Only frequency regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "from sklearn import linear_model\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AGE</th>\n",
       "      <th>SEX</th>\n",
       "      <th>MEDIC_PROB</th>\n",
       "      <th>INJURY_SURGERY</th>\n",
       "      <th>DRUG_HISTORY</th>\n",
       "      <th>AVG</th>\n",
       "      <th>CATEGORY</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.125000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.616764</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.142857</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.371342</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.142857</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.736266</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.160714</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.726260</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        AGE  SEX  MEDIC_PROB  INJURY_SURGERY  DRUG_HISTORY       AVG  CATEGORY\n",
       "0  0.000000  0.0         0.0             0.0           0.0  1.000000       0.0\n",
       "1  0.125000  1.0         0.0             0.0           0.0  0.616764       1.0\n",
       "2  0.142857  0.0         0.0             0.0           0.0  0.371342       1.0\n",
       "3  0.142857  1.0         0.0             0.0           0.0  0.736266       0.0\n",
       "4  0.160714  1.0         0.0             0.0           0.0  0.726260       1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the pre-processed data.\n",
    "with open('data_processed_scaled.pickle', 'rb') as f:\n",
    "    data = pickle.load(f)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AGE</th>\n",
       "      <th>AVG</th>\n",
       "      <th>CATEGORY</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.125000</td>\n",
       "      <td>0.616764</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.142857</td>\n",
       "      <td>0.371342</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.142857</td>\n",
       "      <td>0.736266</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.160714</td>\n",
       "      <td>0.726260</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        AGE       AVG  CATEGORY\n",
       "0  0.000000  1.000000       0.0\n",
       "1  0.125000  0.616764       1.0\n",
       "2  0.142857  0.371342       1.0\n",
       "3  0.142857  0.736266       0.0\n",
       "4  0.160714  0.726260       1.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# drop all other columns except age and avg\n",
    "data.drop(['SEX', 'MEDIC_PROB', 'INJURY_SURGERY', 'DRUG_HISTORY'], axis=1, inplace=True)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# divide data into testing and training models\n",
    "from sklearn import model_selection\n",
    "X = data['AGE']\n",
    "Y = data['AVG']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# reshaping since our data has only one column, but the linear model expects a 2D array\n",
    "X = X.values.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# preprocessing the data to normalize results\n",
    "from sklearn import preprocessing\n",
    "X = preprocessing.MinMaxScaler().fit_transform(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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tJDaiZwce+8YkThnaLW7vKRIUhbskjeqaCH9ZupV7X36f0ooqLj6pH5OHdInLe2e2bsXp\nw7uT1kJTGiUcFO6SFF5fv4M7nl/Lxh0fc/Lgrtx6/khNQRQ5DIW7NAsbd+xlzltbqK45eJhl6+5y\nFufvYkDXtsz++kmcM6qHbhoSaYTCXQJXVFrB5Q+9w56Kajq2OXhmSkarFvxk6kiu+NwAMlpqWTqR\nWCjcJVBlFVVcNWcp5ftr+Pv1n2NEz8ygSxIJBYW7BGZ/dQ3ffHQ5m3fuY97VExXsInGkcJdARCLO\nj55ezeL8Xdx7yVg+p+mHInGlB4dJIO5+aT3Prizipi8O58vj+wZdjkjoKNylyf15yQf88fVNXDap\nP98+fUjQ5YiEkoZlpMm4O39bUcjP/pHLWSO6c/sFozWlUSRBFO7SJN4rKGPm83ks3bybE/t34neX\njadlmv7hKJIoCndJqO17Krn7xfU8s6KALm3TufPLY7gku5+CXSTBYgp3M5sC3AekAQ+5+68O0e4r\nwFPABHfPiVuVEriaiBPx2B/SdaA6wpy3NvOH1zdRVRNhxr8N5vozh5LZWo/PFWkKjYa7maUB9wPn\nAAXAMjOb7+559dp1AL4LvJOIQiU4b2/ayXXzcth3oOaIXztldE9unjqCAV3bJaAyETmUWM7cJwIb\n3T0fwMyeAKYBefXazQRmAT+Ia4USqKqaCD99Npcu7dP5Vna/I3rtxEFdmTgoPk9tFJEjE0u49wG2\n1dkuACbVbWBm44F+7r7AzBTuITLv7S1sKt7Hn67M5qyRPYIuR0RiFMtVrYbmqn06+GpmLYB7gRsb\nfSOzGWaWY2Y5xcXFsVcpgdixt5LfvLKBM4ZnKdhFkkws4V4A1P33eF+gqM52B2AM8LqZbQEmA/PN\nLLv+G7n7bHfPdvfsrKyso69amsTdi9azv7qGn54/KuhSROQIxRLuy4BhZjbIzNKB6cD8Tw66e5m7\nd3P3ge4+EFgCXKDZMslt5bZSnlpewDWfH6S1REWSUKPh7u7VwA3Ai8Ba4El3X2Nmt5vZBYkuUJpe\nJOL8/B+5ZHXI4DtnDgu6HBE5CjHNc3f3hcDCevt+doi2px97WRKkp1cUsKqgjHsuHkv7DN3nJpKM\ndJugfMaeyipmLVrHif07ceG4PkGXIyJHSadl8hm/fWUDu/Yd4OGrJtCihR7qJZKsdOYun8otLGPu\n21u4JLsfJ/TtFHQ5InIMdOYulJVX8dtXN/DI4i1ktmnFTV8cHnRJInKMFO4prLomwuNLt3LPy+9T\nWlHFxSf148YvHkfX9hlBlyYix0jhnqJeX7+DO59fy4YdHzN5cBduPW8UY/p0DLosEYkThXsKum3+\nGua+vYUBXdvywNdP4gujemhFJJGQUbinmBVbS5j79hamT+jHL6aNJqNlWtAliUgCaLZMColEnNvm\nr6F7hwxuPX+Ugl0kxBTuKeSp5dtYXVDGLVNH6s5TkZBTuKeIsooqZi1az0kDOjNtXO+gyxGRBNPp\nW4q475UN7C4/wLwLJuriqUgK0Jl7CtiwfS/zFm9h+oT+mu4okiIU7iHn7tz23BrapafpzlORFKJw\nD7kX12znrY27uPELw+nSLj3ockSkiSjcQ6yyqoY7ns9jRM8OXD6pf9DliEgT0gXVJFFZVcPbm3ZS\nVeONN456c0MxBSUVPH7dZFqm6fe4SCpRuDdz7s5zqz/krhfWUVhaccSvnzauNycP6ZqAykSkOVO4\nN2Pvbi1h5oI8VmwtZVSvTGZeOJoema1jfn0LM4b36JDACkWkuVK4N0NFpRXMWrSOZ1cWkdUhg1kX\nncBFJ/UlTSsjiUiMFO7NzNPLC7j12feIOFx/xhC+dfpQPSpARI6YUqMZeXXddn70zGomDuzCrK+c\nQL8ubYMuSUSSlMK9mVhdUMr1j73LyF4deOjKbNrpbF1EjoHmxzUD23aXc83cZXRpl87DV01QsIvI\nMVOKBKxk3wGunLOUqhrniRkT6N4h9tkwIiKHonAPUGVVDdc9kkNBSQV/vnYSQ7tr2qKIxIeGZQIS\niTj/+eRKcj4o4Z6LxzJxUJegSxKRENGZewBKyw8wc8FaFr73EbeeN5LzT9DiGSISXwr3JlRVE+Gx\nJR9w7ysb2FtZxXfOHMq1nx8UdFkiEkIK9ybg7ry+vpg7ns9jU/E+ThnalZ+eP4oRPTODLk1EQkrh\nnmAbtu9l5vNreeP9YgZ1a8dDV2Rz1sjuWupORBIqpnA3synAfUAa8JC7/6re8f8EvgFUA8XANe7+\nQZxrTTortpZw2YNLSE9rwU/PH8XXJw8gvaWuYYtI4jUa7maWBtwPnAMUAMvMbL6759Vp9i6Q7e7l\nZvYtYBZwSSIKThZbdu7jG/Ny6N6hNU9/62TNXxeRJhXLaeREYKO757v7AeAJYFrdBu7+mruXRzeX\nAH3jW2Zy2fXxfq6csxR3Z941ExXsItLkYgn3PsC2OtsF0X2Hci3wQkMHzGyGmeWYWU5xcXHsVSaR\nigM1XDsvh4/KKvnTVRMY1K1d0CWJSAqKJdwbuvLX4FpvZvY1IBu4u6Hj7j7b3bPdPTsrKyv2KpNE\nTcT57hPvsqqglPumj+fE/p2DLklEUlQsF1QLgH51tvsCRfUbmdnZwE+A09x9f3zKSx7uzi+eW8PL\nedu57UujmDKmZ9AliUgKiyXclwHDzGwQUAhMBy6r28DMxgMPAFPcfUfcq2wm3J2iskpqGlikev6q\nQh5Z/AEzTh3MVafoxiQRCVaj4e7u1WZ2A/AitVMhH3b3NWZ2O5Dj7vOpHYZpDzwVnb+91d0vSGDd\nTW51QSkzF+SxbEvJIducf0IvfjxlRBNWJSLSsJjmubv7QmBhvX0/q/Pz2XGuq9n4qKySWS+u428r\nCunWPp1bpo6ga7uMg9q1TU/jrJE9aKF1TkWkGdAdqodQcaCG2W/k8z//2kRNxPnmaUO4/owhdGjd\nKujSREQapXCvJxJx5q8q4q5F6/iwrJKpx/fkx1NG0r+r1jMVkeShcK9j+QclzFyQx8ptpYzpk8l9\n08frOesikpQU7kBBSTl3LVrPc6uK6N4hg19/dSz/Pr6Pxs9FJGmlRLhXVtVQcaDmoP1VNREeWfwB\nD76ZD8B3zxzKf5w2RAtUi0jSC3WKlR+o5oF/5fPAG5uorIocst2F43rzwykj6N2pTRNWJyKSOKEM\n90jEeXZlIbMWreejPZWcd3wvJgxs+FEA4/t3Zmy/Tk1coYhIYoUu3HO27GbmgjxWFZRxQt+O/O6y\n8UwYqIuiIpJaQhPulVU13PT0ap5bVUSPzAzuuXgsF47TRVERSU2hCfeX8rbz3KoivnnaEL571lDa\npoemayIiRyw0Cbh40y46ZLTkpi8OJ01n6yKS4kKzoOc7+buYOKiLgl1EhJCE+/Y9leTv3MfJQ7oG\nXYqISLMQinBfkr8LgMmDFe4iIhCicM9s3ZKRvTKDLkVEpFkISbjvZuKgrhpvFxGJSvpw/6isks07\n9zF5sG5UEhH5RNKHu8bbRUQOlvThvnjTLjq2acUojbeLiHwq6cN9yeba+e16zICIyP9J6nAvKq3g\ng13lGpIREaknqcP9k/H2kxXuIiKfkfTh3rFNK0b07BB0KSIizUqSh/tuJmm8XUTkIEkb7oWlFWzd\nXa7nyYiINCBpw33JJs1vFxE5lOQN9/xddG7biuE9NN4uIlJf0ob74vxdTBrUVePtIiINSMpw37a7\nnIKSCj1PRkTkEJIy3N/ZvBuAybqYKiLSoJjC3cymmNl6M9toZj9u4HiGmf01evwdMxsY70LrWrxp\nF13apXNcd423i4g0pNFwN7M04H7gXGAUcKmZjarX7FqgxN2HAvcCd8W70LqW5O/S/HYRkcOI5cx9\nIrDR3fPd/QDwBDCtXptpwLzoz08DZ5lZQpJ32+5yCksrNL9dROQwYgn3PsC2OtsF0X0NtnH3aqAM\nSEj6Ltbz20VEGhVLuDd0Bu5H0QYzm2FmOWaWU1xcHEt9B+nUphXnjOrBsO7tj+r1IiKpIJZwLwD6\n1dnuCxQdqo2ZtQQ6Arvrv5G7z3b3bHfPzsrKOqqCvzC6Jw9ekU2CRn1EREIhlnBfBgwzs0Fmlg5M\nB+bXazMfuDL681eAV939oDN3ERFpGi0ba+Du1WZ2A/AikAY87O5rzOx2IMfd5wN/Ah41s43UnrFP\nT2TRIiJyeI2GO4C7LwQW1tv3szo/VwJfjW9pIiJytJLyDlURETk8hbuISAgp3EVEQkjhLiISQgp3\nEZEQsqCmo5tZMfDBUb68G7AzjuUki1TtN6Ru39Xv1BJLvwe4e6N3gQYW7sfCzHLcPTvoOppaqvYb\nUrfv6ndqiWe/NSwjIhJCCncRkRBK1nCfHXQBAUnVfkPq9l39Ti1x63dSjrmLiMjhJeuZu4iIHEbS\nhXtji3WHhZk9bGY7zCy3zr4uZvaymW2I/tk5yBoTwcz6mdlrZrbWzNaY2fei+0PddzNrbWZLzWxV\ntN+/iO4fFF10fkN0Efr0oGtNBDNLM7N3zWxBdDv0/TazLWb2npmtNLOc6L64fc+TKtxjXKw7LOYC\nU+rt+zHwT3cfBvwzuh021cCN7j4SmAxcH/1/HPa+7wfOdPexwDhgiplNpnax+Xuj/S6hdjH6MPoe\nsLbOdqr0+wx3H1dn+mPcvudJFe7Etlh3KLj7Gxy8mlXdhcjnARc2aVFNwN0/dPcV0Z/3UvsXvg8h\n77vX+ji62Sr6nwNnUrvoPISw3wBm1hc4D3goum2kQL8PIW7f82QL91gW6w6zHu7+IdSGINA94HoS\nyswGAuOBd0iBvkeHJlYCO4CXgU1AaXTReQjv9/03wA+BSHS7K6nRbwdeMrPlZjYjui9u3/OYFuto\nRmJaiFuSn5m1B54Bvu/ue1JhzVx3rwHGmVkn4O/AyIaaNW1ViWVm5wM73H25mZ3+ye4Gmoaq31Gn\nuHuRmXUHXjazdfF882Q7c49lse4w225mvQCif+4IuJ6EMLNW1Ab7Y+7+t+julOg7gLuXAq9Te82h\nU3TReQjn9/0U4AIz20LtMOuZ1J7Jh73fuHtR9M8d1P4yn0gcv+fJFu6xLNYdZnUXIr8S+EeAtSRE\ndLz1T8Bad7+nzqFQ993MsqJn7JhZG+Bsaq83vEbtovMQwn67+83u3tfdB1L79/lVd7+ckPfbzNqZ\nWYdPfga+AOQSx+950t3EZGZTqf3N/sli3XcGXFJCmNnjwOnUPiVuO/Bz4FngSaA/sBX4qrvXv+ia\n1Mzs88CbwHv83xjsLdSOu4e272Z2ArUX0NKoPel60t1vN7PB1J7RdgHeBb7m7vuDqzRxosMyP3D3\n88Pe72j//h7dbAn8xd3vNLOuxOl7nnThLiIijUu2YRkREYmBwl1EJIQU7iIiIaRwFxEJIYW7iEgI\nKdxFREJI4S4iEkIKdxGREPr/z6CJAfQ2CSIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112adc9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot \n",
    "%matplotlib inline\n",
    "\n",
    "pyplot.plot(X)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(37, 1)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# splititng data into training and testing data\n",
    "X_train, X_test, Y_train, Y_test = model_selection.train_test_split(X,Y)\n",
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.845546092883\n"
     ]
    }
   ],
   "source": [
    "# importing and creating our regression model\n",
    "regression = linear_model.LinearRegression()\n",
    "# training our mdoel\n",
    "regression.fit(X_train, Y_train)\n",
    "# calculating our acccuracy on test data\n",
    "accuracy = regression.score(X_test,Y_test)\n",
    "\n",
    "print(accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10cfa3f98>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rlwznvSP/H3tt38dldCh8dILo+W8Fjmv2vC9QF6mMmeUBhcD2AOoWkThI5kRk\nW/r08buEX38dzj0X5t1TSP0DI8n910lwyNJin0OqCCL4LwcGmll/M+sCXAQsalFmEXBp6PHXgSUa\n7xdJXam+eezkk32+oBdfhJMH5bJx4WCOWHQBPy0ZyfhTU6ONqS6QTV5mdgFwB5ALPOCcu8XMfgVU\nOecWmdkRwCPAMHyP/6KmCeJItMlLRKLhHCxaBBUVsG4dnHkm3H67TyCXjaLd5KUdviKSEQ4cgAcf\nhBtvhLo6GDfOp5Ae0nLheYbTDl8RySp5efDtb8P69f4Eseefh6FDYepUqE2PPV8JpeAvIhmlWzef\nJG7DBrjqqsiJ47Kdgr+IZKRevWD2bKiu9ofIzJjhN4fNng179ya7dcmn4C8iGa1/f5g7F1auhLIy\nnzhu8GCfTO7QoWS3LnkU/EUkKwwbBosX++RxPXvClCkwfLhPJJeNFPxFJKuMGgVVVb7n39AAY8b4\nZHIrViS7ZYml4C8iWScnBy6+2O8LuOMOWLXKDwldfLE/XCYbKPiLSNbq2tUniduwwR8tWVnJYYnj\nMpmCv4hkvcJCuPlmqKmBb30L7r4bTjrJX9u9O9mtiw8FfxGRkD594L77Pkkc94tfwIAB/tqBA8lu\nXbAU/EVEWhg82CeOW7bMfwP47nfhlFP8tRTNiNNhCv4iIhGceSa88IKfCzDzm8VGjPDZRNOdgr+I\nSBvMYPx4WL0a7r8f3nwTzj7bX1u7tv3XpyoFfxGRKERKHPftb6dn4jgFfxGRDmiZOO7hhz9JHNfQ\nkOzWRU/BX0SkE8IljjvppPRJHKfgLyISg3CJ40pK/LVUThyn4C8iEoDmieOOPhouuQRKS/21VFwe\nquAvIhKgpsRx8+bBBx/A2LGpmThOwV9EJGA5OTBpErzxhk8c99prfkho0qTUSRyn4C8iEictE8c9\n8YTfPXzVVclPHKfgLyISZy0Tx91zT/ITxyn4i4gkSFuJ4/bvT2xbFPxFRBIsUuK4mprEtSGm4G9m\nR5vZM2a2PvR7zzBlTjWzl81sjZn908z+M5Y6RUQyRfPEcQMGwHHHJa7uWHv+FcBzzrmBwHOh5y3t\nAb7pnPssMBa4w8yKYqxXRCQjNCWOe/JJP0GcKLEG//HAQ6HHDwETWhZwzv3LObc+9LgO2Ab0jrFe\nERGJQazB/1jn3NsAod+PaauwmZ0GdAE2RPh5uZlVmVlVfbLXQYmIZLC89gqY2bPAp8P86OcdqcjM\nPgM8AlxjctiZAAAEoElEQVTqnAub8cI5NweYA1BWVpaCG6JFRDJDu8HfOTcq0s/M7F0z+4xz7u1Q\ncN8WodxRwJPADc65VzrdWhERCUSswz6LgEtDjy8FnmhZwMy6AAuBh51zf46xPhERCUCswX8mMNrM\n1gOjQ88xszIz+32ozDeALwGXmdlroV+nxliviIjEwFwq5hrFj/lXVVUluxkiImnFzFY458raK6cd\nviIiWShle/5mVg+8GcBb9QLeC+B90oXuN7PpfjNXUPd6gnOu3b1UKRv8g2JmVdF8BcoUut/MpvvN\nXIm+Vw37iIhkIQV/EZEslA3Bf06yG5Bgut/MpvvNXAm914wf8xcRkdayoecvIiItZEzwN7OxZlZt\nZjVm1upcATPramZ/Cv38VTPrl/hWBieK+73GzNaGDtB5zsxOSEY7g9Le/TYr93Uzc2aWtitEorlX\nM/tG6O93jZnNS3QbgxTFv+XjzWypma0K/Xu+IBntDIqZPWBm28zs9Qg/NzO7K/Tn8U8zK41LQ5xz\naf8LyMWniT4RnzL6H8CQFmW+D9wbenwR8KdktzvO9/tvQLfQ4+9l+v2GyvUA/g68ApQlu91x/Lsd\nCKwCeoaeH5Psdsf5fucA3ws9HgJsTna7Y7znLwGlwOsRfn4B8L+AAWcAr8ajHZnS8z8NqHHObXTO\n7QMexR8001zzg2ceB841M0tgG4PU7v0655Y65/aEnr4C9E1wG4MUzd8vwK+B24GPEtm4gEVzr1OB\nu51zOwCcc2Gz6aaJaO7XAUeFHhcCdQlsX+Ccc38HtrdRZDw+EaZzPgtyUShrcqAyJfgXA1uaPd8a\nuha2jHPuALAT+FRCWhe8aO63uSvwPYl01e79mtkw4Djn3F8T2bA4iObvdhAwyMyWmdkrZjY2Ya0L\nXjT3Ox2YYmZbgaeAHyamaUnT0f/fndJuPv80Ea4H33IZUzRl0kXU92JmU4Ay4MtxbVF8tXm/ZpYD\nzAYuS1SD4iiav9s8/NDPOfhvdC+Y2SnOuYY4ty0eornfScCDzrn/NrMvAo+E7jfsoVAZICGxKlN6\n/luB5ufe96X1V8OPy5hZHv7rY1tfvVJZNPeLmY3Cn7g2zjm3N0Fti4f27rcHcArwvJltxo+TLkrT\nSd9o/y0/4Zzb75zbBFTjPwzSUTT3ewXwGIBz7mXgCHwenEwV1f/vWGVK8F8ODDSz/qHDYy7CHzTT\nXPODZ74OLHGh2ZU01O79hoZB7sMH/nQeE4Z27tc5t9M518s518851w8/xzHOOZeOOcGj+bdciZ/Q\nx8x64YeBNia0lcGJ5n7fAs4FMLOT8cE/kw/5XgR8M7Tq5wxgpwudlR6kjBj2cc4dMLMrgcX41QMP\nOOfWmNmvgCrn3CLg/+C/Ltbge/wXJa/FsYnyfmcBRwJ/Ds1rv+WcG5e0RscgyvvNCFHe62LgPDNb\nCxwEpjnn3k9eqzsvyvv9CXC/mV2NH/64LI07bpjZfPyQXa/QPMaNQD6Ac+5e/LzGBUANsAf4Vlza\nkcZ/hiIi0kmZMuwjIiIdoOAvIpKFFPxFRLKQgr+ISBZS8BcRyUIK/iIiWUjBX0QkCyn4i4hkof8P\nZ59stDEPRGUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113b735c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the linear regression line\n",
    "pyplot.scatter(X,Y)\n",
    "pyplot.plot(X, regression.predict(X), color='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}