005-Linear-Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression  \n",
    "supervised learning: simple linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEDCAYAAAA4FgP0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X9UVHX+P/DnyDDySwWUwaA011ol1A1cW5W0RIyNjoVu\nBhGonU5bW2aav5BTwedDgr++mh7dULC2dD07Lmuute7ClnqOWwid0Y+GZzb88T18aDQYEgyC+Sg0\nnz/8MDLMLwbm3jt37vPxF3N/zH29c3de977f7/t6qywWiwVERKRYQ6QOgIiIpMVEQESkcEwEREQK\nx0RARKRwTARERArHREBEpHBqqQPwlF6vlzoEIiJZmjp1qsPtsksEgPPG9DAYDIiLixMpGt/D9rP9\nbD/b35erm2hBE8HmzZuh1+vR1dWFl156CZMnT8batWvR3d2NqKgobNmyBRqNxuacoqIinDt3DiqV\nCnl5eZgyZYqQIRIRKZ5gieD06dO4ePEidDodWlpasGDBAsyYMQNZWVl4/PHHsW3bNpSXlyMrK8t6\nTk1NDerr66HT6XD58mXk5eVBp9MJFSIREUHAweJp06Zhx44dAIDhw4ejs7MT1dXVmDt3LgBgzpw5\nqKqqsjmnqqoKKSkpAIDx48fjxo0baG9vFypEIiKCgE8EAQEBCAkJAQCUl5dj9uzZ+Ne//mXtCho5\nciRMJpPNOc3NzYiPj7d+joyMhMlkQlhYmM1xBoPB5bXNZrPbY/wZ28/2s/1svycEHyz+7LPPUF5e\njvfffx+PPfaYdXt/at05O8bdQBAHi9h+tp/tVyqfGyw+deoUSkpKUFZWhmHDhiEkJARmsxlBQUFo\nbGyEVqu1OV6r1aK5udn6uampCVFRUUKGSETkE46cNWJLxTe42tqJmPBgrEmdgPSEWFGuLdgYQVtb\nGzZv3ow9e/YgPDwcADBz5kxUVFQAACorKzFr1iybc5KSkqz7L1y4AK1Wa9ctRETkb46cNWL94a9h\nbO2EBYCxtRPrD3+NI2eNolxfsCeCY8eOoaWlBStWrLBu27hxI958803odDrExMQgPT0dALBy5UoU\nFxcjMTER8fHxyMzMhEqlQn5+vlDhERH5jC0V36DzVrfNts5b3dhS8Y0oTwWCJYKMjAxkZGTYbf/g\ngw/stm3fvt369+rVq4UKiYjIJ11t7fRou7ex1hARkcRiwoM92u5tTARERBJbkzoBwYEBNtuCAwOw\nJnWCKNeXZa0hIiJ/0jMOINWsISYCIiIfkJ4QK9oPf1/sGiIiUjgmAiIihWMiICJSOCYCIiKFYyIg\nIlI4zhoiIvIBUhadYyIgIpJYT9G5nnpDPUXnAMi71hAREfWPu6JzQj8tMBEQEUnMVdE5MZ4WOFhM\nRCQxV0XnXD0teAsTARGRxFwVnROjRLWgXUN1dXV45ZVXsHTpUmRnZ2P58uVoaWkBALS2tuLBBx9E\nYWGh9fjDhw9jx44dGDNmDIDbK5r97ne/EzJEIiLJuSo6t6XiGxgd/Oh7s0S1YImgo6MDhYWFmDFj\nhnXbzp07rX+vX78eixYtsjsvLS0N69atEyosIiKf5Kzo3JrUCTZjBID3S1QL1jWk0WhQWlpqt0A9\nAFy5cgVtbW2YMmWKUJcnIhq0I2eNSNp4HONy/4akjcdFW0O4t/SEWBQvnIzY8GCoAMSGB6N44WR5\nzBpSq9VQqx1//UcffYTs7GyH+2pqavDCCy+gq6sL69atwwMPPCBUiERETkk9t783oUtUiz599ObN\nm9Dr9SgoKLDb94tf/AKRkZF49NFHcfbsWaxbtw6ffPKJ3XEGg8HlNcxms9tj/Bnbz/az/YNvf9Gn\n/+1wtk7Rp7WYEPTDoL9fKANpv+iJ4KuvvnLaJTR+/HiMHz8eAJCQkIDr16+ju7sbAQG2o+lxcXEu\nr2EwGNwe48/Yfraf7R98+00/XnGyvcun//s6a79er3d6jujTR7/++mtMnDjR4b7S0lJ8+umnAG7P\nOIqMjLRLAkREYpB6QXkxCZYIamtrkZOTg48//hgfffQRcnJy0NraCpPJhJEjR9oc2zNFdP78+dDp\ndMjOzsbbb7+NDRs2CBUeEZFLUi8oLybBuoYmTZqE/fv3221/66237La99957AIDRo0c7PIeISGxS\nLygvJtYaIiJyYqCzdaQsKT0QTARERF7kS9NO+4u1hoiIvEiMInHexkRARORFYhSJ8zYmAiIiL5Lj\ntFMmAiIiL5LjtFMOFhORLLmamSPlrB05TjtlIiAi2XE1M8d4tQ27TtdLOmtH6CJx3sauISKSHVcz\ncz480yK7WTtS4xMBEcnOQGbm+PKsHWfE6uLiEwERyY6rmTlRoY7vb3151o4jPd1fxtZOWHCni0uI\nxXGYCIhIdlzNzFmSGCG7WTuOiPliGruGiEh2XM3MMQT9gNiYWFnN2nFEzBfTmAiISJZczcyR26wd\nR2LCg2F08KMvRBcXu4aIiHyQmC+mCZoI6urqkJKSggMHDgAAcnNzMX/+fOTk5CAnJwcnT560O6eo\nqAgZGRnIzMzE+fPnhQyPiMhnpSfEonjhZMSGB0MFIDY8GMULJwvypCNY11BHRwcKCwsxY8YMm+1v\nvPEG5syZ4/Ccmpoa1NfXQ6fT4fLly8jLy4NOpxMqRCJSKLmsFyBWF5dgTwQajQalpaXQarX9Pqeq\nqgopKSkAbi9kf+PGDbS3twsVIhEpkJjTMuVCsESgVqsRFBRkt/3AgQNYvHgxVq5cievXr9vsa25u\nRkREhPVzZGQkTCaTUCESkQLJcb0AoYk6a+ipp55CeHg44uLisHfvXuzatQtvv/220+MtFovD7QaD\nweV1zGaz22P8GdvP9rP9ztvvalqmP/x3G8i/v6iJoPd4QXJyMgoKCmz2a7VaNDc3Wz83NTUhKirK\n7nvi4uJcXsdgMLg9xp+x/Ww/2++8/THh15xOy/SH/27O2q/X652eI+r00ddeew0NDQ0AgOrqatx/\n//02+5OSklBRUQEAuHDhArRaLcLCwsQMkYj8nBzXCxCaYE8EtbW12LRpE4xGI9RqNSoqKpCdnY0V\nK1YgODgYISEhKC4uBgCsXLkSxcXFSExMRHx8PDIzM6FSqZCfny9UeESkUHJcL0BogiWCSZMmYf/+\n/XbbU1NT7bZt377d+vfq1auFComICIB/vHnsTXyzmIhI4ZgIiIgUjomAiEjhmAiIiBSOiYCISOGY\nCIiIFI6JgIhI4bhCGRGJSi4loJWEiYCIRNNTArqn+mdPCWgATAYSYtcQEYmGJaB9ExMBEYnGVQlo\nkg4TARGJJiY82KPtJA4mAiISDUtA+yYOFhORaFgC2jcxERCRxwYzBZQloH0PEwEReYRTQP2PoGME\ndXV1SElJwYEDBwAA165dw9KlS5GdnY2lS5fCZDLZHF9dXY3p06cjJycHOTk5KCwsFDI8IhoATgH1\nP4I9EXR0dKCwsNBmwfp3330XzzzzDNLS0vDHP/4RH3zwAdauXWtz3kMPPYSdO3cKFRYRDRKngPof\nwZ4INBoNSktLodVqrdvy8/OtS1VGRESgtbVVqMsTkUA4BdT/CJYI1Go1goKCbLaFhIQgICAA3d3d\nOHjwIObPn2933qVLl/Dyyy/j2WefxRdffCFUeEQ0QJwC6n9EHyzu7u7G2rVrMX36dJtuIwC49957\nsWzZMjz++ONoaGjA4sWLUVlZCY1GY3OcwWBweQ2z2ez2GH/G9rP9QrZ/QhCwbHokPjzTAtOPXYgK\nVWNJYgQmBP0Ag+EHwa7bX/z397z9oieC9evXY+zYsVi2bJndvujoaKSlpQEAxowZg1GjRqGxsRH3\n3HOPzXFxcXEur2EwGNwe48/YfrZf6PbHxQGvPiHoJQaM//6O26/X652eI+qbxUePHkVgYCCWL1/u\ndP++ffsAACaTCd9//z2io6PFDJGISHEEeyKora3Fpk2bYDQaoVarUVFRge+//x5Dhw5FTk4OAGD8\n+PEoKCjAypUrUVxcjOTkZKxevRqff/45bt26hYKCArtuISIi8i7BEsGkSZOwf//+fh27fft2698l\nJSVChUREHuACMsrBN4uJyA7fHlYWJgIiPzTYu3lXbw8zEfgfJgIiP3P8Sht2na4f1N38YN8eZreS\nvHA9AiI/cuSsEf/vX6ZB1wIazNvDPd1KxtZOWHAnER05a+z39UlcfCIgkrmeu29jaydUACxOjvOk\nFtCa1Ak2YwRA/98eZreS/DAREMlY30FdZ0kA8KwW0GAWkGFROvlhIiCSMUd3344MpBbQQBeQiQkP\nhtHBjz6L0vkujhEQyVh/7rIDVCoUL5wsWrcMi9LJDxMBkYy5u8tWAei2WLCl4hvRBmvTE2JRvHAy\nYsODoQIQGx4saiIiz7FriEjGHA3q9tYzZiD2C2Fcl1he+ERAJGM9d98RIYFuj+VykuQMEwGRzKUn\nxCJE07+He87cIUeYCIj8QH9/4DlzhxzhGAGRgMQqteBsymZvnLlDzvCJgEggYpZacDRlM3CIChEh\ngZy5Q24J+kRQV1eHV155BUuXLkV2djauXbuGtWvXoru7G1FRUdiyZYvdwjNFRUU4d+4cVCoV8vLy\nMGXKFCFDJBKMmKUWBvMmMJFgTwQdHR0oLCy0WaB+586dyMrKwsGDBzF27FiUl5fbnFNTU4P6+nro\ndDps2LABGzZsECo8IsGJXWohPSEWX+Qm49iSn+GL3GQmAeo3wRKBRqNBaWkptFqtdVt1dTXmzp0L\nAJgzZw6qqqpszqmqqkJKSgqA28tY3rhxA+3t7UKFSCSowVTwJBKTYIlArVYjKCjIZltnZ6e1K2jk\nyJEwmUw2+5ubmxEREWH9HBkZaXcMkVw46rcHgI6bXSzJTD5FsllDFourOomujzEYDC7PM5vNbo/x\nZ2y/b7R/QhCwbHokSqqb0Xbzzv+WWzpuYV35ORivGpH8s2Fev66vtF8qbL/n7Rc1EYSEhMBsNiMo\nKAiNjY023UYAoNVq0dzcbP3c1NSEqKgou++Ji4tzeR2DweD2GH/G9vtO++PigINfH0fbTdtxgf/p\ntuDg1+149YmHvH5NX2q/FNh+x+3X6/VOzxF1+ujMmTNRUVEBAKisrMSsWbNs9iclJVn3X7hwAVqt\nFmFhYWKGSOR1rM9Pvk6wJ4La2lps2rQJRqMRarUaFRUV2Lp1K3Jzc6HT6RATE4P09HQAwMqVK1Fc\nXIzExETEx8cjMzMTKpUK+fn5QoVHJJr+1OfnGr8kJbeJYOHChZg/fz6eeOIJu64cVyZNmoT9+/fb\nbf/ggw/stm3fvt369+rVq/t9DSJf4eqH3N2yj31XGRO7UiiR266h9957D0OHDsWbb76JF198EeXl\n5ZzSSdSLuzeIHVUIHaq+8389Vy+eEYnBbSKIjo5GVlYW9u7di+XLl0On02Hu3LlYv349mpqaxIiR\nyKf194fcfOsn69+tnbesyYJjCCQ1t11DDQ0NOHbsGP75z39i9OjRePHFFzFnzhzo9XosX74cf/rT\nn8SIk0g0nvbX9+eH3FWy4Bq/JDW3iWDVqlV46qmnUFZWhvDwcOv26dOnIykpSdDgiMQ2kP76/vyQ\nu0oW2zMedDmGQCQ0t11Dhw4dwnPPPWeTBHq89tprggRFJJWB9Nf3Z7F2V+UmuMYvSY3rERD1MpD+\n+v5U/nQ3c4hr/JKUmAiIehlof727H3KWiSZfxkRA1Iu7O/fB4F0/+SomAqJeeOdOSsREQNQH79xJ\nabhmMRGRwjEREBEpHLuGSHFY6ZPIFhMBKQorfRLZY9cQKQorfRLZYyIgRWGlTyJ7onYN/fnPf8bR\no0etn2tra3H27Fnr5/j4eCQmJlo//+EPf0BAgG0NF6LBYKVPInuiJoJFixZh0aJFAICamhr8/e9/\nt9kfFhbmcFUzIm8R8s1hIrmSbLB49+7d2Lp1q1SXJ4Xim8NE9lQWi8Ui9kXPnz+PgwcPYuPGjTbb\nExISkJycDKPRiNTUVDz//PN25+r1eoSEhLj8frPZjKCgIK/GLCf+2v7jV9rw4ZkWmH7sQlSoGksS\nI5D8s2F2x/lr+/uL7Wf7HbW/o6MDU6dOdXiOJE8E5eXlWLBggd32tWvX4sknn4RKpUJ2djZ++ctf\nYvLkyXbHxcXFufx+g8Hg9hh/5o/tP3LWiF2n661dOk0/dmHX6euIjbEvB+GP7fcE28/2O2q/Xq93\neo4ks4aqq6uRkJBgt/3ZZ59FaGgoQkJCMH36dNTV1UkQHfkiTvskEo7oiaCxsRGhoaHQaDQ2269c\nuYJVq1bBYrGgq6sLZ86cwf333y92eOSjOO2TSDiidw2ZTCZERkZaP+/duxfTpk1DQkICRo8ejaef\nfhpDhgxBcnIypkyZInZ45KM47ZNIOKIngkmTJqGsrMz6+be//a317zVr1ogdDskEp30SCYe1hkgW\nOO2TSDhMBCQbXDCGSBisNUREpHBMBERECseuIRIMF4AhkgcmAhIEF4Ahkg92DZEg+CYwkXwwEZAg\n+CYwkXywa4gGxdk4gFzeBOY4BhGfCGgQesYBjK2dsODOOMCRs0asSZ2A4EDb1eV87U1gV/ETKQkT\nAQ2Yq3GA9IRYFC+cjNjwYKgAxIYHo3jhZJ+62+Y4BtFt7BqiAXM3DuDrbwJzHIPoNj4R0IA56+/3\ntXEAZ+QeP5G3MBHQgMlhHMAVucdP5C3sGqIBc1YRFACSNh73ykwcIWf1sKIp0W2iJoLq6mq8/vrr\n1pXHfv7zn+Ott96y7v/yyy+xbds2BAQEYPbs2Xj11VfFDI8GoO84gDffKBbj7WRfH8cgEoPoTwQP\nPfQQdu7c6XDfO++8g3379iE6OhrZ2dlITU3FfffdJ3KENBjuZhJJ9V1E5JzPjBE0NDRgxIgRuOuu\nuzBkyBA88sgjqKqqkjos8pA3Z+JwVg+ROERPBJcuXcLLL7+MZ599Fl988YV1e9+1jCMjI2EymcQO\njwbJmzNxOKuHSByidg3de++9WLZsGR5//HE0NDRg8eLFqKyshEaj8eh7DAaDy/1ms9ntMf5MyvZn\nTQ7Dzi/N+J9ui3Xb0AAVsiaHeRzTQL+L//5sP9vvWftFTQTR0dFIS0sDAIwZMwajRo1CY2Mj7rnn\nHmi1WjQ3N1uPbWxshFardfg9cXFxLq9jMBjcHuPPpGx/XBwQG+OdmT4D/S7++7P9bL99+/V6vdNz\nRE0ER48ehclkwgsvvACTyYTvv/8e0dHRAIC7774b7e3t+PbbbzF69GicOHECW7duFTM88hJvzsTh\nrB4i4YmaCJKTk7F69Wp8/vnnuHXrFgoKCvDpp59i2LBhmDdvHgoKCrBq1SoAQFpaGsaNGydmeERE\niiRqIggLC0NJSYnT/dOmTYNOpxMxIhICSzsTyQvfLCav4hKVRPLjM+8RkH9gaWci+eETgUzIpbuF\nL4ERyQ8TgQwMtLtFiuQhlyUqiegOJgIZGEjNHTH76nsnnPCQQAQOUeHWT3deAmNpZyLfxjECGXDW\nrWJs7cS9uX9Dwn9W2q2zK1Zffd91f1s6bgEqIDw40GeXqCQiW3wikAFn3S09WjpuYU35OQB37vbF\n6qt3lHBudVsQOlSN/8p/zKvXIiJh8IlABhytpNXXrW6Lzd3+YAu2HTlrRNLG4xiX+zckbTxu98TR\ng4PDRPLHRCAD6QmxKF44GbFufsR7//gOZhnGvt09PeMLjpIBK4QSyR8TgUykJ8Tii9xkl8mg949v\n7+ThaV+9J+MLXPeXSP44RiAza1In4A3df+EnB/vmTIyy+TzQgm2edPdw3V8i+WMikJn0hFj8xycX\nbs/O6ePEv72zkI+n7wKwQiiRvLFrSIZaHSQB4HZfftLG40j78IrLAV532N1DpCxMBDLk7M5cBfRr\ngNedwYwvEJH8sGtIhtakTrB5axi4nQQsfY5z9/axK+zuIVIO0RPB5s2bodfr0dXVhZdeegmPPXbn\npaPk5GSMHj0aAQG3uyW2bt1qXcGM7nA0QOvshTPO5ycid0RNBKdPn8bFixeh0+nQ0tKCBQsW2CQC\nACgtLUVoaKiYYclS3zv2pI3HWeyNiAZE1DGCadOmYceOHQCA4cOHo7OzE93d3W7Oov7gAC8RDZSo\nTwQBAQEICQkBAJSXl2P27NnWbqAe+fn5MBqNmDp1KlatWgWVSiVmiLLF+fxENFAqi8XSd4xRcJ99\n9hn27NmD999/H8OGDbNuP3LkCGbNmoURI0bg1VdfxYIFC/DrX//a5ly9Xm9NJs6YzWYEBQUJErsc\nsP1sP9vP9vfV0dGBqVOnOjxH9MHiU6dOoaSkBGVlZTZJAADS09Otf8+ePRt1dXV2iQAA4uLiXF7D\nYDC4Pcafsf1sP9vP9vel1+udniPqGEFbWxs2b96MPXv2IDw83G7fCy+8gJs3bwIAvvrqK9x///1i\nhkdEpEiiPhEcO3YMLS0tWLFihXXbr371K0yYMAHz5s3D7NmzkZGRgaFDh+KBBx5w+DRARETeJWoi\nyMjIQEZGhtP9S5YswZIlS0SMiIiIWGKCiEjhWGJCYr0XfueUTyKSAhOBhHpWAuupGdRTKA4AkwER\niYaJQELOVgL7j08u8CmBiETDRCASR11AzgrCtXTcsi48w6cEIhKaYhOBmH3zzrqARgQHorXT8SIz\nvQ2mnDQRkTuKTARi98076wIKChyC4MAAu32OsJw0EQlFkdNHnf0wb6n4RpDrOfsRb+24ZbcSWHhw\noMNjWU6aiISiyCcCZz/MQt11u1oMvu+6An2fVgCWkyYiYSnyicDZ3bVQd92erBXA9YKJSGyKTARC\nLOJy5KwRSRuPY1zu35C08bjNovH8cSciX6bIriFvL+LSn8Hn/i4Gz5fMiEhsikwEQP9/mPvD1eCz\np9fw5ncREfWHIruGvM2bg89iD2QTESn2iaC/+vPimatZQZ7y5ncREfUHnwhc6OmvN7Z2woI7/fW9\nB4IB7w4+CzGQTUTkiuiJoKioCBkZGcjMzMT58+dt9n355Zd4+umnkZGRgd27d4sdmp3+vnjmzVlB\nnGFERGITtWuopqYG9fX10Ol0uHz5MvLy8qDT6az733nnHezbtw/R0dHIzs5Gamoq7rvvPjFDtOFJ\nf703B5+9+V1ERO6I+kRQVVWFlJQUAMD48eNx48YNtLe3AwAaGhowYsQI3HXXXRgyZAgeeeQRVFVV\niRmeHbFfPCMikoKoTwTNzc2Ij4+3fo6MjITJZEJYWBhMJhMiIyNt9jU0NDj8HoPB4PI6ZrPZ7pjj\nV9rw4ZkWmH7sQlSoGksSI5D8s2FOv+P4lTb80GG22z40QIWsyWFuY5CSo/YrCdvP9rP9nrVf0llD\nFotlQOfFxcW53G8wGGyOOXLWiF2n6639/U0/dmHX6euIjXHcBXPneNv4IkICkT8/3ue7bfq2X2nY\nfraf7bdvv16vd3qOqF1DWq0Wzc3N1s9NTU2IiopyuK+xsRFardYr1/W02qij4wEgRKP2+SRAROQp\nURNBUlISKioqAAAXLlyAVqtFWFgYAODuu+9Ge3s7vv32W3R1deHEiRNISkryynU9fUmLL3URkZKI\n2jWUmJiI+Ph4ZGZmQqVSIT8/H4cPH8awYcMwb948FBQUYNWqVQCAtLQ0jBs3zivX7c9LWr1fHBui\nUqHbQbcVB4mJyB+JPkawevVqm88TJ060/j1t2jSb6aTesiZ1gssa/30LvTlKAnypi4j8lSJKTLir\nNupsTCBApcJPFovgaxoTEUlJEYkAcP2SlrO+/58sFvz/jU8IGRYRkeRYawh8cYyIlI2JACz0RkTK\nppiuIVe8vWIZEZGcMBH8HxZ6IyKlYtcQEZHCMREQESkcEwERkcIxERARKRwTARGRwqksA10UQCKu\namoTEZFzU6dOdbhddomAiIi8i11DREQKx0RARKRwfpcIioqKkJGRgczMTJw/f17qcES3efNmZGRk\n4De/+Q0qKyulDkcSZrMZKSkpOHz4sNShiO7o0aN48sknsXDhQpw8eVLqcET1448/YtmyZcjJyUFm\nZiZOnToldUiiqKurQ0pKCg4cOAAAuHbtGnJycpCVlYXXX38dN2/edPsdfpUIampqUF9fD51Ohw0b\nNmDDhg1ShySq06dP4+LFi9DpdCgrK0NRUZHUIUnivffew4gRI6QOQ3QtLS3YvXs3Dh48iJKSEnz+\n+edShySqjz/+GOPGjcP+/fuxY8cORfz/v6OjA4WFhZgxY4Z1286dO5GVlYWDBw9i7NixKC8vd/s9\nfpUIqqqqkJKSAgAYP348bty4gfb2domjEs+0adOwY8cOAMDw4cPR2dmJ7m77BXf82eXLl3Hp0iU8\n+uijUociuqqqKsyYMQNhYWHQarUoLCyUOiRRRUREoLW1FQDwww8/ICIiQuKIhKfRaFBaWgqtVmvd\nVl1djblz5wIA5syZg6qqKrff41eJoLm52eYfPzIyEiaTScKIxBUQEICQkBAAQHl5OWbPno2AgAA3\nZ/mXTZs2ITc3V+owJPHtt9/CbDbj5ZdfRlZWVr9+APzJE088gatXr2LevHnIzs7GunXrpA5JcGq1\nGkFBQTbbOjs7odFoAAAjR47s12+gX1cfVerM2M8++wzl5eV4//33pQ5FVEeOHMGDDz6Ie+65R+pQ\nJNPa2opdu3bh6tWrWLx4MU6cOAGVSiV1WKL461//ipiYGOzbtw///ve/kZeXp8hxot76+xvoV4lA\nq9WiubnZ+rmpqQlRUVESRiS+U6dOoaSkBGVlZRg2bJjU4Yjq5MmTaGhowMmTJ/Hdd99Bo9Fg9OjR\nmDlzptShiWLkyJFISEiAWq3GmDFjEBoaiuvXr2PkyJFShyaKM2fO4OGHHwYATJw4EU1NTeju7lbc\nU3FISAjMZjOCgoLQ2Nho023kjF91DSUlJaGiogIAcOHCBWi1WoSFhUkclXja2tqwefNm7NmzB+Hh\n4VKHI7p3330Xf/nLX3Do0CEsWrQIr7zyimKSAAA8/PDDOH36NH766Se0tLSgo6NDEf3kPcaOHYtz\n584BAIxGI0JDQxWXBABg5syZ1t/ByspKzJo1y+05fvVEkJiYiPj4eGRmZkKlUiE/P1/qkER17Ngx\ntLS0YMVdZishAAABZElEQVSKFdZtmzZtQkxMjIRRkViio6ORmpqKZ555BgDw5ptvYsgQv7rXcykj\nIwN5eXnIzs5GV1cXCgoKpA5JcLW1tdi0aROMRiPUajUqKiqwdetW5ObmQqfTISYmBunp6W6/hyUm\niIgUTjm3C0RE5BATARGRwjEREBEpHBMBEZHCMREQESkcEwERkcIxERARKRwTAdEg7d69G/v27QMA\n/P73v8fevXsljojIM0wERIP04osv4h//+Ae++eYbnDx5Es8//7zUIRF5xK9KTBBJQaPR4I033sBz\nzz2HkpISBAYGSh0SkUf4REDkBSaTCcOHD8d3330ndShEHmMiIBqktrY2fPjhhzh06BDKysrQ1tYm\ndUhEHmEiIBqkbdu24fnnn8eoUaOQnZ2Nbdu2SR0SkUdYfZSISOH4REBEpHBMBERECsdEQESkcEwE\nREQKx0RARKRwTARERArHREBEpHBMBERECve/fLl1caHzwOcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f74968f0710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "\n",
    "# create random data\n",
    "rng = np.random.RandomState(42)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 1 + rng.randn(50)\n",
    "\n",
    "plt.scatter(x,y)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## choose a class of model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## choose model hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)\n"
     ]
    }
   ],
   "source": [
    "model = LinearRegression(fit_intercept=True)\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## arrange data into a features matrix and target vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 1)\n"
     ]
    }
   ],
   "source": [
    "X = x[:, np.newaxis]\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.74540119]\n",
      " [ 9.50714306]\n",
      " [ 7.31993942]\n",
      " [ 5.98658484]\n",
      " [ 1.5601864 ]\n",
      " [ 1.5599452 ]\n",
      " [ 0.58083612]\n",
      " [ 8.66176146]\n",
      " [ 6.01115012]\n",
      " [ 7.08072578]]\n"
     ]
    }
   ],
   "source": [
    "print X[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## fit the model to your data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__abstractmethods__',\n",
       " '__class__',\n",
       " '__delattr__',\n",
       " '__dict__',\n",
       " '__doc__',\n",
       " '__format__',\n",
       " '__getattribute__',\n",
       " '__getstate__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__module__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__setattr__',\n",
       " '__setstate__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " '__weakref__',\n",
       " '_abc_cache',\n",
       " '_abc_negative_cache',\n",
       " '_abc_negative_cache_version',\n",
       " '_abc_registry',\n",
       " '_decision_function',\n",
       " '_estimator_type',\n",
       " '_get_param_names',\n",
       " '_preprocess_data',\n",
       " '_residues',\n",
       " '_set_intercept',\n",
       " 'coef_',\n",
       " 'copy_X',\n",
       " 'decision_function',\n",
       " 'fit',\n",
       " 'fit_intercept',\n",
       " 'get_params',\n",
       " 'intercept_',\n",
       " 'n_jobs',\n",
       " 'normalize',\n",
       " 'predict',\n",
       " 'rank_',\n",
       " 'residues_',\n",
       " 'score',\n",
       " 'set_params',\n",
       " 'singular_']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## hyperparameters\n",
    "\n",
    "These two parameters represent the __slope__ and __intercept__ of the simple linear fit to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.9776566])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.90331072553111458"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## predit labels for unknown data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xfit = np.linspace(-1, 11)\n",
    "\n",
    "# Xfit = unknown data\n",
    "Xfit = xfit[:, np.newaxis]\n",
    "yfit = model.predict(Xfit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 1)\n",
      "[[-1.        ]\n",
      " [-0.75510204]\n",
      " [-0.51020408]\n",
      " [-0.26530612]\n",
      " [-0.02040816]\n",
      " [ 0.2244898 ]\n",
      " [ 0.46938776]\n",
      " [ 0.71428571]\n",
      " [ 0.95918367]\n",
      " [ 1.20408163]]\n"
     ]
    }
   ],
   "source": [
    "print(Xfit.shape)\n",
    "print(Xfit[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD1CAYAAACWXdT/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEWBYExGJwP8DjNntkYItc+0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f747cff6910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Diabetes dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the diabetes dataset\n",
    "diabetes = datasets.load_diabetes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('shape of the dataset', (442, 10))\n"
     ]
    }
   ],
   "source": [
    "print(\"shape of the dataset\", diabetes.data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.03807591,  0.05068012,  0.06169621,  0.02187235, -0.0442235 ],\n",
       "       [-0.00188202, -0.04464164, -0.05147406, -0.02632783, -0.00844872],\n",
       "       [ 0.08529891,  0.05068012,  0.04445121, -0.00567061, -0.04559945],\n",
       "       [-0.08906294, -0.04464164, -0.01159501, -0.03665645,  0.01219057],\n",
       "       [ 0.00538306, -0.04464164, -0.03638469,  0.02187235,  0.00393485]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diabetes.data[0:5,0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Use only one feature\n",
    "diabetes_X = diabetes.data[:, np.newaxis, 2]  # coloumn 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.06169621],\n",
       "       [-0.05147406],\n",
       "       [ 0.04445121],\n",
       "       [-0.01159501],\n",
       "       [-0.03638469],\n",
       "       [-0.04069594],\n",
       "       [-0.04716281],\n",
       "       [-0.00189471],\n",
       "       [ 0.06169621],\n",
       "       [ 0.03906215]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diabetes_X[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Split the data into training/testing sets\n",
    "diabetes_X_train = diabetes_X[:-20]\n",
    "diabetes_X_test = diabetes_X[-20:]\n",
    "\n",
    "# Split the targets into training/testing sets\n",
    "diabetes_y_train = diabetes.target[:-20]\n",
    "diabetes_y_test = diabetes.target[-20:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create linear regression object\n",
    "regr = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the model using the training sets\n",
    "regr.fit(diabetes_X_train, diabetes_y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Make predictions using the testing set\n",
    "diabetes_y_pred = regr.predict(diabetes_X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAD1CAYAAACiJBXjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f747bfe6190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot outputs\n",
    "plt.scatter(diabetes_X_test, diabetes_y_test,  color='black')\n",
    "plt.plot(diabetes_X_test, diabetes_y_pred, color='blue', linewidth=2)\n",
    "plt.legend(['Predicted line', 'Observed data'])\n",
    "\n",
    "#plt.xticks(())\n",
    "#plt.yticks(())\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD1CAYAAABN5n7dAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wOeqA0KvZDTWwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7479cf8650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "colors = rng.rand(20)\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.scatter(diabetes_X_test, diabetes_y_test,  c=colors, s=40, alpha=0.6, cmap='viridis')\n",
    "plt.plot(diabetes_X_test, diabetes_y_pred, color='blue', linewidth=1)\n",
    "plt.legend(['Predicted line', 'Observed data'], frameon=True, loc='upper left')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAD1CAYAAACm0cXeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTgghJux/Ia4YIbAR2TgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7479cf8e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(diabetes_y_test, '--r')\n",
    "plt.plot(diabetes_y_pred, '-b', linewidth=1)\n",
    "plt.legend(['Predicted output', 'Observed data'], frameon=True, loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 233.,   91.,  111.,  152.,  120.,   67.,  310.,   94.,  183.,   66.])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diabetes_y_test[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Coefficients: \\n', array([ 938.23786125]))\n",
      "Mean squared error: 2548.07\n",
      "Variance score: 0.47\n"
     ]
    }
   ],
   "source": [
    "# The coefficients\n",
    "print('Coefficients: \\n', regr.coef_)\n",
    "# The mean squared error\n",
    "print(\"Mean squared error: %.2f\"\n",
    "      % mean_squared_error(diabetes_y_test, diabetes_y_pred))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Variance score: %.2f' % r2_score(diabetes_y_test, diabetes_y_pred))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}