Analysis-linear regression model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analysis of the features (in drawing board notebook) shows that Overall Quality feature is an important feature that we can use to normalize other continuous features. The resultant normalized features often show very good linear relationship with the Sales Price. In this simple model we use only continous features and ignore all of the discrete features except for Overall Quality. In future models we can use some of the discrete features to categorize houses into different groups and assign each group with a more refined pricing model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as scop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "trainset = pd.read_csv('train.csv', index_col = 'Id')\n",
    "testset = pd.read_csv('test.csv', index_col = 'Id')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figures below shows that houses with higher overall quality (color closer to yellow) has higher prices for a given lot area. There are other continous features show similar patterns. These patterns suggest that overall quality is an important factor to nomalize some continous features. The resultant normalized features usually have improved linear relationship with the sales price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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04zAgfQQTcf87UH13SylOiqX+WuMRvvPhB0iKrh1LQhRlnI5Hun/hRYgR0971\n9+AQtFrZbkc6B7sVeLGljAfrJrMx7qfOgaAk+NooOLNo/9ZGOxIEPEG+NuX7nD3iAgr8RYwMlnF8\nVpxpoa3Y2gY42NpGa2wTmxp+PdTVNfbTQKc+rxCRF4FngXBHoqo+fwDXvB9YICK3AtuBa9yyVovI\nAmANyf1z73QDHSSnWj9BcurzS+4D4DHgd+5kgnrcSQyqWi8i3wWWuufd2zFZwBj+ZuWdxrKGt7oF\nBw8ejsudk/KmxYE6Lnc279W/g9MjeJRlTMBvBXqd/1r1KlrsIG/XT+L0gs2dv8xijgevZyTH5n+R\n3e1v0xav6Fza3y8wNtBOZSyXeGf9FUscRgbq2RHL75yJZmNR5tvN5FANmxOCXzwoMNNZyUiNkpzZ\nf3TJ9GZxRdnNXFF2M3Gnhde2n4X2+CHgEKMy/H9MLfxKH6UYA+GowytVH/DniqXYqlw2+kQuGTUL\nr5VqXb+DN9BgEyTZPXVelzQFBhRsVLUctxtLVetIrrGW6rz7SM5c65m+DDguRXoEuLqPsh4HHh9I\n/Yzh5YrRN7GjbTP1sd0kNIFXvOT48rlmzKcPqtxPjLqBjS2rabPDxJwoPvHjtbzcMPaznec0xzZQ\n0fICCaeF1mgRETtKed1UdrQXcKXtZXd4BGtaRnFS8afwWhmcXvo0a+sfZFXDP9gSzaA+kYWD4CNC\npuVDxU++VcMxoWoCVoKdsUIc96bLLCvC5FANHnfY0nZbbSvjFoV2M37vgU+GOCLsc7qzmQp9sP5z\n5QLe2r2Wdjv5Q2ldcyWvVa/iwdn/elA/6voy0GDzdVXdM+hXN4wUMryZfGPq/Wxo+ZDqSAXFgVFM\nzZlxwGM1HXJ8efzHR37Mew3vsL1tEyMDozm58BwsWlnf8Et2t71Jc2wDyVsrlQJPkJvK8ni64iS2\ntBXTEM/kqYrTCXn8fGbKJAAa4m38qaaGpniJ+/WX/Ecax4vt2FxSUEPc2Tsxsut051J/A5LiS1Pw\nUNv+DmXZlx/U+z3c+Tw55Pg/QlPsQ7oGFws/ozIvHbqKHQHWNlXyz9q1RJy9Y6MRO87Khu0sq9/C\nSYXHDPo1+5v6/HGSrYO4iDgk7/Z/Z9BrYRg9WGIxNWcGU3NmDGq5AU+Q00ecx+luI70hsoJ3q2/H\n0Xi3XS6TIowL1TEjZzcrm4sBCFo+js8by6z88agqv958P43xelJNY3YQamJNFHiFji/Lkb4mtkdH\n4GBh9fX5PmYTAAAgAElEQVTrXHwp6nJ0mln8Axbvuhlbo9jahkcyyPCWMTn/jv4zG31aXr+FhPYe\np2y3Yyyt23zogw3JLq2zVHWdiJwC/BDoe9cowziMqCord/+HO/icmteKc1lpnHYtJdDo59+mXMQn\nx5yMiFDRtpWWxL527hQ2to9gTlZrZ1fZhOBuauI5RB0fNfFcygL1vYKOAkWhswfhHR7+snzjOXfM\nK1SFX6E9UUlOYBrFobOQFAukGgOX68/EZ3lI2N3HLwOWlwJ/eqaW99cvkVDVdQDudgLZ/ZxvGIeN\nmF1HJFHdz1nChKyxPH3GF5iQWcQ1407rHECNOBGsfv4JNdqZrG8fia2Cgw8PDqdlbWJqaBchK0Kr\nHegyNOHBkgBT8r9M0Ft80O/vSOGxQpRlX87k/DsoyZhrAs0gOLdkOlaK1riIcEHpzLRcs7+WTbGI\nfKWv16r6k7TUyjAOAUv8fW6O1sEjAcZkfzLlsbEZx+AMYKB6Z6yQqlgOs3LL2BquZE/CosDbRom3\niaZEDpb3NGbkjMEjfkZlXUa2f9IBvR/DGKhMb4BfnPRpvv7+07QnooDgszz84ITrKQhkpeWa/QWb\nR+nemun52jAOWz5PDgXB2dRFlkKP6dCO46POzmZs1qXkBJLjRrYmeHLrL9jQ+iGZnizOLb6Mq8s+\nxYKdj7k3oar76P2LMYGP6pjDrZN+wgsVT7ElvI6olnJm0ce4cOSVeMTs2GEcWsfljeGvc7/JuuZd\nOKpMzRmVtmnP0P8KAt9J25UNYxiYVvgf/LPyim5pbbafRS3H4rFCrG5fz2t1d3DT2DuojlTyfuMi\nFKU10czzFU9yZtHH+PKUe3lr92ssrvtHr3t4OggO4zNGMzI4mvNKLmVieAr5/kJm5Z1mAo0xZCyx\nmJZb1v+Jg8B8yo2jWk3bawhelBgALYkAi1sn4SAknAgAUaedx7b+hBOYi6NKYyxEzPaS5Yvw5u6X\nmZN/Jh8fdTWL617r4yqKTxzmFt/Izzb8F9WRys4FRv+38vd8cfLdjArtXalJ1WF78x/Z3vIH2hPt\n5AXP4IQRXyDoHZHuvw7DSBsTbIyjWn37ss5AA7jTklN0g2kcR2H5njEk1Oq87SM30M4D6+7CI7jL\n2iS7IXw4HBdsJNuKsyWWxdXjvsTShsVUtu8g4a77FnOiQJSntv2Cb33kh53X+mDPf7K95VVWhouo\nSxQirOOFmju4efxXOS73lLT9XRhGOplgYxzVMv3jqYu8i5JcWiaOh1RjLoIQdzzEnO7HPY7NRH81\nIwPNtDoBtkSKyLGUOws34EHxiCJ48Nov8Lt66Qw0XTXHdrCj9XVKQjOwnQhV4ZdY1jqGZjuIuhOj\nIw48uvlBGiIzGZ85nnkTz+GY7ANfAbunHeE9PLnlDdY1VzIpayS3TDyHY7JTr4RtGAdiQMFGREqA\n7wOjVPVid1fN01T1sbTWzjhqOBon4bThs3LSslRGX8bn3EhFywud67CV+Jqpi2dh032g1MEh0SPQ\nlAYa+dexb+MVG49AlkYo9jUz3auExMbqPDWBRt9gZmAyC2N7NzWzcJiRsYMRvlbW7rmLNRonPziL\nlkQGLW6g6UpRorqZV6qaKa9Zw4Nz/pVZBX1vUT1Q65t3cfuS+cTsODbK5pYa/lGzmp+f9ClOyB9/\n0OUbBgx8W+gnSK6aPMp9vQH4UjoqZBxdbI3x4Z7v8sr2U1m4Yy6v7zyf6ta+xj4GX6ZvHHNKfkXI\nOxoLP8XeZoJWx8yyvQSLnjHwouIPCVjJQANgCXhFqXAUS8DRrvkjnJFRjwcfe9oz+aBuFAU0U+hN\n3vBpaxiHGA2R92l3NOXqAiIQ9MRxUCJOnB+ueXFQ/g5+vPYvtNsxbPeaHeX/aJDKNwwYeDfaCFVd\nICJ3QeeumKmn3RjGfvhwzz1UhV/G0SgAUbuWFXu+xcne+RQETzwkdSgMnczcsr8Ts+v42cbvEXZq\nep3jt/x4e6zNNjrU0Os8VVjZXszfGkcQUQ8jvREuzN5GM3HadDdn5TTwZnwSmxIjmJFTidfqHlQc\nYmR5nJTjRrYjNMf2bo29pbWWuJPAZx1cb/jqxp0p0ze1VJNw7LROhzWOHgP9lIZFpBD3556InArs\na50Ow+hXzG6iqvXvOF0G6AEcjbCpcT4njxycPUva4pXsbHmOtngleYHjKMu+Ep+n++1iIkLAO4Lp\nuadRG/0LiR5733jEQ7bPl9z6WUGxiNo+vN7udV/XXsrOWEFnF1gMm0rHxuM2iwJWgnMKNxKQBB7p\nvTYVQNBKMNpfT2Usv3OFaEfBVqGmPafzvIDlJZKI89yuJbxfv5VxmUX8y9hTGBnK26+/nyxfkIZY\nuFd60OPHc5CLnxpGh4EGm6+Q3KjsGBF5GygiuVmZYRywqF2LiA801utYW3zHoFxjd/s7LK/5IrbG\nAIeqtr+xtuFHTMiZx9SCr/TaqO3cokt4t/4NWuMt2O6kAUE4teBcWitbmVVUQW17Fl5sGuIhgp54\n57pnccdiR6yArr3Tk4J7txDo4LdsTinYyp5YFsWB1pT1/kioimxPhO3REbQ7PlpjIdY3F5PQZPAJ\nWD4uGnUC1779M1rjESJOHJ94WLBjEb+Y8ylm5I8b8N/RteNO54nN5d1WAA5YXq5014AzjMEwoGCj\nqstF5BxgCskR0vWqKabVGMZ+CHlH0/POfUiOj+QFjj/o8lUdVtbeldxOuPsRtjU/jdfK6LZ6cEOs\njl9vvp9wvLWzZZNwBK+l/HP3K8xkLn6PTVlWE1OCu0jgIep4CFkJRGBLpIieM9kyrGjKugnw+p6p\nfLL0fTw4eCxFlc5xIREYE2hgTKABVbDVIlwQ4Pnqs6iKZHFO8UdIODYNsTC2u3pvXG3its29q57j\n2bO+MuBAMW/iOdS0N/HXXcvxWR7ijs25Jcdx57FH326hRvr0t8VA6kWh4FgROdCdOg0DAK+VwcTc\nT7Ol6bfY2u6mCpYEmZT32X3mHYjW+NYu5XanJNja9CST8j6HiNW5XUBNZBeK0/mlb1mwsWkE47K7\nj8/ke9o5NdTMSK+Do7DTtngjnkfPYBO2AwSs3qtKq8LG1pHM3342Z+RvYlxmHR6xyfJEOyccdBAB\nrzjkWu3cOnYJJ478C8XBfC58/b7OQNNVVXsjDbHwgNe48ojFXcddweeP/Rg7wnWMzsinMGBWpTIG\nV38tm4/v49iAd+o0jL5Myvs8QU8pW5oeI+rUkR84gSkFXybLP/Ggy/ZIEO1j+RgAWyPYGsErGVRF\nKqiP1fbagthCKQyG2dRUxBluWqYV5RNZjQQkOQMNgWPE4ea87TzaMLlb/o2Rkczxbu3WlRZ3LN6q\nn4QCjfEM1rSPopY8QJkR2kGhrxWfOL1mvwEICXBWAWcT8vhpoPdYiwJ+z/5PGsjzZ5KXpuXlDaO/\ntdE+daAFi0gQeBMIuNd5TlXvFpEC4BlgPLCN5IZsDW6eu4BbSfatfFFVX3bTZ5Ocfh0C/gb8u6qq\nJDdpfwqYTXLb6mtVdZubZx7wbbc631PVJw/0vRjpIyKMybmSMTlXDnrZGb7RZPrG0xJbn/J4wFOE\nR0IAbG/bRNzp3TMsAlm+KAErDgoN0RBn51Xi6wg0Lo/AJH8Lo7xt7EpkdKY32pmsbhvNjMyKzjSf\n5YAPThyxE6/VNagIGyKlNNSHOKtwA4X+VPvsKHG7EYB/GXMK8zctJNql3l6xOKnwGLK8wRR5jaHS\nlojy54pl/LN2LQWBLK4Zezoz8scOdbUOqQH//BGRS4HpQOenWFXv3UeWKHCeqraKiA94S0ReAj4J\nLFTV+0XkW8C3gG+6N4pe515jFPCaiByrqjbwMHAbsIRksLkIeIlkYGpQ1Ukich3wAHCtG9DuBuaQ\n/KH3noi82BHUjKPH7OKf8c6um4g5dd3SLQkyteDriAjhRAt/2vlEn9sN+C2HY3LriIS9bGgqpjB/\nA95UrQ5RxvjC3YKNhcMof2Pna1Vod7wk8OHz9O4Ci6iP1S2lxNXDJ0pWEPB0b5kpCQpCJwFw/fgz\nWNuc3N7XI8k7c0aHCrhnhpm7M5y0JaLMW/QrqtubiDpxBOHNmrV8aeolfHLs0bP80EBXEPg1kAGc\nC/yG5Ey0d/eVR1UV6Jhq43MfClwOzHXTnwTKgW+66X9U1SiwVUQ2ASeLyDYgR1UXu3V5CriCZLC5\nHLjHLes54JeSHBW9EHhVVevdPK+SDFB/GMj7NY4cGb4xnD/2dbY3/4EdzQuIOHvI9I7j2Px/oygj\n2TH2t6rniKeYEdeho+URtBLMKdpOs3hJKCkDTkxtLBwcLDzYzMjcQb432dVlqxBXD2+3HNvntVSF\nuPpY21LKqflbKAk047c6Ak6AJvsMfrd1NZtbFrI9vIdjc0Zx/wk30mZHKQ3lMz23zMwgG2ae3/ku\n1e2NRJ3kpBN1b5r92bq/cfGoWYS8/n5KODIMtGVzuqrOEJEPVPU7IvJjkl/2+yTJLfXeAyYBv1LV\nJSJSoqpV7inVQMcCTKOBxV2yV7hpcfd5z/SOPDuh80bTJqCwa3qKPMZRRsTD+NybGJ97U8rjq5qW\nDbCgZHfZkvYRfDSrGm+X+2QchbDj4YNIEY479dnGw+q2Mkb7GwhZMRoSmdTEczuPp1LRmlzZ2cHi\nmcpzuHmcMCW0nXXNdbxVN5oPWzKB1zvP3xbeTXntan598m2HbKl4Y/+U16zuDDRdecRibXMFJxYc\n/Pjk4WCgwaZjSk+biIwiOT5S2l8mtwvsBBHJA14QkeN6HFcRSd13cQiIyO3A7QBFRUWUl5cPVVWO\nSooSdSIIELCCpFoA81CY2n4yNqlvsOwqM57DnOrkdOD/23UxBd4oXjdfVD3U2wFm9fEeAlaQTCfK\nGNjn7p4zbQ+I4jgWfifEmF2FVMXCxCPNnIxych/5lr61iNrMon7fg5Fera2tvb5H5rYVMyfRe3af\niLB7xWbKrcG5p2y4G2iw+YsbMH4ELCfZHfboQC+iqo0i8g+SXVk1IlKqqlUiUgrUuqdVAmO6ZCtz\n0yrd5z3Tu+apEBEvkEsyEFayt6uuI095inrNB+YDTJkyRefOndvzFCNN1jav4Ldbf97tq/nTE77M\nlJyDv79mfz2x9UHeb1zc73lzqi9g2chXOl+rQr7VxvGZFYQ8UexEJsvC4+m55KBg8cnRtzA9dxZb\nwxtYVv82G1o/7Fz8s0PHWmqWgO1A1PaT7zuP7a0NbHVq2RePWCya+70BvV8jfcrLy+n5PfJu3Sa+\ntvx3ROy9EzkshLGZI3jmzOuPmm7PAa1FoarfVdVGVf0TMA6Yqqr/ta88IlLkBihEJAR8DFhHciWC\nee5p84A/u89fBK4TkYCITAAmA++6XW7NInKqOx5zS488HWVdBbzujhW9DFwgIvkikg9c4KYZw0Bz\nvJHHtvyUqNNOpMvjN1t/TDjR0u3cmBOlKV6Pk+J+ksFycenV+CWw3/lEoFFD/LN1Mv9omsry8DhS\ntc4Uhxd3/Q8tiSbmFJzJTePvJNNTSHLvGwsLL6rJINMxw81jQcAbY3PrUpwBtLqyfaH9rv/RKmLH\n+d+dS/nqe0/x/Q9fYEPzrrRe7+TCSdw+6XwClpdMb4CQx09ZRiE/m/2vR02ggf5v6jwJ2Kmq1e7r\nW4B/AbaLyD0dA/B9KAWedMdtLGCBqv5FRBYBC0TkVmA7cA2Aqq4WkQXAGiAB3Ol2wwHcwd6pzy+x\nd7zoMeB37mSCepKz2VDVehH5LrDUPe/efupqHCBVZWf7FtoSYcZlTiLkyeg3z/sNqVsRqvB+42LO\nHPExEk6c5yqeYGn9PxHAbwW5suxmTio4q1seRx22hzcRc6JMyDoWv5UMGrVtb7C2/se0xbcT8BRz\nbP6dlGVfkeKqUBIcxZeOvZcfrv9mn/Xqu+Mr+WUR75z/kvrLI64xfrXpPr587L08sHoh79fn4PcI\nIW+ccVn13aZRd/AIFAZbmJY1pXMmUypBy8elI+fwZuVWxmXnMS4nv8/aNsbC7GpvYHSogFx///+v\njjQRO8anFj1MZXs9ETuOhfDSrhXcNf1yLhmdvoVfb5pwNpeXncTqpgpyfRlMzRl1wIEmkogz/8Ol\nPL9pNSLwL5OO4zPTTyLoHd7bk/VXu0eAjwKIyNnA/cAXgBNIdj/1OcdSVT8AZqVIrwPO7yPPfcB9\nKdKXAcelSI8AV/dR1uPA433Vzzh4ddFaHtr8A5rjjVgItia4bNT1zC2+eJ/5Ik5byk3EbE0QsZPD\ngwt2PsbyhkWd58XtOM/s+A3Z3lym5swAoKJtG49s/iFRpx1BcHC4dsxtjAsqy2u/iuMuUxOxq1hd\n9z1sjTIu59qUdeq6LXNPCizfXcZM24ujguUOM9qOELG9+D128t4ZN9CoG5l6fpdE7SiPbHqY9xt8\nRJwEUSfAqIwmLNGUN3BCsmvt05POZUNLFaubKojacUQEWx1CHh8JRwlFS/nVsg8JWOuIOTanjhzD\nw+deToZv7yynhGPzg9X/y8tVKzuXpPn46Nl8bdrHj6rFNp/f+S4VbfWdgdtBiTpxHljzIueNPJ6g\nx5e2a2f7Qpw6YnL/J+6Do8r1f3+GtfW1ROxkN+wvVy7ijYqtLLhkeHfJ9RdsPF1aBNcC892utD+J\nyIr0Vs0YzlSVhzf/gLpoTbf7U/5a9UfKQuOYlD2tz7xTso/ntZoX3W2R9/KIh6nZxxOx23iv4Z1e\nASmuMV6pfoGpOTNIOAke2nQfYbv7QpZ/3DGfc/NbkR7rodkaYUPDLxmbfU3Kf5DhRAsZVhZtTvfy\nVKElHiCuPhKOxeamEUzK3c3O1jyq2nIRd9+aEcEwE3P2uOMtyfK9nh574gg0xLfxkXwPGxuLGZnR\nRE6gvc9AowqTMmeT48vgVyfdyvL6rXzQuIOiYA6z8yfQEA/z981bmP/hMmK2TcxOdgQsrt7B3UsW\n8qMz9wb9Rza+xitVHxBzEsTcmVF/rVxOcTCHTx1zbuoKHIFer/4wZQvREmFtU8WgbEaXTm9WbmVD\nw+7OQAMQsROsrq9hUdUOTh818AVYD7X+ftJ43IF3SLZGXu9ybHi32Yy0qmzfRlO8odeNkDEnxsvV\n+17FaFzGJI7Lmd3Z5QXgtwLMyj+NsowJNMebsCT1Hip1sd0ArGv5gIT2XorG1gQbw72XcAFIOC3Y\n2k5rvJm2xN6g0pZo5OlNN1AbjrC0diyLa8axpr6ElpifiO1lU1Px3utHM6gM51DVlpzCbKuFYlEX\nyWRbSwGQbAml6haDjg3QbI7NraYg2N5rHbQOHa2jqtgiHlj7TWqju5hdOJFPHTOXy0afSGlGPtNy\ny3hmw4fdvngAorbNnzevIeE4blnKczsW9/qSjThx/rD9ndQVOEJl+VKvrOCoknkYrLqwck8V4UTv\nYBmxE7y/pypFjuGjv4DxB+ANEdlDcvrzPwFEZBJmP5ujWpsdxurjt8rG1jU8svkBPjPxq3ik90dM\nRLh5/J2sanqPd+veQEQ4pfAcjsuZDUCBf0TKkQ9BGJ+Z7IZot8OkGklxcLBJTjN1NHmTpMfdoKzN\nyeW/199DbTT5j3JsxkRuGvc53quex6u1E6hsz++8B6YpHqKpoWPQfW9tFGFXW16ve2UcLHa3ZzMu\nqx5HLRrag4zIDPcZdJrjIUZ4Ui1HszfQRGwvHlF2RXbwsw33cPf0nxP0dJ8I0BJPvap0zElw/Vs/\n5+aJZ3LpqFm02anPa4mnXqj0SHXN2NNYXr+128wwQRgRyGZy9sghrNnAjMzIJsPro61HwAl5vIzM\nGNjCq0Olv7XR7hORhSQH+19xZ3pBskX0hXRXzhi+xmYcg52iZQHJ+2c2tqzhjdqXOa/k0pTnWGIx\nM+8kZuad1OuY1/JxSenV/HXXAmLuDp6C4LMCXFyaHCaclDUt5fX9VoDpOefy2Mpilu8uw1GLiTm1\nXDdlBRvsUcScvff6bgtv4mcbvs1EbxsV7fmdG57hXjHVgL+qYKuVch6AIsRsLzXt2YzJaug8RTX5\nsKyu51qE436y/N1XLlCFxmiQTc3Jm0NVIdsXZVpeI+83LOK0Eed1O/+00rG8vnNzr7Dr8Tpsb6vl\nv9f8H1tba5mUPZKNLdW96lwSyO39Rg4Dre1R/F4Pft/+dbCcXjSFm8afxVNb38QnHhQlx5fBT2fP\nG9bjHR0unTCF+5b+o1uaAD7Lw8Xj+l6ZYjjo9/9UxzIxPdI2pKc6xuEi6Alx+egb+XPl71Mu9RLX\nGO/UvdZnsOnP3OJLyPUV8Gr1/9KUaGB85mQuLb2WkcHR1EV3s6JxEWNCE6ho30rcHdvxWwHKQuP5\n1XIf6xrGY7u/jTY3F/OnHScyfVT3e1UUh4gdYV2sGEsUu1dDqXvAUaAt7MfrtQkEEr1mAHgtm53h\nXCbmNODpElhSfYf5rThbWgqZnl+NiGK5Yz8tsQDrm0q6Bb7meJBVDfl8rLT3dtX/76Rzebe6goid\nIO7YyVoKZOcmW00RJ86zOxbzg5nX8/X3n+51Q+meWAv/rF3HWcVTU/5/GG5WbK7k3t+9ys7dTVgW\nfHTWsfzHDeeTGRz4ki+3T/4oV409lQ8ad5DrCzEzfxzWYTJJIssX4JmLr+cL5S+ys7UZUMZl5/PL\nuZ/oNiFkODLjLsYBO6voAnJ8+fx2609TLmLZV8unL+12G+/sWcia5hXk+Qo5p/hCvvGR+7uds7Tu\nnzyz81EcFEdtLDwU+IoYEShhdsEZeBITeaTpT8SdrvURAr4YiRRBMWIrkVgIR1P9qlU82NjufTCO\nbRFuCVGY04IlHZsRJAOShTIxew+5/tQD/j3TqtpyCScCrKwbzciMZjJ9UVrjASpa89BezSahLeFH\n7YJe5U7MLeDVKz/Nb9e8xx83v0dU2sjIjOL17r03x295cFAssXB6/D+JOQme2FJ+WASbHbWN3PHz\n54nEkmNUtgOvvb+R3U2tzP9yykmpfSoIZDG3pO9JLMPZRwqKee2Tn2FXazMiQmnm4bH3kAk2xkGZ\nkTuHEYESdkerSThCfTSTuOMhz5/g/OLTBlxOW6KVH62/i5Z4M3GNIQgrG5dw3djbmFNwJgDhRCvP\n7Hy0syUDYJOg1W7mhpGfY3L2NP606cOU4z17WjMYX+gF6TqLx8uqulGAQ5b7Zd+1RWF1CaAtTSEc\nn5CVHWHyyBqyfFF2teXSGg8Q9CQoy2wk5I0Rc7wEPb3XweopnAgAQtTxsb21sMuR1PfqKMJP1y1m\net5MjukxtjAyM5u7TppLJFDLy7tW9mq9xB2HoMeHz/KQsHv/ANgd6X/4dXXjTh7a+Aobm6sZnVHA\n7ZPO57SiQ9tt8z+vLyee6F7/eMJm1dZqtlXXM35k72B8JBuVlTPUVdgvh0fb0Ri2RISbx/0b0UQ2\ny/eMZWtzITta81ndUMQru8IknIG1bsprX6I53tTZJacocY3x7M7HSbhTddc2r0w5Sy3mRFnekJxV\nNSW/KOXaYw2thfglu9uEhS3NhSTUIqE+Igkfef42BAdQMjxRPJJs1QAkEp7kTLKMKF7LIdMXZ3Lu\nHmaNqOQj+TVk+5NjS5XhPJS9g/x9CVh9BSR169CTELajfG3502gfhd84/iz8Vvffjz7xMC13NLML\nJvZ5P83oUGGvtKgd58PGnewI/3/2zjvOkqpM/99zqurm2zlMT2JyJA1BQNKQMREUV8z6UzGwrorr\noq5xRVdcXbOuuCCIEUGCrIDIMIRhAmEGJjCRmZ7Y07lv31xV5/z+qOrb9/atOzOgg4R+5jOf7j51\n69xTdbvPW+/7Pu/z9vLMQCcfXfW/PN63jUE7w/qhXVy9+tfcv++ZA11iFRzl0l9IB3YXPRQ8t68P\nV1Vfu2VI9vSO85Ve6hg3NuP4mzE1NoM9mRm4WvosLYGrBc8M7uLO3Y8f9HzwlJeDCj01sC/vCRXW\niqsLROnYkc3tHNPSQVgagCYULhKNFomGTD499xqOrT8ddJi8YzJUjFJSANAmA8UElnCJGkWyroWt\nvQK/hJVn0ZRO4uECE+Ip+vOxUi1NOaSAgUKE4WKYnGv6bDjvmNKQd42S/tnkxCByrFHRmrgsYkpF\nLc2CvuIw2zPBOmlz6jr4+rFvpzmcJCwtLGFwcsts/vPYd7B093ZOrj8SK8BYrx3cyT17Vpd+/tPu\nJ7lgydf5+BM38K5lP+Sfn7iBfABt+nsb/1zT8JVDacX/bL6fcx74Ghc99C0uWPJ1bt1ZrSLRl8/y\n/dXLeNd9t/CVFX+lM1XZfurYmROxzOrfgaLjMnNiy0HXMY5/LMbDaOMIhNYaVytMGVzvUo7tmW6G\nAii0edfmzt1P8papJ48Zz/JcejNhI8L0+BykkIRksLaXq2yihteqeEHdMYEaaZa0SqE2gF+cdxlf\nWnUPSwdXogFDCixZ5Cdb7mdZz37SzqSajdKK2kK4LhOiKTpiKQyhMKSXRTGzimmJfvKuia1EqfK/\nVBOTTeJok4JrsivTiKME+WyIvqE6HNfAMBSJRI6OxBCN4RyTYwPszDShEaWcTlaFmBIfYG+2EScg\njyQRB/QWT2+bx/+1Xk13PkXcDNOTzXHB7TeScxxcpYg1asYWyRe1w3c23sW8+jhpO8K3NtxVUxqn\nHP3FNFm3SNw8sK7c9duW8Jsdj5YMVlE5/GDjPdRZUc7vOAaA3ekh3nTXL8k6RQquy4p9O/n9lrXc\nfP5bOaHd0+E9/5S5/O/9q9DeHQNAS81R8zqY0PTyyFu8mjFubMZRgaJy+OHGe7hj9xMUlcOMRBtX\nL7yYYxun1TxHa0p//AFHK35a3ruE23bfhOHTTsMywkdmfpbd2SSuooLFpTU4wi2FziJGjHcfcSU3\nd/7Yn1khEJzR8jqmx0fzBxHDZIu9CeEbCY2mqBT3d60t/Vwb3kbWnasj54SY37i/IrlvSE1UeC2i\nR8ZHvrZH0+xKN2JJl3kN++nsa2bnQDvaNxquazA0FGdoKIYU3paZrM8SiTqliTSCXelGcpkw4ZhN\ntWw9incAACAASURBVDMnqnI2YyGFZEK0AYBLH/gNvbls6YrjAd1BAYbtPD/c8k2eG26mqA5NsiUs\nzYPKu7ha8evtywI9o59vfaBkbK594iGGCvlSCNTRCsdRXL3sXh548wcB+PVzT5M+0sXqFFgp0AYU\n2hRPNXahtEa+DKjLr2aMG5txVOArz/yBR7qfLTV72pbez7888QtuPOVjzEi0B54zI9FGnRUl51ay\nvSLS4o2Tji/9vDu7g9t234Sti9gaiq5kXTrBZXt/iqsl7dEmjkgOYPjaY57XoPnzvj/wriM+CsAx\nja9hZmIeTw+toqiKLKxbRFuksrXS1nQXA8VqFYHqXIHGFK6vAjCyUQmU/70QGqVFaT0jkKJWkEtT\nF8oRNhz2ZBrocpI0tw1RLFikU1GU8kKMIErhtNRgHNvOk0gWSkbLdQ3S6QgypDBNFylHa3Wy2egh\na5ntSA2wOz1UsVblSqSsNjhCaBydI227aA5ubCLS4vIjTj3oWnJukWINL6k7nyp9//CeHYG5tp3D\ngwwV8tSHI/x151aKIUVxjLyYcB12Dg8y7QACpK9UrOrczW1r1lF0XN5w5DzOnjPjJWt0x3M24yih\nJ5/i4TJDM4Ki63Dz9odrnieE4JvHvoO4ESZiWAggaoQ4qmEql04ZLdp8rG8Jjt/DxdWCtf2T6M0n\nvCJJoDuXZMPAhIrkuhCwMfV0xfslrDpObTmXqdHj2TY8TF9htC3Bit4tfPWZW8mPMXzaERT2h9Hu\naNjLQJXkZkaMQDkcFRxC1Dq4dgYgZtpsH25hX7YOKb1CznDEprFlmOA+gYJcJsLQQAzX9SZV2vOv\nBvsSDA3EyGZCZIYj9PfUMZB1yDm1W1iXYyifRziVljGTjqDG2BqJoiM2hBDQEM5U55LwwndxI0xY\nWkSkxVuPOIUPzQ7U061A3AhTbwWrS88q89DiVi0DJwgb3udQFwoO17lKEX+J15gcDnx3yTKu+O3t\n3PnMs/x5w2Y+c/s9fOLWuw8pj/aPwLhnM44S9uT6CUmzJNQ4AoVm23B1QWE5FjZM4a7F/8Zfu9bS\nVxjm2MZpHN80gw1Du/n1jkfZmx0gbPYjJYQM6MvHcUpP+h40kqwTYtgOUxcalVeJGZUyHIPFLJ96\n8ka2pfdjCoOicnjLlJOYkWjl28/eXWUs3Zwk/Wwj4fYciFFD4VL5/mORdsLYSiKFW2FcahkaKTQN\noSz7s3UVFGohvGORaIFcNkh/S1AsWPR1W4QjRVoaU/Rrb9wuhrCLIxupJp4okldFotTeXJXWfPuB\nR7h51RpcpQlh4iYUbp2ikA8RMgT19UVcbLRWTIilmBIfBKA9Okx3rh5Xmdi+JxgxLN4/YzHvnn4G\n/cU09VaM8CGqIwsh+MS81/GNdXdUhNLC0uLjcy8s/fye+cfxvdXLKnTeLGlw/tRZREzvvd6/4AS+\nuOJ+cmVSLaaQLGqbSGs0fkjreaVg18AQv1j5JIUyKnjWtnl0WycrduzilOlT/4GrC8a4sRlHCVNj\nLVWGBsBAMr/u4P3tk1aUS6eMNi7+6761/MfaWykoB43GFBIhJnNU0x7SdrhKXwwADVknVDI2lgix\nuO31FS/54tO/Y1Nqny/E6W08t+1ajqOcwDmV7WVqjERxTA5krNUYW+Mi2D7czNyGbpTyPIQgr2ak\n340UePmOEeGB8pkkmJa3MRimTUNjDmkoXFeSTkUoFjzjUciHcLMmAjFmCo2QikQ8i8mB6eQ/fWQl\nN61ajeOqUi7NSEu0hFCDZEq4jd8tfhtLe+9jafftuIx6SqbUHN/cw9zE5Tzas5nGUJzLp53Kqa1z\nAWiLPH95mwsnLiJuRrhuywPszQ0wK9nOx+ZcwDGNowrFH1p4IpsGevjzjk2EpIGjFAub2/nPU0cN\n0ltmLWRdXxe/2fQ0YcPA1ZppyQZ+tPii572mlzuWPdcZKK+TtW0e2LRt3NiM46WLzkwvq/u3c2zj\nNHak19EW68eSLoPFKL35Nt4z44znNZ+rFdduuLPiadbRCqEN9mWaiRo5JKrKOAghiBgKgxBCaE5p\nPptTmkcl8AeLGZ4a2F6l+FxUo/1kxsJMutQd249WBw6BgZex8bwSTxVgUnwIKWBvNkFRedTlsUrN\nGljX38HCxi4ihh2Y0FEKXEdiWEWamrIIPw/jOhLDUEjDQbkmINg/VB+oIoCWuNpgd66P+aHqTd/V\nil899yg39N5PZD7Y/WEKXVFQEqEF5rDk+DmTuPH8y7CkwQUTLmR9ahl9xR5sVUAgMIXFm6e8m9e2\nnM1H5lwQeI8cpfjVxtX8dvPT2K7ikpkL+ODCEw4ol3J623xOb5tf87ghJd894418+rjT2TTQw5RE\nA3MaK+nMQgi+cvK5fPTok1jXt5/2WJKFTW0vC02zvzfioRBGwHWbUpKMPP+usy8Gxo3Nqxxaa76x\n/g7u3bvab0DmorRFR0IRMR3ajTTTE5qk9fzSe3sy/RTcysSwIVySVgFJlAX1FrsyI4Uo/tM3gknR\nFq495uMMOf1MjEwhaVVuqhmngCEk9kGe7sshRtIxNfckXfraGhmm4FpETZuOWIqI6Xl6HbFhjCFF\nyo5QH8qXnBeNYOtQC1kn7GmSWQUihk3WDZXeUGu/KFRCLGZ7dkPDYH8c2zZBi4o1BHlGI/MoJXiy\nfw/z62dUHf/imt/xwP71GDHvZDkhi9VYIL2h0XsPBZ3DA1g+nT1sRPj03GtY1fcwa4eeIGk2cHrr\neRwRn3XA+/nhJbfz2N5Ocn7I68fPLOe+zs3c+ab3YMq/LQ08OVHP5MSBvaf2WJL22Kub6nzWnBl8\n6c/V46aUXHL0S1OGZ9zYvMpxf9cz3LdvzZg8h2TjYDuLmncjhMbWeZZ238NFk95+SHNuHNrDvz/9\nuwqvpiU8zIz6PrQGQwgGHMVRTRbbUi0M22EEkAxleMPExUyITmQCEwPn7og2EDPCFRLxHjSWdHCU\nMUa9eRTlNTEV42haI2mipo2By9TkIBLts9F8OyU82nN9KI+rBPtzdRQdk90DDeSKYRpiWVCQVZYf\nAPNJ1low0JvAcUbJBplhTSRWwC6ajFpA72s4YuO6Eseuvgbh55tUwEVsG+7ikZ6NFbRuYYAMu1iN\nBez+CNrSNIQr65lCMsxpredxWut5gfdsLJ7p3cdj+0YNDXj9c3akBvjrzq1cOO2lrTz8SkEiHOJ/\n3nYxH7vlrtKY7Sr+4w3nckRTwz9wZbUxbmxe5bht58qAjVtguwZZxyJu2TjaYdPwWuDgxmaomOWj\nj/8vGae8f4pmqBhFoP06Gm9DjJo2Rzbt80UwvY35tt130V/M8+kFbwqcXwrJF458M59b81ts5fh0\nWS+E5hmaUZ8jyJ0ZMThCjASqNG2RFEpLOtONgGR7WtEUzhIyXDJ2iKhZoCM2jNbQm0uwvbuFHBZD\ngyNJaUFXJsy9Q0kaW9JlYTrBYF/cNzSj61AKsulw1doArJBD1HQZ7E9UHheaWCIPAs4ICEetHdwV\nOJ8wwEgWKQ6EMZolVxz5mqrXPB+s7t5HgGIMGcdm1f5d48bmRcRJ06aw/KoPs3z7LmzX5eTpU0iE\nX5ohNDiM1GchxBQhxINCiA1CiPVCiE/4401CiPuFEFv8r41l53xOCLFVCLFJCHFB2fjxQoi1/rEf\nCD9IK4QICyF+74+vFEJMKzvnvf57bBFCvPdwXefLHUGEAMAL9ZRtXk2h1kOa7769awIq3L0eMAOF\nYAqs9CX2wTMCt+xcXhWCK8dpbfO4euGptEbTJMwiI0alksIcHDMbydloLcgXDJSS7M830FOoA79/\njFKSzp5mOgeaSNlR9ucaWNM3hawTYutQK0O7kgz1xyveRzgC9odIbWgkvy+KdgWOI7wwWVD+pcb6\nhDawLJf6pgyG6bUMkNJTHojGCuS66vjkLfdyxvev49/uuIddAx6LrDVShxlQ86IVuEritrpccfwJ\nvGn636bu3B5LYAWEygR4xaMvUdrtKxUh0+TM2dM5d96sl7ShgcNbZ+MAn9ZaLwBOBq4UQiwAPgs8\noLWeDTzg/4x/7HJgIXAh8BMhSkJOPwU+BMz2/49QVD4ADGitZwHfBa7152oCvgycBLwG+HK5URvH\nKC7oOIawrKaxSjRxc5Sl1F/sYUdmS815isqhJ59id66/inoMoBCk7IO03RXQl40zPBzmww/+kTu2\nracYoFI8ZA+wtOdXzKjrJmHV6jQZoJysK783DD/oVHZACI85FokVGeyPk0mPSXoLiEzNQlkJjpGF\nZDhPw5xBkrOGQMPwhnqKuQPTg6Ox6rWHnToQEA47NLcO09YxRHNbikisSH9nPRlXskbvY2dykFv3\nruPi//0VuwaGOKl5FjEzHKjkYIWT/OVt/4+rjjv9b06mnzVlBhGjOiCigb/s3MJ3Vy/7m+YfxysX\nh83YaK33aa2f8r8fBp4FJgEXAzf5L7sJuMT//mLgd1rrgtZ6O7AVeI0QogOo01qv8DuF/nLMOSNz\n3Qqc43s9FwD3a637tdYDwP2MGqhxlOHSKa9hVrKdqOFtqqYwkGhm1VWKPe7ObedHW65hW3pjxbjS\nip9svo/zHvgab374O9yxa1WtZ3b68pW1EK4Wpcp4Vws6hxrZ29VENh1h6a5OPv/YX7joT78ka1cW\nMT7ta54B5ByLWl6CXTQZ7I/R150kNRglnzVRarRrpmlqnzxQfb5haOKJPJnhCEqJEr1ZCKjodK01\nDROHsVpyuAi0qQlPyBGblsZN1YpSe/mgRF0BKV0ECkO6hAywkoO4WQNVFF4BqgJVkAzsT6JCAm3A\niAOnIprBZI6fProSUxr87KQPMTs5gZA0MTAIEeLM6Em8ve047l6zic3dvTXWc+gIGya/f/3bqQ8o\nsMy7Dj9bt4rhYnAL6nG8uvGi5Gz88NYiYCXQrrXe5x/qAkY0UCYB5VKwu/0x2/9+7PjIObsAtNaO\nEGIIaC4fDzhnHGUIGxY/P+nDPNS9gRW9W3m8bzXdeZeYZVftwbYucueeX3PV3K+Vxq7ftoTf7Xis\nSvsqCLYycJTAlJ6pCImp7M72o7WgJ5egc08r5YYj69hsTw1w/YbHed3MJiwRYkpsOrYqov2CQ1M6\nBPWAUQoG+kZDXW5OUsiHqDOGUcpECE0obFOLPCUExBJFYrEi2R1xtG2iJ0u0AYahCIVsigWLsOmQ\ns02ygwmE8PJOVsihri6D7I1ADWcu2ZD1Kvab07gFg+n1vQw4CTL5MJmNDaAEMqw8I2cLdKMLY7VK\nBShL84d161i9fy8/v+xSfnXqx+nKDVJUDrev2swNK56k6G5HADcsf5IrzziJK0792/I2M+ubaY8l\nGQowKpaUbOrrYW3nfn6x4ikGcznmT2jj8+efyTGTOgJmG8erBYfd2AghEsBtwCe11qlyN15rrUWw\nhseLAiHEFcAVAK2trSxduvQftZR/OAzgaDtMc84r3ot3zw90GASCpfuWAmArF5Xu5h0celI4vn9O\naV6B4FgdIut4m7STDK7oN57bycq9W/E8gmU0Ws0cVzwXjWahYwV22dSAW+/FuoSvzqyUQCiNMDzP\nAt9OHSiypDXoVgPlClpkiPfkjwE0MqrRYVHST6OufBKNsDWyDTA0rltp0Qzp5WFKtZQWWPlZFF0D\n7Ur0bAFuZV5HmTo4DqFBJEAouOve+5jX3ooUgoLjYPX2c8W0Sj07Z9cO/vLAMCHj4GreADnbYSiX\nB6A+Gibqy8q802wiVTemal+DdGHlUq+30Nva6wGPxrzskUfY19LkNZbTw961yXrv4l9BSKfTr+p9\n5EA4rMZGCGHhGZpfa63/6A/vF0J0aK33+SGykXjNHmBK2emT/bE9/vdjx8vP2S2EMPF+s/v88cVj\nzlk6dn1a6+uA6wDmzp2rFy9ePPYlLxs4ykWhq5pnPR9csfIbPOOmUAhObO0seSDlaA61cfn8d/PV\ntbfy4P71FEOj+RmtoViwcPxCxXCk3DvSNIczzGnoqZjPFBZntnyEa56+l+5S0r0SjbE0Z0wbzRfF\njQQnNJ3O8r4lrOxuIe9WFxMqBUXXJBwpyx9pyOctouERUoH3uoNJ0eSGIgzbET5tHcF3Up2lySzL\nwXEMtA62ApFwkXwhhBBghWzCEZtwxEFK7aWJNLhpEyPpeMQFA+8vUoNWgszmBlTOb95W7+AmdKDo\nQWifiVACLTTvbG3g82edzfcfWs7Pt+xhLCwp+ddps3jfycexOz3EfZ1b0Fpz3tRZHDFGyPLbDzzC\nzU+upehLooRMg3edcCyfOfd0nuzewzvv/f2ovIyG8H4TnFpBVDhH7eSHZ/8SL1ghvf91X0bGLgs8\n5+WIpUuX8nLeRw4nDpux8XMn1wPPaq3/u+zQXcB7gW/6X+8sG/+NEOK/gYl4RIBVWmtXCJESQpyM\nF4Z7D/DDMXMtBy4Dlvje0n3AN8pIAecDnztMl/qiQmnNbVvXcc+OzXTEk3zwyOO5fvv9PNi1Hlcr\n5tdP4vNHXsrs5PMLWQwVs+zMFHzFY8G+TD0T40MYZQYnJMOcP+FSbtj2IA92raeoKw1NPmcxnIqV\nolpyWNHUnEYamohhM6OuOmdgCINd2S1Yphee8ryA0Q3LkC7TWyrPc7TL7OQCjm04iVT+j6weGCYI\n4YhTaTwERCJ2xfwjisq1oJWfF6raQ0eYZrWRL3iFnSNGWEpNOGKjXMCVZLbUofIGwtTE5w4iI6pE\nPBB4Y8NPN4MWGGmJqrPRSoxaRAUyIxB+IzehBX/YuJqH9AqGtjVW9H0ZvXcKQwpu3riaa1YtKV37\nfz31MFctOp0PH+WF2Lb29HHzqjXknbI22rbDrx5fwyVHz+f4tkl874w38MUVfyVVLKCzGkNJ3Jp6\n2PDs/iyQ90d84kfqq+jwWQijulvoOF5ZOJyezanAu4G1Qog1/tjn8YzMLUKIDwCdwD8BaK3XCyFu\nATbgBTiu1LqkSfIx4Ea8qPU9/n/wjNnNQoitQD8emw2tdb8Q4mvASJvI/9Ba9x+uC32xUHAcTrv1\nZ/TkRuXzf7N5NU1NGYyQd6vWD+3mipXX8YfTr6Il7FVZr+jdwn9tuJ092UHipsk7p5/M+2e8DoBn\nervYlx3mG2vvYMjWhCJeI6/d2QaE1HREUyDAEiavn/BWWqx53LDth1Vy8EJAJGozPAQ+bxrlSjKp\nGK3NBWYkU1hSBPSSEXREW7DkdhZM3sPmPR24SvqtlQWTGgaY3FjZsVGjyDoZjqo/gW8v+iSvW/qf\nFRRurbyQmZS6wtjkcxbZTBjlSqywTTxewLRU6TUjZIUKA6XBdYwDRHtG6nqCnugrLV0+F0JlDYwh\nA5UeJTbooia7pZ7kUZXXKQSYSRsnbRJqKJBszZAZjlDIWWhbYqQlRmbUq9JC45gufWmXIZklFLBo\npTWzJzbz3iV/oDCG6ffd1Y9y3tRZzKhvYsnm53DGykPjhU4f3PIcs9tauHDaXM4/Yg7d2TR/enoj\nP1i6HLemsoNmRsNA9bAwoLAUYm+pcd44Xik4bMZGa/0otQVCArXJtdZfB74eMP4EcGTAeB54a425\nbgBuONT1vhxw9bJ7KwwNeBvywECM5rZUaZMsug537FrFB2edwxN927jqyRtx/EfYYcfhui0Ps6Z/\nPWs66+jJZvxqcE0sLgmVEtqCXekmrxmYcNG5Zr68YDGXPvLtwL4jwRAUCyGuXfRWJsVMfrDlq9i6\nkllmSYs3TjqfX29/lo7EZqY19NEzXEfBNmlKZEiEq5PQSitmJbzCxmQoyi2nfZIvPXMLTw/s9D2s\nEI5tkKgbpRZn0mEy6YgvDQOFXIhi3qKpdRjDKO+fQynEpZUgty2JMDyWWTAUlcmU4GLSkfuhBkKI\n7Nh8iUAVDdy8gREp36w1wlRg+GG3oiQRLWDloNgXQzui5LmMGPG8aVBMRcAEp8HFHCy5Sp7hbHR5\nZqAr8EocpbinczNXHn0yYdPAEIKxJHZDSELm6LYhhWBCPMlREydgShlIVQeImPDR456qPqBHFjeO\nVzrG+9m8jHDfzuA6F6UFrjP6UdraZWvK21C+u/GukqEpvR7J4/299Be6ymRHBJFoEKNMUFQmg8UC\nP9645IDFlo5TneAXQnByy2wmx6Zzbus7MHSYiIwSlhGSZgMfm/l5QtLixye+HwNPObm9LsXU5v5A\nQxOSYU5tOZfmcFtpbGKsiU9NuARnd4y+7jrSqRiFvDXqsSgqDM3IdWktyKSrKbz9PXEG+pL07kpS\nTIcwhmWAVpkmHCkGsNkOsnHWyGl4lmDMMQlOygLbwB0MMaGY4fi2nZy+YBPz53UipUKP/Atp7DYH\npEC5EsN0UQlFscPBaVA49Ypih43ZVCSngvvheN6kd6EXzp8TeClCCC6cPxutNX9avp5LvvwLTv/U\nj/nFHSuYGE0EEg+mNtbzwzcfx6L2AM8GFyJn1b5f43jFYFyu5mUENyCsAQSKNjb5IbTOTHBthdKC\n1vph0j0en9Y0HQxT12Rm5fMWT/fvwqnqdukvQcPw0FhurkaG8px99/fY3e9iK4VgAadObuFLJ53M\nrOQ8pF/1PiHaTEukjd5Cdd+ctlAHyVADYd/QNOpZXL/8CfK2w+LZ01nY0U5nXx/SctHa8tcjGRqI\nU9+QwbaNGtqWArtoMZpHANeVuK6FsCHUZ3psLyUxe/GJVbpEmxZSVzUiqw3P49ERjS5W51IARNgp\n3UsU5PfF0L6m2nEnbKWpOVXywqZM7aF9wiAPLTmKfJuu+kuOJ/LksmFs20QlXBBgSEV7k8OU+rGf\nkwdLSi48wmMWttcluOaN5/GFu+8vdeN0teKaN57LhLokN973ONf9eQX5orfmxzftJhIyueC1M3lo\nZyeu0pwzdwafPvs0JtR5v4tq+IOQ+bl/Lzxlbeq/gZDj9davBowbm5cRGsIRunPV7Y6loTDMyl1v\npFdI0hL0FQK22TF7nWmpmvL7ji1RrsGkSAudhd2BQTQvTyIRQqG1KNGNTcthe+8o+0sDj+7u5Uv2\nGn73+gVsHeri++tuYW9+GxPq+7GMkT4uGonElCHeN/0TTIp513PX2mf5wt03obXGUZrrHnuctxyz\nkMGm3RitBcIpg0Ley4cUCxa93fVYIbsGCUBjGKP3TStIp7w4ojFk+ALM3rqNokTagvB+iZpSpFgI\nlcJt3g0Nmr/ijnvOS1whsxJcjdBiNImvBPmdSaymPNoVFHuiuMMeyy6RzIKGp1fPxC6atE8YYPLU\nHkzTZfLUXp4bbEElRlWjw2EXtKS+MYPrGDiOgWEorJCDMELMb5zAZ49fzDeffAilvc/dkJKPLHwN\nIWVQcBzCpslFR83n9JnTeGjrdtBw5uzpNMaiFG2Hn9+zsmRoRlCwHdSAy+Of+VjgHZDJf0FHL4LC\nEsCCyAUIoy3wtYcKrTUPbNrG759aS95xuOioeVx89AJChoFW/ejMr6D4GBiTEPH3I6yqaPw4XiSM\nG5uXERJWiO5cenRAeKyl+sZshZGwhMGJzTPYOLSHGfFmBgr7K/rGSBQTY0M81z3aL8RxgiOqnqyL\nQgr40NwzeOrJZ8i5LpW7q0Ya0Nw6TCFveT1aTI/63Lu/jqCdeMX+3XzniYf5ybrl3oYrJqB3dXDy\njG1MSOZpDrcyLT6b89ovoS3iMeuGcnm+cPf9Fd0J87bDH9euJXZMLxhQ15AllwlhWi6mpVDuSKhM\nBObxQ2EbpbwwZHo44ns6IIsi0PtwLYFTrtZcRu32vowdL4MAJNjNDkZaIjMCWfpcBHZfBLuvugpU\nCsXqp2ahfKbe0GCcXTvbeO3p62lsSMNga+n9pRC8e8FRnNY+h88+fTMy5GL55BFDSCbHmphXN5H5\nCydx9pQZ3NO5GUcpdu4c4oa/rOYmn8vz4dNew4dPPZHGWLRKsr5rIE0QtIZndx64o6swp4H5/w74\nmueDa+57kNvWrCdne4Zv7d4u7nzmWW58x5nIgUtBpYAi2GvQ+fvR9d9CRsfFRP4RGDc2L3HkHYd1\nfV0kQ2EWtU1kT6GbSDyPa5sIqYhE7FL3yZGn9+F0mPPu+y8MvwYmaeYpKouCMjGFYmJskIwTQpTV\n5Hjei+eZVNWdSDhhciMLmibw3eMv45NP/pq8W5YkRiGEwNGVeR+tQSsZvPFq+OnaFbgjyXR/7Suf\nm8mFCzdSUDOJh8+gzhwVAH1k2w5MKSmMYTwVtE3E7wUwUvlfWpvUJOtzCFeTz0bG/MYL0qkY6VTZ\ngoUf7pJeoeRYuLHgJm1CaJLJLM7mOOQl2Wk1CAUCMMGtV7j1YPWBLJQxysay/BCkUpX1R0oZ5LIh\ndu5oxXUsZk1ootfJsKh1Iv963OnMb/K8he+a7+Fr624jbedxURxdP5Vrjr28pI92RF0jHznqJL67\nZBn3rdtCoYzm/D+PrqQxFuVtxx1VdQktdTFUjfjh5JYXT96+s3+QP6xeV/HwkbMd1u/r5sG113PO\nxEEoURwUkIfUl9CRcxFifOt7sTF+x1/C+OPWdXxh+f1IIVBa0xyJEY06hMIuhCs3XK3BsQ3Sw1Hs\nookQJi3tHkNt2IlhSYfWcBoE7M02YIoI75r1Gpbv7uGZ/t0Iw8VVFfqSJQgB7X41/nFNx/KJeWv4\nS9cjDBZNLKGoC2V4eu9kbG2VnqJdR1IsHrhK3XEBwwu1RaMFhAS7YLB3KMZuNnDrhiLXPvEwd7zp\nXbTHkkghAlWFVVEi/b6f5fcjn7PIpj1tM8tysfoNhCOwEw46yOESYqRbAW7CRQwZiDJSgUYjTYUb\nyKsRSEMTa85jPxfDyCtkykIUBRjgJBQqoUaJav60drNLaJ+oeB+nzgEhMFNeKC+IWK2Uwd49LVxy\n9HF84azXE4RTWudw9+Kr2ZcbJGqEaAonqu+d1vzy8dUV9TTgbdo/e3RVoLGJRUK86ZSF3L18A3l7\n9LxIyOSKN5wcuJbDgVWdu5A1WiM//Fw350wMUjQvgtsJ5szDv8BxVGDc2LxEsa63i39/7C8V/G05\nQQAAIABJREFUTary6RQtDSFglKWlNWQzYXLZUCnM4o0LioXRCnpbmfQURrsbNoWifHT+2Vx1ZIif\nbP4Lv+1chqM0tfLdMdNjbT2wbx3ffnondv9kRFZihhWDhknOHWF1jWyN2pPIPwD5CiAcLhCNFTFD\nLlJCOGzT7SSwbEXWsSm4Dl9e8QD/c/YlnD5zmv8UW779aoQQHKnnslqtB+nZjGymkupcLApodbG6\nTQgL34MJgACjS+C2alRBIXOy/BChfoN8k0KbYy5MaKywCxMV+f1JzN6yHjYumCmJqzyPZixUVGNk\n/cJMBFaqsj4mKJwHMJyKEYvU1bjBHqSQTIo11TxecJwKg1GOvky25nmf+afFRCyTWx95BsdVNCVj\nvOfCE3ho9w7+uGkDZ8yaznnzZv3NnTsPhPpIpEQwKYdlSJpjNX7xtAPiwJ1Ax3F4MG5sXqL45cbV\nFMb0hVFoslmL+piJ7VfvpwZjpYT4WCgV/AcXN8Pc9NorSwbkyrkX8M7pp/HxVTewKb0v8BwDwZ/3\nPMVXn7ydoQ31aFeC8jZtDYhWBx2itA6B8Iohg6BB5EDHoVgMUSyGAE1dY5Zw2MFBMpDxnsJdrXlg\n11bvWvN530aNpTBrtu7Jkk7XE5+dAkMHUp0R4CZdhEt5N+qqtZmuidFV/k6iNIcqGoR7Bfl2FxQI\nx6vBaWjO+F00x67PP9NXAXCTqqrgQAtNxDIpOm5gF07TlDjO2DyZ9z5/Wb2VukGLaMji/OPn0NpQ\n7b3Uwv0bt/KZ2+8JfE+ABRNqJ+8tw+Cqy87k45eeRr5gs2zHTq6+8z4cpXCU4t4NW7hx5VPc/O7L\nKupy/p44c/Z0TFl9rw0hecuiM0EsAV3exsGE0PEIo6XqnHEcfozX2bxE0Z1LB24CQpu8bfKZxI0w\nwrVqGhrwWgwH4aJJJ9Acruzh3hCKH7DXybCd5/ub7iG9K4a2fUMD3oauwRyoNCzVRqES2u+jprXw\n/0uG+uNkdiQYfKoVd2sCs88AB4QrKNg2V/3xHlwUbkxh1zm4UeXnOAS7elI4GZP0njh2ziDQRROg\nwhqZDqqb8RYtB0ZVDkRgcaZXx2L2GoT2WVi9JqF9FsVdMZQDxd4D9+wR1X3lUIYiV0M125SCfz/v\nzIB1eNjRM8DP7l7OD+94lIu+dAN/fWrzAd9/BFu6e/n4H/5Ezqn2agQQsUyuPu+Mg85jGQbhkMnn\n/3Q/eccpqQ5kbZtN+3u4bc36Q1rPC0HYNLnxXZfRlogTD1kkwiHioRDfefPrmTzhYoi9FwiDSAIR\nsBYiGr572NYzjgNj3LN5ieKcyTNZuW9XRRgNvH7v75x5Ch+Zfyb/8vDt3MtzgeebplNTPv91E48N\nHG8IxQPHAVYPbMfWLs5gM1WFmwhPW7FWMX0AhAjY77Ugn7cwfZVkmYNQzkQKwXHf+QkF08aZoEqs\nLqVcqIdQt4lwhWd8BsNke8PQEVzJLhyBYUvUgEI1aIQtENrzLswBs2QMaoWuRq5LFqT3Gv8inIEw\neaGxBw5gbHSZs+XTpo1hAVpQbHcweyXGmDyXozRf+9ODXjItqMjSAVdpXN8L/tKN93Hy/CO459nN\n3LjqKVL5AmfOms7HzzyF9uSo1/ONvzxUUwdiRksT/3XJhSzsaK/xiko8s7crWMDUdrh7/SbefsIx\nhzTPC8GCjjYe+uSHWLd3PwXH4ZhJE0qelEhehY6/H+yNYLQhxvM0/1CMezYvUVw2+ygmJeoruiJG\nTYsrjz6Z5kiMkDR595wTqRULssLBm21MhphdFyzSOSc5oeZ6itr198cDbMJVTkDtvEjNVE45E87/\np4QmW1/AjauSWDD4Xw1w6n1qb056lGUlkVlR7d0oL3cCYDgSa7+BkZIYgxKr10S6ovSeB0PVa7RH\nXaZG6HLEWzIHDY/ynBVYvQbmsImZlt61mNVsNABlgJmm+nq0xsxVvt4wJFf94c98/S9L2drTT/dw\nhtufXs8l1/2K/uxoSGlHf1A1P6Bh4YTWQzY04HkYtUJxMevwtxCQQnD0pAmceMTkqpCdkI2I8Cnj\nhuYlgHFj8xJF1LS4803v5tOLTuPY1g4WT5rOT866mE8sOrX0mtd2HEFbtLqnCC5Eo5WSJKogye2K\nUdjWyHWPPl6x8YzgjPYFRAJaRJfDbM5XbYgajYroAAtSe9MOSuyiwSh4IS5ZBGl7Y3bSQeQFOhww\npfAS7COb/8hXc8DwDM5I4aULVo/0Nnbt9YexJ7g4LS4qdqhab8HGoNb16rJ/I2sz8hJrwMQaMJHF\nEc66f3ZRBhs6DUYerBGD4wu42Q0uw/MdUnMclK8s4ArNsl07S3Un4HlHmWKR3zzxdGls4YS24FAi\nECocWq+b0lwd7dRFqmV/opbF5ccf/bzmGscrF+PG5m/AjtQAn3zobl57y//w5rt/VUpk/70wlM1T\nZ0d435Tj+cEZb+KsyTMqjgsh+L+L38cJbZMQGoxBSWivSXR/iMzaRgrdXkjHSZsMr2ukuD9Gf6/i\np4+u5PU/uZE9g6mK+Y5qmMq5HUeVWkQHITY5jYi6aKFH/5vgNAYxmmrsZhpMLSuf1LVG2tCocsT3\nayJ9mkgvRLs1eEr9B0X5Ri0QWIMmoT0m0R0mDU+ZJHYaRPoglNK4jWVekgoOmwUZVR1RaKvGdY0Q\n5crWYDe52E0HYOVBSeRTGzrYmAkwXAilIdYFsX2C8ACopPb00+o06Zmed1eULpGAhHzBcVm1Y7R5\n7efOP3PUEI9AgZmDNWt3VZ1/IEgh+Nnll9AYjRAPhYhaJmHT4J8WHcnZc2YcfIJxvCownrN5gehM\nDfDGu24i59i4WrM3k+Kfl/6Jz51wJu+Zf9xBz9das3z7Tq5//ElChsGHTzqRY6dMLB3/2bJV/Pjh\nFQghkELwlXse4PtveSNnzp5eMU9rNM6tb3gnX7nnAf64fwMF7fiMKEl+VwJpKfJ74qBGnysKjovt\nKv7rgUf43lveUBoXQvDFI9/CBR3HcNvOlSzt3lC1bmlCbO4QqX316CIIE8xIjYR7LSgIP60w6iW5\ndo22oDWSYeGsXay9YwGosq3f9TwcN6a9+ryy4v2RuWS29k4ulCDcC+V94AqtY2qUwhqd1RW1Lt4B\nL5czOhlIpXGiGuGIUTkb7SVjwgNgOJBt9q5JILAGDOyGGrL72iuisds8q+smFXKsV6HByI0WmHqk\nco0Kl63LNzhm1OATF5/Ot5Y9WvVWhhBMbRotuGxLJIj1QqEO3JAX8TQznvfUZ9amPNfCvPZWHv7U\nFSzb1slgLscJUyczpXGcYjyOUYwbmxeI761ZVjI0I8g5Nt968mEun3PMAdvuaq25/Fe/Z3Xn3tIm\n/cDGbbzx6Ln890VvYN2+/fzk4ZUVldEAn7jtbh791IdJhCs9j4LjcPuaDRUV4AAoQW5PDJ2rXovS\nmke27agaF0JwUstsWsJ1LOvZhK2rN8qmSIQTZ86iMzXAnMYWzpg0nc8+dg9uFQPM2xpL1sEXmIzt\nkhiOgdEHoT4Iz0xzwvFb2fnkRPSYDV8gEEUgXjblyFwacMAcOkDYR0CuDaK9XstiABWiwqdXUY1O\nAc5oOE7jeVoqBCrkZaqE9vrL0BdBC49ZJpTGsAVWGqTjnRdJwfAsxyMcaM/glEJpGkZ7GYDd5hCO\nmhQcBzNVHUaTBQgNjrkmCfmOypsdNgx++KlLOGnKVO7aspH1+7qxy6r8DUPy3tcsKv1smQYT65Ls\n669uPDej44U1MgsZBmeNezLjqIHxMNoLxOP7d1cYmhEordmVHrs7VOLOZzewunMvQo8mpIUW3P30\nJjb1dHPbmnVkogWK7TbFdhsn4XqbnxA8vHV71XxDueo8ygh0wagZwokeoP5hRqKNxlBAzYYWdA/C\n8n2d7BgeZHZDMzuGBgIMDVS4OxqsAUFys0Gke9Q4COCIqfsRUmHnLE/eZgykHaA35rOSzR5Z7ZEw\n5nUSCmXCwtaQoELxRnibvptQaEOjDI2bVBi2xigKT4Sz6MnuhCM2CI3QEOkTxHoE4UHP0HhTCWTB\n88acOu9zwwV7gkuxzcFJKpy4i93ioo/QvP+4E7jmlPO5/YJ30SCjRC3vMwmbBhHTQIRBRUbvpJaa\n7DSFU1f5eVumwaKJkwD42dsv5cRpkyuO267Lv915L9niKMX6qsvOJGwZOBEoJMGOQShk8Km3HJzy\nPI5xPF+MezYvEB3xOnanU1XjjlK0RGpTiAF+8NjymmGnax5ayoZcN05Z8Z9bp1BhjUrpwOZUzfEY\nUcuq8oRAYyRsVM70amPGWJ3pLbWl3YUQXLvoHfzz4zfgakVeeS2Ji7ZkOG0BHgHhh2uWe0/QNQok\nRzixwobENiPQMITCHk27ccoQPc81ocYUg7qxIPKB/xZR0NnyupigiwFlUdI7i/RICu3KI46VMdvc\nBoXb4FtNBWpQIvO+J6Q1wgFWJzBjAucgtZPJLSaZqS467JLYbhDrMcm3Kwrtyi9+hUVNE/nEMa+l\nLuLl1pZ8/APcvX4jnf2DHD1xAufOm+WpF2vNk1v20NU/zJwZzbztr79H2YWS5xI1TL544lklb7oh\nGqmq3NcaNnT18Jk77uHH/3QRAMfPm4I1LYKdyaLQSMAOGTQ1H/j3dxzjeCEY92xeIK48+mSiRqWt\nDhsGFxwxm/rwgQv7Una+5rHO4UFSbr7yk1FgZCQ52+F7Dz7GL1Y8WdHbxpCSfz3ndCLW6HoEHiX1\nxLkT0XZwkca2ngN3yl7YMIW7Fv8bb+04DXtfgsH+GEP9iYq57Br9bbxFlOmKWaBrRLt6dzTguILm\n6QNEG/KIMgVMLXWpcDQQzyNXVHqpEsS2mhhD0qsPqlHgaeSFv2btkQgUWP2axC6X+C6FCgX7kyOe\narzTILHd8LwdJYh2SerXmUhfbWhl7y5e+6Of8dhznQAkI2HefvwxfPa8M3n9wrkl4yGE4IQ5k3nj\nyfOZ09bGvZe8j3fNW8TshmbOnDSd6897C2+bO1rLorXmka07Au/Bks2jdVnfe3AZ/blcqfOqAjLF\nIp+9875DvKPjGMeh47AZGyHEDUKIbiHEurKxJiHE/UKILf7XxrJjnxNCbBVCbBJCXFA2frwQYq1/\n7AfCL3MXQoSFEL/3x1cKIaaVnfNe/z22CCHeeziub/HkGXzppHNIWmFipkVIGpw/dTbfOu11Bz23\nvb7GY7GAtMxXbuCuV7Qo897GvS81zPcffIwv3v3XilPfuuhI/vvS17Owo42mWJTTZh7Bb9/3Nn5y\n9uUYAZIeQFUP+iAkrShr12XI7ItgF2qoFZQPuUARQhjI8gMCslPdwHBf95ZWMvkImYEI+aFw2Ss0\nCI05FFwzI3MeOeCgtTF+rkgb4FhQqAc7IUg8ZxDab3prLp9febkSIw1O2Ms5SdujY4cHFJFBTWKP\non6zg5YHI0OXMeS0QDgQ2TP6Z5eJFfnnP/yppj5ZENpjSb580jncf+kHuOn8t/LajiMqL1fXXlN5\nPcy9GzZX5HXAu1UburpJF6q7pI5jHH8LDmcY7UbgR8Avy8Y+Czygtf6mEOKz/s9XCyEWAJcDC4GJ\nwF+FEHO01i7wU+BDwErgz8CFwD3AB4ABrfUsIcTlwLXA24QQTcCXgRPw/naeFELcpbWuUcX2wvH2\nucdw2ewj2ZNO0RiO1vRolNI8vnkXO7r6mdHRzOK2GTzb2+Mltsv2SKfBZXCMHpqRllXU3JzjcPf6\njfzL4lNKXRABzpk7k3PmVhevzW1rZUNXd+W8QnDW7ENL5m7p6a2i9ZZQNmYMSIysLPECEskQqUTB\nq353wTWDjYJ2JU8umUckr3ArvDCBcCHW7RVhZqeqEt/AKEBis0ExKVFjSzzGKhcIwIB8q1dxb6Ug\nNOSnfbQg1G3i1Pn1NhpC/YJwl2R4gQu2wEqZJHa7ML1sZdqjI0e7HDJTLIxCdffNwG6cCEJDkqz3\noaIt77wVO3ay+ACfR86x+dP2jazr7WJ2QzMXz1xIXai6tgVASokhRGBOsTy8ZhxAJDOwDmoc4/gb\ncNiMjdb64XJvw8fFwGL/+5uApcDV/vjvtNYFYLsQYivwGiHEDqBOa70CQAjxS+ASPGNzMfAVf65b\ngR/5Xs8FwP1a637/nPvxDNRv/97XCGBJg2l1tXMfQ5k8H/zvW9jbN4SjFKaUNNXH0RM1xQ4HWfA2\nJBXxNoaoNMmp0afcWk28LMNg0/7eCmNTC99403m886Y/YCuXouMSsUwSoRCfOef0Q7rGWa3N7B0a\nxhiUXn3KiGSYzwgTRYHMC4xcpYQLOYHlSuy4ItTrtVhWEmRA5O2IYhN7BlIB1+oZnEiPJNwncWIa\n6QgvxCVq53JGWgV40KWQnjah0KAxcyBd4XXMBKxBEwYB16M7ZycrVBSEqSEFkYFgX8HKgxNVGMUD\nhPrGLm0knKhB+OQHJ5hhAUB3Ns3Ff7qZoWKerGMTNS2+s/pRbn/Du5heH6zo/M4Tj+GXq9ZUjb/3\npFFG2iXHLODmVasrcn2GEJwwdRKx0OGv/B/Hqwsv9uNLu9Z6RFa4CxjRxJgElFeS7fbHJvnfjx2v\nOEdr7QBDQPMB5vqH4NrfLWFzqo/eRofBFkVvg8OO9BCRvQIMUDHtPVFLENKThSmHMoML/RylmNRw\nYHn5Ecyf0MZ9V76Pj5z6Gl6/YA6fOutU7v3Y+2ivOzSF4I+feQoR08TMGVi9hmdYbMHCeBsTUkmi\n/RZGupoVVnBcQnmLeE8IoTyjaSfHiDHj9UG58qJTaz5pa7zcjVACy/f00tMcho50KExwUKExG7WC\naBdE90O4G3Aqq/m11DhxsJMaWfAozFr4x0yNDuvRVgC+QdW1/lI0RLpc7LgosbEPZHM0mmK9Lsnp\nmMMSRylOnj615jlff/xBenIZso7HJMs5NkOFPJ9dVju38tnzzuSfFh2FIUTp/ztPOJp/LXvAuPL0\nk5nX3krMsggZBvGQRVsywbUXX1Bz3nGM44VCBDWj+rtN7nk2d2utj/R/HtRaN5QdH9BaNwohfgSs\n0Fr/yh+/Hs972QF8U2t9rj9+OnC11vqNfi7oQq31bv/YNuAk4H1ARGt9jT/+RSCntf52wPquAK4A\naG1tPf6WW275u9+DDbu7AxLjGi29p+yxCBsGtuuOphC0L9tSHvsXnhRIczRGz2Aa23UJmQZtDUkS\n0eDqf9tVGFIENps6FGSKNl2pYfK2gyEFLYk4LfEYjlJ0D2cYCJC/qQnl16gAUgrMkEHIMtCOJpMr\njnmxLm30QnmbvjsSrSyrufFqXnzmm8MYWTaNMj1BNo0ueWUCUVqLCnvjupyhNjKvIzCKmpZkiL7B\nsevz4MS8BZlCYCIp2g5UuF2+SoAc9WwEAiFgUkMd9ZHapJL1/d3BCuDAwub2A4orKK2xXYVlyJqf\nfbZok7NtQqZBMhwcmhvHoSGdTpNIHHqbh1cCzjrrrCe11icc7HUvNvV5vxCiQ2u9TwjRAYwkEvYA\nU8peN9kf2+N/P3a8/JzdwuvxWg/0+eOLx5yzNGgxWuvrgOsA5s6dqxcvXhz0shcMrTUf+er3AllY\nWmqKAZ0EL5gyi4ZInDu2bcDYqzFSgkKjwg2BkTewXINz5s7kjLapfPPWh8gXyzolWibXfugNnH7U\naOx/6Zbn+OLdfyWVL6C05tQZR/CtSy4o0W3/Xnjr9b/lmb1dz+scoSFsmaUukREpMfZrtO3HwAQo\nE1wJdiOoiIubUKgi1eEzB0JdJqGUV2A5dptXJuTbRn4u01JzINrtFW4Oz3NQI9EjAVa/IP6cT3TQ\nmitOnMRvbu+EMdE7ZcDgTAOrIJkzrZkjT2ji1v/bgciNxBs9ckKuCSiLTgnglBlT+diFFx7wPl15\n3fco9ipPkVqCk/TyS6Yp2XjpWw9rg7JxPD8sXbqUv/c+8krBi/1behcwwg57L3Bn2fjlPsNsOjAb\nWOWH3FJCiJP9fMx7xpwzMtdlwBLtuWn3AecLIRp9ttv5/tiLjhXPdtak+9Zqibkt1c8n5r+W2Vvr\ncQzN8EyXYovGrdMUWxyE6/CBRcfx8/9bUWFoAPK2w/dvf6T088auHj5x2//Rnc6QdxyKrsujz+3g\no7+/6+90haP4woWLiVrm6NOz1oT7FfHdLuE+NdJVrAQpBFKK0XbEGnSvQjuVigPFeq+oMTQIIi9R\nEaoNDYDhGXAzV31Y4BddBpDvtOkVM0pbUP+MSXKzQWyHJPGsiZE20ZYfHpMCbYEdCcgqKXDD3ujm\nHX388bbNSKEQcRcM74POtVJhaPzLY+WOXYGtrkfw0Nbt6B5GFamVwOo3aH5MMmOpyebNz8/Aj2Mc\n/ygcTurzb4HlwFwhxG4hxAeAbwLnCSG2AOf6P6O1Xg/cAmwA7gWu9JloAB8D/hfYCmzDC68BXA80\n+2SCq/CYbfjEgK8Bj/v//2OELPBi4paHnuZTP73LKwQMQFAIDaDoKN79zd/SWRii2KRH+5j4jKr0\nJJcv/e4+eocygefv6h5VL7hhxZMUxxR62q5i3d79bO/7+5LzjpnUwW0feAdvOnIeISVoWeNQv8Ul\nsUtRv9WlZY2DLPqbqgbt6Aq2lJnzlI1Hcv4jG3p4wAubWXmId4lSjUoQ7GQtytyBYddDoV7jhkDm\nJcI2sOsE2vQYbLk2yP//9u48uqrqXuD493fOHROSAAmIDKLMqAwGCxZQEQcGJ4oLFXFArXbQ6qud\n7XrSSZ/Vvq5W+15b3yu1zz611oXWAYcnTjihMohYGYIDMkgIECAhdzpnvz/OSUhy782AuVxIfp+1\nssg9w777xuP53T2c3+7pzVQLxpqWbwQSxeJNNmi8cX8AagN+lggyB0haeBDV9+sXX8dpFqixhdr+\nFrHKBN++9W9s3trhEy2V6nC5nI02N8uuM7Mcfztwe4bt7wInZtgeA+ZkKWshsLDNle1gsUSK3y5a\nSiLlENwLie40W1TM4BRnfsaldyLK1ng1iaPTlw/2zoWK2C56Fxawpzb94dA+PQ/MTtu0uzpjX3/Q\ntvh87z6OK80+i+5gDO5Vyl2zprPjje1sjG9vGDcRFyQORR877BkWwPbzPDoFNNyEA7WZWyT1Yyr1\nryPbLPYPdL0gXM+B6FYo/ATixQZxJGM3GrbfhebiRTUDWF4XmRMFJ8u69cZP/ikOpMJejrX69DSx\nHkLNAJtwtgxFrjdAFKoRnBJpEjgClnDGsEEtrpC6aVfmgo3t/SSTDn9/7F2+fcPZWctQ6nCgnb05\nULG1qmEGWTDmfTsXfyVLSXqv66c6NzdCehFLppBsM2H9BxRPGtKXSKjpd4VIKMA3z5/Y8Hr8wP4Z\nE4LGUw7De+duHfbN66vS1k0T/OnDriGUuVGWhcFuNCYfrrKIfO4vT+B3jUW3QdnbXvr9ko31yx80\nnRnmBMCKG9yo668JAyQN9n4Xu/bA1OiMXIOV8DMIxADXG6PZOSJArCxAuLr15daidRa9C7tRGApi\niVAYCnJUURELZkxt8bwBPTNnThbH+3Ecl42fVGY8RqnDieZGy4Ee3aIkkgdaLoE4BHYc2D+gV3di\nJYb1+3Y23AwthOkDhzKp27G8/E4FqZ2G2FGppt/gAQRC1cJGeyc3fWUy9z29jD21MUqLC7jxwklM\n+9KIhkOvmlDOIyvex4m5DV1W0WCAS8tH07OwIEef3svDlU1oj9cqaB6MUhGDlUy/aRvxFw3zCULB\nFpvoNgsrkSJS5f1969kOdNucYueoAMFawfb3hWIQdoKUlRSypWoXhZu8B0RjPYS9Q7IMrBnvw1gJ\n6PFhCvx5F5YD0R0uyZLsSU6bEsK2zXM3zmdpxSdUVO3iuNIeTB02iGAL2cEBvnPGZG569KkDY1uA\nOIZum10ECAQsRg7LvPKqUocTDTY50K+shOKCMNUZurmCtsV350xhwvED+fuG1Ty6YQ1B22be8LGc\nP2gkyZTD7/7xGrHqFNHNFnUD3ANf0QW6VdiIKyRSLpdOOYlLTh9LMuUQDNhp3TGlhQU8dt3l3Pvq\nmyyt+ISSaIT5E8q5aOwJOf38k08ZytI31jd5UNEAqagQ9NPuBOog1SjfY6qbEPCzJYvhwDoypula\nNODN8hNXiG731o9pLiDC6F692bB7R5Pt8WSKHZtqKK60MI43aaHb5iRWnUX16HBa68brcjOIk8CO\ni78F6spsnKikt4bqu+bSOvGEO796LuFAgLNGDOGsVv5+jZ0+9Dj+ffZM7nrhVT7dVY2dMBR85lBQ\naRCBUCjAnFmtzjpVKu802OTI9y+dyo8XPpM20ygUDDB+xDGEbJt5I05i3oiTmuwPBwP8zw/m8utH\nX+WlVRVEdiVJlPhpVHb7s5Fsi7PLhwIgIoSC2f8zHl1SxB3nn9PxH7AFN339TNau30b1nv3UxZJE\no0Gi0RB1RweRZMJLEhoMMHrEAF7c+JH3rV0gVuqlobHi3uJgTkiwkkJkNwf6w4zBjjm4YTvrg5ZB\nLGYMHcZnH+9Om7GXSHn9T+GUQ31QKKmoJVQdp/LUYm8Mp54/KcMJBdlbWoMkUrgmjhspbHocUBQN\n86fvX8zi9e/x0OMf4CRdMEI0FOSu685lwsim+cva46zhgzlr+GBSKYcH/vYWj1esYH8owZgTB3Dj\n9VPp3attD/cqlU8abHJk2rhhrNqwhcffWIPjeg/VIcLd159HuIXgAFBaXMjt13gJPd/7aCs33LOI\nlOOScB2ioSClJQVcO2PCofgYafbUxvjPJ99gyYr12JbFBV8+gWtnTGgyfpQ0LjffMo3d2/dRuX0v\nx/TvyakThxEIWGzYUkXKcRk+oBe2ZbFuexV/fP1tnv9wA0nXxYmAExFvPMYS3DDsP6r+wVavxdNz\nVR1FH8VwCoIkexY0ufHbtjB8aB969izMOPBu73cJ1RgIeN1Xri3E+xQR2V5D/6d2svn80oYWi+C3\nXoJQd1wRTkRIWkmMnV6uawx79sW46bQzuWHyGaz7bAcB22Jov7IWJwC0RyBgc/W8SVwB5a4BAAAM\nq0lEQVQ9b1KHlKfUoaTBJkdEhB/Oncqc00fz5j8/pTAS4syThlJc2L6HKccM6stjP5nP46+vYdOO\nasYN68/0k0ekTQ44FBLJFFf+8kG27drX0EX21yXLWVmxhf+6ZQ518SRX3/EQGyp3eQM3Ipw6+Biu\numxiww13WP9eTcocflQZv549kz+/tZx7X3kTYyAVS2HVQqwIbwqL+GvKUD/BIoXlGGRfAjdokSqJ\ngCVEggEG9OvJT2+9kGA4wL899GLaZ4jsdpoOs4j38GiqZ5RQZQ3hqhTxXhnyggUt3EigxTGa+l22\nZXH8wKOyH6hUF6TBJscG9y1jcN8vNvOrV/duXHfuKR1Uo4O3ZGUFO/fubzIWE086fLipktUfbeNX\nD77Ehu07vZaGH1yWVmziZ394hgXfmNli2VefMo55J49h65593PP3pbyyeiNS6KePqb+Lu4bQnhTh\nKq+ZI0CoOobbK8w1V53OpLGDGHxc74Yy77hmBrcufAbbEowxOI7bMGW5OTdkYwTsRAvr8wDBj3aS\n7FMMwaYD+7ZlMXpQ3xbPVaor02Cj2uz9j7exP55M2+64Lqs2buGDLZVpYxlYsHjFOhbQcrABCAUC\nHFvag7WfVWIMRKogUXwgF1qwFnq9sa9J4yIYsPnNLy5nxIn908o7Y+wQnr/zOl55/yNSjsvE4wcy\n/6t/onZ/hvxmjkEcQ6yshWzHjiG8thL3mB44g8pwhYaJGb/62nkEbH2SQKlsNNioNjumd3ciwUDa\nQl8B26K4INLQddZcCq9VYTe7GRtjWPXSGpYuWkY4EuSsK05n8Jhj6V9Wwue79mG5EKluOBg7CRHb\nxsHrCotEg5w6fXTGQFOvqCDCeROOb3h9yewv8ddHlpFoPHHANQT21rF7VCFu2CISDCAIjut6y3A7\nLuIagnvjFBSGOSVQwCW3zGH5xi0UF0Q4u3xYu7tHlepqNNioNps5fiS/f/JN4slUw+Qw2xJKCiPM\nnDCSO/53CU7zdDHG0I1AxkBz1/zf8dqiZcRq41i2xZO/f575v7iUr86YwJqPP28IalbCULDDwTYQ\n712MlLmM7FnMnMsmMnlaWnKJrPbVxekztJTy8ceyfNnHJJMpL3WOm6SqvACnwKLn2jr69SjhZzfP\n4qlPN7Lis60c26M7Y2qCREM13L1kASPGezMBRw/J28oVSh1xtN2v2qy4MMKfvnMxwwf0JmBbBGyL\n8iH9WfjdSwgHA1w5pdxLuFk/3dsYxMBNF01OK+u9lz9oCDQAruMSr0uw8McPMbikiAVXnENpcQEh\ny6JgewpJGVzHkEw5JFzD+to6xkwa0uaZXv+3fD3n/OA+fv7gC7y+Yyu7jxZq+gXZOzDIrtGFRD9P\n0O/ZXZSs3Edi6TZ+NOcPlNd04+GrL+XOWdOZe/mZdO9d0hBolFLtoy0b1S5D+pXx4K3z2Lc/hmVZ\nFEYOrJ/zrUtOo6y4gPuefIuaZJIegQj/cvFpzJya3vp4bdFbxPenZ9W0bYt3nl3F9KvP4Oxxw3h8\n8Ur+uPAVYrGmY0Wu67LklbV85byT0spobkd1Dbf95VniSQfqixEBf3JZwedJuq/b35AiKJnwsj/c\n+5PHOPm0YXTv2bXWJ1EqFzTYqINSVJB5jGLujJOZO6P1J9pD0RBi+U/yNyKWEIp4g/SWJcTqkiST\n6UlL4/EUO3fVpG3P5IUVG1rcH9key7jkg2VbvP3yWs6ZrU/oK/VFaTeayouzLj+dYIZnhVzHMOHc\n8obXo0/oTzCYnj8sGgky5sQBadsziSWTpJqn6W+L3C1iq1SXo8FG5cWg0QO55o65BCNBIt3CRIsi\nRArCLHj0OxQWH0gSesLIvow9cQCR8IHAFA4HGDakD+PGti0FzOQTB2VczdK2hIBtYQ0oSp+yjddV\nN37KiLTtSqn20240lTezbz6PKZdM4p1nVxGKhJhwbjkFRdEmx4gIty+YzVPPvsfTz63GdQ0zzh7F\nhTPHYmUIEJkM7VfGRaeO4rHX3m/IlRYOBfjKpFFcf+4pbKmq5tW/LeeZB9/yHvy0BBHhhttm6XiN\nUh1EWlqStisZPny4WbduXb6roXLEGMPKii0sfnstADPGj6B8SL8ms9k+rdjOspc+JBC0OXXaKHod\n3b1JGbq+vGpNV7xGRGS5MabVgU1t2aguQUQoH9qf8qHZHwAdOOQoBg7RnGZK5YKO2SillMq5Th1s\nRGS6iKwTkQoR+WG+66OUUl1Vpw02ImID/wHMAI4H5orI8S2fpZRSKhc6bbABxgMVxpiPjDEJ4GHg\nwjzXSSmluqTOHGz6AZ81er3Z36aUUuoQ69Kz0UTkeuB6/2VcRNbksz5tUALsOQLKP5hy2nNOW45t\n7ZiW9mfbVwZUtVq7/Mr1NdJR76HXSH515HXStqerjTGd8gf4MvBco9c/An7UwvHv5rvObfhM9x0J\n5R9MOe05py3HtnZMS/uz7dNrpOPeQ6+Rzn+dNP/pzN1o7wBDReQ4EQkBlwJP5LlOX9STR0j5B1NO\ne85py7GtHdPS/lz/nXPpUNS9I95Dr5H8OuT179QZBERkJvAbwAYWGmNub+HYd00bnoJVXZdeI6o1\neo1k16nHbIwxi4HFbTz8vlzWRXUKeo2o1ug1kkWnbtkopZQ6PHTmMRullFKHCQ02Simlck6DjVJK\nqZzTYJOFiIwUkT+IyKMi8o1810cdnkSkUETeFZHz8l0XdfgRkSkistS/l0zJd33yqUsFGxFZKCKV\nzTMFZMoObYz50BjzdeBiYFI+6qsOvfZcI74fAI8c2lqqfGrnNWKAGiCClzKry+pSwQa4H5jeeENL\n2aFF5ALgado+fVod+e6njdeIiJwN/BOoPNSVVHl1P22/jyw1xszA+1Ly00Ncz8NKlwo2xphXgV3N\nNmfNDm2MecK/UOYd2pqqfGnnNTIFOAW4DLhORLrU/09dVXuuEWOM6+/fDYQPYTUPO536oc42ypQd\neoLfvzob7wLRlk3XlvEaMcbcCCAi84GqRjcW1fVku4/MBqYB3YHf5aNihwsNNlkYY14GXs5zNdQR\nwBhzf77roA5PxphFwKJ81+NwoM1+2AIMaPS6v79NqXp6jajW6DXSCg02nTM7tOpYeo2o1ug10oou\nFWxE5CHgTWC4iGwWkWuNMSngRuA54EPgEWPMB/msp8ofvUZUa/QaOTiaiFMppVTOdamWjVJKqfzQ\nYKOUUirnNNgopZTKOQ02Simlck6DjVJKqZzTYKOUUirnNNgolYWI1LTj2Fn12cLbePzJInLPwdWs\nSTlREXnFzzqMiNwtIh/4/2ask4hcJiIJEfnXZtvPFpHlIvK+/+/URvteEJEeX7S+quvSYKNUx5iF\nl1q+TYwx7xpjbuqA970GWGSMcfzX1wOjjTHfy1QnP4B8399+lohc1Wh3FXC+MWYUcBXwQKN9DwDf\n7ID6qi5Kg41S7SAix4rIiyKyWkSWiMgxIjIRuAC4W0RWicjgZufMEZE1IvKeiLzqb5siIk/5vy/2\nz1slIntE5CoRsf3WyTv+e30tS5XmAf/wy3kC6AYsF5EFzeskIqOAXwDTjDEVwEzgMhGZBmCMWWmM\n2eqX+wEQFZH6tPhPAHM74m+ouibN+qxU+9wL/MUY8xcRuQa4xxgzy7/RP2WMeTTDObfh3eC3iEj3\n5juNMTMBRGQc8GfgceBaYI8x5kv+Df91EXneGPNx/Xl+Dq5BxphP/HIuEJEaY8xYf/9xGeo0sdH7\n1uKlv8/kImCFMSbuH7tbRMIiUmqM2dmGv5NSTWjLRqn2+TLwoP/7A8DkNpzzOnC/iFwH2JkOEJEy\nv7zLjDF7gHOAK0VkFbAMKAWGNjutDKhu9ydohYicAPwSaN6aqgT6dvT7qa5BWzZK5Zgx5usiMgE4\nF6+La1zj/f7g/sPAz4wx9evaC/AtY8xzLRRdh7e2fYcRkf7AY8CVxpiNzXZH/PdUqt20ZaNU+7yB\nlz4evPGSpf7v+4CiTCeIyGBjzDJjzG3ADpquewJwJ7DaGPNwo23PAd8QkaBfxjARKWx8kjFmN2CL\nSLaAk7VOWerZHXga+KEx5vVm+wToA3zS1vKUakyDjVLZFfgp5Ot/bgG+BVwtIquBK4Cb/WMfBr4n\nIiubTxDAG6R/X0TW4AWr95rt/y5wTqNJAhcA/w38E1jhn/dHMvdEPE/2rryW6pTJjcAQ4LZGdent\n7xsHvOWn0leq3XSJAaWOYCJSDnzbGHNFjt/nt8ATxpgluXwf1Xlpy0apI5gxZgXwUv1DnTm0RgON\n+iK0ZaOUUirntGWjlFIq5zTYKKWUyjkNNkoppXJOg41SSqmc02CjlFIq5zTYKKWUyrn/B+fSMrkp\nVbO4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9b81470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure\n",
    "ax = plt.gca()\n",
    "ax.scatter(trainset.LotArea, trainset.SalePrice, c = trainset.OverallQual)\n",
    "ax.set_xscale('log')\n",
    "plt.xlabel('Lot size (ft^2)')\n",
    "plt.ylabel('Sale Price ($)')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = trainset.groupby('OverallQual').SalePrice.agg('mean')\n",
    "oqmap = a / a.loc[5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The map above calculates the influence of OverallQual on the sales price. This map is based on known sales price therefore could be overfitting the training set. A less variant model would be using a log linear relationship between overall quality and sales price as the figure below suggests. For now we use the oqmap function above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x9b812e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(trainset.OverallQual, trainset.SalePrice, '.b')\n",
    "plt.xlabel('overall quality')\n",
    "plt.ylabel('slae price ($)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LotArea</th>\n",
       "      <th>LogLotArea</th>\n",
       "      <th>LotArea_Q</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.697945</td>\n",
       "      <td>0.215848</td>\n",
       "      <td>0.263843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LogLotArea</th>\n",
       "      <td>0.697945</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.335918</td>\n",
       "      <td>0.388520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea_Q</th>\n",
       "      <td>0.215848</td>\n",
       "      <td>0.335918</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.851368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>0.263843</td>\n",
       "      <td>0.388520</td>\n",
       "      <td>0.851368</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             LotArea  LogLotArea  LotArea_Q  SalePrice\n",
       "LotArea     1.000000    0.697945   0.215848   0.263843\n",
       "LogLotArea  0.697945    1.000000   0.335918   0.388520\n",
       "LotArea_Q   0.215848    0.335918   1.000000   0.851368\n",
       "SalePrice   0.263843    0.388520   0.851368   1.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trainset = trainset.assign(LotArea_Q = np.log(trainset.LotArea) * trainset.OverallQual.map(oqmap))\n",
    "trainset = trainset.assign(LogLotArea = np.log(trainset.LotArea))\n",
    "trainset[['LotArea', 'LogLotArea', 'LotArea_Q', 'SalePrice']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table above shows that when normalized the linear relationship greatly improves. The reason could be that overall quality represents the factors that are not related to lot area. When those factors are taken out we are essentially comparing houses under the same condition but with different lot area. The normalization distilled the more simple intuitive relationship between lot area and sale price that we see in the figure below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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I/FtEfhCRHSKyQUTGi8itItKolvcYqqpHq2p/5/m9wCRV7QpMcp4jIj2By4FewAjgWREp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x9b25ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure\n",
    "ax = plt.gca()\n",
    "ax.scatter(trainset.LotArea_Q, trainset.SalePrice, c = trainset.MSSubClass)\n",
    "plt.xlabel('log(LotArea)*oqmap(OverallQual)')\n",
    "plt.ylabel('sale price ($)')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure above also shows an example that other discrete features (in this case MSSubClass) can help us further refine the relationships between normalized continous features and the sales price. A refined model would consist of a classification model that puts a house into a specific category and each category has its own regression model (maybe linear). The regression model is each category has reduced error than a general regression model with all houses.\n",
    "\n",
    "In this model we consider only linear regression over all houses and the refinement discussed above will be investigated in the future.\n",
    "\n",
    "Below we create a few more normalized continous features that is based on the overall quality. In addition we add the logarithmic of OverallQual as a continous feature. We also added a feature TotBR represent the total number of bathrooms. It is a feature that is naturally ordered and has a good linear relationship with sales price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "trainset = trainset.assign(FFSF_Q = trainset['1stFlrSF'] * trainset.OverallQual.map(oqmap))\n",
    "trainset = trainset.assign(GLA_Q = trainset.GrLivArea * trainset.OverallQual.map(oqmap))\n",
    "trainset = trainset.assign(PosOutSF = trainset.WoodDeckSF + trainset.OpenPorchSF + trainset.ScreenPorch)\n",
    "trainset = trainset.assign(POSF_Q = trainset.PosOutSF * trainset.OverallQual.map(oqmap))\n",
    "trainset = trainset.assign(LogQ = trainset.OverallQual.apply(np.log))\n",
    "\n",
    "trainset = trainset.assign(TotBR = trainset.BsmtFullBath + trainset.BsmtHalfBath * 0.5 + trainset.FullBath + trainset.HalfBath * 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LotFrontage</th>\n",
       "      <th>LotArea</th>\n",
       "      <th>MasVnrArea</th>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <th>1stFlrSF</th>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <th>FFSF_Q</th>\n",
       "      <th>LotArea_Q</th>\n",
       "      <th>GLA_Q</th>\n",
       "      <th>TotBR</th>\n",
       "      <th>Fireplaces</th>\n",
       "      <th>GarageCars</th>\n",
       "      <th>POSF_Q</th>\n",
       "      <th>LogQ</th>\n",
       "      <th>SalePrice</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.426095</td>\n",
       "      <td>0.193458</td>\n",
       "      <td>0.392075</td>\n",
       "      <td>0.457181</td>\n",
       "      <td>0.080177</td>\n",
       "      <td>0.416649</td>\n",
       "      <td>0.359309</td>\n",
       "      <td>0.400998</td>\n",
       "      <td>0.220092</td>\n",
       "      <td>0.266639</td>\n",
       "      <td>0.285691</td>\n",
       "      <td>0.237748</td>\n",
       "      <td>0.230435</td>\n",
       "      <td>0.351799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>0.426095</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.104160</td>\n",
       "      <td>0.260833</td>\n",
       "      <td>0.299475</td>\n",
       "      <td>0.050986</td>\n",
       "      <td>0.226289</td>\n",
       "      <td>0.215848</td>\n",
       "      <td>0.216391</td>\n",
       "      <td>0.204764</td>\n",
       "      <td>0.271364</td>\n",
       "      <td>0.154871</td>\n",
       "      <td>0.197817</td>\n",
       "      <td>0.097750</td>\n",
       "      <td>0.263843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>0.193458</td>\n",
       "      <td>0.104160</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.363936</td>\n",
       "      <td>0.344501</td>\n",
       "      <td>0.174561</td>\n",
       "      <td>0.465630</td>\n",
       "      <td>0.452811</td>\n",
       "      <td>0.485121</td>\n",
       "      <td>0.319557</td>\n",
       "      <td>0.249070</td>\n",
       "      <td>0.364204</td>\n",
       "      <td>0.347806</td>\n",
       "      <td>0.374281</td>\n",
       "      <td>0.477493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>0.392075</td>\n",
       "      <td>0.260833</td>\n",
       "      <td>0.363936</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.819530</td>\n",
       "      <td>-0.174512</td>\n",
       "      <td>0.788815</td>\n",
       "      <td>0.599942</td>\n",
       "      <td>0.579591</td>\n",
       "      <td>0.414468</td>\n",
       "      <td>0.339519</td>\n",
       "      <td>0.434585</td>\n",
       "      <td>0.474575</td>\n",
       "      <td>0.504216</td>\n",
       "      <td>0.613581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>0.457181</td>\n",
       "      <td>0.299475</td>\n",
       "      <td>0.344501</td>\n",
       "      <td>0.819530</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.202646</td>\n",
       "      <td>0.830897</td>\n",
       "      <td>0.565636</td>\n",
       "      <td>0.598228</td>\n",
       "      <td>0.390557</td>\n",
       "      <td>0.410531</td>\n",
       "      <td>0.439317</td>\n",
       "      <td>0.456603</td>\n",
       "      <td>0.437098</td>\n",
       "      <td>0.605852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0.080177</td>\n",
       "      <td>0.050986</td>\n",
       "      <td>0.174561</td>\n",
       "      <td>-0.174512</td>\n",
       "      <td>-0.202646</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.031611</td>\n",
       "      <td>0.262289</td>\n",
       "      <td>0.490218</td>\n",
       "      <td>0.375160</td>\n",
       "      <td>0.194561</td>\n",
       "      <td>0.183926</td>\n",
       "      <td>0.215624</td>\n",
       "      <td>0.292110</td>\n",
       "      <td>0.319334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FFSF_Q</th>\n",
       "      <td>0.416649</td>\n",
       "      <td>0.226289</td>\n",
       "      <td>0.465630</td>\n",
       "      <td>0.788815</td>\n",
       "      <td>0.830897</td>\n",
       "      <td>0.031611</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.885672</td>\n",
       "      <td>0.867546</td>\n",
       "      <td>0.473020</td>\n",
       "      <td>0.411636</td>\n",
       "      <td>0.537132</td>\n",
       "      <td>0.658076</td>\n",
       "      <td>0.697657</td>\n",
       "      <td>0.793815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea_Q</th>\n",
       "      <td>0.359309</td>\n",
       "      <td>0.215848</td>\n",
       "      <td>0.452811</td>\n",
       "      <td>0.599942</td>\n",
       "      <td>0.565636</td>\n",
       "      <td>0.262289</td>\n",
       "      <td>0.885672</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.897974</td>\n",
       "      <td>0.525137</td>\n",
       "      <td>0.407133</td>\n",
       "      <td>0.597824</td>\n",
       "      <td>0.686783</td>\n",
       "      <td>0.865553</td>\n",
       "      <td>0.851368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GLA_Q</th>\n",
       "      <td>0.400998</td>\n",
       "      <td>0.216391</td>\n",
       "      <td>0.485121</td>\n",
       "      <td>0.579591</td>\n",
       "      <td>0.598228</td>\n",
       "      <td>0.490218</td>\n",
       "      <td>0.867546</td>\n",
       "      <td>0.897974</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.567686</td>\n",
       "      <td>0.434253</td>\n",
       "      <td>0.539791</td>\n",
       "      <td>0.676252</td>\n",
       "      <td>0.731183</td>\n",
       "      <td>0.837414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotBR</th>\n",
       "      <td>0.220092</td>\n",
       "      <td>0.204764</td>\n",
       "      <td>0.319557</td>\n",
       "      <td>0.414468</td>\n",
       "      <td>0.390557</td>\n",
       "      <td>0.375160</td>\n",
       "      <td>0.473020</td>\n",
       "      <td>0.525137</td>\n",
       "      <td>0.567686</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.331652</td>\n",
       "      <td>0.483578</td>\n",
       "      <td>0.439799</td>\n",
       "      <td>0.521937</td>\n",
       "      <td>0.631731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fireplaces</th>\n",
       "      <td>0.266639</td>\n",
       "      <td>0.271364</td>\n",
       "      <td>0.249070</td>\n",
       "      <td>0.339519</td>\n",
       "      <td>0.410531</td>\n",
       "      <td>0.194561</td>\n",
       "      <td>0.411636</td>\n",
       "      <td>0.407133</td>\n",
       "      <td>0.434253</td>\n",
       "      <td>0.331652</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.300789</td>\n",
       "      <td>0.344928</td>\n",
       "      <td>0.384360</td>\n",
       "      <td>0.466929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageCars</th>\n",
       "      <td>0.285691</td>\n",
       "      <td>0.154871</td>\n",
       "      <td>0.364204</td>\n",
       "      <td>0.434585</td>\n",
       "      <td>0.439317</td>\n",
       "      <td>0.183926</td>\n",
       "      <td>0.537132</td>\n",
       "      <td>0.597824</td>\n",
       "      <td>0.539791</td>\n",
       "      <td>0.483578</td>\n",
       "      <td>0.300789</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.418162</td>\n",
       "      <td>0.576119</td>\n",
       "      <td>0.640409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>POSF_Q</th>\n",
       "      <td>0.237748</td>\n",
       "      <td>0.197817</td>\n",
       "      <td>0.347806</td>\n",
       "      <td>0.474575</td>\n",
       "      <td>0.456603</td>\n",
       "      <td>0.215624</td>\n",
       "      <td>0.658076</td>\n",
       "      <td>0.686783</td>\n",
       "      <td>0.676252</td>\n",
       "      <td>0.439799</td>\n",
       "      <td>0.344928</td>\n",
       "      <td>0.418162</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.535201</td>\n",
       "      <td>0.645248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LogQ</th>\n",
       "      <td>0.230435</td>\n",
       "      <td>0.097750</td>\n",
       "      <td>0.374281</td>\n",
       "      <td>0.504216</td>\n",
       "      <td>0.437098</td>\n",
       "      <td>0.292110</td>\n",
       "      <td>0.697657</td>\n",
       "      <td>0.865553</td>\n",
       "      <td>0.731183</td>\n",
       "      <td>0.521937</td>\n",
       "      <td>0.384360</td>\n",
       "      <td>0.576119</td>\n",
       "      <td>0.535201</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.732961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>0.351799</td>\n",
       "      <td>0.263843</td>\n",
       "      <td>0.477493</td>\n",
       "      <td>0.613581</td>\n",
       "      <td>0.605852</td>\n",
       "      <td>0.319334</td>\n",
       "      <td>0.793815</td>\n",
       "      <td>0.851368</td>\n",
       "      <td>0.837414</td>\n",
       "      <td>0.631731</td>\n",
       "      <td>0.466929</td>\n",
       "      <td>0.640409</td>\n",
       "      <td>0.645248</td>\n",
       "      <td>0.732961</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             LotFrontage   LotArea  MasVnrArea  TotalBsmtSF  1stFlrSF  \\\n",
       "LotFrontage     1.000000  0.426095    0.193458     0.392075  0.457181   \n",
       "LotArea         0.426095  1.000000    0.104160     0.260833  0.299475   \n",
       "MasVnrArea      0.193458  0.104160    1.000000     0.363936  0.344501   \n",
       "TotalBsmtSF     0.392075  0.260833    0.363936     1.000000  0.819530   \n",
       "1stFlrSF        0.457181  0.299475    0.344501     0.819530  1.000000   \n",
       "2ndFlrSF        0.080177  0.050986    0.174561    -0.174512 -0.202646   \n",
       "FFSF_Q          0.416649  0.226289    0.465630     0.788815  0.830897   \n",
       "LotArea_Q       0.359309  0.215848    0.452811     0.599942  0.565636   \n",
       "GLA_Q           0.400998  0.216391    0.485121     0.579591  0.598228   \n",
       "TotBR           0.220092  0.204764    0.319557     0.414468  0.390557   \n",
       "Fireplaces      0.266639  0.271364    0.249070     0.339519  0.410531   \n",
       "GarageCars      0.285691  0.154871    0.364204     0.434585  0.439317   \n",
       "POSF_Q          0.237748  0.197817    0.347806     0.474575  0.456603   \n",
       "LogQ            0.230435  0.097750    0.374281     0.504216  0.437098   \n",
       "SalePrice       0.351799  0.263843    0.477493     0.613581  0.605852   \n",
       "\n",
       "             2ndFlrSF    FFSF_Q  LotArea_Q     GLA_Q     TotBR  Fireplaces  \\\n",
       "LotFrontage  0.080177  0.416649   0.359309  0.400998  0.220092    0.266639   \n",
       "LotArea      0.050986  0.226289   0.215848  0.216391  0.204764    0.271364   \n",
       "MasVnrArea   0.174561  0.465630   0.452811  0.485121  0.319557    0.249070   \n",
       "TotalBsmtSF -0.174512  0.788815   0.599942  0.579591  0.414468    0.339519   \n",
       "1stFlrSF    -0.202646  0.830897   0.565636  0.598228  0.390557    0.410531   \n",
       "2ndFlrSF     1.000000  0.031611   0.262289  0.490218  0.375160    0.194561   \n",
       "FFSF_Q       0.031611  1.000000   0.885672  0.867546  0.473020    0.411636   \n",
       "LotArea_Q    0.262289  0.885672   1.000000  0.897974  0.525137    0.407133   \n",
       "GLA_Q        0.490218  0.867546   0.897974  1.000000  0.567686    0.434253   \n",
       "TotBR        0.375160  0.473020   0.525137  0.567686  1.000000    0.331652   \n",
       "Fireplaces   0.194561  0.411636   0.407133  0.434253  0.331652    1.000000   \n",
       "GarageCars   0.183926  0.537132   0.597824  0.539791  0.483578    0.300789   \n",
       "POSF_Q       0.215624  0.658076   0.686783  0.676252  0.439799    0.344928   \n",
       "LogQ         0.292110  0.697657   0.865553  0.731183  0.521937    0.384360   \n",
       "SalePrice    0.319334  0.793815   0.851368  0.837414  0.631731    0.466929   \n",
       "\n",
       "             GarageCars    POSF_Q      LogQ  SalePrice  \n",
       "LotFrontage    0.285691  0.237748  0.230435   0.351799  \n",
       "LotArea        0.154871  0.197817  0.097750   0.263843  \n",
       "MasVnrArea     0.364204  0.347806  0.374281   0.477493  \n",
       "TotalBsmtSF    0.434585  0.474575  0.504216   0.613581  \n",
       "1stFlrSF       0.439317  0.456603  0.437098   0.605852  \n",
       "2ndFlrSF       0.183926  0.215624  0.292110   0.319334  \n",
       "FFSF_Q         0.537132  0.658076  0.697657   0.793815  \n",
       "LotArea_Q      0.597824  0.686783  0.865553   0.851368  \n",
       "GLA_Q          0.539791  0.676252  0.731183   0.837414  \n",
       "TotBR          0.483578  0.439799  0.521937   0.631731  \n",
       "Fireplaces     0.300789  0.344928  0.384360   0.466929  \n",
       "GarageCars     1.000000  0.418162  0.576119   0.640409  \n",
       "POSF_Q         0.418162  1.000000  0.535201   0.645248  \n",
       "LogQ           0.576119  0.535201  1.000000   0.732961  \n",
       "SalePrice      0.640409  0.645248  0.732961   1.000000  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "contset = ['LotFrontage', 'LotArea', 'MasVnrArea', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF', 'FFSF_Q',\n",
    "           'LotArea_Q', 'GLA_Q', 'TotBR', 'Fireplaces', 'GarageCars', 'POSF_Q','LogQ', 'SalePrice']\n",
    "trainset[contset].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The feature LotFrontage and MasVnrArea have decent correlation coefficients with sales price. However, both features have a few null values in the training set. In the MasVnrArea the null values are in the houses without masonary vaneer so they can be filled by 0.0. \n",
    "\n",
    "We can use other features to estimate the missing values in LotFrontage. The table above shows that LotFrontage and a number of features has decent correlation coefficients (higher than 0.2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "trainset.MasVnrArea.fillna(0.0, inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model 1: estimating Lot Frontage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\theya\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:15: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([  5.40172899e-07,   7.96236357e-03,  -4.73246899e-04,\n",
       "          1.66199535e-03,   1.66199535e-03,  -2.06200434e-03,\n",
       "          1.29772058e-03,  -1.17215088e-06,  -1.91005107e-03,\n",
       "         -1.06409275e-06,   2.95469789e-06,   1.08034580e-06,\n",
       "          8.36543315e-04,   5.95659238e-07]),\n",
       " 1.0097419586828951e-28,\n",
       " {'funcalls': 8,\n",
       "  'grad': array([  9.16892133e-15,   9.09207565e-11,  -4.94109472e-13,\n",
       "           1.25946912e-11,   1.25946912e-11,  -2.15290556e-12,\n",
       "           1.44981048e-11,   9.42726821e-14,   1.11489220e-11,\n",
       "           2.04013366e-14,   1.16898880e-14,   1.83378427e-14,\n",
       "           3.97696051e-12,   1.60398929e-14]),\n",
       "  'nit': 3,\n",
       "  'task': 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL',\n",
       "  'warnflag': 0})"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def lrCost(theta, X, y):\n",
    "    \"\"\"linear regression cost function \"\"\"\n",
    "    m = X.shape[0]\n",
    "    return np.dot((np.dot(X, theta) - y).T, np.dot(X, theta) - y) / 2.0 / m\n",
    "\n",
    "def lrGradient(theta, X, y):\n",
    "    \"\"\" linear regression gradient \"\"\"\n",
    "    return np.dot(X.T, np.dot(X, theta) - y) / X.shape[0]\n",
    "\n",
    "contset.remove('SalePrice')\n",
    "ind = trainset.LotFrontage.notnull()\n",
    "X = np.concatenate((np.ones(shape = (trainset.shape[0], 1)), \n",
    "                    trainset[contset[1:]].values.reshape(trainset.shape[0], len(contset) - 1)), axis = 1)\n",
    "theta0 = np.zeros(shape = (1, len(contset)))\n",
    "w = scop.fmin_l_bfgs_b(lrCost, theta0, lrGradient, (X[ind, :], trainset.LotFrontage.values[ind]))\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\theya\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:4: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n",
      "C:\\Users\\theya\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n"
     ]
    }
   ],
   "source": [
    "lotfront_para = w[0]\n",
    "lotfrontage_predict = np.dot(X, lotfront_para.T)\n",
    "ind = trainset.LotFrontage.isnull()\n",
    "trainset.LotFrontage[ind] = lotfront_para[ind]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We filled the missing LotFrontage values from the model above. Next we build a linear regression model between the continous features and the sales price. We remove sales price from the feature list for obvious reasons. We also remove LotArea and instead using LogLotArea since the latter has better linear relationship with sales price."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model 2: Sales Price model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "contset.remove('LotArea')\n",
    "contset.append('LogLotArea')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ -1.24883663e+04,  -4.93581209e+01,   2.25868737e+01,\n",
       "          1.85343492e+01,   4.84428662e+01,   1.63739395e+01,\n",
       "         -2.23078555e+01,   1.21138339e+04,   5.49194889e+00,\n",
       "          1.28092456e+04,   6.20480609e+03,   1.24967318e+04,\n",
       "          1.07804182e+01,  -3.92693174e+04,   6.42887535e+01]),\n",
       " 561464052.65125704,\n",
       " {'funcalls': 1467,\n",
       "  'grad': array([   42.35360841,  -278.28024839,  -456.87119629, -1105.88833641,\n",
       "         -1245.50883893,  -281.79405356, -1933.79704006,   340.65292909,\n",
       "         -2846.25407888,  -259.18078066,  -109.51519165,   -49.0765471 ,\n",
       "           344.42076048,    46.103245  ,   406.69181388]),\n",
       "  'nit': 1280,\n",
       "  'task': 'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH',\n",
       "  'warnflag': 0})"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.concatenate((np.ones(shape = (trainset.shape[0], 1)), trainset[contset].values.reshape(trainset.shape[0], len(contset))), axis = 1)\n",
    "theta0 = np.zeros(shape = (1, len(contset) + 1))\n",
    "w = scop.fmin_l_bfgs_b(lrCost, theta0, lrGradient, (X, trainset.SalePrice.values))\n",
    "w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we estimate the relative error of the model over the training set. The relative error is define as:\n",
    "\n",
    "$err(y, y_0) = \\frac{|y - y_0|}{y_0}$, \n",
    "\n",
    "where $y_0$ is the known sales price and $y$ is the predicted sales price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Hk+xPcu2465GkpWxBvFU3yTLgd4B/ChwEPp9kd1XtG29li8e43ujr23ylhWmhHHlsAvZX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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc073518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sp_predict = np.dot(X, w[0].T)\n",
    "err = np.abs(sp_predict - trainset.SalePrice.values) / trainset.SalePrice.values\n",
    "plt.hist(err)\n",
    "plt.xlabel('relative error')\n",
    "plt.ylabel('count')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16228493767104593"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.dot((np.log(sp_predict) - np.log(trainset.SalePrice.values)).T, np.log(sp_predict) - np.log(trainset.SalePrice.values)) / sp_predict.size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure above shows that most of the price predictions has a relative error less than 0.5%. This is not a bad model. We use the model parameters to estimate the sale prices for the test set hosues.\n",
    "\n",
    "First we filling the null values in different features. For LotFrontage we use the same method shown above. For the MasVnrArea,  BsmtFullBath and BsmtHalfBath we use 0 to fill the null values since in all three cases the null value represent no corresponding feature present in the house as shown below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MSZoning        0.002742\n",
       "LotFrontage     0.155586\n",
       "Alley           0.926662\n",
       "Utilities       0.001371\n",
       "Exterior1st     0.000685\n",
       "Exterior2nd     0.000685\n",
       "MasVnrType      0.010966\n",
       "MasVnrArea      0.010281\n",
       "BsmtQual        0.030158\n",
       "BsmtCond        0.030843\n",
       "BsmtExposure    0.030158\n",
       "BsmtFinType1    0.028787\n",
       "BsmtFinSF1      0.000685\n",
       "BsmtFinType2    0.028787\n",
       "BsmtFinSF2      0.000685\n",
       "BsmtUnfSF       0.000685\n",
       "TotalBsmtSF     0.000685\n",
       "BsmtFullBath    0.001371\n",
       "BsmtHalfBath    0.001371\n",
       "KitchenQual     0.000685\n",
       "Functional      0.001371\n",
       "FireplaceQu     0.500343\n",
       "GarageType      0.052090\n",
       "GarageYrBlt     0.053461\n",
       "GarageFinish    0.053461\n",
       "GarageCars      0.000685\n",
       "GarageArea      0.000685\n",
       "GarageQual      0.053461\n",
       "GarageCond      0.053461\n",
       "PoolQC          0.997944\n",
       "Fence           0.801234\n",
       "MiscFeature     0.965045\n",
       "SaleType        0.000685\n",
       "dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nullpercent = testset.isnull().sum() / testset.shape[0]\n",
    "nullpercent[nullpercent.values > 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Id\n",
       "1692    NaN\n",
       "1707    NaN\n",
       "1883    NaN\n",
       "1993    NaN\n",
       "2005    NaN\n",
       "2042    NaN\n",
       "2312    NaN\n",
       "2326    NaN\n",
       "2341    NaN\n",
       "2350    NaN\n",
       "2369    NaN\n",
       "2593    NaN\n",
       "2658    NaN\n",
       "2687    NaN\n",
       "2863    NaN\n",
       "Name: MasVnrType, dtype: object"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testset[testset.MasVnrArea.isnull()].MasVnrType"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Id\n",
       "2121    NaN\n",
       "2189    NaN\n",
       "Name: BsmtQual, dtype: object"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testset[testset.BsmtFullBath.isnull()].BsmtQual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Id\n",
       "2577    Detchd\n",
       "Name: GarageType, dtype: object"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testset[testset.GarageCars.isnull()].GarageType"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One house is missing GarageCars feature and this house has a detached style garage. We use the mean value for GarageCars for this garage type in training set to fill this missing value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>count</th>\n",
       "      <th>min</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageType</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2Types</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Attchd</th>\n",
       "      <td>1.964368</td>\n",
       "      <td>870</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Basment</th>\n",
       "      <td>1.578947</td>\n",
       "      <td>19</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BuiltIn</th>\n",
       "      <td>2.250000</td>\n",
       "      <td>88</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CarPort</th>\n",
       "      <td>1.666667</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Detchd</th>\n",
       "      <td>1.576227</td>\n",
       "      <td>387</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                mean  count  min  max\n",
       "GarageType                           \n",
       "2Types      3.000000      6    2    4\n",
       "Attchd      1.964368    870    1    4\n",
       "Basment     1.578947     19    1    2\n",
       "BuiltIn     2.250000     88    1    3\n",
       "CarPort     1.666667      9    1    2\n",
       "Detchd      1.576227    387    1    4"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trainset.groupby('GarageType').GarageCars.agg(['mean', 'count', 'min', 'max'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "testset.MasVnrArea.fillna(0.0, inplace = True)\n",
    "testset.BsmtFullBath.fillna(0, inplace = True)\n",
    "testset.BsmtHalfBath.fillna(0, inplace = True)\n",
    "testset.TotalBsmtSF.fillna(0.0, inplace = True)\n",
    "testset.GarageCars.fillna(1.6, inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "testset = testset.assign(LotArea_Q = np.log(testset.LotArea) * testset.OverallQual.map(oqmap))\n",
    "testset = testset.assign(LogLotArea = np.log(testset.LotArea))\n",
    "testset = testset.assign(FFSF_Q = testset['1stFlrSF'] * testset.OverallQual.map(oqmap))\n",
    "testset = testset.assign(GLA_Q = testset.GrLivArea * testset.OverallQual.map(oqmap))\n",
    "testset = testset.assign(PosOutSF = testset.WoodDeckSF + testset.OpenPorchSF + testset.ScreenPorch)\n",
    "testset = testset.assign(POSF_Q = testset.PosOutSF * testset.OverallQual.map(oqmap))\n",
    "testset = testset.assign(LogQ = testset.OverallQual.apply(np.log))\n",
    "\n",
    "testset = testset.assign(TotBR = testset.BsmtFullBath + testset.BsmtHalfBath * 0.5 + testset.FullBath + testset.HalfBath * 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we fill the missing LotFrontage values using the model established with the training set data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\theya\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:8: FutureWarning: in the future, boolean array-likes will be handled as a boolean array index\n",
      "C:\\Users\\theya\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:8: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n"
     ]
    }
   ],
   "source": [
    "contset = ['LotFrontage', 'LotArea', 'MasVnrArea', 'TotalBsmtSF', '1stFlrSF', '2ndFlrSF', 'FFSF_Q',\n",
    "           'LotArea_Q', 'GLA_Q', 'TotBR', 'Fireplaces', 'GarageCars', 'POSF_Q','LogQ']\n",
    "\n",
    "X = np.concatenate((np.ones(shape = (testset.shape[0], 1)), \n",
    "                    testset[contset[1:]].values.reshape(testset.shape[0], len(contset) - 1)), axis = 1)\n",
    "lotfrontage_predict = np.dot(X, lotfront_para.T)\n",
    "ind = testset.LotFrontage.isnull()\n",
    "testset.LotFrontage[ind] = lotfront_para[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "contset.remove('LotArea')\n",
    "contset.append('LogLotArea')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we use the model we established with the training set to estimate the sale prices for the houses in the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.concatenate((np.ones(shape = (testset.shape[0], 1)), \n",
    "                    testset[contset].values.reshape(testset.shape[0], len(contset))), axis = 1)\n",
    "test_SalePrice = np.dot(X, w[0].T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "testset = testset.assign(SalePrice = test_SalePrice)\n",
    "testset.to_csv('houseprice_v1.csv', columns = ['SalePrice'], index = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After submitting the results we got a mean squat root error for the logarithmic of the sales price of 0.175."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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