{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# What is Simpson's Paradox?\n", "\n", "An overview of Simpson's Paradox in the cases that we address in this project and how to detect it as well as breif complexity analysis of the problem" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pylab as plt\n", "import seaborn as sns\n", "\n", "# for outputting all alone variables\n", "# from IPython.core.interactiveshell import InteractiveShell\n", "# InteractiveShell.ast_node_interactivity = \"all\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's generally discussed in terms of two variables, both discrete, though binary or mulit level cases are both poputlar. A popular example is the berkeley admissions data set. the claim was that it was iased againt women because t the univerisyt sclae it ws, but fom os depeartments they actually admitted wmen at much higher rates but the departments tha had low aceptance rates wer the ones with most of the women applicants" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regression Based SImpson's Paradox\n", "\n", "\n", "It can manifest in how a decision variable relates to others that $x_k$ is predicted differently for different values of $x_j$ \n", "another way Simpson's Paradox could manifest is through latent clusters. It can manifest in relationsships among variables. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/smb/anaconda2/envs/simpsonsparadox/lib/python3.6/site-packages/ipykernel_launcher.py:7: RuntimeWarning: covariance is not positive-semidefinite.\n", " import sys\n" ] } ], "source": [ "# \n", "N = 100\n", "# sample data from 2 clusters\n", "mu = np.asarray([[1,1],[5,5]])\n", "\n", "z = np.random.randint(0,2,N)\n", "x = np.asarray([np.random.multivariate_normal(mu[z_i],[[.6,-1],[0,.6]]) for z_i in z])\n", "\n", "latent_df = pd.DataFrame(data=x,\n", " columns = ['x1', 'x2'])\n", "\n", "# now we add somoe more columns\n", "color_z = {0:'r', 1:'b'}\n", "char_zy = {0: {0:'x', 1:'o'}, 1:{0:'o', 1:'x'}}\n", "\n", "latent_df['color'] = [color_z[z_i] for z_i in z]\n", "y = np.random.choice([0,1],N,p=[.7,.3])\n", "latent_df['y'] = y\n", "latent_df['char'] = [char_zy[zi][yi] for zi,yi in zip(z,y)]" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "sns.lmplot('x1','x2', data=latent_df, hue='color', ci=None,\n", " markers =['x','o'], palette=\"Set1\")\n", "# adda whole data regression line, but don't cover the scatter data\n", "sns.regplot('x1','x2', data=latent_df, color='black', scatter=False, ci=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "in this, if we ignore the color, x_1 and x_2 are posiiely correlate, show by the black line, but in each color, they're negatively correlated. This is a type of plot that we will want to generate a lot, so we've included it in the package" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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D/NLhWNPrbojrS1DLlgGCuNtvQ0pZ7nVNT+8Vo6AaskxUVY6GlJLTd9yJ64cfMCQnI4Qg5pprEELU2bcIZE5JuCOl5KOPPuKxxx7js8/KljVTU1OZPXs2DzzwQER/YGVwKxRVYO7bl6S+ffH85RGK1rzqNcSPHsX55Vc4v/wKY4cOZRnitTDEhRAY4+Mx9+uHuV+/ck/rJdu3Y4iLq3EADVTmdlU5GtZZM7EtWYrrhx8AgWX8eABd0Ky33Vonz8HXX3+xaGpCUVJSwuuvv86CBQv4+eef9faLLrqIefPmMXHiRKKiokLYw8CgZhYKRS3RDfGMDJyffV72htlcZoj371fjQOj7m/MdV/F1rfrSgMztmmYnwmpFs9ko2b5dn11ouaeI6tuH6P796zS7aMozC5vNxrJly3jyySc5dOiQ3j5ixAjmz5/P6NGjK37GiP7AIfUshBCJQog3hRC/CCH2CCEGh7I/CkV16Ib4yle8GeKzZiISEsDlwvH2O+SOv5acseO8hrjDUfV1hCg3iFR8XRMNzdz2LSf5D9o+U9sQF0fctKlYZ83E3K8fMi8fLTcXQ3Irovv3r5Pf4Otn0dq15RIHi9aujejEwZMnT/LII4+QmprKgw8+yKFDhzAYDNx444189913/Pe//2XMmDERL4YVCenMQgiRAXwlpXxRCGEGYqWUeVUdr2YWinBDczhwrFuHffkKSnbs0NtFQgKxE28kbvp0TF27BOx+gfYs/PMqrLNmYjAY9Hs4v/+eku3bkXllIb618VX8OX3f/WgFhSS9vAyDwYCmaZy+5TYMLeJJeubpiAqr3b9/P0888QQvv/yybljHxMRwyy23MHv2bM6puTR+eH6wWhKymYUQIgG4FFgGIKV0VScUCkU4YrBYsN58MykfrCfl3XVYJkwAsxmZn4/9hRfJHn4puZOn4PjoI6TH0+D7VTYr8EU21cbzqHgt/4gl+9IXdKGwvbiMku3bib31Vkzdz0EkJiLz8uocoht1wQVoJ7P1a9uXvoB2MpuoCy7A9srKiAir9UU29ezZU49satmyJX/+8585dOgQzz77bG2EIuIJ2cxCCNEHWArsBnoD3wMPSCntFY6bBcwCSE1N7e+/NqhQhCOeU6e8hvgrK/EcPaq3Gzt0KMsQb9WqQfcI5BN5Zb6CsVMnTH36YDAY9HZPTi7mfn3rVJKkKs/COmsm9qUvBDT5L5BUF9n08MMPc+uttxIXF1fXy0b0zCKUYjEA+AYYKqX8VgixGCiQUj5S1TlqGUoRblQ3aEuPh+JP/+s1xD//ouwksxnL1VcTNyOdqH59w2LZpaJhnrz+/YAN5tWF6Iab+d3IkU2h/0E3gFAa3EeBo1LKb0tfvwn0C2F/FIo6UVNynDAasYweRfKqlbT56kusM2/3M8TfJuea8eRceRX2Na9Wa4g3NpUZ5valLyCs1gYvd1VnxgeqVHsgsNlsPPXUU3Tr1o2pU6fqQjFixAg2btzIjz/+yJQpU5pECGx9CZlYSCmzgCNCiJ6lTSPxLkkpFGFPXbOTTV27kPh/f6Ht91tJXLSQqF69ACjZsYO8OXPJGnAx+X/9G+6DB4P+Oaoqde4r/VGxUGFlYbOVlR+pqYy6pmkh34/DP7LpoYce4siRIxgMBiZOnMjWrVubbGRTfQh1NFQf4EXADPwG3CKlPFPV8WoZShFONGQZRUpJyQ/bsS3PwPH+++By6e9FX34Z1vR0Ykb+DmE0Nlr/fTS0ymx15wNBK1hYFw4cOMDjjz9+VmTTrbfeyuzZs+nWrVtj3DaiFUcl5SkUDSAQ25p6cnPLDPFjx/R2Y8eOXkN80s0NNsRror6GeW1CeYFKrx2KUuhbt25l4cKFvPXWW2iaBkDLli255557uO+++2jdunWj3LcUJRbBQomFIpwIlEHrGzy9hvin2Jdn4Pziy7IDzGYsv/+91xDv26dBT9yNkdfQ0BlWY+dZSCn58MMPeeyxx/j888/19gZGNtUHJRbBQomFIlwIVHJcVU/X0uFAy8uj6PU3kAUF+vFRF12INX06sePHIyyWOvW5sXfWa+gMK9CUlJTw2muvsWDBAnb4JUz27t2befPmceONNwbbsI5osVAlyhWKehCI5LjqTHJhsZDgM8QXLiDqggsAKPl5B3kPz+XEgIvJ/9v/w52ZWel1K772v5dvv2/fvTyFhQ0ylRtafiTQ2Gw2Fi9ezDnnnMO0adN0oRg5ciQbN25k+/btTJ48uVlHNtUHNbNQKBpAQ5dRaruEI6XEte177CtW4Hh/fXlDfMTlWNPTiR5xOY5XX9NnDz58s4fYKZMDVnq8sv6HOrnu5MmTPPPMM/znP//hzBlvnIzBYGDChAnMmzePAQMGBKUf1RDRMwtVolyhaAAVB8K6Doy1LeEthCD64gFEXzwAz1/+t6xk+vHjOD/7HOdnnyMSE4jq1w8tKwtN0zAYDLh++AHPkSNYxo9HSom5Xz+c//0MDXTB8A3s9fELqpphSSnLzbAas+bT/v379cgmZ+m+I0GIbGp2qJmFQhFCGmQOu90Uf/opBf/8F+59+8veMBpBCJASQ+sUrLfdRvyddwDomy/VVBywrjMm//eDFeW0detWFixYwFtvvaUveSUlJXHvvfdyzz33NHZkU32I6JmF8iwUihBRU9JaTQ9ywmQiZvRoYm++GWOP7hg7dQKDATwecLvB40HLy0MkJiAdxdiWLKX43XdrLA5Yn21b/WcQjbmVqpSSjRs3MmLECAYOHMibb76JlJLOnTuzePFiDh8+zF//+tdwFIqIRy1DKRQhoqolHEBPaPOnsqd7/3OK1q6FnBwoKfEKBoCjmII58yj8+z8wX3QRUcOG4Xj9dbScXEypnfDg3aXP/x6+wR44y4OoaYYRqJ38KuKLbFq4cGG5mk2+yKaJEydiqsMWt4q6o5ahFIoQU9mST9Gq1XVaytE0jeyBl6DlngK3G9GmNTGjR1P89jtIm+2s4w3t25Oy6SscL718lhkdiPyRQIXS2mw2XnzxRZ544gmOHDmit48cOZJ58+YxatSokIfo1oGI6WhlqGUohSLEVDbY1WUpx7ehkMzLR1gsiDZtMPe6EPePP2J94H4MaWne5Sm/+2jHj5N76eVIj4foUaPKmdENLfAXiFDa7Oxs/vznP1dZs+mTTz6pbNtSRSOixEKhCDP8czYc69aRM+6qKkNRfRsKuffswTx0KG137SB+5u14srMwtG6DMT6e1l9+joiOhuhoMJsxDxsGgOfIEQr/8U9s//4Prm3bcP34o37N+g72DfVh9u/fz1133UXnzp159NFHOXPmDBaLhbvvvpt9+/bx2muvhUMIbLNELfIpFGFIXUJqDXFxWG+9Rd8WVa/HZLV6cytuuU0/FqMRERNDyuf/peiVVRS94c0QL3rjTYreeJOo3hdh7NwZ92+/EXvddeU8i6r6AGVLafUNpa0usunee+8lJSUlgN+uoj4oz0KhCEPq6htU5ntIKTl9y224Nm3CPHQoSS8vO+s1xcU43n4H2/IM3Hv26OcLi4XY9OnEpU/H2KlTtX5JZaGyhc8vwRgfj3XqlCpDaYXVylfJrViwYEG5mk2dO3fWazZZrdYAfaNhQUSvmamZhUIRZlSXFQ1VzzAqvhZCYGgRrwuDwWDQBcPQIh6DwQCxsVinTiF2ymRcW7diX56BY8MHSIcD+/NLsC9ZSvSIEVjTpxPzuxGV9rWy6Knid9/FMn48mqad9f6ZZ59jzZIlPHsql93Hj+vXqi6yKRgFBxXVo2YWCkUYEsjENl82d1WvK+I5eRL76jUUrVyF58QJvd2Ymop1+jRib7oJY1JLvb2mWZDv/dy33mLl0SMsyczkWOkeElBzZFMoSpk3EhGtbkosFIowpSFZ1LU5vsb7u90Uf/wx9uUrcH79ddkbMdHEXnMN1vTpmPv00e9VVahsdnY2Tz/9NM8uXEheSQngrdl04403MnfuXPr371/tZwqX2lMBIGI6WhlKLBSKJkBjP32X7N+PPWMFRW+8iSws1Nuj+vTGmj4dz8kcitev19st48dz4ncjeOKJJ1i+fLles8liMHBzx448ePtMLvzzn4Ca62kFat+QMCCiOlsRJRYKRYRTn93q6otmt3sN8YwM3Ht+KXvDaMQ8cCCJjy/k6+ee44nly1l/8qQe2dQyKorbLryQu266mZQWLcplhPuM8Jo+Y7jtl1EPIq7D/iixUCiaAOUS906dRmqaXiAQCPgav5QS13ffeQ3x99cjPR4+cxbzrM3GNy6nflznzp2599LLmNq/P7FmM8XvvquXRfeviFvdLEHNLMIDFQ2lUDQB/PMypKaVKxBoW7KUorVrib322rItXBvoZwghiL7kEgz9+vFerwtY8PdH2X36lP7+BaYo7u7ShUkPPEDC5EmIxET9PMe6dfr9KxrhFT0XX//rEhmmaBzUzEKhaAJUfPr25OQCEkNyMvL0GUznnaeHzwbCzygsLOTFF1/kySefLFez6dJOnbi3SxcG7ztQNoibTMROuB5r+nSiLrqo0uWk6jwXQEVDhQGq3IdCEeFUVmIj7nZvrShPTg7S40E7mY196QsNLhmenZ3Nn/70J1JTU5k9e7Zes+mmm27iiz/8kTcu6MXYSZNJ+exToi4e4K1J5XZT9Nrr5Iy7mqyBg9DOnEFqGuCdNfjnYlRWCyt2yuRyMwjfLCrChCLiUctQCkWEU7HEBpSGzSYmIAxGRFJLDK3bNKhk+L59+1i0aBEZGRllkU0Wi74bXdeuXcv2vXjpZWwvLsOYkkz8nIcRCQnYnlqMlpODVpqEZ7AXYTr3XIreeAMA66yZQO3Lmqulp+CjlqEUiiZCxTX+mGuuIf7OO3TPQss9hTElGah9NNF3333HggULePvtt/Xrt2rVinvuueesmk2+EiPZAwch8/IQiYm0+e4b7EtfoGjtWgzWOLSCfNy/7vNuzlSK6bxzSfjT/xA1fDinfn+N3p68/v1qkwf97xsh2d1h2anaosRCoWhiVFz/95Uwd+/Zg6FVElBznakPPviABQsW8MUXX+jtaWlpPPzww9xyyy1YrdaztlJ1FxRgMBhwrFuHJycXLTcXYbFg7JxK7LXX6rMerTRD3L5yJVpWtn59YbEgEhMwtGyJMJkwtG5DzBUjiZs2tU6f1b70Bd3PCDPhCJuO1Ae1DKVQNDH8B0lfCXPtZDbWW2+pNprI5XLx6quvsnDhQnbu3Klfr2/fvsybN48bbrhBr9nkP0gDuAsKsD/9DBgE8fffj6Zp2B5bgHQ40HJzsc6aqd/H2KYNLR56kPh776H4o4+xLV+Oa/MWpMPhPf5MHoakJEr2/gpA7JTJlc4wKtalElYrxZ98inYyW69L5S8cioahxEKhaIL4m8HVbd0qhKCwsJAXXniBJ598kqNHj+rXuOKKK5g3bx5XXHHFWcs8FYsDCiG8ZramYXv7bTh1GpGcjBAgDEbsS184ayYjoqKwXDUOy1XjyF/0OEVvvOn1NIqLdW/DvXcvxW+/g+XqqxAxMWd9Rv8tXD05Oci8fMxDh2KdNbNcQcMwm2FEJGoZSqFoBlS2rp+dnc0zzzzDs88+S15eHoC+G93cuXPp169ftdcrnwTowXrbbdjfeQdOnUY7lUvMqNG0XPIc9qUv1KqWk6Zp5Iy9Ei0vz7s9rLMsuc+QlETs5ElYp03F1LHjWX3JvmRwaYSVN1wYQMvNxdyvH0lLng8XoQiLTtQXNbNQKJoB/oPlr7/+yuOPP35WZNNtt93G7Nmz6dKlS62uF3fHLIrWrkVqHmRePq5vvsFgMOBxFIEErfTaFWcyleFbLhNGI8ZWrTAkJWHu2xft9GmKN36Idvo0tn//B9uzzxEz8ndYZ6QTfemlIIQ33LY0EVEkJqLl5CKRkF+AuRrBU9QNJRYKRTPh22+/ZcGCBbzzzjvlIpvuu+8+7rnnHpJLn8hrg76BkRAYkpPx2Ow4v/gCQ3Iyps6dESmt9dyOuDtm1bqcR2W1rRL+7y8UrXkV+6pVaFnZFH/8CcUff4KxSxdM55yD59gxb16JlNgWP4202bw7Aia3qnMeiaJqlFgoFE0YKSUbNmxgwYIFfPnll3p7Wloac+bM4ZZbbiE2NrbO16w4uJ+uwX3tAAAgAElEQVSadQfOjz/Bt9LSavlLurlc0xJQTb6KqV07Wsx+iPj77qX4w4+wLc/AtWULnoMH8Rw8CCYTJfv2IaxWZEkJIi4OQ4sWxN4yg+J339WvV5+lqAgKy210lGehUDRBqops6tOnD/Pnzy8X2VQfKkZD2ZYsxfbiMoTBgKFVEpbx4/U9wStS1QBcl4G5ZO9eb8n0N99C2u1lb0RFYWjTBkNiArHXXadXtY2dMrnOg3wjlH2PaJVR5T4UiiZEYWEhTzzxBN26dSM9PV0XilGjRvHxxx/zww8/cPPNNzdIKMAbnusvFI5164i7/TbafLsFy/jxONat08uL+GNfuUov6QFlsxT7ylU1bhXrT1TPniT+41Ha/rCNhEf/rpvalJSgHT2Ke++v2J5fgszPxzJ5kn6P2uIf8VVZCZJIesgOFCFfhhJCGIFtwDEp5dWh7o9CEYlkZ2ezePFinn32WfLz8wH0mk1z5sypNrKpvvgG85pCc31UtV+3/94WdX36N8TFETcjHYxGSnbt8hriGz7wikZODrZ//4fiDz9ClriInVL7JL2KYbn1LZPSlAj5MpQQYjYwAGhRk1ioZSiFojyBiGwKBLVZQqpYjsRHoAZg3z3dx09w5uGHcW3eUq6siLFLF+LSpxM78UYMCQm1vmYAN12KaIUJqVgIIToCGcCjwGwlFgpF7QhkZFN9qYvHUNHjyBl3FZ6cXITBQJtvtwT8SV1KyckrxyHz8715IH6+hoiJwXL9dVjT0zH3uqDaawRY2CJaLEK9DPUUMA+Ir+oAIcQsYBZAampqkLqlUIQfVUU2denShdmzZ+s1m4KBb/D3mdh6KK3VelYtJ//lJ5+geHJykXl5kJiAbcnSKjdAqg/+Yb0iMRFDYiLmwYORxcU4Sg3xotVrKFq9BnP//lhnpGO5ahwiOvqsa6hNl8oImVgIIa4GTkopvxdCXF7VcVLKpcBS8M4sgtQ9hSJsqK5m0/z585kwYUKDDeu64Bv87S+9jHPLNyS9vEyvLGts0xagnGD41v+llNiXLUPm5SMSEzCPuBxcJfoAbJ01s8G1nGrK2Wiz7Tscb7+NffkK3Pv24fr+e1zff0/+//2V2Ek3Y50+DVOHDrUqk9LcCNkylBDin8A0wA3EAC2At6WUVZaYVMtQiuZEVTWbRo0axbx58xg5cmTIBi1fJVvXpk3eSrHJyRjbtNWL+FX25F1WlsODaNUK63XX6QITc8VIpN1eq7IgNVGbkFcpJa7NW7Atz6D4ww/B4/GebDAQM+oKb4b4sGEgRCDzLCJaYUJucAOUzizmKM9CoYCsrCyefvrpSiOb5s6dS9++fUPcQy+appE98BJknrePpu7nVCsUvid834Abc801CCEoWrtWPz7QZndVr/3xnDiBfdVq7KtWo508qbebunbFOn1anQzxGohosVB5FgpFmPDrr78ya9YsOnfuzD//+U/y8/OxWCzce++97N+/n9WrV4eNUPhqORn8jHRPTvlS5P7H+i8Ftf5gA5bx4yl+992zBvFAeQF1ydkwtmtHizkP0/bbLbR87j+YB10CgPu338j/v7+S1f9izsybT8mu3Q3uVyQTFjOL2qJmFoqmSFWRTffffz933313UCKb6oJv8PctIWkns3XD2jx0KEkvLzsrc7uyTYpsS5ZSsn07niNHdNEIZR6Dfx/dv/yCLWMFRa++BiUl+jHmAQOwzpiOZVx5Q7yWRPTMItTRUApFs0TTNH03uoqRTb7d6OpasylYCCEQVms5j8I6a6a+G19le1f4b8jkG5QBPEeO6MtRrh9+CFm0UWUJg6a0NEw9umPq1An3/gO49+/HtW0brm3byE/+m9cQnzYNU4f2QetnKFEzC4UiiLhcLtasWcPChQvZtWuX3t6vXz/mzp3b4JpNwcT2ykqk3V7llqaV4b8kZezUiai+fRFClMviNsbHh2Rnu+ryKgBcmzZjy1hxtiE+ehTW9HSihw+rSeAiemahxEKhCAJVRTaNHj2auXPnhjSyqSHUpyqr/zKWv7Ht8ztC+T3UJmPbc/wE9lWrvIZ4To7eburWzWuI33hDVYZ45P2A/VBiEUI2/5rDqs2ZHD/joH1LC1OGpDGkR0qou6UIIJVFNhmNRn03usY2rMO1xLbtlZUULl6MITkZIQTJ698P+X7Zdc3Yli4Xjg82Yl++HNd3W/V2YbFguf564tKnE3XB+f6nhP6LbwAqGipEbP41h0Ub9pBb6KSFxURuoZNFG/aw+decmk9WhD179+6tNLLpvvvuY9++fUGJbKquwmso0TSN4k8+Reblo+XmIqXk9C23hbSia8WIrZQN6/Xquf7foT/CbCZ2/DWkvPM2rT/+COu0qYjYWKTDQdGqVZwcPYaca6/37ibocgX9MwWayFgcDSGN9fS/anMmUUYDFrMRwPtfl7ddzS4il2+++YYFCxawdu1afYBJTk7mvvvuC2pkU2NUeA1Uv+xLX8CTnYV56FA9ksqz/wDmoUMrDb0NBg3N2I46/zwS//VPWvzPHyl68y3sGSu8hvjWrbi2biU/5W+0+/GHYHyURkMtQ1WD7+k/ymggJspAcYlGiUdjzrjzGjygX/fkl7SwmM5aIihwuHnnoUsb2nVFEPFFNj322GN89dVXenuoI5saoRBeQPCvK5V7lTcP15OTS/wD959VVyrYBGrZTkqJ8+tN2FesoPjDj8DjocOxIxG9DKVmFtXQmE//7VtayC106tcGKC7RaN/S0qDrKoJHdZFN8+fP5/rrrw9pZJPv6dhfLGojFI3tc1inTtEjp3wYU5KRdnvIPZW6JPPVdJ2Y4cOIGT7Ma4ivXBmI7oUUJRbVcPyMgxaW8l9RTJSB42ccDb72lCFpLNqwB1yUm7VMGZLW4GsrGpeCggI9sunYsWN6++jRo5k3bx6/+93vwsJE9s0s/PGv8FoZjbCVaKX9si99odlUdDW2b0eLeXMB+P7771ubTKYXgV6Ep2esATvdbvft/fv3P+n/hhKLamjMp/8hPVKYAyoaKoI4ceIETz/9NM8991y5yCZfzaY+ffqEuIdl1KfEdrB8juZc0dVkMr3Ytm3b81JSUs4YDIaw8wA0TRM5OTnnZ2VlvQhc4/+eEotqaOyn/yE9UpQ4RAB79+5l0aJFrFixAldpVEtsbKy+G11aWlpoO1gJ9RmQg7mVqH9Gt/+9m7JQlNIrXIUCwGAwyJSUlPysrKxeFd9TYlEN6um/eVNVZJOvZlOrVq1C3MPqqc+AXF+foz4Eyh+IMAzhKhQ+Svt31hKZEosaUE//zQtN0/Td6MIpsqm+1HVAro/PoQgts2fPbh8XF+f529/+lt2Y91FioVAQ/pFNwUBtJdo8KCkpISoqqs7nhaMbr1AEjYKCAh5//HG6du3KjBkzdKEYM2YMn376Kdu2bWPixIlNXiigap/DMn58kzeew5F///vfrXr06HF+z549z7/22mu77N271zxo0KAePXr0OH/w4ME99u3bZ654zubNmy29e/c+t0ePHuePGjWqW05OjhFg4MCBPW+99dZOvXr1Ou/vf/97m/r0p9q/ACFECyBFSnmgQvtFUsqf63NDhSIciKTIpmDSjI3nsGLbtm0xixYtardly5Zf2rVr587OzjZOmjSpy5QpU07dd999p5566qlWd911V6dPPvmk3Ng8Y8aMLk8++eThq666yvbggw+2nz9/fvuXXnrpCIDL5RI7d+7cU98+VTmzEEJMBH4B3hJC7BJCXOz39vL63lChCCV79+5l5syZpKWl8a9//Yv8/HxiY2O577772L9/P6tWrWq2QuGjmRrPYcWHH37Y4ve///2Zdu3auQHatGnj2b59u3XWrFmnAe66667T33//fZz/OadOnTIWFhYar7rqKhvAzJkzT33zzTf6MZMmTTrdkD5VN7P4H6C/lPKEEGIg8IoQ4o9SyncIUfVEtxbWQQSKMCbSI5vCkXCtaKuonPj4eK0h51fnWRillCcApJTfASOAPwsh7gdCMmofyC7kn+/uIjPHForbhy2bf83hnuVbue7JL7ln+VZVubYUTdN47733uPTSSxk8eLC+bWnXrl3597//zaFDh3jkkUeUUNSDcK1o21QYM2ZMwXvvvdcyKyvLCJCdnW3s27ev/cUXX2wJsGTJkqQBAwaUGwhbtWrladGihWfjxo1xAMuWLWs1ePDggA2W1c0sCoUQ3Xx+RekM43JgLXBBoDpQF6SEdd8fZd33RxnaI4XJQ9Lol9ayWT/N+Bc79C91Pgeabcivy+Vi9erVLFy4kN27d+vtzSmyqTEJ14q2TYkBAwYUP/zwwyeGDx9+rsFgkL169Sp6/vnnD0+fPj1t8eLFbVu1auVesWJFZsXzXn755YN33XVX5/vvv9+QmprqXLNmzVnH1Jcqq84KIXoDRUCUlHK3X3sUcLOU8pVAdaK2dDvvItn3zn9z9HRZbaae7VowZWgavzu/DSZj8wvuumf51rNKkjhcHpLjo/nPjIurObPpUVBQwNKlS3nqqafK1WwaM2YM8+bNY8SIEWoQCxDhWtE2zBE//fRTZu/evXND3ZGa+Omnn5J79+6d5t9W5egqpfxJSrkPeF0IMV94sQBPAHc3blcrp6XVzGv3DecfN/Xmwk6JAOw9UcD/vvkzExZ/xerNmdiL3aHoWsg4fsZBTFT5H2Ogih1GCidOnOCPf/wjqampzJ07l2PHjmE0GpkyZQo//vgjGzduDJvifk0F/9IgPpRQNG1qMxe/BHgM2AzEA6uAoY3ZqeowGgS/O78tvzu/LTuO5LF6cyZf7MkmO7+Ypz/cy7LPDzC+f0duGpRKm4SmV+674mZM1mgjxSVasyx1XlXNpttvv53Zs2fTuXPnEPew6aIyvZsftRGLEsABWIAY4KCUskGueqC4sFMi/7ypD0dPF/HqlkO8v/0Ydqeb1Zszee2bQ4y8oC1ThqbRs12LUHc1IFTmTxQ6XPofZ3Mpda4im0KLyvRuntRGLLYC64CLgWTgeSHEBCnljY3aszrQMSmWOVedx8wR3Vi77Sivf3uIUzYXH+04wUc7TjCgSxKTh6Qx6JxkDIba/RI31naqDaHSzZgwE2UUJMSaw6qvgUbTNNavX8/ChQvL1Wzq2rUrc+bMIT09PaJqNkUyzbnEeHOmxm1VhRADpJTbKrRNC4XBXdttVV1ujY92nGD15kx+O1kWOZaWYmXy4DTGXNSO6Chjlec35naqDaE5bsXqcrlYtWoVCxcuZM+esuTT/v37M2/ePCZMmIDRWPXPUtF4qDyLOhPRBneNM4uKQlHaFnShqAtmk4Gr+3bgqj7t+fbAKVZtymTrb6fIzLHzj3d38dyn+7hxYCrXX9yJROtZ5VUadTvVhtCctmKtLrJp7ty5yrAOA1Smd/OiSceaCiEYdE4yz6QP4JW7BnNl7/YYDYIzdhdLP9vP+Ce/YMH7uzl8yl7uvHCNMJoyJI0Sj4bD5UFKicPlaXL+xIkTJ/jDH/5Ap06dqoxsGjlypBqYFIp6snfvXnP37t3rnCvXbDKTurdtwV+uv5C7Rnbn9W8Psfb7o9iK3by99QjvbDvCpT1bM2lIGr1TE8P2Cb4pb8a0d+9eFi5cyCuvvFIusmnmzJk8+OCDYbkbnULR2EhNQxgMVb4OJs1GLHy0Tojh3tE9ueWybrz3w1Fe/eYQWXnFfPHLSb745SQXdExgQJckPtpxAgi/CKOmthnTli1bWLBgAevWrVORTQqFH4XPP58sbXZj/OyHsoXBgNQ0Cp94so2Is3ri77yzQb6H2+3mmmuu6bJz587YHj16ON54443MmmpHNellqOqwRpu4eXAab94/nL/f2JvzO3jDa3cdzSfjq4M43RqaJskrKiE5Pjrk5nZTwlezafjw4QwZMkQPge3atSvPPvsshw8fVjWbFM0aqWlIm93oWL8hqfCJJ9v4hMKxfkOStNmNUmtY9kJmZmbMvffee/K3337bFR8fry1cuLDGwa1JzyxqE/5qMhq4oldbRl7Qhp8Oe5P8vtp7ktM2F6dxER9j4oIOCXRvGx+iTxFcGjNkuLrIJl/NJhXZpFCAMBiIn/1QNoBj/YYkx/oNSQCWq8ad9s00GkLbtm1do0ePtgNMmzbt1NNPP90aqHZb1iYrFnUtsCeEoE/nlvTp3JJDuXZe3ZLJhh+PU1jsZsXXB1m9JZPRF7Zj8pA0zmnTNIWjsYoS+iKbnnzySY4fP663jx07lnnz5nH55Zcrw1qhqIBPMHxCARAIoYD6RbKFbBlKCNFJCPGZEGJ36eZKDwTy+v7hr0IILGYjUUYDqzZn1nhu52Qr839/AWtnX8bMEd1oaTXj9kg2/Hicqc9u5oEV2/h2fy415ahEGg35ziqjYmTT8ePHy0U2ffDBB6q4n0JRBb6lJ/8235JUQzlx4oT5k08+sQKsWrUqaciQITWWMg/lzMINPCyl/EEIEQ98L4T42L/CbUM4fsZBC0v5j1fX8NeWVjO3XX4OU4Z2YeNPx1mz5RCHcu18e+AU3x44Rbc2cUweksboXu2IMkW+/ROI7wzgl19+YdGiRZVGNj300EOqZpNCUQP+HoVv6cn3Gho+w0hLSyt+5plnWs+aNSu2e/fuxXPmzKlxE5yQiUXpxkq+zZUKhRB7gA5AQMQikOGvMVFGrh3QiWv6dWTzPu+a/vbMMxzItvH/3tnJ85/s48ZLUrl2QCdaWKIC0f2QUN/vzOdz7PhhK0e/fo2D27/U30tJSdEjm5KSkqq5ikKh8CEMBkSc1ePvUfg8DBFn9TREKHr27Ok6ePDgrjr3KRyWUoQQacCXQC8pZUGF92YBswBSU1P7Hzp0qFbXbOySHb8cz2f15kw+3ZWNp3S7V4vZyO/7duDmwZ1p3zLy6hTV5zv7+pds5i56if2frSH3tx16e4fUNP78x/mkp6djsTS9DHOFoh7UudxHqPIsKiv3EXKxEELEAV8Aj0op367u2NrWhvIRjGKAWXkOXvvmEOt+OEqR0wOAQcCI89swaUgavTomBvR+jU1tvzOn08nq1at5+M//jzPHD+rtrVLPpcfIyaT1u4yWcZYmlzyoUDSApl0bqjEp3XXvLWBVTUJRH4KRwNY20cIDY8/ltsu7se57b5JfToGTT3dl8+mubHqnJjJ5SBrDerbGWMuKt+FMQUEBS5Ys4amnnioX2dThgkFcMGoybXv2x1bs5tCpYjxSbfWqUDQVQiYWwhsCswzYI6V8IlT9CBRxMVFMGdqFmwZ15pNdWazenMmvJwr56XAePx3+kY5JsUwa3Jmr+nQgxs8TCKdS6NWFzqbFlbB48WKef/55Cgq8K4VGo5FuA0eTdulE2nXpqV8nt9CJySjCrhCjQqGoP6GcWQwFpgE7hBA/lrb9j5RyQwj71GBMRgNjL2rPmAvb8f3B06zenMnmfbkcPV3EwvV7WPrZfiZc3IkJA1PZe7ygUfIa6ktl1XYLjhzi9tsf58C3GyuNbDrmjGXRhj04XB7d53BrGm0TYspdOxwKMSoUivoTymior4HIX5epAiEEA7q2YkDXVhw8aWP1lkw2/nSc/KISXvriN1ZuyqRFTBRmU/iUQvcPnT15YAc7P1rJkZ/KNhqqLLKpM5xV3DDKKCjxlPfCwqEQo0KhqD9NNoM7nOjSOo4/je/FnSO789Z3h3nzuyMUOErItTkByHeUkBRnJtZsDOkTeLuEaH7+5jP2/XcNJw/8rLe3aN2Rx/76pyojmyp6Q77lLFzhV4hRoVDUDyUWQaRVXDSzftedacO6sP7H4zzz4V6cbg27043d6SY6ykBcdBSdk4MbduuLbPrgH/8i88CvenvL1HPpPuJmFs2/g+Hnta319ZpyKXWFoimhaRpSylrVZFNiEQIsZhM3DEylbYsYHn13F0VON063hrNEw1nixKNprNqUyfj+HYiLabwkv/z8fH03Ov/IptQLB9Np2EQuungIU4d2qdcg39RKqSsUoeDTnVktVm/ObHuyoDi6dYsY5+QhaVkje7UtqPnMqtm7d695zJgxPfr27WvbsWOHdcOGDft69Ojhquk8JRYhZNi5rXnEIFi1OZPMHDseTSPfUUJeUQnPfLSXZV/s59r+nbhpUCoHsm0Be1I/fvx4pZFNkyZNYs6cOfTu3TuQH1OhUNSDT3dmtVj84S+pJoOQ1mij+4zdGbX4w19SgcMNFYzDhw9HL1u27ODIkSMza3uOEosQU/EJ/NjpIl775hDvbT9GkdPD6s2ZvLolk+goIwmxUSRYouodNbVnzx69ZlNJSQlQv5pN4RTuq1A0VVZvzmxrMggZHWXUAKKjjBolHsPqzZltGyoW7dq1c40cOdJe85FlKLEIMzokxTJ73HncPuIc1m47wuvfHia30InD5cHh8lBQ5DXDTaUzkpoG6c2/5rAoYx1b1i0na9cmvT0lJYUHHniAu+66q041mzb/msOj63ZiK3bj0TRO25w8um4nfxrfSwmGQhFAThYUR1ujjW7/NrPJoJ0sKI5u6LVjY2PrXLpWiUWY0sISxfThXZk0OI2rH/8ch8uDy61R5PJQdNqB2WQgv6gEZ4mH6KizzSlN01i4ZBULFizgdOZOvd2a3IG77n2Av827t141m5795FfyilwYDQaMRgNSQl6Ri2c/+VWJhUIRQFq3iHGesTujfDMLAJdbM7RuEeMMRX+UWIQ5USYD57SJJ6egGCnhlN1JkdMrHC63xrVPfskNAzsx4eJUEq1mnE6nvhvdL7/8ol+nVedz6TV6KikXDKMoIVYXitouKfmO25/tLXtvEBKDEAgBUggOnyoKzheiUDQTJg9Jy1r84S+plHgMZpNBc7k1g1uTYvKQtKxQ9EeJRQQwZUianundKSmWAoebvCIXLrfGGbuLFz47wEuf7CTh6Fd8v3E1J7PLfpfanz+IXmOm0LZHP4QQSCn1PI7Kyns8um4nLa1m7E6PLh6AfpwAJOAuTbprCvWuFIpwpNSXOBzoaKiePXu69u3bV+cS5UoswoTqnvAry1uYe9V5nNM2nhc3bGXpc//h6Lfv4XF6n+4NRhNXjp+AtffvoWXnKvenqFjew6NJ8opc2Jxu0pKtupEeW7pjnnfnPIHLI3XBEIAmoUuQc0MUiubAyF5tCxoqDoFCiUUYUJu9rytGTe3Zs4c/PvSHcpFNRrOFlL5jaTvoOnITWhObGEuhw4WUUVjMxrMyqSvujHfa5sQgBJom9W1VccHhU0V0SbEC0DrBwvEzRUjpnWEIgyDBbOTuK3oE5btSKBShQYlFGFBZAb+qakRt2rSJhQsXsm7dOr3NEt+StGHXM+jKmxhwbme2HTzN7mP5uo9gd3qIiTLStXUc04eVJdlV3BmvxOP10aKM3s1VbMVuThUW43JrZObYSWkRQ1yMifYtY70eCtCrY6IKnVUomgFKLMKAmva+1jSN9957jwULFrB582b9mI6du5A88Hq6XnIlcVYL9hKNT3Zl8fCV52KNiWLN5ky+3HtSN8N3HMnjkTd/pmvrOG65tKvuhfhqOBmEoMSjIdDYl1WIpkkMAswmA25NciKviLYJFkxGA63iowO266BC0YzQNE0TBoMh9FuUVoGmaQI4K7S28ffnU9RI+5YWikvK/2yKSzTaxBl56aWXuOCCC7j22mt1oTjvwr6MvvsfpN3yLC0uHIMwmfVloyijgdVbDtGnc0sem9SX1+4bxpDuyYDXk7A73ew4ksef3viJ42eKmDPuPKKMgoM5dtweDU2CW5N4NK8v4ZEQH2OiXWIMJqOBnEInyUooFIr6sjMnJyehdEAOOzRNEzk5OQnAzorvqZlFGFDxCb+goIA9n7/N4c1vsyT/lH7c2LFjuWryHXya2xKzyYj9TBGalGTnOwALcTGms6rWpray4nRrdEyKpbjEwxm7C48mcbg8LNrwCz3axnPa7qJtQgw5Bd4lp9ItxRHCu0Wsw+UhpUUM1mgTBQ43/5lxcZC/IYWiaeB2u2/Pysp6MSsrqxfh+bCuATvdbvftFd9QYhEG+KKdlq7fyuZ3VpK55V1Kir2Z+MJgJLX/FXS7/CYeuf1qVm3OxGzy+gxmowG3RwMhOG1zEhdjqnTfCN8yV1yMiaQ4MwVFJZy2e0Nvf80qBMBe7Mbt0TAaBcbS2YXJIBAGoXsZak8KhaJh9O/f/yRwTaj7UR+UWIQBe/bsYdmiRaz2i2wymS30GH4N5428ibiktjhcHj101udvJMWZyc4vRtM0XG7Yl1WA0WBgdK/y5cT9jWyDECRazZhNBko8Gln53mQ/p9srCB63pNTfRgKaJokyCBwuT1D2pFB1pxSK8ESJRQjZtGkTjz32GO+9957e1rp1a1r1/z0XjbyBmLgEvd23vOQ/8MfFROFwuTll8wqM2WQkLtrE+p+Oc16HBH2QrbjMVVzirelU7NaQviUnvOIAUDqRINpgwK1pWMwmkuOjG33grk0IsUKhCA3huGbWpNE0jXXr1jF06FCGDRumC8U555zD888/T2ZmJiMm3oE0x5U7z7cENGVIGiUeDYfLg5QSm9OD0QAdk2LpnGylVXw0UUYDqzZn6ucO6ZHCnHHnkRwfTYHDTZRR6Ia6yW8WYcDrUfhwlHhwa5LenVty18jujT5g+4cQ+xv2/p9FoVCEBjWzCBJOp5OVK1eycOFC9u7dq7dffPHFzJ8/n2uvvVbfraqymYBvCahiNreU0DbBa277qGxrVv+kvnuWb0VixyRAGAwINNwSpPTmWPzlugvJyi/m9W8PkZ1fzGe7s/lsdzYXdkpkytA0hvds3ShlPmoKIVYoFKFDiUUjk5+fz/PPP8/ixYs5ceKE3j5u3Djmzp3LZZddhhDlB96atiWtOPDnFpYvQlmTEX38jLdqrcejIQQYjQYMgNujcWGnREaWeh43DUrlv7uzWbUpk70nCthxJI8/vPojHZNiuXlwZ67u04EYc83bMdaWikmCtfksCmQ5woYAABoMSURBVIUiOAgpwzY35CwGDBggt23bFupu1Ipjx47pu9EVFnojjkwmE5MmTWLu3LlceOGFAbmP/zq//yykujyIe5Zv5XCunbwiFwJviKxHgkEI/nVTn7POk1LyQ+YZVm/OZNOvOXp7C0sU11/ciRsHptIqvuoS+3WpbFvXz6JQRBBhmVtRW5RYBJjdu3ezaNEiVq5cqUc2Wa1WfTe61NTUgN+zrhFEvkG5xK1hc7pxuTWMBkH6sC7cNuKcau91MMfGms2ZbPz5BC63rzyIYOxF7Zk0JI2urct7LXUVABUNpWjCKLEIFuEsFlVFNt1///113o0uGDR0UD5lc/LWd4d5a+sR8otK9PbB3ZOZMiSN/l2SEELoy2T+S0sOl4fk+GiV3KdobiixCBbhJhZV1Ww655xzmDNnDunp6cTExISwh41PscvD+h+P8eo3hzjitwFSj3bxTB6SxvOf7CMhNqqcLyOlpMDh5p2HLg1FlxWKUKHEIliEi1jUJbKpueDRJF/vPcnqzZn8dDhPb48yGrBGG0lpEaNHUKmZhaKZEtFioaKh6oAvsumpp54iK6tsN7px48Yxb948Lr300rMim+pDJK7bGw2Cy85rw2XntWHn0TzWbD7EZ7uzKPFo5BVp5DtKSIyNItZsQkKjZ4IrFIrAosSiFlQV2TR58mTmzJkTsMgmaBpZzL06JvLoxESOn+nOa98c4p1tR0u3gC3hjL2Evp1b0tJqDnU3FQpFHVDLUNVQWWRTXFycHtnUqVOngN8zHAzhymY2UHXeR00UOEpYu+0Ir397uFxOSN+0lkweksbQ7ikY1F7eiqZPRP+SK7GohKoimx588EHuvPNOWrZs2Wj3vu7JL2lhMYXMEK4s1NVWXIKUEqPBUOdQW39K3Bof7zzB6s2Z7M+26e2dk63cPKgzV/ZpT0xU8/J6FM0KJRbBojHForrIprlz5zJ9+vSgRDY11syitj5IZfc/eNKGVvp74p/EB5CWbMXu9NRptiGl5LvfTrF6UybfHijbr6Ol1cyEizsxYWCqWqZSNEWUWASLxhALp9PJK6+8wqJFi86KbJo3bx7XXXddUCObGiOLuS7XrGxmsz+rAI/mTb7zLRd5NEmJRxIdZSAt2Vrvfu7PLmTN5kw+3HECd6kCRZsMjOvTnpsHp9E52Vqvz6xQhCFKLIJFIMUiLy+PJUuWNHpkU30IdDRUXWYrVc0snG6NaJPQvxNniYbEKyDd2sRXe83akFNQzJvfHeadbUcocLj19mE9U5gyJI0+nVuG7OehUASIiP4FDmk0lBBiLLAYMAIvSin/1dj3PHbsGE899RRLlixp9Mim+uJfKDAQ1KWaa2UVb+NiTLiLXHgkGIW3Oq0EjAZvHkVN16wNKS1iuOuKHqQP78r7271JfsfPOPh6bw5f783hvPYtmDw0jRHntcFkVJX1FYpgEzKxEEIYgf8Ao4CjwFYhxLtSyt2Ncb/du3ezcOFCVq1aFbTIpnChLtVcK6t4+8CYnuw5lk/G1wdxezTMRgNRRoFHk7g9GgeyC0uT70ykNnDZKDbaxMRBnZkwMJUv9mSzenMmO4/ms+d4AY+88TNtE2O4eVBnft+vI9ZoFfmtUASLkC1DCSEGA/8npRxT+vqPAFLKf1Z1Tl2XoaSUbNq0iQULFpwV2fTAAw9w1113NWpkU7gQKB/Ef3kMJFl5xRiNAoMATXq/71sv7VanCKna8PNhb8XbL345qe/sFxdj4tr+HZl4SWdaJzTtkiqKJkNEL0OFUixuAMZKKW8vfT0NuERKeW+F42YBswBSU1P7Hzp0qMZra5rGu+++y4IFC9iyZYve3r17d+bMmRO0yKZgURuPo6E+SMXz84tcFDhKsBW7KfFoRBkNxMWY6NTK2mj5IEdO2Xl1yyHe//EYztKd/owGwahebZk8JI0e7Vo0yn0VigChxKJeN66lWPhT08yiqppNAwcOZP78+YwfP77J1WwKxh4Qld3j6Oki2ibEEG+J0o8LVj5IfpGLt7Ye4c3vDnPa5tLbB3RNYsqQNAadk6zMcEU4EtG/lKFc9D0G+BsFHUvb6kx1kU3z589n+PDhTXbw8N+3GvD+1+VtD5RYVLyHR5NoUnLsjINYu4ukuGjiYkxB29UuIdbMrZd1Y8qQND7a4U3yO5hjZ9tvp9n222m6to5j0uDOjLmoPWaTMsMVikAQypmFCfgVGIlXJLYCk6WUu6o6p+LM4ujRoyxevDisI5sam8ryIgodJeQUOmkVFx2Q0Fv/e9iK3WTnO0oFA0yl4VFJcdGYjIaQ7GqnaZJvDuSyelMm2w6e1ttbxZm5YWAq11/ciYRYleSnCDkR/cQaspmFlNIthLgX+BBv6OxL1QmFP1VFNs2aNYsHH3ywSUc2VaRipJOt2E1WvgNTAAsR+t/jtM2JEALfA7vJaMDp1nC4PPx1wgUhKXZoMAiGdE9hSPcU9p4oYPXmTD7ZmcUpm4sl/91PxlcHubqvN8mvY1Js0PunUDQFIiop79xzz5Xdu3fn/fff19vatGmj70bXHCKbKlLRT8jMsePWJO0SY4iL8foJDS0X4n+PY6ft+iymTYL3HjV5FaEouZ6d7+D1bw+zdttR7E5vkp8QcNm5rZkytAsXdkps1PsrFJUQ0TOLiBILIYTe2e7duzN37lymTZvWpCKb6oP/YHzK5iQl3ky8pWzZJRDGs+8eO47kIQSkxEfXSoyCYcBXh73Yzbs/HOW1bw6RlV+st1/YKZHJQ9K49NzW+qZMCkUjE9G/aBEnFpdccgnz58/nmmuuaXKRTYGgsUuc13XwD4eS6wBuj8Znu71JfnuOF+jtHZMs3DSoM1f37YDFrJL8FI2KEotgce6558o9e/Y02cimQBCsUNraLiuFuuR6RaSU/HjoDKs2Z/L13hy9vYXFxHUDUrnxklSS46OD3i9FsyCiB66IEotw2YM73AmnbVnDZWZRGZk5Nl7dcogNPx3n/7d358FV3ecZx78vWpFYxI7QdokXbIzZF0l4nMWxgx3HS/ACoum0kxm3M12SaTvdMv0jnU5nMplJ+18nnaSddoIE3mI7dmrH29ixL5tZzWJssO/VAkJsYhPa3/6hy4U4GCFA55x79XxmNKAfXN0HCfRwzznv73T3Dgz55eUY35g7g9U1VekNEkVuEJVFUFQWmSfscxZX48TZLp7b0sRzmxtp7+hJr1ffPJm62hhLvjRRr2blRsjov0QqCxl2UXqlcyWdPX38345DNGxI0Hi8I71+y/SxrK6p4t45peRpyE+uncoiKCqL4GTKN/jh0N/vvPfxUerjCXYkT6bXp4wt4InqKh5ZVP4725yIXCWVRVBUFsHIhENHQdnbcor6eIK39rTSn/qnUpSfw0MLy3miuiqQ7U0ka6gsgqKyCEaUT0qH5dDJ8zy9MclL25rp6O4DYJTBV2dPZ83yGLPLxoecUDJARpeFLiyX3zOUO+uNFDMmjOb799/Gd79yEy9sbebpTUmOnu7izT2tvLmnlQVVE1hdG+OuW6ek71Mukk1UFvJ7hnJnvZFm7Og8vnPXTFZVV/HGnlbq4wk+aT3D9uRJtidPUjmpiNU1Me6fP4PCPA2NSvbQYSj5PTpncfXcnQ8+O8Ha9xNsPHAsvV5SlMfKJZWsXFrBxDEa8hMgww9DqSzkskby1VDX6uCRMzRsSPLarkP09A38u8rPHcX98waG/GJTxoScUEKmsgiKykIywbEzXTyzqZFfftDI6fO96fXlt05hzfIYC6omaMhvZMroL7rKQmSYnO/u5eXtLazbkKTlkosDbpsxjjW1Mb46exq5ORryG0FUFkFRWUgm6ut33vnoCA3xJB82tafXp48v5InqKh5eWE5xoa41GQFUFkFRWUim29V4kvp4gnc+auPCP73iglweWVTOE9WVTBuvK86ymMoiKCoLyRZNx8+xfmOSl7cforNnYMgvZ5Tx9TnTqauNMat0XMgJZRioLIKispBsc6qjm+e3NPHM5kZOnO1Ory+eOZG62hjVN0/WkF/2yOgvpMpCJAK6e/t5bdchGjYk+bTtbHo9NqWYupoY35hbSoGG/DKdyiIoKgvJdu7OxgPHqI8n2fLp8fT6hOJ8Hl9WycolFYwvyr/CR5AIU1kERWUhI8nHh09TH0/w+u5W+lJb3hbkjeLB+WWsqqmiYlJxyAlliFQWQVFZyEjUdqqT9ZuSvLi1mbOdA0N+ZnD3rKnULY8xt6JEQ36ZIaO/SCoLkQxxrquXX21rZt3GJK3tnen1OeXjqauN8eXbp5Gjk+FRltFfHJWFSIbp7evn7X1HaIgn2NtyOr1eNmE0T1ZX8eCCMooKNOQXQSqLoKgsRC5yd3YkB4b83vv4aHrIb9zoXB5dXMFjSyuZMq4w3JByKZVFUFQWIpeXPHaOdRsS/HrHIbp6+wHIzTHuu7OUutoYN08bG25AAZVFcFQWIld28lw3z21u5LktTZw8d3HIb9lNk6hbHmPplybpZHh4MvoTr7IQyUKdPX28unNgyC957Fx6/eZpY6irjXHvnFLycrXjbcBUFkFRWYgMTX+/E//kKGvfT7A9eTK9PmVsAY8vq+SRxRWMG50XYsIRRWURFJWFyLXb13KK+niCt/YeSQ/5jc7P4aGFZTxZHdM91oefyiIoKguR63e4/TzrNyZ5aWszHd0DO96OMvjq7OnU1VZxR3lJyAmzlsoiKCoLkRvnzPkeXtzazPpNSY6e7kqvz6ssoa42xl2zpmrI78bK6E9mKGVhZj8GvgV0AweBP3b39is/SmUhMhx6evt5Y08rDfEEH7eeSa9XTCpiVXUV35xfRmG+dry9AVQWQ35Ss/uAt9y918x+BODufzfY41QWIsPH3dn62Qnq4wninxxLr48vymPlkgpWLq1k0piCEBNmPJXFdQUwexR4zN3XDPZ7VRYiwfis7Sz1GxK8uvMQPX0D3yPyc0exYm4pq2tjzJwyJtR8GUplcV0BzH4FrHf3X3zBrz8FPAVQWVm5KJlMBhlPZEQ7fqaLZ1NDfqfP96TXl986hbraGAtjEzTkd/Uy+hM1bGVhZm8A0y/zSz9w9xdTv+cHwGLg234VQfTKQiQc57t7eWXHIdZtSNB84nx6fVbpONYsj/G12dPIzdGQ3yBUFtf0xGZ/BPwJcI+7d1zNY1QWIuHq63d+u7+N+niCXY0Xr0mZNr6QJ5ZV8ciicooLtePtF1BZDPlJzVYAPwG+7O5Hr/ZxKguR6PiwqZ36eIJ39h0hNeNHUUEOjyyq4MnqSqaN15Df56gshvykZgeAAuDCTYY3uvufDvY4lYVI9DSf6GDdhiQvb2+hs2dgyC9nlHHPHdOoq53JbTPGhZwwMlQWQVFZiETXqY5uXvigmWc2N3LszMUhv0UzJ1JXG6Pm5smMGtlDfhn9h1dZiMgN1d3bz+u7D1MfT3DwyNn0emxKMatrYqyYW0pB3ogc8lNZBEVlIZI53J3NB4+zNp5g88Hj6fUJxfk8vrSSby+poKQ4P8SEgVNZBEVlIZKZPmk9TUM8yW92H6Y3NeRXkDeKB+aVsbq2ispJxSEnDITKIigqC5HM1na6k2c2NfLCB02c6ewFwAzunjWV1bUx5lWWZPOQX0b/wVQWIhK4jq5efrW9hXUbkhxuvzjkN7tsPGuWx/jybVOzcchPZREUlYVIdunt6+edj9pY+36CvS2n0uulJaNZVV3FtxaWUVSQNUN+KougqCxEspO7s7OxnYZ4gnf3t3Hh29LYwlweXVzB48sqmTKuMNyQ109lERSVhUj2azx+joZ4kl/vaKGrtx+A3BzjvjtLWV0T45bpY0NOeM1UFkFRWYiMHO3nunl+SxPPbG7k5Lnu9PrSmyZRVxtj2U2TMu1keEaF/TyVhYhEWldPH6/uOkzDhgSJo+fS6zdNG8Pqmhj33VlKfm5GnAxXWQRFZSEycvX3OxsOHKM+nmDrZyfS65PHFvD40koeXVLBuNF5ISYclMoiKCoLEQH46NBp6uOf8eaeI/SltrwdnZ/DgwvKWFVdRdnEopATXpbKIigqCxG5VGv7eZ7e1MgLW5vo6BrY8XaUwVdun0bd8hhzyktCTvg7VBZBUVmIyOWc7ezhxa0tPL0pyZFTnen1uZUlrKmNcdesqeSEv+Nt6AGuh8pCRLJGb18/b+5ppT6eZP/h0+n18olFrKqp4sH5ZRTmh7bjrcoiKCoLEbka7s62xAnq40ne//jizTjHjc5j5ZIKHltWyaQxBUHHUlkERWUhIkP12dGzNMQTvLrrMN2pIb+8HGPF3BnU1caYOXVMUFFUFkFRWYjItTp+tovnNzfx7JZGTnX0pNdrb5lMXW2MRTMnDveQn8oiKCoLEblend19vLKjhXUbkzQd70iv31o6lrraGF+/Y/pw7XirsgiKykJEbpS+fue9/W3UxxPsbGxPr08dV8iT1ZU8vKicMYU3dMhPZREUlYWIDIfdzQM73r699wipGT+KCnJ4eGE5T1ZXMb1k9I14GpVFUFQWIjKcDp3sYP3GJC9ta+F898CQX84o4547plFXG+O2GeOv58OrLIKishCRIJw+38MLHzTx9KZGjp3pSq8viE2grjbG8lumMGroQ34qi6CoLEQkSD29/by++zBr4wkOHjmbXq+aXMzqmirunzeDgryrHvJTWQRFZSEiYXB3Nn96nIZ4go0HjqfXJxTn89jSClYuqaSkOH+wD6OyCIrKQkTCduDIGerjCX7z4WF6+wa+fxbkjuKB+TNYVROjanLxFz1UZREUlYWIRMXR0508u7mR57c0caazFwAzuOvWKaxZPpN5lSWfH/JTWQRFZSEiUdPR1cvL2weG/A6dPJ9en102jrramXzl9qkXhvxUFkFRWYhIVPX1O+/sO8LaeII9zafS69NLCllVXcWqmpjKIigqCxGJOndnV1M79e8neHd/Gxe+xW784Tcyuixyww4gIpJNzIx5lROYVzmBxuPnWL8hycs7WsKOdd30ykJEZJid6uhmfFF+Rr+yGJatFUVE5KLxRYPOYEReqGVhZn9tZm5mk8PMISIiVxZaWZhZBXAf0BhWBhERuTphvrL4N+Bvgcw5aSIiMkKFUhZm9jDQ4u47w3h+EREZmmG7dNbM3gCmX+aXfgD8IwOHoK7m4zwFPAVQWVl5w/KJiMjVC/zSWTO7E3gTuHDz23LgELDU3Vuv9FhdOisiGSyjL50NfCjP3T8Epl5438wSwGJ3PxZ0FhERuTqasxARkUGFvt2Hu8fCziAiIlemVxYiIjIolYWIiAwqozYSNLOjQHKID5sMROXkeZSyQLTyRCkLRCtPlLJAtPJEKQtcOc8xd18RZJgbKaPK4lqY2QfuvjjsHBCtLBCtPFHKAtHKE6UsEK08UcoC0ctzI+kwlIiIDEplISIigxoJZfGfYQe4RJSyQLTyRCkLRCtPlLJAtPJEKQtEL88Nk/XnLERE5PqNhFcWIiJynVQWIiIyqKwvCzN73Mz2mFm/mYV2SZuZrTCz/WZ2wMz+PsQc/2VmbWa2O6wMlzKzCjN728z2pr5O3wsxS6GZbTaznaksPwwryyWZcsxsu5m9HIEsCTP70Mx2mFno2z+bWYmZPWtmH5nZPjOrCSnHrNTn5MLbaTP7fhhZhlPWn7Mws9uBfuCnwN+4e+B/yc0sB/gYuBdoBrYAq919bwhZ7gbOAv/r7nOCfv7L5CkFSt19m5mNBbYCj4T0uTGg2N3Pmlke8B7wPXffGHSWSzL9FbAYGOfuD4aVI5UlQYR2iDaz/wF+6+4/M7N8oMjd20POlAO0AMvcfagDxJGW9a8s3H2fu+8POcZS4IC7f+ru3cA64OEwgrj7u8CJMJ77ctz9sLtvS/38DLAPKAspi7v72dS7eam30P43ZWblwDeBn4WVIarMbDxwN/BzAHfvDrsoUu4BDmZbUcAIKIuIKAOaLnm/mZC+IUaZmcWABcCmEDPkmNkOoA143d1DywL8OwP3qe8PMcOlHPiNmW1N3cEyTDOBo8B/pw7T/czMikPOBLAKaAg7xHDIirIwszfMbPdl3kL537sMnZmNAZ4Dvu/up8PK4e597j6fgTs4LjWzUA7VmdmDQJu7bw3j+b/AXe6+ELgf+LPUIc2w5AILgf9w9wXAOSC0c4EAqUNhDwHPhJljuIR+P4sbwd2/HnaGQbQAFZe8X55aEyB1fuA5YK27Px92HgB3bzezt4EVQBgXAywHHjKzB4BCYJyZ/cLd/yCELAC4e0vqxzYz+yUDh1ffDSlOM9B8ySu/Zwm5LBgo0W3ufiTkHMMiK15ZZIAtwC1mNjP1v49VwEshZ4qE1EnlnwP73P0nIWeZYmYlqZ+PZuCChI/CyOLu/+Du5ambg60C3gqzKMysOHUBAqnDPfcRTokC4O6tQJOZzUot3QMEflHE56wmSw9BwQgoCzN71MyagRrgFTN7LegM7t4L/DnwGgMncJ929z1B5wAwswZgAzDLzJrN7Lth5LjEcuA7wNcuufTwgZCylAJvm9kuBgr+dXcP/ZLViJgGvGdmO4HNwCvu/mrImf4CWJv6es0H/jWsIKkCvReIxCvj4ZD1l86KiMj1y/pXFiIicv1UFiIiMiiVhYiIDEplISIig1JZiIjIoFQWIilm9qqZtUdhh1eRqFFZiFz0YwZmPkTkc1QWMuKY2RIz25W6f0Vx6t4Vc9z9TeBM2PlEoigr9oYSGQp332JmLwH/AowGfuHukbgZlEhUqSxkpPpnBrb06AT+MuQsIpGnw1AyUk0CxgBjGdjVVUSuQGUhI9VPgX8C1gI/CjmLSOTpMJSMOGb2h0CPu9en7pkcN7OvAT8EbgPGpHYq/q67B75LsUgUaddZEREZlA5DiYjIoFQWIiIyKJWFiIgMSmUhIiKDUlmIiMigVBYiIjIolYWIiAzq/wHDpscOkXrtegAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sp_data_util import sp_plot\n", "\n", "sp_plot(latent_df, 'x1','x2','color')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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x1x2
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" ], "text/plain": [ " x1 x2\n", "color \n", "b x1 1.00000 -0.53890\n", " x2 -0.53890 1.00000\n", "r x1 1.00000 -0.50993\n", " x2 -0.50993 1.00000" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "latent_df['x1'].corr(latent_df['x2'])\n", "latent_df.groupby('color')['x1','x2'].corr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, we can see that the correlation between $x_1$ and $x_2$ is positive in the whole data set and negative in each subgroup. This is Simpson's paradox. So, to detect Simpson's Paradox in a data set with $d$ continuous variables and $c$ discrete variables, we can compute correlation matrix for all of the data, one $d \\times d$ matrix. Then for each of the $c$ discrete variables with $k_c$ levels we compute an additional $d \\times d$ matrix$ for each level of each variable. \n", "\n", "So, we need to compute $1+ \\sum_{i = 1}^c k_i$ correlation matrices of size $d \\times d$ and compare the signs of each element in the lower half of all the $\\sum_{i = 1}^c k_i$ for subgroup levels to the first one. " ] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }