{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# HIDDEN\n", "\n", "from datascience import *\n", "import numpy as np\n", "from scipy import stats\n", "\n", "import matplotlib\n", "matplotlib.use('Agg', warn=False)\n", "%matplotlib inline\n", "import matplotlib.pyplot as plots\n", "plots.style.use('fivethirtyeight')\n", "import warnings\n", "warnings.simplefilter(action=\"ignore\", category=FutureWarning)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# HIDDEN \n", "\n", "galton = Table.read_table('galton.csv')\n", "heights = galton.select('midparentHeight', 'childHeight')\n", "heights = heights.relabel(0, 'MidParent').relabel(1, 'Child')\n", "hybrid = Table.read_table('hybrid.csv')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# HIDDEN\n", "\n", "def standard_units(x):\n", " return (x - np.mean(x))/np.std(x)\n", "\n", "def correlation(table, x, y):\n", " x_in_standard_units = standard_units(table.column(x))\n", " y_in_standard_units = standard_units(table.column(y))\n", " return np.mean(x_in_standard_units * y_in_standard_units)\n", "\n", "def slope(table, x, y):\n", " r = correlation(table, x, y)\n", " return r * np.std(table.column(y))/np.std(table.column(x))\n", "\n", "def intercept(table, x, y):\n", " a = slope(table, x, y)\n", " return np.mean(table.column(y)) - a * np.mean(table.column(x))\n", "\n", "def fit(table, x, y):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * table.column(x) + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visual Diagnostics ###\n", "Suppose a data scientist has decided to use linear regression to estimate values of a response variable based on a predictor. To see how well this method of estmation performs, the data scientist must how far off the estimates are from the actual values. These differences are called *residuals*.\n", "\n", "$$\n", "\\mbox{residual} ~=~ \\mbox{observed value} ~-~ \\mbox{regression estimate}\n", "$$\n", "\n", "A residual is what's left over – the residue – after estimation. \n", "\n", "Residuals are the vertical distances of the points from the regression line. There is one residual for each point in the scatter plot. The residual is the difference between the observed value of $y$ and the fitted value of $y$, so fr the point $(x, y)$,\n", "\n", "$$\n", "\\mbox{residual} ~~ = ~~ y ~-~\n", "\\mbox{fitted value of }y\n", "~~ = ~~ y ~-~\n", "\\mbox{height of regression line at }x\n", "$$\n", "\n", "The function `residual` calculates the residuals. The calculation assumes all the relevant functions we have already defined: `standard_units`, `correlation`, `slope`, `intercept`, and `fit`." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def residual(table, x, y):\n", " return table.column(y) - fit(table, x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Continuing our example of using Galton's data to estimate the heights of adult children (the response) based on the midparent height (the predictor), let us calculate the fitted values and the residuals." ] }, { "cell_type": "code", "execution_count": 42, "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", "
MidParent Child Fitted Value Residual
75.43 73.2 70.7124 2.48763
75.43 69.2 70.7124 -1.51237
75.43 69 70.7124 -1.71237
75.43 69 70.7124 -1.71237
73.66 73.5 69.5842 3.91576
73.66 72.5 69.5842 2.91576
73.66 65.5 69.5842 -4.08424
73.66 65.5 69.5842 -4.08424
72.06 71 68.5645 2.43553
72.06 68 68.5645 -0.564467
\n", "

... (924 rows omitted)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatter_fit(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A *residual plot* can be drawn by plotting the residuals against the predictor variable. The function `residual_plot` does just that. " ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def residual_plot(table, x, y):\n", " x_array = table.column(x)\n", " t = Table().with_columns(\n", " x, x_array,\n", " 'residuals', residual(table, x, y)\n", " )\n", " t.scatter(x, 'residuals', color='r')\n", " xlims = make_array(min(x_array), max(x_array))\n", " plots.plot(xlims, make_array(0, 0), color='darkblue', lw=4)\n", " plots.title('Residual Plot')" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CwYMwrlrlcVxcJTIAQDhyhF2P5wGjsVXj4gt/hx6Jt9/OxPmsVkg6HcQQLxJJ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\nOyJOozFPKXNHiM9G1bMhNxdcUpKgehoSAkNmppAvEHsgYCGprdcj/ME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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "residual_plot(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The midparent heights are on the horizontal axis, as in the original scatter plot. But now the vertical axis shows the residuals. Notice that the plot appears to be centered around the horizontal line at the level 0 (shown in dark blue). Notice also that the plot shows no upward or downward trend. We will observe later that this is true of all regressions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Regression Diagnostics ###\n", "Residual plots help us make visual assessments of the quality of a linear regression analysis. Such assessments are called *diagnostics*. The function ``regression_diagnostic_plots`` draws the original scatter plot as well as the residual plot for ease of comparison." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def regression_diagnostic_plots(table, x, y):\n", " scatter_fit(table, x, y)\n", " residual_plot(table, x, y)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VE+4J+t1G/9prr7F8+XKMRiN5eXmUl5czd+5c9bzJZGLGjBl8/vnn/SiloDN0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\nsTY2UVJe49uvIhNVGk1UaTQ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k+PHjWK1WZs0SiYJ6gp4ofhCo0ELrAgezp47n4ikZvP3B\npwyNiWT8uBQUhU4XDgkmb+uCFrKskJw0lJjoCCQkRo1MDFqk2V8xBm/hEEVRWPCdqUw7PyOgzG3n\n4MkHb0EjaUgYGk1ZRRXNdic6rZb0sSO45xff47prLuW8cckcyc6ntLyGmCGR/PLmRay690cUFldS\nUFyOdfO/uPt7x1h84X+4+bI9DI20+pW9M5ivupLH12Wy7cQ1LFz+ARIatYDLsoWzOF3fwN792TRY\nmwDQaTUkxA3h9puvZnx6qk/hkKqaeprtdnRaLQlDozl//Bgiwy1kjB2pzpGiKNz50N/4v+ffUQuy\nLF80m3e37qahsZnU4Ql8/OajSJLkt9BMaxt6mMnA8IRY5s5oP//npadQU1ODJczCgu9czMVtntXb\nLQVMPGPSesY8Y5JaSMYSZmL0yEQyxozw235vcLYW/elNgq7o8/Ly1H/feuut/OIXv0Cj0TBv3jy/\nAVSpqak9LZ8gCN5yb3GxUeQVV/DW5l1cd82laDQaNblV6wCZQ9mnuG6hJx1uT8uRX1JJxtiRFBRV\nICsKI4d5Qva9ZewC0VrW1oRqp207B29/8CnXXePxG7956Uy/gTHrN+0kv6SC9LSRKHIjt01bAhXw\nyu3A7SEPOyAut4YFf/iNT5KvS6d7VsTfu+oSNBpNu8Ijf167marTDWqSB7fb4w751gefopG0XHfN\npWfmOW0kYWYjCorfwiMAdz70t3Z7H9OmZJI0LJZRKYnYHU7e+ddnnv6DFGPvKLBKkiSunjslYABS\noF8EwdxdBT1PUEV//vnnt9th/+Mf/8jjj/uWEfP66IrI2L4lFJt7XxcSSR4ejyIravRob7vvdXZ8\nkrucn0+9pkfT9e46EsePVs9j0XenAWeidI0GPZHhYe1cQ/2Nocnu8LW9o1BVU4dOq2XDls/aFT3v\naJ797X1ERlj8zlVni5R0BuHOeXYQVNH/5S9/Ea5OZzGh2Nz7IkDGpw9nz6dACLlvP+PTOI8QUdWz\nhev/uuVS/vavNL7NL0GSNJiMeuJjzxQU8ZFnXEqHc5GVlszHOw/42N49G63QYPMURVm/aWen5tnv\n3keAufJ3rKfeG7FyPzsIquivv/56PvzwQ1JSUsjKyvJ7zdGjRykoKODKK6/sFQHPRUL1dw+l0EJv\nr6hkWWbP/mOcKigj3GLith9ezZ79x3nhja1+i450NL7O+vq3Hd8P5jUR3hJ1emE4UNX9Ma756E7M\n0XNYtnAW6zftZOO+3cTHumm2Oygpr6apyY6tqZnd+48iywqHs0+BAldfdlG7YhreNtom81IUhQ1b\nPuXzg9koioJepycqykKExax6Lq248wZef/cTDuYUEB1pYf2mHfzlH5sYlhDD0itnqoW+FUXhwolp\nvP/hHurqraSOSOSJ3/+UdRt38Pn+4zTZnYSZjXz/qku4fvEcdf4yxoxQn92E9FSWXT2L7G+LOvXe\ndCdWo6OCNb3Z92AnqKJ/6623uPvuu9m9e3fAa8LDw7nllltYs2YN3/ve93pcwHORUP3dA9noW9Pb\nK6q7Hn6BjR/vRa/TUddg408vbaKipradD39rgo2vs77+xsa/8fOp958JTKoNeGnITLrlYg6djECn\n1RAXG8XELAN2xw7VR99o0HMkp4C6hkbcbhm7w0lFVS3rNu7E5ZbRaiUUBT7edZC7H/m7jy/+3gPH\n2XswW405KCytRJIkrl88B0mSqLdaGRIdpSZCa53T5+5H/s7hE3m4XTJVNXV8k1+KViORV1ROUWmV\n+qzXb9rJo39eh7WxGUmCorIqlv5sFV8eOkGT3eN/39hk5zerXkSr1arze8eK59n48Rm7viS1f3Yd\n0Z1YjUDxH33R92AnqKJfv349N9xwAykpKQGvSUlJ4Qc/+AFvvvmmUPQ9RHcKhPQ1bW3BhWVVhLfk\nYA9UrLs7xcFNdXdibPxHj47higd/yH92lyG3KZnolhVsjXZVltZ+9bZGTwFvl9uNJEm4XJ588Ioi\nI6FDkjzXtPXFP5SdF7BYeGufdI8NHh8b/AtvbFULtiC19CXpcMtyu3ZsjXY0rX4l5Zwqxu5w+Yyv\n2eHymd+uFFpvS3feye72fzZ8Hs5Wgv4u+vrrr7nssss6bGTOnDkcPHiwx4Q61wm1gELm2JFqoYv8\nonI1BL0vaVtkZGTi0A6LdQcbX9tzv7vmT2oB66jS6B5R8i99+RZzH7iL+SvvY+4Dd5GUdB5GQ/s1\nj1YjYQkzemSxO7GYjBw7UUBJWTWWMCOSJKkugzqdFo1GgyRpUFCQFQVLmLFdMY2JGakBi4V7x15c\nVs2x3EKGJ8bw8N03qiYZ71zrtFpQ8PSlKGg1mnbtWMKMyIqCgsdRIn3U8HZjNBl0PnPflULrbelO\n8Y/u9i8KjwQm6IrearUSHd1xlr3o6Gis1u77Ggs8hGpXVxSFunobtkY7ljBjp4t49wRti5ysfuBn\n3Lk9RJAAACAASURBVP3I31tyxkQx9fx01SvLS7Dx9bRHDID56vn8bPl8xmeMYvmi2Vy7AJxug1oA\n/aLJ43C53Lz23jb1HqNBx/KFs9WxlZbXYGtsRqf3rKC/O+t8QGLbnq9psDai1WoxGnQoskJ1rRWN\nRmL0SI9t/DerXvJJdvbW5l1s2PIZZRU1DEuIQVZk3nx/O8dyC6ioqqOiqg6XrPD6e9vY/eVx9mx6\nCq1Wy5MP3uIphH6ymGHxMQxPjKWyuk610Xvn0VtQ/a+vfKAW3n5qxS288d427n30JdVG/8Tvfqru\nD6zftBNLmIn4mGhq621qofXO0vrZZo715At6cPWrIdnMAxXM6UzfsiLz11c2Y7U1+xRMP9cJquhj\nY2MpLCxk+vTpQRspKirqVABCeXk5Dz30EB9//DFWq5VRo0bx5JNPMmOGJ4Ly9ttvb1fR6qKLLuKj\njz4KuY+BTKh29ff+vQe7w+WpfORw8d6/93DDkrl9IOEZ/PnBT78gi/ySSowGPW99sAuN5Os3ro5P\nkYkqi4GynpVp7gN3kTo8nmO5eQyJjmLaFCfjM0a1k8HRkt3xL//YTG29FYNeh8PpQqvRoNVqOVVQ\njlavpbKmnoqqWjRaDZLDiSXMRHRUBFlpyRSUVlJdU8+3+aU02x24XDIulwtLmJmj3xSw9Ger0Oq1\nPn7+Xnv8us070Gg1/HntJhQU9DodJRW1uF0u5Jbv7NxTxWpOmrc/+BStXsv5E8Z40hEH8W2/Ycnc\ndu+CXq/n4gsyVU8arVbrkaNV4ZWKmlpGDotDq9eqMQmdofW72zaGA4LbzAPFVHSm730Hcyguq0av\n07Hx471IktStNgcLQRX9tGnTePPNN1m2bFnQRt544w2mTZsWUod1dXVcccUVzJgxg3feeYeYmBjy\n8vKIi4vzuW7u3Lm88MIL6ipVr9eH1P65hAR4F0iSpKYZ6XcC2kqVZqLKEnu0r8Lqkdzy7A3kfFOE\nrakZS5iJ9DEeW3iY6UzR6mA5cprsDmyNdtwtWTc9aRA8du3zx4/xFOHWnjGT1NXbfIqPeHPyKAq4\n3W5AwuV2YzIZ1DbaytG2fxRolpwYdFpszjO2dI32TE6a7tqgA93fW3ln+sNm3hP7DIORoL9pbrvt\nNnbs2MFvf/tbHA5Hu/NOp5P777+fnTt3cvvtoYUUPvPMMwwbNoxnn32WyZMnk5yczOzZs9tF1hkM\nBoYOHUpcXBxxcXEhmZDONZZcOYP42GjPT+7YaJZcGTinTF/itZXGhDfw7wce55kf/NJjY+8BJe8w\n/8ingPWWb/+C3eEkPNyM0+VSc6ZMzEj1KVqdOXYk6zbu4MHVr7Ju4w4yx470KbZtCTOibUnl7Els\n5rFr2x1OIiLCkACDXockSSTFx3DsRD71DTbsdicRFjOSJKHRSGg0WmRFweVyY2tsYlxqEs12B8Vl\n1RxtKV6uKIqPPdls9BQij7CY0Wo16Fs2ZDUaT+YYb06a7tqgA+3peNttO4fdtXH3h828J/YZBiNB\nV/RTp05l1apV/P73v+ftt9/msssuY+RIz8tRWFjItm3bqKmpYdWqVSEnPNuyZQuXX345P/nJT9i1\naxeJiYn86Ec/4pZbfO2Be/fuJS0tjaioKGbOnMkDDzzA0KFDuzjMwYl3k+5siTrUOA8RUTW7R0vi\nNUX+AYcl8CIiUNGQZQtn8acX31aLViuKErCYyeJ50z2Fqrd8xvFvCtHptMxpsWu//cGnHMnJ4+uj\nJ7E12bGYjUhaiZxTxTTbHYwakcDEjFSmjB9LSVk1JRXVFJVWoiARbjZyw9I57Dt4gpP5ZQyJtJBX\nVMH6TTt9bNmL53lMo8dzCygsKWVYQjz/2fUVtfU20kd7Coe3Hmt3nreE56efRPs9k0CFV7pKf0TF\ndtfOP1gJWhzcy2effcYzzzzDp59+SlOTJ+mS2Wzmkksu4Y477lBt66GQmJiIJEncfvvtLF68mMOH\nD3Pvvffy0EMP8bOf/QyA9957D7PZTEpKCgUFBaxcuRJZltmxY8egMeH0RIHizgaYhHp92wIV7699\nkJMnT7aTV+vYS3j1/G6NoS22Ieuw67+r9p82ahiKW+GbgjLSRw3n3Rd/77O5GWgMiqLwzN/foqq2\nma+PniTnZDF6g46stJEe84wMmWkjVQXkdruZevWvOVlYDkB0ZBgLL59GacVpNJLEkitncN01l7Li\nydfUFAeKouB2yZRVnlY3PSPCzeTmlXiFoLCkkhMni3HLMkaDnrGpSSiyQkNjE263m8y0ZJZeORMU\neHfrbk6czKeg5EwqkZkXZrLpHw+h0WhCDgYKFDj0wBP/5L1/76a+RZkvmT+Dlb/5kXpfVwOWBlqx\n7YEmb08QUprimTNnMnPmTGRZVqtIxcTEoNVqO92hLMtccMEFPPDAAwBMmDCBb7/9lhdffFFV9EuW\nLFGvz8zMZNKkSUyYMIEPP/yQBQsWdLrPwUpnA0xCvd5fgYqnfn8j+qYNhNX+tEfH0DB0F7J+gm//\nN61Q+//si+OAx2yy58Bxxn/nNuxOZ4dj8BbEKC6vpbyihv/f3nnHR1Fuffw327KpEFI2nVBSCIEA\nEYQgKEiVIh1soEj0Bd8rcrmickVEeFUkWFEQxHalKU0R0AuKlNA7SAhLKi2N1N1ks23ePzY77G52\ns5u2jfP9fPhjZ2eeOTOzc3hynnPOTyDgc7nuvt5iMGCMhDo+XLudc/IAUF5Zjf9s/xNeXh7w9BBx\nhU2GrQHybxXpsnFqasEwwE+7DyM5sTP4Qj48REJcysjB7aIybkxFrQqXM/PA4+kctFbLoqS0Clcy\n88ACqJBVo7raWLkt/bTu/j81YbDNC5uWCofOX85CQVEpeDweqqsVOH85y+i45hYsEc5LozRjeTxe\nvUXTxiKRSBAbG2u0LTY2Fl9++aXFY0JCQhAWFobs7OwGx5ZKpc2yzd40196T5zPAAFCr1WDqPjc0\npq37X5HmgWWBf066jvdmXQfwXwCftEjV6TnZPmhgsN4iAwBjG65I87hSfj36FM2Ssgr4+XhZvYb0\nk+chEgpQUVGlm/myAJ/Pw93SCnh5CCAJbAO5XM7tm3+7yKy9GrUGWqEWlTI50k+exz9mjERBYRyy\n8gpQVeWNm7eLdUEQVjeJuVtejimjUpCVV6DbaA6WBVsncKLWaFApq4ZKreH+IzLlijQP6SfPQ61S\nQq1ScjYnJ4SZ3d/SviVlZRCJBNBotBCJBCgpKzO6d439PRlyv7179qQl/vqwuzh43759691kqVTK\nxf7NUVJSgjt37kAikTQ4tiv9OdYSfz726dGFm4Gp1Gr06dGlwTGt7S+SrYJn1Zso2dYss4wY8c4/\nMH7EEG722dGGYxJi2nMzej16LdxA/zbcjL6ha+7fpwcyc/aiTRtfFBaVAgygUWshCW4HvkCAu+XV\nnFBH/z49cOJ8Nq6ZUVzi1xVC+fl4o3+fHoiNjeUmKpt/PoglH/0ARWklGEY3EerTowteeWEqAF1L\nge+3/QGt9p7D1y20snUFU7oe7QIBH7UqDVgwMPefQ0JMe/Tv0wM3Cu+1De7fp4fFZ21p3wd7JuBO\n8b3n/2DPBKMxGvt70uNqoRBXs7clsFl4pKWIjIzEBx98AB6Ph9DQUBw8eBDLli3D/Pnz0bNnT8jl\ncixduhS+vr7QaDS4ePEi5s6dC61WixUrVriNVm1LiB+YE+1oqCDFdP/V87LhUzYZYtn7EMveh1D5\nZ7PsAYByyV0ofN/At3/0w7+/igLLCtGlcyQS6wQtbGHKmAGcQEaHyGC09fWGXKFEdLgEp3Z/jINH\nL+FueRUSOkfhmw//aTaOnBAbhQPpZ6FUaeHj5Qkty0IgEMBTJISHhwg8hsGdglKo1Br0TorByrdm\nYauBSIanpwjTxgyEfxtfhEsC8OyUoZg8+iE8/twSvP3RBvz3rzN4519PI9C/DbLzC+AhEiK+UySi\nwoNRVFKBrnHtMfzhZNy6UwJpzi2o1VoIBXz07hGLAb0TUFYph4+3GMndYxAWEoCamlqolGowDGv0\nH0NKchf88s1idIuPBljgyrUbEPB4iO8ciYSYSPxzyVosX/0Ttv16BBnXb6CopBxTxgzghFv0AiAA\nUFpWhRNnM1Fdo0C3+A717p2xYE03PNgzDj/tPmIkSGIKy7L4z7b92HPgXIP7ORMkPGIHevbsiQ0b\nNmDJkiVIS0tDREQEFi1ahJkzZwIA+Hw+rly5gi1btqCiogISiQQDBw7Et99+C29vbyuj3180qsCE\nZeFT/gS++Z/f722rad751cJkyAP/MNqmf8UNC5K2/HqoUc3Vtu5O5wQy8m8Wgc9nMfDBRNQqVXjt\n3W90RUOJuqIhS0U9P+46jFuFZZAE+aNWqYIksC0uXctFTa0SJWUVEAkF4PP5qJTX4NNvfgaPx8Nr\nL001Ett4qE+i0dhjDNYOjp3NwPjnl2LXd0vw5PhBXHGQNPc2Ll/LA6CLi3+27CXw+XxupnxFmo/Y\nDuG4uG81N+4ri9fg9EWpTlavQgahkI+2fj5QqdWI7RjOrYUxDAOVwT3duOMALl3LhVqthUJRi5yb\nhbhkQWB7888H8dm3v6CmVgmhUIC7ZZX17l1DgjXmxgSMxcGpkZjzYndHDwBDhw7F0KFDzX4nFoux\nbVsLxg7uV1gVvMqfh1DxS4sN+fv5bvho12OI6xhhVaWqOcUy5oqJ9ONYEuw2N4a+QZiHSIjiymoj\nwXGlSg2hgTh4QyIcejJzblkU127oeq0V8fj5eHG2VVbJwWN4Zvc1Pce5a/lckzMej4dKWXWDAjSW\nmqlZun+2NtYzvM/USMw5oSYQ7oJWBu+SIfcagBUENdvJy9t+i4rQcnx58mc8OP9/8NGux2wufGlO\nsYy5YiL9OKZNwiyNmxATZVQw1b1LNALa+SGuUwQC2/nBx9MDWq0WGo0WYrEQCTFRVm2O6xAOrVYn\nDGJOuNvSsdaKeBJi23O2+fl4oc7P19vX9BxxHcKhUqvB5/Oh1Wrh5+PFnZtl2XoFYpaaqVl7Bo25\nz9RIzDlxyIyeaAG0cojka+ApW9piQ8oC9kAjSjHIpz6O7vEFWPlWKgoKC7jiI9PCF9O87Umj+uOH\n7X/iwpUs8Pl8PNA9pq5FAGskPK0XuzhxLhOXMu/lbpsWE7Esix2/HYOIL0CfHnF4sGc8Mq7faLAI\nZ/Loh7B2w684dzkLcR3CkbZoFrbuTr83Jljs3HsMLIDxI/pBo9Hg8+9+RVFxGSTB/njp2dFgWRZv\nfvAdVyyVGB+F24V3kX+nBL7eXnhi3MPQaDSYt+RLbN+TDnlNLfg8HiRBbbF1z2Gkn/4bp85fQ96t\nQqiUGgiEfCR3j6nXLMzwevsmdUDOzVIcPHG5XlM40wKkyaMfwvx31uHc31koKCqDUqmGRqXB5NEP\n1UuxnDJ6AB7sEYcDxy5Co9EgPDTA6JkAxnn0tgqPTB070Oi3MWXMACOhFUeIf5AASX1sKpgiWp7G\nrvwz2jKI5GvgIUsDA/NpeI2lKvA4tML4ettfWbzGKPti3LB+eOnpRy3aaxjPrVWqcPvOXWTn39H1\nftFq0a6ND7p37chJ3xnFf69ko6KqGt5eYu5cpusOpuPbIlX4yuI12L43HR4eIovjGo6/5KMfUFyX\nPSMUCLh8eGnObRQWlcJT7AGNVregqmsGBgQHtEWgvx+Onc3gJAAB3TqFSCSEWq2BRmuwnWEQGtQW\nb8172qL9UqkUZ67cbtT1mntefr7eXGEXALAaFkqNGiWllbh5pxiRoUEIaOdnNLa5cWxZAzL8LTfl\nWbU01my4H7NuKHTjpDCaAogr/82FYvwKO0AsW95kJ88yvqgMzjDqE2POyQONbwxlGs+9UVACnr5v\nDMNAVq2w2NBLL+DR0LmaEu+/eDWXi0dbuwZDoQ59tkpmzi1dw7KqavB4PKg1GrAsixqFEnw+Dzwe\nDzW1SmTm3IJGazxXYqGrLtayWuMTsSxkNbVW7W/s9Zp7XqahF7ZuLMPGZY1dS7AFZxD/cAYbnA1y\n9M4Gy8Kjcgn8iuLhIf+8ycOohX1RIbnFOfXKkBtg+aE2HdvYxlCmTiUyJBBafSdIloWPl7ie8LR+\nf72AR0Pnakq8v3t8NDR1s2xr12BJqENRqwSPz4NKpeb+0/IUi1BdU4sqWQ2UtUrEdggHn2c+7bDe\nNuheOGsCMY29XnPPa8qYAYgOD0bx3QpEhwdj/Ih+VhuXOVp4pKVwBhucDbvn0RM6LOXy8lXn4FUx\nu9HjZd3tD16HM6j1+zdqfV+HyutpgGlazYG5/PyysjKLucdd49ob5W2vfGsW0k9dgVxRi4iQQIwf\nmYLBKT24WKnh/hNH9kcbX28olJZrAUzHtyXmOuzhXriUcR0seFZrDLrGtUe7tr7Izi+AWCTEY4P7\n4JuP/omT5zJx43axLr2RZdAzsRP69oxDVn4BxB5C+LfxxfPThqOdvw+ycu9Aq9VCJOBD5CGEn48n\n/Hy84OMthlKlm1F7e4kRFhKAvj3jdXnxZigtLcXAfj0bdb3mntePuw7jyOkr8PP1wt3yKiTGRaNb\nXDS8vcToGBmC+E4RGJRiPHZj6zIMbdb/NpryrFoaazZQHj3hcFjG+h9ZamE/1Pq+CrVoENeQPtC2\nybr187Msftx1GH6+3njhyZE2vajmcuR3fbek3rj6BTL9jJZlWZw8n4k2vl42n8ucveYW3hiGQVKX\naESGh3FZKHPfWl2nfCXGSzPG4InHH+HOx+PxMLh/Ete98adfj8DXxwuJBg45rmMEWJZFeEggZLIa\n8AV87Pj9GLp0jsSEx/rjzAUpruffAQMGkiB/MAyDKlkNQoMDoNFqIRDwuVz6hhYsrdUcmLtm01i6\nafgi4/oNqymxhnn0TV3QbG0xeltwBhucDXL0ToZW0B0Kn39BVP0NeFpdAzmVx1DU+vwLGtGDrX5+\nSw2xWnLcfYfOgoWuUlW/MHjRQqGPNZssfWdayLNh+584c1kKlVoDlgWWfbyRU77Sj2G4UHkxMxfR\n4boWCfpFvYSYKBw/m4Gbd4ohFAhQdLcMZWWVKCguw7Wsm1Cp1WBZoBYqZGbdBMPjQSjkQ63S9bHx\n9hKjvFKG85ezcCkzt8n32JZnZNh8rSnhi9b6HRCOgRy9s8HwUOv7Jmp933TI6VtrIct8EZTKJkWj\nhmxqSDXJsJDn3LV8sCzqREVgtChqSWHJz8eL61mvn9X+nZkLHy9PVFZVg8fwIRKJIJPVQKvV6sav\nW5dQa7QQMgw8PUSQaxTgC3hgGAYRoUGQ1SgQ7N22wXvc0IzalmfU3F7wtKDpXpCjJ4xo7kzQlnE9\nPUTcjL68SmZV0aghmyx9p5t9/w1v3CsuOnNZWicTCPh4ehjte/Fqjq4FgaE9se3rzWKr5DWQVdfA\nw0MIeXUNlEol2rVrAx6PB0ar5RZhBXwewDCoqb2XpdM+IhgB7fwQHR6M3FtFDd7jhmbUtjyj5oYv\nWut3QDgGcvQuTGsUhkwdO1BXoLT3KIR8AVdUY6sN+iKeixm58Pb0QFLXjkiM02WBALqZ4uPD+uLE\n2au6wpzYaPRI7ISuBopGpvF8jUaDa9dvorSiCgH+ftCyGmi1Wvy46zD+vpaH6PBgI1UklmWh1WpR\nWlaFOwVlUNaFa3y9vSAU8tHGzxsvzRjDnW/q2IFQq9X49wffoUpWjaxaNSSBbXH09N9Y+eVWSHN1\nvdn5PB46tZcgXBIAeU0tJIFtERrcDvGdI9ErsRNOX7im64DJApLAtmjj5438W8VgGCBUEoBH+nVD\n11jdvfhx12Gj56YXe7mcmQOhUAhFrRJalkV0ZAjCJbq/driCpoxcyOTVqKlVws/XC1pWa1T41BK/\nF1v/ImBZFrsPnEXpz8epOMmJIUfvwrRGHFW/kGnakMxS73NTGzZs/xOXruVCo9aiRlGL7JuFRk2+\nAF1BS97tYgQHtkWtUoWuJjNn03j+7cK7qJLXQKtlcaeoDMs+3oST564ZzYoNi2I2/3wQn37zM0rK\nqlAlU0Cj1YLP54EB0K9Xl3oLxQzD4NOvf0FFVTUAoFpRi0MnLgMAV94P6Iq/ruXcQWiwP7ondESt\nUoWJjz1kdN5P1u9E0d1y1NSqIC+4Cy2rhbenJ4pKy1Elq+H2NX1OerEXw8IrAJBm34JGrcH4ESmc\nMIhGrYW8WgG+gI/qmlp89vUv3HpDQzTm92LrXwTU1Mw1oDx6F8Ye8XRr45rum5lzC0KBAGqNBjwe\nD1VV9RttWRvfNJ5fo9DF9HUzRV3R0cWruQ3G7RUKla6HfV3REsuy9RqRGXKjoMRoJqpUqbm+NqZ4\nCIWI6xiBaWMeNprpXpHmIyo8GGGSgLqZNgsvTzEA6wVIhg3TDFFrNIgIDcTUsQO5gia1RgMw4GoV\niksrsHbjXmz++WCDf321xu+Fmpq5BuToXZjWKgxpzLiWGm0J6hpt+fp6mY2rNzS+aVMzT7EIYPRF\nSDrR7YaamyXEREEsFuqce126ql64xLARmSGRIYFGTlIkFFjUS30kpTve+dcznDi7kd0qFcJCAhAd\nKUFSl446pwzrBUiGDdP0MIwuXBQeEgCGYbiCJgGfD7C6dMgahRLVNbVQqtTYvOsgtvxyyOI5WuP3\nQk3NXAMqmHIQLVG00VrFKebGtWSv6b5LX30G+TeLoFZr0TEqBI/0625ULAXoREFOnL0Kac4tXLmW\nj137T2D1d78iOMAPifHROpGSujFHP9oHg/snISe/EKxWi+hICf71P5Mw/8WJFq+9a1x7+Hh54k5B\nMWKiwyEUCMBjeAgJ9keNQolPv/4Z32zZh407/8L5v7Mw7OFeeG7qUHy/9Q/UKJTw9fbEzKlDEdMx\nHHJ5DUorZAB0PWweTIpBh6hQFBSX4auNv2HFmm04e0mKsgoZrkjz4ekhQmVVNfg8PiaNfgi+Xp5Q\nKFUY2CcRD/aKx0+/mhfymDp2INJPXkFFZRVqlffCRb4+nkjuHoNHH+rBFTSp1Vp0bB+KTlGhqK1V\nQhLUDmEh7SAQ8HX3IyXJ5ucK6MIvP/56uEnCIV3j2qO0tBTeXt4OK5BqLPdjwRQ1NXMQrtZYqSXt\n1TedOnkuE9U198SwvcQifLj4xRaL8Zo229I3LtOoNWABiD2EEItFGDesH/r26mK2EZZhg6z8m0Vg\nwaJ9hASXrmSjvEoOby9PyKtr0NbXG90SOiLvZiEYMJxMoblxGmr29dy85fh532kjlakBvbvWW1cw\nvZdNbSLWEk3I7uffsqtAi7GE3dHHihUKpdF2hVLdajFew8Zl+vmyWq3hYud+vt4W8/HNiaDIamqh\nj/SwrO4zoBMx0ctsWRqnoVh2ZvZtbi0CAHg8BnKD/wxNaW6+/N/X8lBSWgmZrAY+Pp74u27hnHAv\nKEZP2B19rFgsNu7FIxYJWi3Ga9i4TB9YEAj4XOzcUvzakgiKj6eHvvsEGEb3GQA8PASorVUi8/pN\n5N0s5No92Bofj+sYBl5dkzSG0YmHd+8SbfG69Nkx5tYMbKFKVo2bd4ohr1Hg5p1iVMmqG3U84RrQ\njN6FsZQX3dz8enPHNwZ9vveFjBz4eIqN8uQNBTQSOkdi6+4jOqFsTzH+77XpXB682dz8q7lIjI0C\nGAaXr+YZ5embXqNGo8GL/16LmwVliOsQju1fvYn0U5ex/bejUPMYtPHzQZikHXy9POHtJUb6qcu4\nei0PRaUV4PP4UKlUmDSqPzQaDaRZt1Alr0a3Lh0wbcxArPlhLwRCAcIlAahW1ELOsiitkOFyRg6i\n6jpGqlQaiD2EYKFTerpSl+/v6+NlVDNgyoIXxuLS1ZvIvlEIoYCPqWMHYOVbqWZ74xgKhehFWywt\nIFvCUMbQ11vXiK052PrbI3EQ+0KO3oVpqM9Lc/LrzR1vKY/eHPp8b0ui1fpZ6LTHH8a7rz9X73hT\nYWp9br5QIMClqzlgwMBDJLSYpw/o8tIvXMkFn8/HsbMZ6D/uX+DxGXiIRBB7AAFtfdEjoSNybxXh\n4InLyMy6AZVKlyGj1WqQfioDKY/PR5W8mhMkOXc5C8UlFSgqLYdQIEBJaQVUKjVUai0YBrhVWIqi\n0kq09fOGRqOFQCjAzr3HuJoEW2LgH6z9BSXllQjw94VKrQaP4eGnX4+YfZ76+ywUCJCdryvqslks\nvo6E2Pa4mJmLsJAArhq4Odj626NeOvaFHL0L01Cfl+bkS5s7vjGOXp/vbYtotS3n14tgA4BWy4IB\n22CePlBfyPtGQQkkAW2NxLH1QuO6XjXGOQkMdLn1Qj4fvLqZJsuyuFFQAh8vcd1n1Dn5ulALdBW5\n2roCrfJKOUKD2jXqWWRm364n/mFp/aAlhEKaG+M3pTGi4tRLx35QjN6FsSWu3JTc5uYer8/3Nida\nDaCecLVpkY+l3HxAtzjJ4/GM8vQVtUpUVsmNxjMV8o4MCawnjq3Pxffx8eTi4npY6HLrTQVJIkMC\nOVt0soO8OvtZsAB8vMQIkwRA7CHCkP5JmDAypVH3Mq5jWD3xD0vPoyWEQpob4zfF1NYunSPNPmsS\nB7EvlEfvIFozj765+fWNyaM3hz7fW6XWoFNUKAalJGGwgciF/s/28ko5LmRkgwFj1PfdUm6+olaF\nR1OSkFinHqXP0/f29EDuzSKUV90bb+mrz+C/h05DqdaiR0JH7Nv0f/D19kJFZTXCggPw7JShmP/i\nBDBg4O0lRkx0GGqVSlTJaiAU8vFgr3js3/QuAv3bGAmS/LjmDeTfKoaiVoVB/brjuanDcPGKLvTw\nQFIsXnl+HHx9vDBxZH/Mf3EiEuOjG/UsunQIgqxabST+YWmMpgqFtDQNCY8AwJZfD9V71o4UKKE8\nesJuuFoub0va+1baf4yEq+M6RlgVxWjseEvmP41P1v2I0kolEmKizDYSawmREwBGDdhYlsXO346B\nBTBhZEqjZ8mW7rMzL1429Nto6WfdErjau9cSUIyesDst3QLX3HimzbaOn83gmqA1dfHP3AIi3vFd\nHAAAGnlJREFUAKMGbOWVMihVOgGSG3eKWkztyFUXL6ndsXNAjp6wOy29AGhuvMUrfzBqtqVfeNV/\nbsrin6UFRMOCKnl1LTw8dJ8VChW3T3Nn5K66eNnSz5poGuToCbvT0pqe5sYzFR7pHh9tVezDGpZm\np4aCKt5eHtyMXiwWcvs0d0buqjNj0m91DsjRuzCtFbdtbMGUaeHOyrdS8dOvR/D3tTxObDvBoGCq\npW0zN+aUMQPw+1/HkXurFD6eYvj6eDZYsKTPBNq+9ygYAONHpmDq2IFGcf0pYwaAZVls33sUojpR\nFsMZ6+PD+uLYmQzsOXAKDIA+SbHcMdv2pCM3vxA+Pp4Ik7Rr9Ix88uiH8MO2P3Dm4nX4+XhCy2ps\nEhshCIAcvUtjDyFvWwqmTAt3snLvgC/k1xPbbgn7bL3mH3cdxq3CMqjUGly6lovyKjkC2vlZLFja\n8sshfPL1ThSVVIBhgBt3inHi3NV6cX2GYaAyEWUxFB45fUEKsLoc+5MXruHHXYcBQNdeQF6NSlk1\n1Go1Jozo36jrnv/OOpz9+zpUag1qFLVY9vEm8Bg+zZYJm6A8ehfGGYRHgPqFO5k5t+qJbbek0IWt\nBTkiocBmG/RiJXp9V31Blem5rAmV19QqwePxwOfzuBi9qSBJVGhwo2PVF6/mcuLmPIYxEjcnCGuQ\no3dhnEF4BKhfuBPXIZwrRFKp1VbFv1vDNr0ghq026MVKzBVUGZ6rofMnxETB00MErVYLjUbLxehN\nBUkmPNa/0SGX7vHRYBhdWZaWZY3EzQnCGhS6cWFaK6PB3LjXr1+3uP+Hi18AAJti9EB98W8AyLh+\nw6Z1hiljBuD42QzuXHrRcXPXUFBYgLsVtfVsMNcMTN9MraEYvalsoOk2Q2F1fR69tWNs5cPFL4Bl\nWfx1/BJ8vMVG4uYEYQ2HFEwVFhbi7bffxr59+yCTydChQwesXLkSKSkp3D7vvfcevv/+e5SXlyM5\nORlpaWmIj4+3t6mthqsVbbSG8IiHSGhRqMOWY63tb8nmVxav4dYUVGo1xg3r1+hmYK2Fq/0uANez\n2dXsbQnsHrqpqKjA8OHDwTAMtm7dipMnT2L58uUICgri9vn444+xevVqrFixAgcOHEBQUBDGjx8P\nuVxub3OJVsAwzq1QqHSCHrBtPaAl1iVaohkYQbgSdnf0n3zyCUJDQ/HFF1+gR48eiIqKwsCBA43+\nh12zZg3mzZuH0aNHIz4+HqtXr4ZMJsPWrVvtbS7RChjGucViXf45YNt6QEusS7REMzCCcCXsHqPf\ns2cPhgwZgpkzZ+Lw4cMICQnB9OnTkZqaCgDIzc1FYWEhBg0axB0jFouRkpKCEydOYMaMGfY22e60\nlnhDa+Xdq9VqpDw+HzcKShAZEoj0nWnYtueoxfMYrgGMG9YPgHGMviEauy5h7ppN1xT0ny0dx60j\nSPNRKas2ysVnWZaL93eLi8aDPeNwNetmPYGQeW+vxcFjF+Ht7YmXZozGE+MesfhMzYmMtBTO3DOH\naD3s7uhzc3Oxfv16zJkzB/PmzcOlS5ewYMECMAyDWbNmoahI1x/EMJQDAEFBQSgoKLC3uQ6htcQb\nWivvPuXx+biWcwsMw+Bazi0kPjobXWKjLJ6nOdWSjT3W0jVbi8kbHvffQ2fAgIFAwMeNO8WICA3i\nhFSOn83g4v1Xr9/Afw+dQfeEjvUEQn7afRgqta5iduknG8Hj8cxex56/zuGvk5mt1tPGVXvmEM3D\n7o5eq9UiOTkZixYtAgB069YNWVlZ+OqrrzBr1qxmjS2VSlvCRLthyd70k+ehVimhVim5z+YKlmzd\nr6n722pv/u2iOv1UFgwDlJRVNOs8LUlTr9nwOEMdVQZAWXkl2vqKkX7yPM5czgYD3V81Wq0WVbJq\nbi1Jf66T5zN0vfFZ3fFVsmqLdmTlFbTqvWvub8AS7vLuOSMtsXBsd0cvkUgQGxtrtC02NhZffvkl\nACA4OBgsy6K4uBjh4eHcPsXFxQgODm5wbFdaSW9o5b9/nx64UXgvs6R/nx5m97V1v6bub6u9UWHB\n3IyeZVkE+reBQChq0nlaEqlU2uRrNjzO18eLm9HLa4rh39YPAqEI/fv0AF/gwc3oeTw1fH284O3t\nbXSuPj26IPdmCTRaLVgW8PXxsmhHp/YhuFFY0Wr3rjm/AUu4WhaLq9nbEtjd0fft27fe/6ZSqRSR\nkbo4aHR0NCQSCQ4cOIAePXoAABQKBY4dO4Zly5bZ21yHYGscurHx6tbKuz/680qrMXpH0dRrNruO\nYCZGr8/jtxSjB/Q58DCK0Vuy47FHeiJEEtJq9466Sd6f2D2P/ty5cxg+fDhee+01TJgwARcuXMDL\nL7+Mt99+GzNnzgSgy8z58MMPsWrVKnTq1AlpaWk4fvw4Tp06BW9vb3ua22q42qzC1ewFyGZ74Wo2\nu5q9LYHdZ/Q9e/bEhg0bsGTJEqSlpSEiIgKLFi3inDwAzJ07FwqFAgsWLOAKprZv3+42Tp4gCMKe\nOKQFwtChQzF06NAG93nttdfw2muv2ckigiAI94WamhEEQbg51NSMcCmo4IcgGg85esKloIIfgmg8\nFLohXApXFckmCEdCjp5wKVpLbIUg3BkK3RAuBRX8EETjIUdPuBTNaYhGEPcrFLohCIJwc8jREwRB\nuDnk6AmCINwcitG7MFQ8RBCELZCjd2GoeIggCFug0I0LQ8VDBEHYAjl6F4aKhwiCsAUK3bgwVDzU\nNGhtg7jfIEfvwlDxUNOgtQ3ifoNCN8R9B61tEPcb5OiJ+w5a2yDuNyh048LYEmumeHR9aG2DuN8g\nR+/C2BJrpnh0fWhtg7jfoNCNC2NLrJni0QRBkKN3YWyJNVM8miAICt24MLbEmikeTRAEOXoXxpZY\nM8WjCYKg0A1BEISbQ46eIAjCzSFHTxAE4eZQjJ5oNlSURRDODTl6otlQURZBODcUuiGaDRVlEYRz\nQ46eaDZUlEUQzo3dHf37778Pf39/o3/x8fHc93PmzKn3/bBhw+xtJtEIpo4diGljHkZcxwhMG/Mw\nFWURhJPhkBh9bGwsdu/eDZZlAQB8Pt/o+0GDBmHt2rXc90Kh0O42ErZDRVkE4dw4xNHz+XwEBgZa\n/F4kEjX4PUEQBGE7DonR5+XloUuXLkhKSsLzzz+P3Nxco++PHz+OmJgYPPDAA5g7dy5KSkocYSZB\nEIRbYPcZfe/evfHFF18gJiYGxcXFWLFiBYYPH44TJ06gbdu2GDp0KMaOHYv27dsjPz8fS5cuxdix\nY3Hw4EEK4RAEQTQBuzv6Rx991Ohz7969kZSUhI0bN2LOnDkYP348951+1t+tWzf8/vvvGD16tL3N\nJQiCcHkcXjDl5eWF+Ph4ZGdnm/0+JCQEYWFhFr83RCqVtrR5rQrZ2/qQzfbB1Wx2JXtjYmKaPYbD\nHb1CoYBUKsXAgeZT8kpKSnDnzh1IJBKrY7XEDbEXUqmU7G1lyGb74Go2u5q9LYHdF2MXLVqE9PR0\n5OXl4fTp05gxYwaqq6vxxBNPQC6XY9GiRTh16hTy8/Nx+PBhPPnkkwgODqawDUEQRBOx+4z+9u3b\nSE1Nxd27dxEYGIgHHngA+/fvR0REBBQKBa5cuYItW7agoqICEokEAwcOxLfffgtvb297m0oQBOEW\n2N3Rr1+/3uJ3YrEY27Zts6M1BEEQ7g/1uiEIgnBzyNETBEG4OeToCYIg3Bxy9ARBEG4OOXqCIAg3\nhxw9QRCEm0OOniAIws0hR08QBOHmkKMnCIJwc8jREwRBuDnk6AmCINwccvQEQRBuDjl6giAIN4cc\nPUEQhJtDjp4gCMLNIUdPEATh5pCjJwiCcHPI0RMEQbg55OgJgiDcHHL0BEEQbg45eoIgCDeHHD1B\nEISbQ46eIAjCzSFHTxAE4eaQoycIgnBzyNETBEG4OeToCYIg3Bxy9ARBEG4OOXqCIAg3hxw9QRCE\nm0OOniAIws0hR08QBOHm2N3Rv//++/D39zf6Fx8fb7TPe++9hy5duiA0NBSjR4/G1atX7W0mQRCE\n2+CQGX1sbCykUimuXbuGa9eu4ejRo9x3H3/8MVavXo0VK1bgwIEDCAoKwvjx4yGXyx1hKkEQhMvj\nEEfP5/MRGBiIoKAgBAUFoV27dtx3a9aswbx58zB69GjEx8dj9erVkMlk2Lp1qyNMJQiCcHkc4ujz\n8vLQpUsXJCUl4fnnn0dubi4AIDc3F4WFhRg0aBC3r1gsRkpKCk6cOOEIUwmCIFweuzv63r1744sv\nvsC2bdvw6aeforCwECNGjEB5eTmKiorAMAyCgoKMjgkKCkJRUZG9TSUIgnALBPY+4aOPPmr0uXfv\n3khKSsLGjRvxwAMP2NschxETE+NoExqFq9kLkM32wtVsdjV7WwKHp1d6eXkhPj4e2dnZCA4OBsuy\nKC4uNtqnuLgYwcHBDrKQIAjCtXG4o1coFJBKpQgJCUF0dDQkEgkOHDhg9P2xY8fQt29fB1pJEATh\nutg9dLNo0SKMGDECERERKC4uxooVK1BdXY1p06YBAGbPno0PP/wQnTt3RqdOnZCWlgYfHx9MnDjR\n3qYSBEG4BXZ39Ldv30Zqairu3r2LwMBAPPDAA9i/fz8iIiIAAHPnzoVCocCCBQtQXl6O5ORkbN++\nHd7e3vY2lSAIwi1gysvLWUcbQRAEQbQeDo/R20phYSFmz56Nzp07IyQkBP369eMqatVqNRYvXoz+\n/fsjPDwc8fHxSE1Nxc2bN53WZlNeeeUV+Pv7Y9WqVXa20hhbbL5+/TqeeeYZtG/fHmFhYXjkkUcg\nlUqd0l65XI5XX30VXbt2RWhoKJfe6yi6d+9erwWIv78/pk6dyu3jbC1AGrJZo9E45btny33W4wzv\nni32Nue9s3vopilUVFRg+PDhSElJwdatW9GuXTvk5uZy+fbV1dW4dOkSFixYgMTERFRWVmLhwoWY\nPHky0tPTwePZ//8zazYb8vPPP+Ps2bMICwuzu52G2GJzXl4eRowYgSeffBILFiyAn58fpFKpQ0Jr\ntti7cOFCHDp0CGvXrkVUVBSOHj2Kl19+GYGBgZgyZYrdbf7rr7+g0Wi4z3fu3MEjjzyCCRMmALjX\nAuSLL75A586dsXz5cowfPx6nT592WPiyIZvlcrnTvXvWbDbEWd49a/bm5uY2671zidDNO++8g2PH\njmHv3r02H5OZmYm+ffvi6NGj6NKlSytaZx5bbc7Pz8fIkSOxc+dOTJw4ES+88AL+93//105WGmOL\nzampqWAYBmvXrrWjZeaxxd6UlBSMHTsWr7/+Ordt1KhR6Nq1Kz744AN7mNkgaWlpWLVqFTIzM+Hh\n4YH4+Hi8+OKLmDdvHgBd1llMTAyWLVuGGTNmONhaHaY2m+Lod88c5mx2pnfPFFN7m/veuUToZs+e\nPUhOTsbMmTMRExODAQMGYN26dQ0eU1lZCYZh0LZtWztZaYwtNms0GqSmpuLVV191iiIOazazLIvf\nfvsN8fHxmDRpEjp37ozBgwdjx44dTmkvAPTt2xe//fYbbt26BQA4ceIELl++jKFDhzrC5Hr88MMP\nmDp1Kjw8PFymBYihzeZw9LtnDlObne3dM8XQ3pZ471zC0efm5mL9+vXo0KEDtm/fjtmzZ2PJkiX4\n6quvzO6vUqnw5ptvYuTIkQgNDbWztTpssfndd99FYGAgnn32WYfYaIo1m4uLiyGTyfDhhx/i0Ucf\n5WZCqamp2Ldvn9PZCwDLly9H165dkZiYiKCgIIwZMwZLlixxCkf/559/Ij8/n5upu0ILEFObTXGG\nd88Uvc3Tp0/ntjnbu2eI6T1uiffOJWL0Wq0WycnJWLRoEQCgW7duyMrKwldffYVZs2YZ7av/n7qq\nqgpbtmxxhLkArNt8+PBhbNq0CUeOHHGYjaZYs1mr1QIAHnvsMcyePRsAkJiYiPPnz2PdunV2d562\n/C7WrFmDU6dOYcuWLYiIiMDRo0fx5ptvIioqCoMHD7arvaZ899136NWrFxISEhxqR2NoyGZnefdM\n0dvctWtXAHDKd88Q03vcEu+dS8zoJRIJYmNjjbbFxsbWW9nXaDSYOXMmMjIy8Ms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CwYMwrlrlcVxcJTIAQDhyhF2P5wGjsVXj4gt/hx6Jt9/OxPmsVkg6HcQQLxJJ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\nOyJOozFPKXNHiM9G1bMhNxdcUpKgehoSAkNmppAvEHsgYCGprdcj/ME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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(heights, 'MidParent', 'Child')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This residual plot indicates that linear regression was a reasonable method of estimation. Notice how the residuals are distributed fairly symmetrically above and below the horizontal line at 0, corresponding to the original scatter plot being roughly symmetrical above and below. Notice also that the vertical spread of the plot is fairly even across the most common values of the children's heights. In other words, apart from a few outlying points, the plot isn't narrower in some places and wider in others.\n", "\n", "In other words, the accuracy of the regression appears to be about the same across the observed range of the predictor variable. \n", "\n", "**The residual plot of a good regression shows no pattern. The residuals look about the same, above and below the horizontal line at 0, across the range of the predictor variable.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Detecting Nonlinearity ###\n", "Drawing the scatter plot of the data usually gives an indication of whether the relation between the two variables is non-linear. Often, however, it is easier to spot non-linearity in a residual plot than in the original scatter plot. This is usually because of the scales of the two plots: the residual plot allows us to zoom in on the errors and hence makes it easier to spot patterns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "Our data are a [dataset](http://www.statsci.org/data/oz/dugongs.html) on the age and length of dugongs, which are marine mammals related to manatees and sea cows (image from [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Dugong_dugon.jpg)). The data are in a table called `dugong`. Age is measured in years and length in meters. Because dugongs tend not to keep track of their birthdays, ages are estimated based on variables such as the condition of their teeth." ] }, { "cell_type": "code", "execution_count": 52, "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", "
Length Age
1.8 1
1.85 1.5
1.87 1.5
1.77 1.5
2.02 2.5
2.27 4
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2.26 5
2.35 7
2.47 8
\n", "

... (17 rows omitted)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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LBweHUrfT5QcppaSkJLNpC8D2mAJTaZOtm5u6BwGlEkonJ9G6TaU9hmYSF6lzc3Nx+fJl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\nEsWAICIiUf8PXVfCvXHmy5YAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(dugong, 'Length', 'Age')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While you can spot the non-linearity in the original scatter, it is more clearly evident in the residual plot.\n", "\n", "At the low end of the lengths, the residuals are almost all positive; then they are almost all negative; then positive again at the high end of lengths. In other words the regression estimates have a pattern of being too high, then too low, then too high. That means it would have been better to use a curve instead of a straight line to estimate the ages.\n", "\n", "**When a residual plot shows a pattern, there may be a non-linear relation between the variables.**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Detecting Heteroscedasticity ###\n", "\n", "*Heteroscedasticity* is a word that will surely be of interest to those who are preparing for Spelling Bees. For data scientists, its interest lies in its meaning, which is \"uneven spread\". \n", "\n", "Recall the table `hybrid` that contains data on hybrid cars in the U.S. Here is a regression of fuel efficiency on the rate of acceleration. The association is negative: cars that accelearate quickly tend to be less efficient." ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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p6QQHBzN79myHHD8vL4+kpCSio6Pp2LEjgwcPZs+ePXaP\nw2AwsHDhQvr160fHjh3p168fCxcuxGAw2PzYaprWwlwsVVVVzJs3jxtvvJGIiAhiY2OZMmUKZ8+e\ntXssV5o+fTrBwcH84x//cEgcx44d44EHHqBr16506tSJm2++maysLLvHUlpayl/+8hd69+5NeHg4\nAwYMYNmyZVaPIz09nVtuuYXIyEiio6O57777+Pnnnxu0s8d121wsbb1unT7RHzhwgDVr1tCnTx+H\nHL+wsJA77rgDRVHYsGED+/fvJzU1tcFzAPbwyiuvsHr1ahYvXsyBAwdITU1l1apVpKen2/zYaprW\nwlwsZWVlHD58mNmzZ7Njxw7ee+89zp49y//93//Z5AOxufNSa/PmzXz//fd06tTJ6jG0JI5Tp04x\ncuRIunXrxtatW9m7dy9z587F19fX7rHMmTOHr776ihUrVrB//35mzZrF/Pnz+eCDD6wax549e5gy\nZQpffvklW7Zswc3NjbFjx6LT6Uxt7HXdNhdLW69bpy7dFBYWcvPNN/Paa6+xaNEievXqxcsvv2zX\nGF588UX27t3L559/btfjNmbixIm0b9++Xu8nKSmJS5cusX79ervF0blzZxYvXsykSZNM22JjY3n8\n8ceZMWMGUDOSKiYmhoULF/LQQw/ZNZYrHT16lEGDBrFnzx7i4uLsHsvp06cZNWoUH3/8MRMmTOCx\nxx7jySeftGscU6ZMQVEUVqxYYbPjtjSWIUOGcPfdd/PMM8+Ytt1111307t3bpr/fpaWlREZGsm7d\nOu644w7AcddtY7FcyZLr1ql79NOnT2fcuHH87ne/c1gMn332GQkJCUyePJmYmBiGDh3Km2++6ZBY\nBg8ezM6dO01/bmdmZrJz584mLxR7Ufu0FkVFRSiKQlBQkN2PXV1dzZQpU/jLX/7isAd0jEYjX3zx\nBbGxsdxzzz1ER0dzyy23sGnTJofEM2jQIL744gvOnTsHwL59+/jpp5+4/fbbbXrc4uJiDAaD6Tpw\n5HV7ZSyNseS6dcjwSmtYs2YN2dnZrFq1yqFx1MYwdepUZsyYYfrzSlEUHn30UbvGMn36dEpKSrjh\nhhtwdXWlurqamTNn8sgjj9g1jiuZm9YiNzfXQVHVqKysZO7cuYwaNYrw8HC7H/+ll16iQ4cOPPzw\nw3Y/dq2CggJKSkpIT0/nueee44UXXmD79u1MmTIFPz8/myfYK6WmpjJ9+nT69OmDm5sbiqLw8ssv\n2zyOZ555hn79+jFw4EDAsdftlbFcydLr1ikT/bFjx1iwYAH/+te/cHFx7B8lBoOBhIQEnn/+eQCu\nvfZajh8/zsqVK+2e6D/66CPWr1/P6tWr6dmzJ4cPHyY5OZmuXbty//332zUWZ1Dbmy4uLub999+3\n+/F37tzJe++9x65du+x+7Lpqa7x33nknSUlJAPTp04cffviBN9980+6Jfvny5Rw4cID333+fzp07\ns2fPHubOnUtkZCS33HKLTY45Z84c9u/fzxdffNHojLr21FwsrblunTLR79+/n4sXL3LDDTeYtlVX\nV7Nnzx7eeustfv31V9zd3e0SS1hYGD169Ki3rUePHrzxxht2OX5d8+bN46mnnmLs2LEAxMXFcfr0\naV555RWHJvq601pERESYtjtyWovq6momT55MZmYmn376qUPKNrt37yYvL6/e9VNdXc28efNYvnw5\nP/30k13iaN++PW5ubvTs2bPe9h49eti9fKPX61mwYAFr165lxIgRAPTq1YtDhw7x2muv2STRP/vs\ns3z88cds3bqVyMhI03ZHXLdNxVKrtdetUyb6xMRErr/++nrbpk6dSnR0NDNnzrRbkoeaeuKVQ9Cy\nsrLo0qWL3WKoVVZW1uAvHBcXF7sMrzSn7rQW8fHxwP+mtVi4cKHd46mqquKRRx7h6NGjfPrpp3To\n0MHuMUDNDdDaD+Va48eP55577rHpjb4rubu7c/311ze4jo8dO2b367iyspLKysoG17Grq6tNruPk\n5GQ2b97M1q1b6d69e73X7H3dmosF2nbdOmWiDwgIICAgoN42Hx8fgoKCGvRKbG3q1KnccccdLFmy\nhPHjx/Pjjz+yYsUKXnjhBbvGATBy5EiWLl1KZGQksbGx/Pjjjyxbtozf//73Nj+2mqa1MBdLeHg4\nDz74ID/++CPvvfceRqPRNP11QEAAXl5edoulc+fOtG/fvl57Nzc3QkNDG/1Ft2UcTz31FJMnT2bw\n4MHcdNNN7Nixg02bNrFu3TqrxtGSWG688UZeeOEFfHx86NKlC7t27WL9+vUsWLDAqnHMmjWLDz74\ngHfffZeAgADTdeDr62saVmqv67a5WKqrq9t03Tr18Mq6Ro8eTVxcnN2HVwL8+9//Zv78+Rw/fpzO\nnTvz2GOPMWXKFLvHUVpayt/+9je2bt3K+fPnCQsLY8KECcyePRsPDw+bHltN01qYiyU5OZl+/fo1\nWja5r5IAAAhlSURBVPt8/fXXzQ7DtHYsteelrn79+jFlyhSrD69sSRzvvfceS5Ys4ddff+Waa65h\n5syZjBs3zqpxtCSWgoIC5s+fz7Zt27h06RJdunThwQcf5E9/+pNV4wgODm70OkhOTiY5Odn0tT2u\n2+ZiOX36tOmviiu15LrVTKIXQgjROKceRy+EEKJ5kuiFEELjJNELIYTGSaIXQgiNk0QvhBAaJ4le\nCCE0ThK9EEJonCR6Iah5iCc4OJjdu3fb/diHDx9m0aJF9Ra8qBUcHExqaqrdYxLaIoleiN84atbC\nw4cPk5qa2mii/+qrr3jwwQcdEJXQEqec60YItausrGzx5HpGo7HJD5mEhARrhiWuUtKjF3Z38uRJ\nHn/8cfr160d4eDjx8fHMnDmz0R7trl27GDduHJGRkURERPC73/2Od955p16bNWvWMGzYMMLDw4mK\niiIxMZEDBw6YXr98+TLz5s2jX79+hIaG0q9fP5YsWYLR2PzsH5988gm33347nTp1omvXrjz88MMN\nFmTu27cvjz32GO+88w4DBw4kNDSUL7/8EqhZWGTYsGFERkbSvXt37r77bg4ePGh677p160zz2lx3\n3XUEBwfTrl07zpw5AzReuvnqq68YMWIE4eHhREZG8oc//IFjx47Va3PXXXcxatQotm/fzrBhw+jU\nqRNDhgxh69atzX7PQnukRy/sLicnh06dOvHSSy8RHBzMqVOnSE9PZ+LEifzrX/8ytfv000956KGH\nGDx4MK+++irt2rUjMzPTlAQB5s6dy+uvv85DDz3EnDlzcHFx4cCBA5w9e5YBAwZQXV3N+PHj+eWX\nX5g9ezZxcXEcPHiQl19+GZ1OZ3ZGxNWrVzNz5kweeOABkpOTKSkpISUlhcTERHbv3l1v4exdu3bx\n008/8cwzz9ChQwfTXOK5ubkkJSXRuXNnysrK+OCDD7jrrrv45ptviIuLY+TIkcyaNYslS5awdu1a\n0+LgHTt2bDSmr776iokTJ3LzzTfz9ttvU1JSwt/+9jdGjRrFzp07Te9TFIWTJ0/y7LPP8vTTT9Ou\nXTtee+01HnnkEQ4cOEBUVFSrf37C+UiiF3Y3ZMgQhgwZYvr6hhtuoFu3btx5550cPnyYa6+9FqhZ\nhKFfv35s2bLF1HbYsGGm/588eZKMjAyefPLJegm77opIH374Ifv27eOzzz5j0KBBANx0000YjUZe\nfvllpk+f3mCqYKiZCfSFF17ggQce4O9//7tp+/XXX0///v355z//yRNPPGHaXlhYyI4dOxrMEV73\nvQaDgVtvvZUff/yRtWvXkpKSQrt27ejWrRtQszpZcwl44cKFdOvWjQ8//NA0Z3v//v3p378///jH\nP+rNk37x4kW++OIL0z779u1Lz5492bRpk2mxa3F1kNKNsLvKykqWLFnCwIEDCQ8Pp0OHDowaNQrA\nVILIysrizJkzZm9EfvPNNxiNRrOLdHz99dd06dLF1Luv/Td8+HAqKirqlXjqOnDgACUlJdxzzz31\n3tepUydiYmLYs2dPvfb9+/dvdCGIb775htGjR3PNNdfQvn17OnTowPHjxxuUWlqirKyMQ4cOMW7c\nuHoLc3Tt2pUbbrihwYih7t271/vg6NChAyEhIQ1KT0L7pEcv7O6FF15g5cqVJCcnM2DAAPz9/Tl3\n7hz3338/er0eqOmNAmYXPq5tU1vuaExBQQGnT59uNAkrimLaR2PvMxqNjBkzptH3BQcH19sWFhbW\noN2PP/7Ivffey2233cY//vEPOnbsiIuLC3/+859N36cldDodRqOx0bJOWFgY3333Xb1tjS0z5+Hh\n0apjC+cmiV7Y3aZNm5g0aRJPP/20aVtxcXG9NrXllJycnCb3U7dNUysytWvXjqioKN5+++1Gb752\n7dq1yfdBzULVja1a5u/vX+/rxkbNbNmyBXd3d9555516PXCdTteqNWqDgoJQFIW8vLwGr+Xl5TX4\n8BGilpRuhN2VlZXh5la/j/HOO+/US5bR0dFERkaydu3aJvdz8803oygKb7/9dpNtbr31Vs6dO4ev\nry/x8fEN/jWVHAcOHIi/vz/Hjx9v9H0tWeqvrKwMV1fXetu2b9/eoHTi6ekJ1IwOMsfHx4f4+Hg2\nb95c70Pr9OnT7N+/n6FDhzYbk7g6SY9e2N1tt93Ge++9R1xcHNdccw1btmxptFaekpLCgw8+yOjR\no5k8eTLt27fnl19+oaCggGeffZaoqCimTp3KsmXLKC4uZtSoUbi6uvLdd9/Rs2dPxo4dy7333su6\ndeu4++67+dOf/kSfPn2orKzkxIkTfPHFF6xbt8603mbd5Onv78+LL77IX/7yF86fP89tt91GQEAA\nOTk57N69m6FDhza7buhtt93G8uXLeeKJJ0xDINP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t2bBnD1V3VW5oLtKlSxeTrtNMNU9pU0OYQkUbGGvSdAdUMxltPYUzZ85wVlIy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\nOhQvv/wytm3bhiFDhmDKlClo1aoV8vLycO3aNRw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "regression_diagnostic_plots(hybrid, 'acceleration', 'mpg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how the residual plot flares out towards the low end of the accelerations. In other words, the variability in the size of the errors is greater for low values of acceleration than for high values. Uneven variation is often more easily noticed in a residual plot than in the original scatter plot.\n", "\n", "**If the residual plot shows uneven variation about the horizontal line at 0, the regression estimates are not equally accurate across the range of the predictor variable.**" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [Root]", "language": "python", "name": "Python [Root]" }, "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 }