3bicFB4+SPadNIxPv++/H4\n5S892L2bVG5MnizhV7+Kx9NP+9DZySE1Fdi8OQFdXRz27XOiuFg0nGPlsyxf7qEEsLrag1//Og6l\npSJWrCBR+tmzPJYvT1TTFq+84oHdLhuqJoazZqA/LoeDvgk2NPDg+Wno6xNM650ZkYEJ8jhkuI0g\nka4dNTY+0ANElcftc+d4tLfzVK5X+V15uQhBII/uDgePrCwJiYkkup4+XUJ3N5nioU1p7NnjRE6O\nhN/8xooVK7z46isB6elEbLxeWtwnTSIexAsXJmLFCi+Vg+7s5LF+vRsHDlipyR+B0gc7d7rw9NM+\nqmFEGVXV3MwDoD2ktU8KHEf7ckycKBlqmhVjpEBWqArDKTnTf/eyTD9Z9PdzWLlywojq2BlDwwR5\nHDLcRpBI147qoy79AFHlcdvh4AwmPtqSuLIyCadOCXj+eb9t5pYtbjgc5LFaSSnk5EiorPSipYWH\nJHH4h38YxIIF/kqIb78led+NG93o6iL1xg4Hh//1v3ymjnZeL4fXX09QPTq0kz/Ky0V8+iltXH/t\nmtGwqK+PbCsvTzI9x6IIiCKH7m5g8WK/yO7d6zQ0n1y7xpnmrSPRlqwcl+JtfeUKh9paJ3p7gfh4\nYPnypIjuj2EOE+RxSKz4COijLovFPCXicBhzvR6PvyRu9my6CWLpUi+eecYvxEpKobLSS0Wnmza5\nTSPK6moPNmyIx5tvelBS4s9fK452Z8/y8HrJQh95XCceHUeP+qd119UJGBigj7moSEJuLv2zmTN9\n2LfPB56X1HZyWabbz7WfRfnOyA2Dzk9Pnx7aTL2RtMqbVWhMmCCjq4scG6tJji5MkMchsVLUr48G\nA82CKy6W8H//LzHxsVjIaCZFDJWbifYzAaCEWBkmGh9P/37CBNk0ooyPl/HRR06kpcl48EHJcLwA\nqOnSFRU+HD3qo1I4TU0cBIGeWJ2aKmPOHAm1tcSwKDdXQlKSjL/5G387+bFj/ejt5dTuxbVr3Vix\nwovSUpH6zu67TzJNIfF84POoMJJWef3N/MQJAU88QY7j4kUf7rvPwiouoggT5HFIrPoIBEqJVFT4\n65uViFF/M9F+ptRUWoiTk0lFgyT5I8e8PBEpKSQ9oa+EmDZNwmOPBY4alTI65fw98AAZnHrwoEX9\nb7tdxoULRLh2745DWxt/u86YCLwyPLWqivZj7u4mPh1K5K7kvufMGcSnn5LFxcJCMgpK2Z+y+DnU\neVTo6KDz0drBsUNhNrj2yhXSHm+zXRoXJvCxDBPkcchY8xHQHm+g6E/7mrNneWzc6MbEiTK6uznk\n5Ulq3fInnzhx6pSA2bP9k6Lz8kQ1J5ueLmLCBOMx6LvbrFZSYtbfD/zXfwlYuNCfi/7mG17tuFMm\nQq9Zk4CCAtng96FPxWjTM9rI/emnfZQ1qL4+OZxFNP08vtpa59Bvuk15OTGMOnGCGONv3x6HDz5w\nh/x+xshggsyIKuHkM/WG7YFeW1oq4eZN4+DQzk5i1ZmZKaO11b8gppgQKVGrmcjpH/O1grhuXeBc\n9OrViYiPJyVyFouM1lba72P79jj1ZlBcTKJnJT2jjdz1i4HaWuvOTph27wVC72LncHCBX6yD54kP\ndXIyiYw/+MCt3hQ5zmIoT5w5kzw9KMemPE2wSSHDgwkyI6qEk88M9bU8D7S1Getkc3L8Hssff0y3\nC0+d6q/wUJowDhywBHRO0wqi4uWsz0UrFRSDgxx++MMUNRpV/DaUnPbPf56Eri5O7SpU0jO5uRI1\nvilQrXVyMsLKCY90DSHQE5bDkY36egt1U6qtdRoabYZj98kgMEFmRA1RBHp6MGRnmUI41SEZGXrP\nDM0Ye60AACAASURBVImKDDdvjldzslOn+s3lt26Nx5IlXqp++PBhp0EQJ0+W1PbnuDiSi54yhd7n\nQw8N4tNPfWht5bFpkwubNyfA4eCwc6dbjdbr6iyorPRSn514Vgi4eJF0LRYVSWht5dQZeunpxO1u\nyxYXJk6UDZ2KQ1XNRGsNoaXFilu36O9Iby2q/29WIhceTJAZUaOuTjD4NgSL1sKJ7JKTabvO5GQZ\n99zjTxWcOSPg0iUBeXkilZv98EMnrl+nRePiRR6iCOzc6cK1axyKiiQIgoy//dsUKvJLS6P3OTBA\ne1won6+sTITTSXLJ6ekSrFbglVc8uOceGWfPkn1rqziU9MjatS7YbMC1azxsNhmyLGPp0mSDsf5Q\nES/P+0W/qYkDEJnuutzcQfT2xuuORT9mauRjp+5mmCAzooY+4k1NDR6thRPZtbfzlF3njh1OzJ/v\nU604bTYZW7eS1mbtMfT0GB3psrIkvPJKojoKKi8PBtEmeVPaInTjRhf1mpQUkkPVTlXR56OVEU1a\n0/jsbAn/5/8MoKREuj1lmtiMrl3rAUAc53bvdqK/P/SINxpDRjMy2pGcXIg9e5zo7iY55LIy+jsb\nauwUIzhMkBlRQx/xlpRIQaO0cKpDzKJpxYrz44+tWLx4AIsWeQ3m8AUFHlit8VSky/MyXn7ZC5+P\nw+7d8diwgQtoWan9WV6eUdjr6+kqC20+OjOTTCW5eZOMk9K2RX/6qVOtClEWDBsayMnq6uJgsUD1\nAREEMjcw2OLncJuDgi3CSpIPZWVK3bZfaPXfmdl3GMm5juMZJsiMqBHNeuhA2y4vF6mxS9q5f3a7\nDIfDgitXBCrSrapyY+3aRKpyorfXvPxO60PR3MxRBvrd3RxEUUZ6uvkC3ZIlXrXuWF+frB9F1dcH\nzJoloqrKo6ZknnqKpFDWr3cbFtb0ddXB0j/BxDFYZB3IqzkUohGxj0eYIDOiRjTroYPlSbWLe8rc\nv4ICWRUEfU5WsZXUVk5kZcHUslL7ea5fFyj/iZoaD5YsScD777vU8U45ORL6+jhs3uyCxeIvbdPX\nJ2dm0gI6e7aIhATi/1FQIFELe/qFtRMnBCQlQZ1kPVTqIJg4BousHQ7aqzlUURVFGCbJsMU+c5gg\nM2KSgQHgxAlBHV//6KMiOI6O7CwW2VRYzKJDrdBs3Rqv5kEnTZLUaDlQm3QgMjKICAsC3e5ts8lY\nuJDOIRcWioiPp+uTa2udaGnhMWGCDKcTWLfODY4D8vIk2GwS/uqvUqkoWHmvfqyUzYaATnpmohdM\ndINF1i0t1mGJal2dYLBQZYt95jBBZsQkJ04IhvrWlBS6HnfPHqepQJilM7TDUZWcbHGxhPh4Ce+8\n41YXqRQfZi3KI35PjwyLhUNzM/GpyMoS8dBDosGGUz8YNS5OxvLlSRAEkivu6vI3iSxfnkgJ98yZ\n/Xj00TgcOKA3svenS4qKJBw86MSf/+zvptuwwR2yWAYT3WBpptzcwWGJalOT39C/r49DRUVoN7y7\nESbIjJhEX896+TKPuDj/I39mJvHsrapyq6JkNjRUQT8w9cIFAWvWJODIESeefFKEskgliv6uOLtd\nRm8vSS8sXZqItWs9eO45/0Lcrl0uZGTIqvmO0uBx+TJPCdfAAIe2NqLyX31FJoAor9dXoWRktAPI\nN4imNoUiisDXX/MoLxfR3c1j506SgglVLIOJbrA0U0ZGO44cSQx7TaCggLjFrV5N8vRHj/rYgl4A\nmCAz7iihrrbr61m9Xo6yu1yyxEvVANfWOoMKRFYW8MILdL7XLJLU51cVn4rqag/a24mAKr7Lvb1A\nQgIoE6CDBy3YtClBFf+yMjIJG8Dt9IKs7tesCkWSfACCi6ZZDri0VAp5AXW4uX1J8g3rfbFqdhWL\nRFyQd+3ahQMHDuDs2bPo7e3F2bNnkZOTE+ndMMYooa62P/qoqNpYKt7EALBnjxO9vWTyh75OOFjU\npYjC+fOA0ylg69Z400hSn191u6HmiQsKJOTliVi8eACvv56AmhoPXn7ZL/LHjvXDbpexaJEXHEfK\n7554woctW9zo6CB2oLducThwoB9dXTwEwSiily+T4wgmmoFywEOJ5WiVno01s6vRJOKC7HK58MQT\nT+Cv//qvUVVVFenNM8Y4odbHWizA44+Lhrxxejrw5JM+nDolDPmIrhegigoREyZcwc2b0/DGG27T\naE0ftRYXS1S98N69TjQ382p9sfaz6AeD7t7thCwDsiwjJYXDokXJaiWGNrLX22sOxXC9KkK5GbJ6\n4dEl4oL80ksvAQDOnDkT6U0zYhzlYr5wIfAwTL2YTJ8uBa1tDVZvHO5oezI5Ofhjt3a7druMzk5a\ndL/8UlBL1vTDT/WDQc+eJflipQnFTMRPnBCQnIyQyse0x3j4sBMXL/LIzJTQ3MxBlgXTBUktodwM\nWb3w6MJyyIwRowjx+fM8+vs5bN3qdzfTX8x6IfX5aF+HUAd2hvIYbCZAZWXBP4u+vjknR8L69W7c\nukXKzRITZWzYQHLEEydK2LvXiY4OHhkZEhIS6NpiJV+sGMXn5YmGySCKAbzyObTNF5MmyXA4OEyZ\nIuPRR0VYbl+tsgy4XIDHAzQ2CqovcyRc4GJl/NfdChNkxrDQPtrqp3wo3W5mF7NeSPXlXZEUgIIC\nWc359vYCdrsMnh/6T14bJW7e7KK64tavd6OtjceaNQl4800Pbtzwm8Hn5YnYt480hAwOcmqeOi2N\n+GqsX+9GVZWy4Ac88ICI1asTKQN4ffNFdTVJcdTWOvH446J6fNrzrQxhHWoySChPFXdi/BdLiwQm\nJEF+8803sXHjxoC/5zgOv/vd7zB37tyIHRgjttGKlr4NWOl2C+Vinj6djkCLiiTDa4Z7AevbqK1W\nGfv3FyA/Xw750V5fUxwfT4yM0tJIbfGiRQPq70WRg9cLeL3E6/iFF7yYOVPE5MkyJk2ScOMGh+Zm\nAatXk6qLd991UQbwgLH5oq+PU8v+lCYZvQG9MoR1qMkgoTxV3ImKCJYWCUxIglxZWYkf/vCHQV9z\n7733juhAGhsbR/T+aBGrxwWM7rFduDBNFQV9G3BZ2SA++6wPaWntaGz0Bd2O05mH117z21weOtSD\nxsZm6jXd3bmYNy9d85prsNtbAJBHfIcjGy0tVuTmDiIjo10tHQOA9vZplHj9z/9YYbX2q+8320ZB\nwQDWr+dx6xZnSDHk5zsxeXILurtz0dWVTOWRlyzxYtEiukMvKcmNpKQWlJWRz2G1+htBioqcSE1t\nUSsrACA3N9eQ9rBaZWRkyHjuuWRYrTL27XOapkba2oBPPpFNz0M42GxQUzvaYwMi8zen/dsZHORw\n8SKZ1zdSYvFaDXcGYUiCPHHiREycOHFYBxQqsTg8sbGxMSaPCxj9Y+vr81c5KG3AimdEWtplFBbm\nA8gfcjt1dXTKorMzEYmJxVQ0bHxNEubOJZ/91ClB56+QSEVb2uNUcrba95tto7bWqaYptOZE5Hji\nwPPTUVgIdWyU8nt9KV5qqoyHHopDfX2xOqvv+PF+NDby1LZEETh3ThmNRLbX2wskJxNfjk8/dWLd\nugR1uz09JF/c0KDk7ElqpL9fwMqVKabnIRJE6m9O/53cd59lxNsd7eshUkQ8h+xwOHD16lU0NjZC\nlmU0NDTg5s2byMnJwQSz6ZKMMUmgEfUAgkbF+vSDMlBUuTjtdqM/RbC85lCLUOXlIj77rB89Pbxa\nq6xPi+i3oe0SVMyJFiygP5Py+K9FX4pXUkLsOPWfR9mW4tfhcgEtLQKVq9Y+xv/3fws4c0YAQJ5E\nenp45OeLWLhwEKdPC3jjDbeaQgl0HszSPrI8Orlc1igSmIgL8gcffID169eD4zhwHIdnn30WALBt\n2zYsXLgw0rtjjBJm+chQyt70+cPjx/upi7OjAwaBnT/fF/ACNhNrvfjEx0O1vVTETotxG8ObelFe\nLuLYsX50d5MhoLIMQ3u0VigVv44VK7zq75X/b2jg1c87caKEnTtdaGgQVOP9N95wU80gp04J6Ooi\n7zc7ZrO8LceFN6svUrBGkcBEXJBXrVqFVatWRXqzjBglWLWF2QWuj0YbG3ksWODTXJzGho9gF7BZ\ntHXmDC0+775LLzrW1/PgOKg3DP02hjv1gucBSaKbQwIZ3ZNzQSJxm00Gx9F5+P5+DpWVSWozys2b\nHDZsiA94kxgq6jR7klD+rf0ZE8nRhZW9MUZEsGoLbZSniN9QZVV6YXngATFo44iZWOvFx26nI16P\nh8NTTyWrNwyzbQw3gjNOrzY3ugf8fh3btsVjxQoPdu924to1ICMDVPrhyy/J4FOlXG7OHBHl5aJp\nJ2K4Dm/RLnFjhAcTZMaI0AqQvtpCG+Up4jdUJKcXx1OnzEukgpXC6cUnI4O8r76eh8fj9y2ORkSo\n37fS+GF2M1H8OpqaeOTlEc/nK1ca0ddXTKUfbDYgPh6w2SQ8/LB/O2bnhiyCCujoIN+HshgZKOpn\nudzYggkyY0RoBUiptmhv9yE93WK6yBRu/rCjA2rrsc0mq80PwWpZ9aJfWkpm+elzpiOJCAPdEPSt\n12vXxuPpp31obQVu3QKcTuI8R7oBgZQUICVFRkoKVLEuLydCfeKE3+/4gw/cmDVr6DQEx5HzUlPj\nURtWlNTJY48Fn4Ay1GeLJfTHmJY2PqRsfHwKRkQJ54I0i3gvX75kiPKGK342GwzCAgSvrggk+uXl\nIg4duobOzqQRR4T6G8KePU6kp5N9KK3XZ8/yWLp0gDInqq724IUXEgIuqtls5Pgfe0xEcjKJrvXN\nIwp2u7FCRTkvoXhmBPqex0Ljhv4YDx3KRmHhaB/VyGGCzDAQzgUZTPwi8Tis70pzOMi/h9Piy/OA\n3d5C1SAPF/0N4cwZv/G8IrSZmTLWrnVjxQovbDaSK1Y67wItqikNGaE8SehN93t7/edFb3yk98wA\njN9zoHrqWFzs05//1lYrxkOjMBNkhoFIGMxEqrQpkPBGupY13Md0Y65YNghtZaWHKrerqfEAoJ8Y\nRrKopjfdP3rUqZ6Xzk5g3z4nTp6k0x5a9N/ziRMC1q5NNAyBjcXFPv35z80dBBA32oc1YpggMwzc\nCYOZUAkkvJGuZQ33MV05Ln23XF6eDJeLCK0+bZCSImPCBEkVTsC4qKZvVTZDFIEzZwQ0NPD46CMn\nEhJkTJok48YNHh9+aEVRkYgpU8jNYc4cEb29ME17mC1AAsCBA1bs3etEayvxzpg5M7bSFYDx7yIt\njYy+GuswQWYYiJVOKiVqDVSlEEkCLZA1NXGYPl2Cz8cZjmP2bOJz8ac/WbBo0QDS0mQMDspYujQJ\n1dUeTJ1Kl9uVlEgGkR/OTaWuTqAsS2tqPCgqEvHss+Rn69e7DV1/+gVBwLgAuXQpMT1asGBQ3Vas\n5pD1N+ShPFPGCkyQGQZipZPqTi4u6aNFbQu3XuC03hZNTRxWrUpUt/Puuy7V0a22tl+tEElLkzEw\nEJknDWOtM3GDU3526xb9e30jjIL2e5YkYOdON65cGRs55FAYC9UiepggM2KWkeSyFZ8IxbJSMXjX\nGsAHKlfTt3DrBU7JtZp34vmj4qYm3iDWjzxitBcNF/3NIy1NRna2/2dpafTv9Y0wZmjFOZTxWGOB\nsVAtoocJMiOm0Ldi5+WJaG4WwhYGxSdCG9U+/rhoMIAP3K0nBBQ4Jddq1omnbcCYNIl+X1GRiLo6\nxdWNR3GxNOTYJbPzUlQk4fBhJy5c4GG3S0hJkfFP/+Q3vi8t9eHwYSfOnRteI0woKatIRp/RimTH\n4vQTJsiMmCJQKVa4uWytY5sSrT7+uGgwgA90kWpFqajIPx06I0NGczOPqioP0tJkTJ0qY+ZMybTt\n2ueD2olXUCAhPp5E14Fc3cI5L0eOOPH884MASLrhrbe8uHKFu93JRxpheH54jTChpKwiGX1GK5KN\npcXpUGGCzIgp9FGNmfVlKBgd20iqIDd3MKSL1NzfAvjqKwHLlydS4hEIZXK2MnrpwAGLIf2hvyEE\nSqkMtxFGuZEoC5MHDlgiEoVGMvqMViQbK4vT4cAEmRFTRCqq0fpEKDlkAMjIaMeRI4lhX6RKTvry\nZR41NR5s2xaPtjY+LPEoKJDR02NcPNSKZKCUynAbYZSuQYeDdqEbaRQayegzWpFsrCxOhwMTZEZM\nEamoRh+dKkiSL+SLVJvbnDRJxg9+QA8fXbMmIaB4mOVFy8tFCAJps+7u5jF1qoSXX05Uc+RHjjjV\nlEpOjoTKSq9aITFcS1AlHbBihTeiUWgko8+xGMlGCybIjJgilqKaYNaiCQmkM+6BB8wX6gLlRcvK\npNtiDZw9y2Px4gEq2lZSKsuWebByZaLh/aGeF+WGcPas33NZG4VOny4FtTUdikh+T7H0nY82TJAZ\n44ZIr9YHshbNyxORlyehqYlDf7+AlhbekFcONilEL9br1rnh85H6X4DD8eP9OHtWoN7f0MCbphiG\nMgiqqfGonss1NR6kpsooLpbQ28th/vw7VxIW7LsZi/XC0YIJMmPcEOnVer216L59TrS08MjNlaj0\nxSefOJGZKaOtzW8cFM4cwLg4YNUqpfIiEUeOOJGZKelyzeb1y4E+s7KPbdviUV3tQWIiqQZRJqr8\n+c9CRFMYQxHsuxmL9cLRggkyY0yjja7S0mSDMEY6T8rzIg4coKdgnzoloLLSi1WrElXxDZYX1Yt1\nZqZkEMeiIonq8svIMM9VB6pQUPYBkJSA1Uq/Rz9MINolYcEqKcZivXC0YILMGNPoo6uaGg8ljCMh\nUG7TzJQnKUnGtm0uFBdLlNeF/r0DA4DXK+PDD524do1Hfr6E1FRj5cXFizxmzCDGQFlZQGmpP0IO\npXlGuSFcvw5DdUVBgYw334wzjISKJsGeGMZivXC0YILMGNPoo6vUVBk7djijulof6kQPM/QdhLt2\nuZCa6s87T54sYunSZKryYtYsMrJKWYRTjICU15g1zyg3BH00r0zxVnwrtCOhokmwJwZWZeGHCTJj\nTKOPrkpKpJCEMRChLDCFOtHDDH0HYVcXB6uVwxNPiCgvB44f5/Hcc4Ow2Uj1hfL4rn8SqK72YPXq\nxCGbZ8yiz9Goagi2T1Zl4YcJMmNME67vQlZWLgoLETAiDHWBabgiou8gzMyU8dxzyeqkkR/9iE6/\nKI/v+ieBvj6yvaEe8Vn0ObZggswY08gyGV4aDFpkk4Ku4gdaYIpUadbDD4vYt8+JK1d4ZGbK2LzZ\nb/yj7FP5/9RUv4DqI905c0Rs2+aC3S7BYpEhSeY3GRZ9ji2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_scatter(-0.55)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating $r$ ###\n", "\n", "The formula for $r$ is not apparent from our observations so far. It has a mathematical basis that is outside the scope of this class. However, as you will see, the calculation is straightforward and helps us understand several of the properties of $r$.\n", "\n", "**Formula for $r$**:\n", "\n", "**$r$ is the average of the products of the two variables, when both variables are measured in standard units.**\n", "\n", "Here are the steps in the calculation. We will apply the steps to a simple table of values of $x$ and $y$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
x y
1 2
2 3
3 1
4 5
5 2
6 7
" ], "text/plain": [ "x | y\n", "1 | 2\n", "2 | 3\n", "3 | 1\n", "4 | 5\n", "5 | 2\n", "6 | 7" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.arange(1, 7, 1)\n", "y = make_array(2, 3, 1, 5, 2, 7)\n", "t = Table().with_columns(\n", " 'x', x,\n", " 'y', y\n", " )\n", "t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Based on the scatter diagram, we expect that $r$ will be positive but not equal to 1." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t.scatter(0, 1, s=30, color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Step 1.** Convert each variable to standard units." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
x y x (standard units) y (standard units)
1 2 -1.46385 -0.648886
2 3 -0.87831 -0.162221
3 1 -0.29277 -1.13555
4 5 0.29277 0.811107
5 2 0.87831 -0.648886
6 7 1.46385 1.78444
" ], "text/plain": [ "x | y | x (standard units) | y (standard units)\n", "1 | 2 | -1.46385 | -0.648886\n", "2 | 3 | -0.87831 | -0.162221\n", "3 | 1 | -0.29277 | -1.13555\n", "4 | 5 | 0.29277 | 0.811107\n", "5 | 2 | 0.87831 | -0.648886\n", "6 | 7 | 1.46385 | 1.78444" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_su = t.with_columns(\n", " 'x (standard units)', standard_units(x),\n", " 'y (standard units)', standard_units(y)\n", " )\n", "t_su" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Step 2.** Multiply each pair of standard units." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
x y x (standard units) y (standard units) product of standard units
1 2 -1.46385 -0.648886 0.949871
2 3 -0.87831 -0.162221 0.142481
3 1 -0.29277 -1.13555 0.332455
4 5 0.29277 0.811107 0.237468
5 2 0.87831 -0.648886 -0.569923
6 7 1.46385 1.78444 2.61215
" ], "text/plain": [ "x | y | x (standard units) | y (standard units) | product of standard units\n", "1 | 2 | -1.46385 | -0.648886 | 0.949871\n", "2 | 3 | -0.87831 | -0.162221 | 0.142481\n", "3 | 1 | -0.29277 | -1.13555 | 0.332455\n", "4 | 5 | 0.29277 | 0.811107 | 0.237468\n", "5 | 2 | 0.87831 | -0.648886 | -0.569923\n", "6 | 7 | 1.46385 | 1.78444 | 2.61215" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_product = t_su.with_column('product of standard units', t_su.column(2) * t_su.column(3))\n", "t_product" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Step 3.** $r$ is the average of the products computed in Step 2." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.61741639718977093" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# r is the average of the products of standard units\n", "\n", "r = np.mean(t_product.column(4))\n", "r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, $r$ is positive but not equal to 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Properties of $r$\n", "\n", "The calculation shows that:\n", "\n", "- $r$ is a pure number. It has no units. This is because $r$ is based on standard units.\n", "- $r$ is unaffected by changing the units on either axis. This too is because $r$ is based on standard units.\n", "- $r$ is unaffected by switching the axes. Algebraically, this is because the product of standard units does not depend on which variable is called $x$ and which $y$. Geometrically, switching axes reflects the scatter plot about the line $y=x$, but does not change the amount of clustering nor the sign of the association." ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t.scatter('y', 'x', s=30, color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The `correlation` function ###\n", "We are going to be calculating correlations repeatedly, so it will help to define a function that computes it by performing all the steps described above. Let's define a function ``correlation`` that takes a table and the labels of two columns in the table. The function returns $r$, the mean of the products of those column values in standard units." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def correlation(t, x, y):\n", " return np.mean(standard_units(t.column(x))*standard_units(t.column(y)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's call the function on the ``x`` and ``y`` columns of ``t``. The function returns the same answer to the correlation between $x$ and $y$ as we got by direct application of the formula for $r$. " ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.61741639718977093" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(t, 'x', 'y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we noticed, the order in which the variables are specified doesn't matter." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.61741639718977093" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(t, 'y', 'x')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calling ``correlation`` on columns of the table ``suv`` gives us the correlation between price and mileage as well as the correlation between price and acceleration." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-0.6667143635709919" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(suv, 'mpg', 'msrp')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.48699799279959155" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(suv, 'acceleration', 'msrp')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These values confirm what we had observed: \n", "\n", "- There is a negative association between price and efficiency, whereas the association between price and acceleration is positive.\n", "- The linear relation between price and acceleration is a little weaker (correlation about 0.5) than between price and mileage (correlation about -0.67). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Correlation is a simple and powerful concept, but it is sometimes misused. Before using $r$, it is important to be aware of what correlation does and does not measure." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Association is not Causation ###\n", "\n", "Correlation only measures association. Correlation does not imply causation. Though the correlation between the weight and the math ability of children in a school district may be positive, that does not mean that doing math makes children heavier or that putting on weight improves the children's math skills. Age is a confounding variable: older children are both heavier and better at math than younger children, on average." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### Correlation Measures *Linear* Association ###\n", "Correlation measures only one kind of association – linear. Variables that have strong non-linear association might have very low correlation. Here is an example of variables that have a perfect quadratic relation $y = x^2$ but have correlation equal to 0." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "new_x = np.arange(-4, 4.1, 0.5)\n", "nonlinear = Table().with_columns(\n", " 'x', new_x,\n", " 'y', new_x**2\n", " )\n", "nonlinear.scatter('x', 'y', s=30, color='r')" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(nonlinear, 'x', 'y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Correlation is Affected by Outliers ###\n", "Outliers can have a big effect on correlation. Here is an example where a scatter plot for which $r$ is equal to 1 is turned into a plot for which $r$ is equal to 0, by the addition of just one outlying point." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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te5cvX9bTTz+tsrIyrV+/vsuxVs5db7NJsc/doDoFNNRuI1FbW6tp06YpISEh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\nogAAwFAUAAAY6v8BrN4i2xACiusAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "line = Table().with_columns(\n", " 'x', make_array(1, 2, 3, 4),\n", " 'y', make_array(1, 2, 3, 4)\n", " )\n", "line.scatter('x', 'y', s=30, color='r')" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(line, 'x', 'y')" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "outlier = Table().with_columns(\n", " 'x', make_array(1, 2, 3, 4, 5),\n", " 'y', make_array(1, 2, 3, 4, 0)\n", " )\n", "outlier.scatter('x', 'y', s=30, color='r')" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(outlier, 'x', 'y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ecological Correlations Should be Interpreted with Care ###\n", "Correlations based on aggregated data can be misleading. As an example, here are data on the Critical Reading and Math SAT scores in 2014. There is one point for each of the 50 states and one for Washington, D.C. The column ``Participation Rate`` contains the percent of high school seniors who took the test. The next three columns show the average score in the state on each portion of the test, and the final column is the average of the total scores on the test." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
State Participation Rate Critical Reading Math Writing Combined
Alabama 6.7 547 538 532 1617
Alaska 54.2 507 503 475 1485
Arizona 36.4 522 525 500 1547
Arkansas 4.2 573 571 554 1698
California 60.3 498 510 496 1504
Colorado 14.3 582 586 567 1735
Connecticut 88.4 507 510 508 1525
Delaware 100 456 459 444 1359
District of Columbia 100 440 438 431 1309
Florida 72.2 491 485 472 1448
\n", "

... (41 rows omitted)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sat2014.scatter('Critical Reading', 'Math')" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.98475584110674341" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "correlation(sat2014, 'Critical Reading', 'Math')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "That's an extremely high correlation. But it's important to note that this does not reflect the strength of the relation between the Math and Critical Reading scores of *students*. \n", "\n", "The data consist of average scores in each state. But states don't take tests – students do. The data in the table have been created by lumping all the students in each state into a single point at the average values of the two variables in that state. But not all students in the state will be at that point, as students vary in their performance. If you plot a point for each student instead of just one for each state, there will be a cloud of points around each point in the figure above. The overall picture will be more fuzzy. The correlation between the Math and Critical Reading scores of the students will be *lower* than the value calculated based on state averages.\n", "\n", "Correlations based on aggregates and averages are called *ecological correlations* and are frequently reported. As we have just seen, they must be interpreted with care." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Serious or tongue-in-cheek?\n", "\n", "In 2012, a [paper](http://www.biostat.jhsph.edu/courses/bio621/misc/Chocolate%20consumption%20cognitive%20function%20and%20nobel%20laurates%20%28NEJM%29.pdf) in the respected New England Journal of Medicine examined the relation between chocolate consumption and Nobel Prizes in a group of countries. The [Scientific American](http://blogs.scientificamerican.com/the-curious-wavefunction/chocolate-consumption-and-nobel-prizes-a-bizarre-juxtaposition-if-there-ever-was-one/) responded seriously whereas\n", "[others](http://www.reuters.com/article/2012/10/10/us-eat-chocolate-win-the-nobel-prize-idUSBRE8991MS20121010#vFdfFkbPVlilSjsB.97) were more relaxed. You are welcome to make your own decision! The following graph, provided in the paper, should motivate you to go and take a look." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CFKBAmUCzDKqha4uIqGC4IAtHDh6CfkpXuJbdsqwl/o4f0zIAna4sLaRsN1co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\nxRd86eP5+A4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# HIDDEN\n", "\n", "from IPython.display import Image\n", "Image(\"../images/chocoNobel.png\")" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }