2017-10-24 - 09 Train Test and Overfitting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Train / Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We'll start by creating some data set that we want to build a model for (in this case a polynomial regression):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgwAAAFkCAYAAABMyWOlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3XuQXGd9p/HnJ3yRsS3ZjIIMAVUEToizSTASQkwIMoQM\nMrBL4k0qQWvLG6gsRSJTWLsmhF1iI7OFuNkixHbWu0vAWEFZFykKkjWamZAgBzLIQuISEoOxbGNu\nEtYYZK3B2KB3/zhnpJ6ennn7fpvnU9UlzTmnT79zuqfP97y3EyklJEmSFrKk1wWQJEn9z8AgSZKy\nDAySJCnLwCBJkrIMDJIkKcvAIEmSsgwMkiQpy8AgSZKyDAySJCnLwCBJkrKaDgwR8eaIuDMiHo6I\nwxHx0Yj4uRrbXRsR346IH0TEZEScX7X+9Ii4MSKORMSxiPhIRDy52XJJkqT2a6WG4YXAnwHrgV8H\nTgUmIuKMmQ0i4k3AFcBrgecBjwDjEXFaxX7eC7wC+C1gA/BU4K9bKJckSWqzaNfNpyJiBfBdYENK\n6dPlsm8D704p7Sh/XgYcBv5jSum28ucHgVellD5abvMs4C7g+SmlO9tSOEmS1JJ29mE4B0jAQwAR\nsRo4D/jkzAYppYeBvcBouei5wClV23wVeKBiG0mS1GOntGMnEREUTQufTin9a7n4PIoAcbhq88Pl\nOoCVwGNlkJhvm+rXGgE2AvcDj7ZceEmSFo+lwM8A4yml6Uae2JbAANwE/ALwgjbtbyEbgb/swutI\nkjSsLgU+3MgTWg4MEXED8HLghSml71SsOgQERS1CZS3DSuDzFducFhHLqmoZVpbrarkfYOfOnVxw\nwQWtFn/R2Lp1Kzt27Oh1MQaOx61xHrPmeNwa5zFr3F133cVll10G5bm0ES0FhjIs/AZwUUrpgcp1\nKaX7IuIQ8BLgS+X2yyhGVdxYbrYf+HG5TWWnx1XA1Dwv+yjABRdcwJo1a1op/qKyfPlyj1cTPG6N\n85g1x+PWOI9ZSxpu0m86METETcAm4JXAIxGxslx1NKU0U5D3Am+JiHso0szbgG8CH4OiE2REvB+4\nPiK+BxwD3gd8xhESkiT1j1ZqGF5H0anxU1XLXw18CCCl9K6IeCJwM8Uoin8EXpZSeqxi+63AT4CP\nAKcDu4EtLZRLkiS1WdOBIaVU15DMlNJbgbcusP5HwOvLhyRJ6kPeS2KR2LRpU6+LMJA8bo3zmDXH\n49Y4j1l3tW2mx26JiDXA/v3799vZRZKkBhw4cIC1a9cCrE0pHWjkudYwSJKkLAODJEnKMjBIkqQs\nA4MkScoyMEiSpCwDgyRJyjIwSJKkLAODJEnKMjBIkqQsA4MkScoyMEiSpKxWbm891MbHx9m7dy+j\no6OMjY31ujiSJPWUgaHKwYMHWb/+BUxPHz6xbGRkJfv2TbF69eoelkySpN6xSaJKERYeBXYCDwA7\nmZ5+lHXrRntcMkmSesfAUGF8fLysWbgRuBR4evnvDUxPH2ZycrKn5ZMkqVcMDBX27t1b/m9D1ZqL\nAJiamupqeSRJ6hcGhgrr168v/3dH1Zo9AIyO2iwhSVqc7PRYYePGjYyMrGR6eguQKGoW9gBXMDKy\n0tESkqRFyxqGKvv2TTEyshTYDKwCNjMyspR9+2yOkCQtXtYwVFm9ejVHjhxicnKSqakp52GQJAkD\nw7zGxsYMCpIklWySkCRJWQYGSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQ\nJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJ\nWQYGSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQJElZBgZJkpTVdGCIiBdG\nxMcj4lsRcTwiXlm1/gPl8srH7VXbnB4RN0bEkYg4FhEfiYgnN1smSZLUGa3UMJwJfAH4QyDNs80n\ngJXAeeVjU9X69wKvAH4L2AA8FfjrFsokSZI64JRmn5hS2g3sBoiImGezH6WUHqy1IiKWAa8BXpVS\n2lMuezVwV0Q8L6V0Z7NlkyRJ7dXpPgwviojDEfGViLgpIp5UsW4tRWD55MyClNJXgQeA0Q6XS5Ik\nNaDpGoY6fIKieeE+4JnAduD2iBhNKSWKJorHUkoPVz3vcLlOkiT1iY4FhpTSbRU//ktE/DNwEHgR\n8A+t7n/r1q0sX7581rJNmzaxaVN1NwlJkhafXbt2sWvXrlnLjh492vT+OlnDMEtK6b6IOAKcTxEY\nDgGnRcSyqlqGleW6Be3YsYM1a9Z0prCSJA24WhfRBw4cYO3atU3tr2vzMETE04AR4Dvlov3Aj4GX\nVGzzLGAVMNWtckmSpLymaxgi4kyK2oKZERLPiIhnAw+Vj2so+jAcKrd7J3A3MA6QUno4It4PXB8R\n3wOOAe8DPuMICUmS+ksrTRLPpWhaSOXjunL5LRRzM/wycDlwDvBtiqBwdUrp8Yp9bAV+AnwEOJ1i\nmOaWFsokSZI6oJV5GPawcJPGxXXs40fA68uHJEnqU95LQpIkZRkYJElSloFBkiRlGRgkSVKWgUGS\nJGUZGCRJUpaBQZIkZRkYJElSloFBkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIkZRkYJElSloFBkiRl\nGRgkSVKWgUGSJGUZGCRJUpaBQZIkZRkYJElSloFBkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIkZRkY\nJElSloFBkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIkZRkYJElSloFBkiRlGRgkSVKWgUGSJGUZGCRJ\nUpaBQZIkZRkYJElSloFBkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIkZRkYJElSloFBkiRlGRgkSVKW\ngUGSJGUZGCRJUpaBQZIkZRkYJElSloFBkiRlNR0YIuKFEfHxiPhWRByPiFfW2ObaiPh2RPwgIiYj\n4vyq9adHxI0RcSQijkXERyLiyc2WSZIkdUYrNQxnAl8A/hBI1Ssj4k3AFcBrgecBjwDjEXFaxWbv\nBV4B/BawAXgq8NctlEmSJHXAKc0+MaW0G9gNEBFRY5M3AG9LKf1tuc3lwGHgN4HbImIZ8BrgVSml\nPeU2rwbuiojnpZTubLZskiSpvTrShyEiVgPnAZ+cWZZSehjYC4yWi55LEVgqt/kq8EDFNpIkqQ90\nqtPjeRTNFIerlh8u1wGsBB4rg8R820iSpD7QdJNEr23dupXly5fPWrZp0yY2bdrUoxJJktQ/du3a\nxa5du2YtO3r0aNP761RgOAQERS1CZS3DSuDzFducFhHLqmoZVpbrFrRjxw7WrFnTpuJKkjRcal1E\nHzhwgLVr1za1v440SaSU7qM46b9kZlnZyXE98E/lov3Aj6u2eRawCpjqRLkkSVJzmq5hiIgzgfMp\nahIAnhERzwYeSil9g2LI5Fsi4h7gfuBtwDeBj0HRCTIi3g9cHxHfA44B7wM+4wgJSZL6SytNEs8F\n/oGic2MCriuX3wK8JqX0roh4InAzcA7wj8DLUkqPVexjK/AT4CPA6RTDNLe0UCZJktQBrczDsIdM\nk0ZK6a3AWxdY/yPg9eVDkiT1Ke8lIUmSsgwMkiQpy8AgSZKyDAySJCnLwCBJkrIMDJIkKWtg7yWh\nvPHxcfbu3cvo6ChjY2O9Lo4kaYAZGIbQwYMHWb/+BUxPn7yNx8jISvbtm2L16tU9LJkkaVDZJDGE\nirDwKLATeADYyfT0o6xbN9rjkkmSBpWBYciMj4+XNQs3ApcCTy//vYHp6cNMTk72tHySpMFkYBgy\ne/fuLf+3oWrNRQBMTXkjUElS4wwMQ2b9+vXl/+6oWrMHgNFRmyUkSY2z0+OQ2bhxIyMjK5me3kJx\nE9GLKMLCFYyMrHS0hCSpKdYwDKF9+6YYGVkKbAZWAZsZGVnKvn02R0iSmmMNwxBavXo1R44cYnJy\nkqmpKedhkCS1zMAwxMbGxgwKkqS2sElCkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIkZRkYJElSloFB\nkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIkZRkYJElSloFBkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIk\nZRkYJElSloFBkiRlGRgkSVKWgUGSJGUZGCRJUpaBQZIkZZ3S6wIsZuPj4+zdu5fR0VHGxsZ6XRxJ\nkuZlYOiBgwcPsn79C5iePnxi2cjISvbtm2L16tU9LJkkSbXZJNEDRVh4FNgJPADsZHr6UdatG+1x\nydSK8fFxrr32WiYnJ3tdFElqO2sYumx8fLysWdgJXFouvRRITE9vZnJy0uaJAWONkaTFwBqGLtu7\nd2/5vw1Vay4CYGpqqqvlUeusMZK0GBgYumz9+vXl/+6oWrMHgNFRTzKD5GSN0Y0UNUVPL/+9genp\nwzZPSBoaBoYu27hxIyMjK4EtFFek3yj/vYKRkZVta46wPb076q0x8v2QNOjsw9AD+/ZNsW7dKNPT\nm08sm2nzbpXt6d01u8bo0oo1RY3RqlWrWLHiPN8PSQMvUkq9LkNDImINsH///v2sWbOm18VpyeTk\nJFNTU22dh6E4OT1KUUW+geJEtoWRkaUcOXKoLa+h2U4e8xsoahb2UNQYLQXw/ZDUNw4cOMDatWsB\n1qaUDjTyXJskemhsbIyrr766rc0Qtqd33759U2U42AysAjYzMrKU6657p++HpKFhYBgiwzQCY5Da\n/FevXs2RI4eYmJhg27ZtTExMcOTIIb7+9a+XWwz++yFJ9mEYIrn29EEYgTHIfTDGxsZm1RYNw/sh\nSTM6WsMQEddExPGqx79WbXNtRHw7In4QEZMRcX4nyzTMujUCo5OGaU6DYXg/JGlGN5okvgysBM4r\nH786syIi3gRcAbwWeB7wCDAeEad1oVxDab729HaMwOi0YeyDMcjvhyRV6kaTxI9TSg/Os+4NwNtS\nSn8LEBGXA4eB3wRu60LZhs5Me3onRmB0Wj19MAbld5kxyO/HsPIusVJzuhEYfjYivgU8CkwBb04p\nfSMiVlPUOHxyZsOU0sMRsRcYxcDQkur29EEwzG3+g/h+DJtB7h8j9YNON0l8Fvg9YCPwOmA1cEdE\nnEkRFhJFjUKlw+U6LTK2+auThql/jNQLHa1hSCmNV/z45Yi4E/g68DvAV1rZ99atW1m+fPmsZZs2\nbWLTpk2t7FY91slZMLV4eZdYLUa7du1i165ds5YdPXq06f11dVhlSuloRNwNnA98CgiKDpGVtQwr\ngc/n9rVjx46Bn+lRc9nmr04Yxv4xUk6ti+iKmR4b1tXAEBFnUYSFW1JK90XEIeAlwJfK9cuA9RTd\n5LWI2eavdhrm/jFSt3Q0METEu4G/oWiG+GlgG/A48FflJu8F3hIR9wD3A28Dvgl8rJPlkrS4zPSP\nmZ7eQtF1qvKeH/aPkerR6RqGpwEfBkaAB4FPA89PKU0DpJTeFRFPBG4GzgH+EXhZSumxDpdL0iJj\n/xipNZ3u9JjtgZhSeivw1k6WQ5LsHyO1xntJqO850Y7ayf4xUnMMDOo7MwFh1apVXHXVHzvRjiT1\nAQOD+sbcmfiWAGdTjJ3fANzB9PQW1q0b5ciRQz0rZydYiyKp3xkY1Ddmz8T3NOBFnLwRFQzjRDtO\nVyxpUHTjbpVS1tw7Vf6gXDP/RDvDwOmKJQ0KA4P6wtyZ+J5Z/ntH1ZbDM9HOMN7OW9LwMjCoL8ye\niQ/g54CXA69nWG9EVc90xZLULwwM6gu171T5Soqmic3AKmAzIyNLh2ainbkhacbw1KJIGh52elTf\nmG8mvuuvfxf3339/XSMIBmm0gdMVSxokBgb1jVZm4uuH0QbNhJVaIWnZsnOHphZF0vCIlFKvy9CQ\niFgD7N+/f7+3t+6SQbhqX7HivHK0wY3MzNkAWxgZWdrxORtaDSsHDx7kOc9Zx7Fj32vq+ZJUr4rb\nW69NKR1o5LnWMGhe/XDVXo+Tow120os5G2YPjWx8gqn161/AsWPHm36+1G6DcJGg7rPTo+Y1KHME\n9HK0wdyhkT8EngS8pa6hke0eWjk+Ps61117rkEw15eDBg6xYcR4XX3wx11xzDS996UtZseI87rvv\nvl4XTX3AGoYOG7SkPlPeU089tadX7Y2YPdrg0oo1nR9tcDKs/DLwCuD2irVLuP322xc8TvWEnXqO\nc6u1QdWf015+bgftb2aYtFpbpiGXUhqoB7AGSPv370/97J577kkjIysTRff3BKSRkZXp3nvv7XXR\naqpVXliS4EsJUsXjgQSkbdu29brIsxRlX57g1rKMtyZYnkZGVra03927d6dt27aliYmJedcXx+rC\nBE9KsLN8/Z0Jlqdly87N7r94/s6q43xrAuZ93Wonf//Zr5/7/Wu97xGn9uRzO2h/M8OmXZ9F9bf9\n+/fP/H2tSY2efxt9Qq8fgxIYmv0C75X5ylucCPv/y+Pee+9t68mmkZPX2Wef29IX7TnnrKgZds45\nZ0VdZW3li37u+35hzz63nf6byYW/xW7btm3l5+iBgbhIUHMMDH1m0JJ6rrzw7rZetXfSxMREW04K\njZy8rrzyypa+aIvAcPqscAKn1x0Y6vmir3WynPu+f7Vnn9tO/s1Yc1GfQfveUnNaCQx2euyAQZvy\nN1deeCODMtPi2NgYV199dUtt3412RLz44ovL/zU+Y+P4+Djf//4R4P3A3RR9IO4G/jff//6Rujov\nzp0x8m7gE8D/AeC6695bsxPb3Pf9YNXPMzr/ue3k30wjnXcXc6fR2rOtDtd07GqNgaEDBm3K31x5\nt2/fzrZt25iYmODIkUN9NaSyExo9ebXyRTv7tX4WeFn5b/0nypOv/wfAc4BnUdyH443AE3j44Z9Q\n62Q5933v3Q2/OvU3U2/4c3RAYd++KUZGljKs07GrRY1WSfT6wQA0SaTUuU54nTJo5e2kZqpmm+1D\n0a5q4HvvvbfsrNhYP5S57/uFqdbnYNmyczve/t+Jz2C97fKD1ueo09rVtKf+Yx+GPtTuTnidNmjl\n7bRmT17NfNG240SZ74dyd82TZa33vXqURLdGTXTiM1hPIOu3tns7Z6qTDAx9bNCS+qCVt1O6GaDa\n8Vq5K2m4fc6JcPv27SeeX/2+z/xcjADp7pV3uz+DuUDWL6MD7JypbmglMDhxU4eNjY0NVGehQStv\np7RyI6xGzExStGvXrQBNv1Zu8ir4F+AXy5/fACzhscceO7FV9fs+NjbG8ePHy/tbdHfyrnZ/Bue7\nC+pMu3wvJ/6q5KRJ6ncGBmkBnQpQ7bxPx0zoOPvsczl2bO6tsuEcig6QbyyfcSHwUM0TYeUsi+2Y\nhbJy5tDHH3+8J7M35sJfP9xmvNf3Q5HqYWCQeqAdV5O1QkfEqaS0uWKrJwBLgXcDTwa+C/z3OSfC\nWvtatuzc8n+NX3nP3t8S4Pis/X7hC/vbOtqmnumkFwp/uVqITmvXFOFSRzXahtHrBwPWh0Gq1unp\noM86a3k644yzZrWFF9N8z98uPv9Mn6c01SHz5P5qT5kNp6Rbbrml6WM4o93t/r3qw9NvHS81vOz0\nKA2QdnSyy4+KOGvOSfqMM86ueeLJ7yvqPiHv3r07XXbZZeW2787ut9VOfcM0HNKhzeoGOz1KTejV\nXRHb0ckuPzvnH1DdFv7DH26mlvy+Pgg8CFzN2WefzpEjhxgfH+fWW2890Tdh1apVXHXVH89q0iia\nQBbab2J6+pGmO/W1o92/n+6M2etmESnHwKBFp50dDpvRjk52+VER/7bqGfO3hef3NUox++RKjh3b\nzPLlT+Lhh79Xsd2S8vdYRnHyfhrwIor+EgvtF+B1TE+/p+FOfQcPHuSSS367/Kl2INm+fTtAzf22\n8hnoVMhodGROP4UdLRKNVkn0+oFNEic4wUtz+qEaux1zL8xXhV30V2isLbz2vp6U4OVVTSZLahy7\nc2u85svL5TN9GKr3e2H5e++puxlmbnln+mnM1+TReJ+NhT4D/TJPQr+UQ4PJPgyLjF8Yzeu3zmWt\ndLKbL3QsWzYz2VL9t8uuta/ipP5QxTF6V+YEvadi2UMJfq1cvqTGfs8pQ0Xjx332e/jyGoFkprNl\n7SDQ7GegH4Jmu8rhxcbiZWBYZPrli2sQ9cusfu1UHToauV129Ylj7gyPlSfiJy547OCNNU/Al1xy\nSTrjjDOryvNrCf5HU5/b2e/hQ2VoqNz3M6uCzuwg0MxnoNNBs94TeKvl8GJDBoZFpN+ukAfNX/zF\nXwz18Zv9+RhPsC3BxJzfL3fiqFXjUISIhWoYlqWFevjfcsstc4Z7NnOyqv03MJ7g36e5NR1zg0Az\nf0OdCpqNnsBbLYcXGzIwLCLDeIXcTcUX5umpaF9v7WZP/Vile/LzMdMcwKyfG707Y3Xtxfx9HX4p\nVddqzHfia8dcByfL8ec1ftfqppS5QaDRIYydCuqNnsDrvZlWrePrxYZSMjAsKv7RN+/ksbs5za3G\nXpIuueSSga/SLX7HJWUgmtsxsdW7M9bu67DkxHG45ZZbuhKkTpajVifMyj4MtYPABz7wgXTGGWc3\n9D62e56E1vtSzO2jUv3eLFt2brryyitPhDQvNmRgWGSc4KU5c78w707FXRz31H3i6FaVbrM1GPWc\nhFo9cezevTtdfvnl6fLLL0/bt2/vWU1LfsKpue9nrcB3xhln1TXrZLvvYNrs+zBfOYq+K7XC05IT\n4cGLDRkYFplu3np5mORPMHsWDADdqN1ptQajnpNQs79Hv9Wu5H7XF7/4xXN+l3YEvnZNH93q56my\nHPnP9nsSLE8Rp6ZOXmz0a1OdTjIwLFK9mvd+kNWunTk3zZ5voPYXdjeqdFs9odV7Emqmlmq+si1b\ndu68n8NWTyALPb/RDqz92JzXrtrC3GezqEkrfs+TnVfbF/r6LUxqfgYGqU612+B/Lc3uJFc7AHRj\naF079l/PSajRWqpGq/9bPYHU8/xGO7CePKnekormqNYDX6uBqF21hfn35+5Zv2e7LzYcfTE4DAzq\nukGpepyvnBMTE2nz5s0Nn6A72X+kXTUYjZyE6j1x5K9gb5l1kmj1BJJ7fq4Da3WfhHvuuaeiDX/m\n8fJUBMXi/W7k7pn9eJfM/GydnalJ6ceaG83PwKCuGZSqx3rL2WgA6GT/kXZ/8bbzKrK+K9jKn5v/\nPZrruDm7A2t1uKodQGamqC5ut91I6OvHK+r5Z+v8UvZz3QpHXwwWA4O6ph+/KGupt5zNBoCZk9bb\n3/72DlXt9t8ImPwV7MmTRCsnkHZ33MyHnQtOlLme9zG3v8svv7xno0a2bduWtm/fnq688sqO9FWY\n73WtYRgcBgZ1xaB8MTRTzkavxjtV09LPI2Dqu99Ed2oYUqo/XNXXnMKCYaayaav2/qZT9QRS3Xrf\nFvosdqtjdD8HXc1mYFBXDErV4yCMZsjp5xEwC99vYqbG4cIa65rpw9B6x818DcO7Tzy/+njXOhnX\nns9g5u6c3a9564dav34OuprNwKCuGOYahn7a/6C4995758yWeLIj4ZdS9V0qI05Ne/bsqXvf7ey4\nOX9zyoXlif70mifY+U7Gs+cz+FTPPg/t+Cy2swNzPwfd+QxKB+52MTCoawal6nEQRjMMg5MnrDem\n2UMVZ67e35SKKv/3NHX823UCWmhKa1iSzjlnRcM1E9V9BHrxeWjlszgoHZg7ZaHff5hDRCuB4RSk\nBuzbN8W6daNMT28+sWxkZCX79k31sFRzdbKc69evL/93B3BpxZo9AIyOjrb8GoNi48aNjIysZHr6\nfwK/DCylOA5XABcC76jYeiXT05uZnJxkbGys5v7Gx8fZu3cvo6OjjI2NnXi0avXq1Rw5cojJyUmm\npqY47bTTuOuuuwC47LLLar7G3r17y/9tqFpzEQBXXXUlo6OjfOhDH2Lnzp10+/MwPj7O1772tfKn\nxl97/foXMD39KLCT4ne8g+npLaxbN8qRI4fqev3K92rQzPf7P/OZzyKlx09sN/O9sXr16l4VtX80\nmjB6/cAahr4wKFWPnSpnv9a09OLKaP6r9y/VfdXbj1e7jVT3d/PzMPdYLWn4tVtpyujH96pR9U2l\n3b+jwFphk4TUZf3WyasfvsQrh5o2ejJqtONet4JRvUGgm5+Hucfq5lTvrcVntNKU0Q+dLFtV31Ta\n9YeoQWJgUNsMc9tdJ/RLTUu9X+L9dqKdKVO9AaPbwajRINDpz0O75oBotoZhWDr81j8RWX0hapAY\nGNSyfrhCVXPq+RLv5vu7e/fuhiYOauRqt5Wr21bCUr8Ew3Z2uG2mGWWYOvzO9/sXI2cGNwzlDHxg\nALYA9wE/BD4LrFtgWwNDBwxDNeNiVc+XeDfe3/nmLLjyyisX/LKt96p1WG7L3Yp2XeHPhLrq+2vk\njsuw1DCkVLv2qBguu6yhEDVoBjowAL8LPApcDvw8cDPwELBinu0NDG02TF8Ci1Hu/WumT0EzWgkl\n9VztNnt1O2xhuJUOlrXC09ln50Ndu16/H1XWHvVb36ROGPTA8FngTyt+DuCbwB/Ns72Boc2GqZpx\nsVroS7wb72+robOeL+pmXmMYw3ArJ7V2hKfFcFLtlyaoThjYeRgi4lRgLfD2mWUppRQRfwcsnsHs\nPea8AoNvoXkn7r777nJJc+9vPePtc3MWTE1NLThWv3qehFqvdXLOhy0U33cXMTPnw8jIyqbmUsiV\nqx/Vc6xqGR8fZ3r6MMW8AzOfg0uBlJ0fox2vP0jaNf/H0Gk0YbTzATwFOA6sr1r+TmBqnudYw9AB\nw1bNuFjNd2XUzPvbSNt/t67kG726HcYahmZZk6iUWqthiFSchHsiIp4CfAsYTSntrVj+TmBDSmnO\npU9ErAH2b9iwgeXLl89at2nTJjZt2tThUg+n++67r7xCPXximTOcDY9m3t8VK84rZ8K7kZmZ8GAL\nIyNLa84EeHL7G5h99V97+1Y0cnXbzXLN6MdZEMfHx7n44ouZXcNA+fNmJiYmOlrWfjwmw27Xrl3s\n2rVr1rKjR49yxx13AKxNKR1oaIeNJox2PoBTgceBV1Yt/yDw0XmeYw1DBw1z253qf3+buTLv17bt\nbpar30e9JSaYAAAJAklEQVRk9KImsd+PyWIzsH0YUkqPR8R+4CXAxwEiIsqf39fLsi1Wtt0Nt3rf\n33ra/o8fPz7rirFf27a7Wa5W78/Qab24F0y/HxM1oNGE0e4H8DvAD5g9rHIa+Kl5treGQeqwXA1D\no+P3F4NB6i/RrZrEQTomi0UrNQxLuhlOakkp3QZcBVwLfJ7ilncbU0oP9rRg0iI2MyKhmFNtJ/CN\n8t8riDiVhx8+Xv78ALCT6elHWbducY+mqadWpl+MjY1x9dVXd7wGaJCOifJ6HhgAUko3pZR+JqV0\nRkppNKX0uV6XSVrs9u2bYmRkKbAZWAVs5uyzl1Dc+vdGio5zTy//vYHp6cNMTk72rsA9Nnt4cqXF\nOzzZYzJc+iIwSOo/M23/ExMTbNu2jYmJCa666spyrVeM1RaqlZlvnohh5zEZLj3t9Cip/1V2lDx+\n/Hi51Em+aulFp8J+5zEZHgYGSXVrZrbFxaRfR4r0ksdkePR04qZmzEzctH//ftasWdPr4kiLjpN8\nSYPrwIEDrF27FpqYuMkaBkkN8YpRWpwMDJKa4iRf0uLiKAlJkpRlYJAkSVkGBkmSlGVgkCRJWQYG\nSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmS\nlGVgkCRJWQYGSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQJElZBgZJkpRl\nYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQ\nJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKUZWCQJElZBgZJkpRlYJAkSVkGhkVi165dvS7C\nQPK4Nc5j1hyPW+M8Zt3VscAQEfdHxPGKx08i4o+qtnl6RPzfiHgkIg5FxLsiwhDTAf5hNcfj1jiP\nWXM8bo3zmHXXKR3cdwLeAvwvIMplx2ZWlsHgduDbwPOBpwK3Ao+Vz5MkSX2i01fz/y+l9GBK6bvl\n44cV6zYCPw9cmlL655TSOPAnwJaI6GSQkSRJDep0YPjjiDgSEQci4qqIeELFuucD/5xSOlKxbBxY\nDvybDpdLkiQ1oJNX8n8KHAAeAn4FeAdwHnBVuf484HDVcw5XrPviPPtdCnDXXXe1s6xD7+jRoxw4\ncKDXxRg4HrfGecya43FrnMescRXnzqWNPjdSSvVvHLEdeNMCmyTggpTS3TWe+3vAzcBZKaXHI+Jm\nYFVK6WUV25wBPAK8rGyiqFWG/wD8Zd2FliRJ1S5NKX24kSc0WsPwHuADmW3unWf5neXr/QzwNeAQ\nsK5qm5Xlv4cW2P84cClwP/BopiySJOmkpRTn4ZoX5QtpKDCklKaB6UZfpPQc4Djw3fLnKeC/RsSK\nin4MLwWOAv+aKUNDqUiSJJ3wT808qSN9GCLi+cB64B8ohlL+CnA9cGtK6Wi52QRFMLg1It4EPAV4\nG3BDSunxTpRLkiQ1p6E+DHXvNOI5wE3As4DTgfuADwE7KsNARDwd+HPgRRR9Fz4IvDmldLzthZIk\nSU3rSGCQJEnDxWmYJUlSloFBkiRlDVRgiIgtEXFfRPwwIj4bEdXDMlUlIl4YER+PiG+VNwF7Za/L\n1M8i4s0RcWdEPBwRhyPioxHxc70uV7+LiNdFxBcj4mj5+KeIuLjX5RokEfHH5d/o9b0uSz+LiGuq\nbmx4PCLmHVmnQkQ8NSJuLWdf/kH597qmkX0MTGCIiN8FrgOuoRii+UVgPCJW9LRg/e9M4AvAH1JM\nrKWFvRD4M4pRPr8OnApMlJOKaX7foJjUbQ2wFvh74GMRcUFPSzUgyouf1zL/DLea7csU8/acVz5+\ntbfF6W8RcQ7wGeBHFPdxugD4L8D3GtrPoHR6jIjPAntTSm8ofw6KL6n3pZTe1dPCDYiIOA78Zkrp\n470uy6AoA+l3gQ0ppU/3ujyDJCKmgatSSrnJ3ha1iDgL2A/8AcUN+D6fUvrPvS1V/4qIa4DfSCk1\ndHW8mEXEO4DRlNJFrexnIGoYIuJUiquWT84sS0XS+TtgtFfl0qJwDkXNzEO9LsigiIglEfEq4IkU\nE7RpYTcCf5NS+vteF2SA/GzZzHowInaWQ/Q1v38HfC4ibiubWg9ExO83upOBCAzACuAJ1L5Z1Xnd\nL44Wg7IW673Ap1NKtpFmRMQvRsQximrPm4BLUkpf6XGx+loZrC4E3tzrsgyQzwK/R1G1/jpgNXBH\nRJzZy0L1uWdQ1GB9lWJG5T8H3hcRmxvZSSfvVikNupuAXwBe0OuCDIivAM+muEX9bwMfiogNhoba\nIuJpFIH0153dtn5VNyb8ckTcCXwd+B3y9zparJYAd6aU/qT8+YsR8YsUgevWRnYyCI4AP+Hkzalm\nrGThG1VJTYmIG4CXAy9KKX2n1+UZBCmlH6eU7k0pfT6l9N8oOvC9odfl6mNrgZ8CDkTE4xHxOHAR\n8IaIeKys4VJGebuBu4Hze12WPvYd4K6qZXcBqxrZyUAEhjJ97wdeMrOs/GN6CU3eREOaTxkWfgN4\ncUrpgV6XZ4AtoZgaXrX9HfBLFE0Szy4fnwN2As9Og9IjvcfKTqPnU5wUVdtnKG7VUOlZFDUzdRuk\nJonrgQ9GxH6KW2VvpehU9cFeFqrfle165wMzVyvPiIhnAw+llL7Ru5L1p4i4CdgEvBJ4JCJmarWO\nppS8nfo8IuLtwCeAB4CzKW5BfxFFe6lqSCk9QtWdeSPiEWA6pVR9NahSRLwb+BuKk91PA9uAx4Fd\nvSxXn9sBfCYi3gzcRjFs/PeB/9TITgYmMKSUbiuHuF1L0RTxBWBjSunB3pas7z2X4q6hqXxcVy6/\nBXhNrwrVx15HcZw+VbX81RQ3UFNtT6b4TD2F4hb1XwJeas//hlmrkPc04MPACPAg8Gng+Sml6Z6W\nqo+llD4XEZcA76AYunsf8IaU0l81sp+BmYdBkiT1zkD0YZAkSb1lYJAkSVkGBkmSlGVgkCRJWQYG\nSZKUZWCQJElZBgZJkpRlYJAkSVkGBkmSlGVgkCRJWQYGSZKU9f8Br2ZMM7oVSl8AAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1995ef10eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from pylab import *\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# generate some random data\n",
    "np.random.seed(2)\n",
    "pageSpeeds = np.random.normal(3.0, 1.0, 100)\n",
    "purchaseAmount = np.random.normal(50.0, 30.0, 100) / pageSpeeds\n",
    "\n",
    "# plot the date\n",
    "plt.scatter(pageSpeeds, purchaseAmount)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now we'll split the data in two - 80% of it will be used for \"training\" our model, and the other 20% for testing it. This way we can avoid overfitting. Now this is actually a very naive approach. In real live, we would use random sampling to split the data.\n",
    "\n",
    "```python\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgwAAAFkCAYAAABMyWOlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZ0MLuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x199615600f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# naivly split data into 80% training and 20% test data \n",
    "\n",
    "# Training and Test inputs\n",
    "X_train = pageSpeeds[:80]\n",
    "X_test = pageSpeeds[80:]\n",
    "\n",
    "# Training and Test outputs\n",
    "y_train = purchaseAmount[:80]\n",
    "y_test = purchaseAmount[80:]\n",
    "\n",
    "# Plot the training data\n",
    "plt.scatter(X_train, y_train)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgwAAAFkCAYAAABMyWOlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngUGSJBUyMEiSpEIGBkmSVMjAIEmSCv1/7/Tf36CyzigAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19961622898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the training data\n",
    "plt.scatter(X_test, y_test)\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now we'll try to fit an 8th-degree polynomial to this data (which is almost certainly overfitting, given what we know about how it was generated!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       8         7         6         5        4        3        2\n",
      "0.734 x - 17.01 x + 165.7 x - 881.9 x + 2788 x - 5315 x + 5898 x - 3442 x + 838.4\n"
     ]
    }
   ],
   "source": [
    "x = np.array(X_train)\n",
    "y = np.array(y_train)\n",
    "\n",
    "testx = np.array(X_test)\n",
    "testy = np.array(y_test)\n",
    "\n",
    "# fit an polinomial regression to the training data of degree eight\n",
    "p4 = np.poly1d(np.polyfit(x, y, 8))\n",
    "\n",
    "print(p4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's plot our polynomial against the training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAFkCAYAAACq4KjhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nE8iSBGOMMcYEsiTBGGOMMYH+D5+YhrNtHDS1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19962c439e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the model on our training data\n",
    "xp = np.linspace(0, 7, 100)\n",
    "axes = plt.axes()\n",
    "axes.set_xlim([0,7])\n",
    "axes.set_ylim([0, 200])\n",
    "plt.scatter(x, y, c='c', marker='x', label='training')\n",
    "plt.scatter(testx, testy, c='c', marker='D', label='test')\n",
    "plt.plot(xp, p4(xp), c='r', label='model')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Doesn't look that bad when you just eyeball it, but the r-squared score on the test data is kind of horrible! This tells us that our model isn't all that great... And if we look at the ends of the model, this gets pretty obvious. While there is no test data here, the fitted line runs up very steaply, creating strong predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.300181686118\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "# calculate R² for our test data\n",
    "r2 = r2_score(y_test, p4(X_test))\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "If we look at our training data, the fit is much better (which we could expect since we used that data for training purposes. Now in fact, however, we see that our model predicts random noice rather than real variation. We'd better go back and reduce the degree of our function to get this model more reliable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.642706951469\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "# calculate R² for our training data\n",
    "r2 = r2_score(y_train, p4(X_train))\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Try measuring the error on the test data using different degree polynomial fits. What degree works best?"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}