5_Data_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data Analysis\n",
    "===\n",
    "\n",
    "Data analysis is the process of asking and anwering questions of our data. Is it faster to go through self check-out or employee checkout? Is a home's value related to its size? This module will provide a very brief introductions to a few topics to get you started analyzing data.\n",
    "\n",
    "\n",
    "Statistical Significance\n",
    "---\n",
    "\n",
    "A common question you might ask of your data is, are two things different? Take, for example, checking out at a grocery store in a self-checkout line versus getting checked out by a human employee. In the dataset provided below each row represents one persons checkout time (in seconds) going through both self checkout (U-Scan) and getting checked out by a store employee (Employee_Checkout)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>U-Scan</th>\n",
       "      <th>Employee_Checkout</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>341</td>\n",
       "      <td>169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>450</td>\n",
       "      <td>164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>199</td>\n",
       "      <td>243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>57</td>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>33</td>\n",
       "      <td>51</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   U-Scan  Employee_Checkout\n",
       "0     341                169\n",
       "1     450                164\n",
       "2     199                243\n",
       "3      57                 53\n",
       "4      33                 51"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# data set originally from http://www.math.hope.edu/swanson/statlabs/data.html\n",
    "checkout_times_df = pd.read_csv('checkout_times.txt', delim_whitespace=True)\n",
    "checkout_times_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just by looking at the first 5 data points we can see that for some people self checkout was faster and for others employee checkout was faster. The best we can do to answer the question \"which is faster\" is to figure out which is faster on average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total data points: 24\n",
      "\n",
      "Mean check out times\n",
      "U-Scan               146.916667\n",
      "Employee_Checkout    122.125000\n",
      "dtype: float64\n",
      "\n",
      "Standard Deviation of checkout times\n",
      "U-Scan               103.073176\n",
      "Employee_Checkout     69.417021\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x11362c590>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x1136ca710>]], dtype=object)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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N40I/jXOMWcmkjZVBG3b/No0NdffsZ4C9HfP2sMK5/5TSMrDcfty+E2dqamrFjlre0587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\nfFy/crdwDTMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1135a6710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('total data points: %s\\n' % len(checkout_times_df))\n",
    "\n",
    "print('Mean check out times')\n",
    "print(checkout_times_df.mean())\n",
    "\n",
    "print('\\nStandard Deviation of checkout times')\n",
    "print(checkout_times_df.std())\n",
    "\n",
    "%matplotlib inline\n",
    "checkout_times_df.hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on this sample of checkout times from 24 customers, on average employee checkout is faster than self checkout. The average difference was 25 seconds, but if a different set of customers performed the same experiment what's the likelihood that they would come up with contradictory results? We can answer that question with a test of statistical significance.\n",
    "\n",
    "The precise definitions for tests of statistical significants can be a little convoluded, but their purpose is to help quantify the reliability of your findings. In performing these tests we usually assume the opposite of what we want to prove. The opposite of what we want to prove is called the null hypothesis. In the case above the null hypothesis would be that there is no difference between self checkout and employee checkout. We then calculate the probability that our data supports the null hypothesis. The probability that the null hypothesis is true is called the \"p-value\". A low p-value means the null hypothesis is unlikely, which means the thing we're trying to prove *is* likely. We'll use a t-test from scipy's stats module to get the probability that this null hypthosis is valid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.270406420767\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "pval = stats.ttest_rel(\n",
    "    checkout_times_df['U-Scan'],\n",
    "    checkout_times_df['Employee_Checkout']\n",
    ").pvalue\n",
    "print(pval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The p-value is 0.27 which means there's a 27% chance that the checkout times between self checkout and employee checkout aren't different at all. Most statisticians would claim that, based on this data, there's not enough evidence to reject the null hypothesis. In other words, we can't say that either employee checkout or self checkout is faster based on our data.\n",
    "\n",
    "In most cases you've performed an experiment (or gathered data) with hopes of rejecting the null hypothesis (or actually proving something). In general small p-values mean we can make a statistical claim about two things being different. But how small is small enough? There's not a great answer to that question, but the rule of thumb for many researchers is that if p is smaller than 0.05 you can claim statistical significance and if it's larger than 0.05 you can't."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation\n",
    "---\n",
    "\n",
    "Let's return to the nbs sql database and look at data measuring engagement with musicians and bands on social media across Facebook, Twitter, YouTube and Instagram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "there are 3760 rows in the data table\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FaceBookPageLikes</th>\n",
       "      <th>TwitterFollowers</th>\n",
       "      <th>YouTubeViews</th>\n",
       "      <th>InstagramLikes</th>\n",
       "      <th>InstagramFollowers</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>artist_id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>4797.0</td>\n",
       "      <td>1395.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>744</th>\n",
       "      <td>NaN</td>\n",
       "      <td>224.0</td>\n",
       "      <td>44287.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>952</th>\n",
       "      <td>4142.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>130279.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1017</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2966.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1086</th>\n",
       "      <td>28980.0</td>\n",
       "      <td>43405.0</td>\n",
       "      <td>402054.0</td>\n",
       "      <td>56832.0</td>\n",
       "      <td>7653.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           FaceBookPageLikes  TwitterFollowers  YouTubeViews  InstagramLikes  \\\n",
       "artist_id                                                                      \n",
       "500                   4797.0            1395.0           NaN             NaN   \n",
       "744                      NaN             224.0       44287.0             NaN   \n",
       "952                   4142.0              64.0      130279.0             NaN   \n",
       "1017                     NaN               NaN        2966.0             NaN   \n",
       "1086                 28980.0           43405.0      402054.0         56832.0   \n",
       "\n",
       "           InstagramFollowers  \n",
       "artist_id                      \n",
       "500                       NaN  \n",
       "744                       NaN  \n",
       "952                       NaN  \n",
       "1017                      NaN  \n",
       "1086                   7653.0  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sqlite3 as lite\n",
    "\n",
    "con = lite.connect('nbs.db')\n",
    "query = 'select * from social_data'\n",
    "social_df = pd.read_sql(query, con, index_col='artist_id')\n",
    "con.close()\n",
    "print('there are %s rows in the data table' % len(social_df))\n",
    "social_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x115773dd0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1wH3dyqrabWs7JkmSNJ1GDUGnbLqJJEnS5Br1jtHnjbsjkiRJM2nkmyUmeWKS05N8LMlu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\nIEmS1EuGIEmS1EuGIEmS1Ev/HwNhcMqXCzS7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1153463d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "social_df['YouTubeViews'].plot.hist(bins=50, alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1158d56d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9jBUGrAYeyqKuCFAXeN778y6gGvBphnaTgRuA5kBboAnwTlqlmRUFvgB+AOoB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\n4FoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115825390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "social_df.drop('YouTubeViews', axis=1).plot.hist(bins=750, alpha=0.3, xlim=[0,50000])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many statistical methods assume that data is normally distributed so it's always nice to find that normal looking histograms. The distributions of all five social features, however, are very right skewed. Fortunately there are ways to transform non-normal data to make it look normal. In this case we'll try taking the log of all of the values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KvA/4i6TzSc3jq5P2Zz/SsXmGav8bs1ZyHen7vjXpdvyaa4Da2EFV\ngqZbgT2VxiybBTwYEbfkdICTJV1MuiR3aUTcK+kE4PjcEfvPpADrdaT+OGeQ7vzrC98mfY+vzPXi\nXNK+bUgKXCqLiBsl/Q74fO6gfR3pVv6PkPoNzSjkDUnXkoZluTnyEAgs60u2FfCz0iZ+RuoMfr7S\nOFIzSC1y/0bqTzkWuHsVxfyV0jh300hDM2xOqqduioiHurO/bafRt+/51fWL+kMOvFgn30QKtwST\n7iqZTKp4FpGae89hxVt2P0UKcF6mMPwA6Qs8g9T0+wSpL9OEYp7COj5H6tC4kPRF3pXUCnVFIc+4\nvOx+dco+gjRu05N5e9eSxneZRv1hC/Zb2TEqHxNg3ULaTOrfWhzAuYVjPLOwzGZ5/ldK6z80p59a\nSFuDNO7VP/Jxf5pUIX6ZPExC1f+NX341y4uVDDlQyHNn/j78eyFti5z2QJ389YYceEP+/i9gxVv+\nT8h1xFJKww+Qxju6jnTX7TzgHtKYZ1sU8txAYViW0na7nFfK93rgf0g3mSwg1ZG7l/KscsiBnDY8\n79NMlnUKP4HCcCqFvF/K6zy9lD49p+9aZ5nhpP6i9+R6Zg6pA/nRpG4EsGzIgdPqLH8AqY9mrZ6a\nSRrHab1Gfx4b/VI+QGZ9Il+yehq4JCI+3ejymJmZ9RX3abIey8Pwl+9O+xjpDpppA18iMzOz/uOW\nJusxpWfVnUEa9HEO6fbiT5L65uwQ6S4xMzOztuCO4NYbM0mDSn6e1Lr0LKmD9NcdMJmZWbtxS5OZ\nmZlZBe7TZGZmZlaBgyYzMzOzChw0mZmZmVXQkh3B823uG5IGMjOz1jEKeDLarDOl6ySzltTt+qgl\ngyZS5TRoHxho1uI2Io00305cJ5m1pm7VR60aNM0DeOyxxxg9enSjy9LvOjs7mTJlChMmTKCjo6PR\nxWkbPq79o6vjOnfuXDbeeGNoz9aYSnWSP3P9x8e2/7Tjse1pfdSqQRMAo0ePHjRB08iRIxk9enTb\nfGCbgY9r/xjMx3VVddJgPjb9zce2//jYLtPSQZO1js2+flnlvDNPfk8/lmTVWqmsZtb/ulMnVOW6\nozX57jkzMzOzChw0mZmZmVXgoMnMzMysAgdNZmZmZhW4I7g1HXfENjOzZuSgyczMBp3+uCPO2p8v\nz5mZmZlV0OctTZKOAj4AbAMsAK4HjoyI+wt5VgO+BxwAjAAmA4dFxKy+Lo9ZTfnMcsTQ4JSdYLuJ\nk1m0RA0qlZmZtYr+aGl6JzAJ2BkYD3QAUyStXshzBvBeYP+cf0Pgkn4oi5mZmVmf6POgKSL2iIjz\nI+LvEXEHcBCwCbADgKQ1gU8CX4qIqyLiVuBgYFdJO/d1ecysfUk6StLNkuZJmi3pUklbl/KsJmmS\npDmSXpR0saQxpTybSLpM0vy8nlMluc+nmS1nIPo0rZnfn83vO5Ban66sZYiI+4BHgV0GoDxm1j56\n3bItaShwGTAc2BX4OOlk74T+L76ZtZJ+PZOSNAQ4E7guIu7OyRsAiyPi+VL2WXlevfWMIPV9qhkF\n6SGCnZ2dfVvoJlTbx1be1xFDo1/W251jUi7DiCGx3Ht/b3+w6Orz2h/HKiL2KE5LOgiYTTo5u6bQ\nsn1gRFyV8xwM3Ctp54i4AZgAbAu8O/ervF3SscB3JU2MiMV9XnAza0n93fw8CdgOeHsv13MUcHw5\nccqUKYwcObKXq24dU6dObXQReuyUnfpnvZdffnmvy3DijksHZPuDTfnzOn/+/IHYbKWWbUm1lu0b\n8vtdpRtRJgM/At4A3FbeSE9P5NrhBKhZdffY9teJXFWt9Blox89tT/dFEf3zwZF0NrAP8I6IeLiQ\n/p/AX4FXF1ubJD0CnBkRZ9RZV70K6vFnnnmG0aNH90v5m0lnZydTp05l/PjxdHR0NLo4PbLdxMn9\nst67J+7e4zKMGBKcuONSjr1lCIuW9v/dc90payvr6vM6d+5c1l13XYA1I2JuX283t2z/CVgrIt6e\n0w4EzouIEaW8NwFXR8SRkn4CbBoRuxfmjwReAvaKiCvqbGsidU7kfv3rXw+qEzmzVjV//nwOPPBA\n6GZ91B9DDgg4C9gXGFcMmLJbgU5gN+DivMzWpM7iM+qtMyIWAYsK2wCgo6OjZYOInmjl/e2vW/q3\nOnZKN3LXL8OipRqQIQda9X/XU+XP6wDsf1+1bFdxEnB6YXoU8PiECRNWeiLXDidAzaq7x7a/TuSq\naqWTqHb83M6d27Pztv64PDcJOJDUyjRPUq2f0gsRsSAiXpD0M+B0Sc8Cc0lB1ozcv8DMrFtyy/be\npJbtxwuzngKGS1qr1I9yTJ5Xy1O+eDumMG8FvT2Ra+UToGZX9dg2emy2Vvz/t9Pntqf70R9B06H5\nfVop/WDg/Pz3F4GlpJamVwa37IeymFkb66OW7RnA0ZLWj4jZOW086YTunv7dA+trHqzW+lOfB00R\nscpPa0QsBA7PLzOznuqLlu0ppODol5K+RrqL91vApNyiZNbn/GDy1uTB28yslfW6ZTsilkjam3S3\n3AxSB/ALgOP6q9Bm1pocNJlZy+qrlu2IeATYqw+LZmZtaCBGBDczMzNreQ6azMzMzCpw0GRmZmZW\ngYMmMzMzswrcEdzMzJpW1VvzRwyNfnvGpVmNW5rMzMzMKnDQZGZmZlaBL8+ZDRCPAGxm1trc0mRm\nZmZWgYMmMzMzswocNJmZmZlV4KDJzMzMrAIHTWZmZmYVOGgyMzMzq8BBk5mZmVkFDprMzMzMKnDQ\nZGZmZlaBRwS3HuvOCNdmZtYzfppA83BLk5mZmVkFDprMzMzMKnDQZGZmZlaB+zSZmdmAcn9Ia1UO\nmmwFrtAazx0/zcyajy/PmZmZmVXgoMnMzMysAgdNZmZmZhU4aDIzMzOrwEGTmZmZWQW+e26Q8B1x\nZmbtz3fe9i+3NJmZmZlV4JYmsxZX9czSZ5XWn9yabYOBW5rMzMzMKnBLk5mZ2SBUtXXwHydO6OeS\ntA63NJmZmZlV4JYmMzPrkvsqmS3joKmHfFuntTN/vs2sZruJkzllp/S+aIlWmrfd6wNfnjMzMzOr\nwC1NZmZm1ifavZW6YUGTpMOBrwIbAHcAn4uIm/pjW42+Jt/uHyKzdjCQdZKZtaaGBE2SPgycDnwW\nuBE4ApgsaeuImN2IMpnZ4DXY6qRGn0iatapGtTR9CfhpRJwHIOmzwHuATwAnN6hMTaFeZTZiaFTu\nhGfWFf9QrpTrJLMB1opXYQY8aJI0HNgBOKmWFhFLJV0J7DLQ5TGzwa1d6iQHxdbOmiXAakRL07rA\nUGBWKX0WsE29BSSNAEYUkkYBPPvss3R2dq5yg8NefqlHBW0Ww5YG8+cvZVjnEJYsdUtTX/Fx7Rtz\n5sxZbrqzs5P58+czZ84cOjo6XkmfN2/eQBetqgGrk2rH5k1HX8KiPv7MDfa7evx97j+tdmzLdVI9\nPa2PWuV7dhRwfDlx8803b0BRGuPARhegTfm49t663+v2IqOAuX1fkgE16OukZuTvc/9ppWPbzTqp\nW/VRI4KmZ4AlwJhS+hjgqS6WOYnUSbNobeDZvi1a0xoFPA5sBDTt6XoL8nHtHys7rqOAJwe8RCs3\nkHWSP3P9x8e2/7Trse12fTTgQVNELJZ0K7AbcCmApCF5+uwullkELColt/qZamXSK82h8yJi0Ox3\nf/Nx7R+rOK5Nd5wHsk7yZ67/+Nj2nzY+tt3el0ZdnjsduEDSLcBNpNt7VwfOa1B5zGxwc51kZqvU\nkKApIn4naT3gBNJAcrcDe0REuSOmmVm/c51kZlU0rCN4RJxNF03ftoJFwDdZ8XKA9Y6Pa/9oyeM6\nQHVSSx6bFuFj2398bDNFRKPLYGZmZtb0hjS6AGZmZmatwEGTmZmZWQUOmszMzMwqcNBkZmZmVoGD\npiYm6ShJN0uaJ2m2pEslbd3ocrUTSV+XFJLObHRZWp2k10r6laQ5khZIukvSjo0uVzORdLikmZIW\nSrpR0k6NLlOrcz05MFxXJg6amts7gUnAzsB4oAOYImn1hpaqTUh6C3AIcGejy9LqJL0auA7oBPYE\ntgW+DDzXyHI1E0kfJg2i+U1ge+AOYLKk9RtasNbnerKfua5cxkMOtJA8+N5s4J0RcU2jy9PKJK0B\n/A04DDgGuD0ijmhsqVqXpJOBt0XE2EaXpVlJuhG4OSL+O08PAR4DzoqIkxtauDbierJvua5cnlua\nWsua+X2wPKi4P00CLouIKxtdkDbxPuAWSb/Pl0huk/TpRheqWUgaDuwAvPJ5i4ileXqXRpWrTbme\n7FuuKwsaNiK4dU8+Kz0TuC4i7m50eVqZpANIl0fe0uiytJHXAYeSLj99h3RsfyBpcURc0NCSNYd1\ngaFA+bEss4BtBr447cn1ZN9yXbkiB02tYxKwHfD2RheklUnaGPg+MD4iFja6PG1kCHBLRHwjT98m\naTvgs4CDJhsorif7iOvK+nx5rgVIOhvYG3hXRDze6PK0uB2A9YG/SXpZ0sukjqSfz9NDG1u8lvUv\n4J5S2r3AJg0oSzN6BlgCjCmljwGeGvjitB/Xk33OdWUdbmlqYpIEnAXsC4yLiIcbXKR28FfgjaW0\n84D7gO9GxJKBL1JbuA4o3+b9euCRBpSl6UTEYkm3ArsBl8Irl5J2ww8u7xXXk/3GdWUdDpqa2yTg\nQGAfYJ6kDXL6CxGxoHHFal0RMQ9Yrq+DpJeAOe4D0StnANdL+gZwEbAT8Jn8suR04AJJtwA3AUcA\nq5N+iKznXE/2A9eV9Tloam6H5vdppfSDgfMHtCRmKxERN0vaFzgJOA54GDgiIi5sbMmaR0T8Lt8O\nfwKwAXA7sEdElDuHW/e4nrQB43GazMzMzCpwR3AzMzOzChw0mZmZmVXgoMnMzMysAgdNZmZmZhU4\naDIzMzOrwEGTmZmZWQUOmszMzMwqcNBkZmZmVoGDJjMzM7MKHDSZmZmZVeCgyczMzKwCB01mZmZm\nFThoMjMzM6vAQZOZmZlZBQ6azMzMzCpw0GRmZmZWgYMmMzMzswocNNmAk7SWpJD0rQaW4XZJlzZq\n+2Zm1nocNLUISVdIek7SmDrz1pT0L0k3Suqz/6mkPXJws6rXwr7aZg/LeUIux44ryfPVnOcdA1k2\nMzNrH8MaXQCr7DDgbuAM4MDSvO8A6wJ7RMTSPtzmHcBHS2mnAbOAUwtpS/pwmz1xIXAs6bjc0kWe\nA4FHgel5eicg+r9oZmbWLhTh341WIelrwHeB3SNiSk57C3ADcFpEHDkAZXgQeDAi9ujFOtYCngO+\nHRHH9FG5bgFeA2xcDhwlbQPcC5wcEUf1xfbMzGzw8eW51nI6cCfwQ0mrSRoKnAM8AnyzlknSVpIu\nkfS8pPmSrpc0obgiSZ/Nl6s2KKXXLsnt3N3CSbpU0u110s+U9HwXy3xG0kOSFkiaUe8Sm6TNJV0o\n6WlJCyXdIemAUrZfARsC4+ps5iP5/cLCOlfo0yRpdUknS3pY0iJJMyV9U9KwQp6rJF1VWm56+dKf\npN1z2i55+lV53f/M+/C0pKslva3ecTEzs+bjy3MtJCJelvQZ4HrS5ajZwPaky3LzASRtlOcPA34A\nPA98Arhc0vsi4vKGFL6+95EuK56dpz8H/FXSmyLiYQBJmwE3AnNJQeMLwD7AbyStFhHn52V/S7p0\neCCwXFAD/BdwZ0Tc3VVBJHUAU4DtgB8DDwI7AscAmwIH5azTga9K6oiITkkjgLcAS4GxwDU531hg\nAcsuF54GHAL8iHTZcy1gZ+DfgetWepTMzKwpOGhqMRFxo6QfAl8FFgG/iYjJhSxHA+sAb42ImwEk\n/Qz4OynoaKag6d+AN0TEAwCS/ge4ixQQfiLnOY0UML05IubltB9KugI4SdIvI2JJRDyVW4A+KOmw\niFic1/lWYAtgVZcuDyEFPztFRK217CeSHgJOlnRqRPydFDQdRwqoZpD6Rg0HLiYFSjVjgRsiojNP\nvwf4bUR8rltHyMzMmoYvz7Wmo4E5pNaNL5bm7QVMrwVMABHxAnAusLWkLQeslKs2tRYwAUTEvcCV\npH0gt+K8F7gEGCFp3doL+F9gA2Cbwvp+RWrB2auQdiCpw/dvVlGW/YGbgcdL2/lrnj8uv88AXgZq\nl+LGkgLSPwK7ShoqaTgpmKp1OofU4vdmSZuuohxmZtakHDS1oIiYC9wPPBYRs2rpebiBjfO8snvz\nezP9aP+jTtoDwBhJq5HKOpzUqvZ06XVmzr9+Ydn/IV0SOxAg9/n6EHBNRDy2irJsBexaZzu14HN9\ngIh4CbiNZa1KY0nB0TXAKOA/SC1Wq7F80HQUsAnwsKTbJH07d1A3M7MW4ctzg1dXt00ObaJ11oL6\nc0iXv+q545WNR8yT9EdgH0mjSH2GNiBdTquyrRkryftw4e9rgYNzP6hdgV9ExKOSHiUFUa8itUbN\nKJTtCklbAO8HxpP6b31V0v+LiIsqlM/MzBrMQVMbiYilkh4Dtq4zu9aq8Uh+fy6/rwU8VcjXm5ao\n54A310nvap1b1Ul7PTArIhbmIKQTiIi4smIZLgQOAPYF3gUsBv5QYbmHgLUqbmc66bLo/wNGs6xF\n6RqWBU1/y61Sr4iI2cBPSH2l1gJuIgVpDprMzFqAL8+1n8uBsZK2ryVIGg18Crg/Ih7MyQ/l9+Jt\n8h3Ap3ux7YeAjSVtXljnFsDuXeQfL+n1hbzbAO8GrgDIdwReBnxM0uvKC0tar846JwPPAAeTAqfL\nI+K5OvnKLgK2lfShOttZI18urLk2vx8JzIyIx/P0dFLQtCvLX5pD0jrF6Yh4HpgJjKhQNjMzawJu\naWo/3wb2A66U9APSnWcHk8Ywem8tU0TcKuk24DSlR7PMJY1n1JvRvX8BHA9cJulHpFasw4B7gM3r\n5L8XmCbpLECkS1bzgeIz6b5IGrzzNkk/IfV5Wo/Ub+jNwGbFFeZhAC7K24XC2Eyr8CPgg6ShDN5D\nGuZgBLAtqV/UDqRhCIiIpyXdR2q9+2VhHdewrI/VckETqYP5JaT+UC8AbyNdpjuxYvnMzKzBHDS1\nmYh4PA+Y+F1SwDEcuB3YqzQ0AaTLWOeQ7sZ7lnTp6GbgLz3c9mO5peZk0lAB/wAOJd15Vi9o+hPp\n0SZfJwV1twOfj4haKxgRMTMPeHk8qYP3eqQO2neRxlCq50JS0DS36r5ExOI8AOjX8nYOAOaRAqWT\ngSdKi0wnBU3XFtZxn6SnSWNPXVvKfzqwB2nogQ5SH6kvs6xDu5mZNTk/RsXMzMysAvdpMjMzM6vA\nQZOZmZlZBQ6azMzMzCpw0GRmZmZWgYMmMzMzswq6FTRJmigpSq/7CvNXkzRJ0hxJL0q6OI8BVFzH\nJk4C2YIAAAl6SURBVJIukzRf0mxJp0ry0AdmZmbW1HoSrPydNGpzzcuFv88gjUOzP2kAv7NJT6h/\nG7zyANXLSI/t2BV4DWlAxE7gG1ULIEmkcX3m9aD8ZtY4o4Anw2OdmFkL6tY4TZImAu+PiDfVmbcm\nadDBAyPiDzltG9Koz7tExA2S9iQNNrhhRMzKeT5LGohxvYhYXLEcrwUeX2VGM2tGG0VEebBQM7Om\n15OWpq0kPQksJD3F/aiIeJT0mIkO4JUHnuYRkh8FdiE9CmMX4K5awJRNJj3C4g2kR0xUMQ/g3HPP\n5f3vfz8dHR092I320NnZyZQpU5gwYYKPg48D0LzHYu7cuWy88cbgFmIza1HdDZpuBA4C7iddWjse\nmC5pO2ADYHF+EGnRrDyP/D6rznwKeVYgaQTLP9h0FMDIkSN51ate1VQ/DANt2LBhPg74OBQ167Ho\n7OxsdBHMzHqlW0FTRFxRmLxT0o3AI6QHmi7oy4KVHEUK0FYwderUftxs6/BxSHwclmm2YzF//vxG\nF8HMrFd6dddaRDwv6QFgS2AqMFzSWqXWpjGkjt/k951KqxlTmNeVk0gPPK0ZRe7TNH78+KY6mx5o\nnZ2dTJ061cehD4/DdhPLzzXu2t0Td+/VtvpDs34m5s6d2+gimJn1Sq+CJklrAFsAvwRuJd0Ftxtw\ncZ6/NbAJqe8T+f1oSetHxOycNp70NPp7utpORCwCFhW2+8q8jo6OpvphaJT/3979h9pd13Ecf772\nw/1hElG5sCUSlBALJGtpP5AS6cek6C+lf6KgMjWxwpgS5SLYkFiWjv6QsFEh1T9B7I/Jgoh0bU6d\nGfVHfzhLS81r2GXTqXfv/jjnunXn8nO3e8/nnnOfDzhs53u/55zXPtsfr32+n/P5Og4DCzEOR2by\n6icd93lL1VL7N7GUskjSqZhXaUryXeDXDC7JnQNsBmaAu6rq2SQ/ArYleYZBEboN2FNVfxi+xd0M\nytFPknydwTqm7wDbh8VIkiRpSZrvTNM64C7g9Qy2F/g9cFFV/Wv4868ARxnMNK1h8M24q2dfXFUz\nSS5n8G25PcAhYAfwzdP4M0iSJC26+S4Ev/JVfv48cM3wcbJzHgU+Pp/PlSRJ6s3bl0in4bxNO5vP\nPbh14yImkSQtNm/YK0mS1MCZJi0b85kVkiRpLmeaJEmSGliaJEmSGliaJEmSGliaJEmSGliaJEmS\nGliaJEmSGliaJEmSGliaJEmSGliaJEmSGliaJEmSGliaJEmSGliaJEmSGliaJEmSGliaJEmSGlia\nJEmSGliaJEmSGqzqHUBaLs7btLP53INbNy5iEknSqbA0aazNFpE1K4tbNsD6m3dxZCadU0mSJpGX\n5yRJkhpYmiRJkhpYmiRJkhpYmiRJkhpYmiRJkhpYmiRJkhpYmiRJkhpYmiRJkhpYmiRJkhpYmiRJ\nkhpYmiRJkhpYmiRJkhpYmiRJkhqs6h1Amuu8TTt7R5Ak6QSWJmkJmk9xPLh14yImkSTN8vKcJElS\nA0uTJElSA0uTJElSA0uTJElSA0uTJElSA0uTJElSA7cc0Ei495Ikadw50yRJktTA0iRJktTA0iRJ\nktTANU3SmJu7XmzNyuKWDbD+5l0cmcnLx73diiSdHmeaJEmSGliaJEmSGnh5TqfMbQQkScuJM02S\nJEkNLE2SJEkNLE2SJEkNXNOkE7hWSZKkE3UrTUmuAW4A3gQ8BHy5qvb1yjPpLEKSJJ2eLqUpyRXA\nNuAqYC9wPbAryflV9VSPTNKkm09xdiNMSTpRr5mmrwJ3VNWdAEmuAjYCnwO2dsq0JMx3Ruhkuz9L\nkqSFNfLSlOQM4EJgy+yxqjqaZDdw8UleswZYc9yhswAOHz7M1NQUq1evXsTEo7XqpUPzO/9ocfjw\nUVa9uIKZo8u3NDkOxyzEWExNTS1wKpienl7w95SkUUpVjfYDk3OAx4H3VdWe447fAlxSVe99hdfc\nDHxrZCElLaZ1VfV47xCSNF/j8u25LQzWQB3vXOBhYB2wnP8LexbwGI6D43DMUh6Ls4B/9A4hSaei\nR2l6GpgB1s45vhZ44pVeUFVHgCPHH0vyt+Fvp6vqPwsdclwkL19+cRwGlvU4wJIfi6WWR5KajXxz\ny6p6AbgfuHT2WJIVw+d7TvY6SZKknnpdntsG7EiyH9jHYMuBM4E7O+WRJEn6v7qUpqr6eZI3At9m\nsLnlAeCjVfXkPN7mCLCZOZftliHHYcBxOMaxkKRFMPJvz0mSJI0jb9grSZLUwNIkSZLUwNIkSZLU\nwNIkSZLUYCxLU5JrkhxM8nySvUk29M40akluTHJfkukkTyX5VZLze+fqLcmmJJXk1t5ZRi3Jm5P8\nNMlUkueSPJzk3b1zSdKkGLvSlOQKBvs8bQbeBTwE7Epydtdgo3cJsB24CLgMWA3cneTMrqk6SvIe\n4IvAH3tnGbUkrwPuAV4EPga8A/ga8O+euSRpkozdlgNJ9gL3VdW1w+crgL8Dt1XV1q7hOhrue/UU\ng5se/653nlFL8hrgAeBq4BvAgaq6vm+q0UmyFXh/VX2wdxZJmlRjNdOU5AzgQmD37LGqOjp8fnGv\nXEvEa4e/PtM1RT/bgZ1VtftVz5xMnwD2J/nl8HLtg0k+3zuUJE2SsSpNwBuAlcDcncOfZLCz+LI0\nnG27Fbinqv7UO8+oJbmSwaXaG3tn6eitwJeAvwIfAX4I/CDJZ7qmkqQJ0uvec1pY24H1wAd6Bxm1\nJG8Bvg9cVlXP987T0Qpgf1XdNHz+YJL1wFXAjn6xJGlyjNtM09PADLB2zvG1wBOjj9NfktuBy4EP\nVdVjvfN0cCFwNvBAkpeSvMRgkfx1w+cr+8YbmX8Cf55z7C/AuR2ySNJEGqvSVFUvAPcDl84eG16a\nuhTY0ytXDxm4HfgU8OGqeqR3pk5+A7wTuOC4x37gZ8AFVTXTMdso3QPM3XLi7cCjHbJI0kQax8tz\n24AdSfYD+4DrgTOBO7umGr3twKeBTwLTSWbXdD1bVc/1izVaVTUN/M86riSHgKlltr7re8C9SW4C\nfgFsAL4wfEiSFsDYbTkAkORa4AYGi78PANdV1d6+qUYrycn+4j5bVT8eZZalJslvWWZbDgAkuRzY\nArwNeATYVlV39E0lSZNjLEuTJEnSqI3VmiZJkqReLE2SJEkNLE2SJEkNLE2SJEkNLE2SJEkNLE2S\nJEkNLE2SJEkNLE2SJEkNLE2SJEkNLE2SJEkNLE2SJEkNLE2SJEkN/gvcYYRDKtELrgAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115786810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot\n",
    "\n",
    "log_df = np.log10(social_df)\n",
    "log_df.hist(bins=20)\n",
    "pyplot.tight_layout()  # this line is usually necessary when you have multiple subplots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like that did the trick! Now that our data is normally distributed we can check whether any of these variables are correlated. Pandas dataframes have a built-in correlation method that gives correlations coefficients between every pair of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>FaceBookPageLikes</th>\n",
       "      <th>TwitterFollowers</th>\n",
       "      <th>YouTubeViews</th>\n",
       "      <th>InstagramLikes</th>\n",
       "      <th>InstagramFollowers</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>FaceBookPageLikes</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.410080</td>\n",
       "      <td>0.298984</td>\n",
       "      <td>0.466838</td>\n",
       "      <td>0.525900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TwitterFollowers</th>\n",
       "      <td>0.410080</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.189475</td>\n",
       "      <td>0.540367</td>\n",
       "      <td>0.691184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YouTubeViews</th>\n",
       "      <td>0.298984</td>\n",
       "      <td>0.189475</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.221682</td>\n",
       "      <td>0.322739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>InstagramLikes</th>\n",
       "      <td>0.466838</td>\n",
       "      <td>0.540367</td>\n",
       "      <td>0.221682</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.851220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>InstagramFollowers</th>\n",
       "      <td>0.525900</td>\n",
       "      <td>0.691184</td>\n",
       "      <td>0.322739</td>\n",
       "      <td>0.851220</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    FaceBookPageLikes  TwitterFollowers  YouTubeViews  \\\n",
       "FaceBookPageLikes            1.000000          0.410080      0.298984   \n",
       "TwitterFollowers             0.410080          1.000000      0.189475   \n",
       "YouTubeViews                 0.298984          0.189475      1.000000   \n",
       "InstagramLikes               0.466838          0.540367      0.221682   \n",
       "InstagramFollowers           0.525900          0.691184      0.322739   \n",
       "\n",
       "                    InstagramLikes  InstagramFollowers  \n",
       "FaceBookPageLikes         0.466838            0.525900  \n",
       "TwitterFollowers          0.540367            0.691184  \n",
       "YouTubeViews              0.221682            0.322739  \n",
       "InstagramLikes            1.000000            0.851220  \n",
       "InstagramFollowers        0.851220            1.000000  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not surprisingly Instagram like are highly correlated with Instagram followers. We could also get correlation coefficient and the corresponding p-values from stat's personr method. In this case we have to do a little bit of extra work to drop any rows that have NA values. Let's dig into the correlation between Instagram likes and Instagram followers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8512202450831523, 2.4120520518988779e-57)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dropping any rows that have NA values for either InstagramLikes or InstagramFollowers\n",
    "log_df_inst = log_df[['InstagramLikes', 'InstagramFollowers']].dropna()\n",
    "\n",
    "stats.pearsonr(log_df_inst['InstagramLikes'], log_df_inst['InstagramFollowers'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first value in the resultig tuple is the correlation coefficient (which matches what we got from panda's corr method), and the second is the p-value. The very very small p-value means that we can be very confident that these two features are indeed positively correlated.\n",
    "\n",
    "Let's go a step further and plot the results in order to make a conjecture about the relationship between the two variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11a0d7410>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fL6jT8IAMBEkDh3vxqkR+xf/Zmdkg4IvAnCQHNLMrgGuA7zrnPpuwXSK5k2Zy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\njf+zPQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a08a850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_df.plot(kind='scatter', x='InstagramFollowers', y='InstagramLikes', title='log10-log10 axes')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relationship looks linear. Let's try to fit a few functions to the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the slope and y-intercept of the best fit line are 1.06814198321 and 0.643323493171\n",
      "the coefficients of the second order polynomial are -1.27052575888, 2.41263664103, and -0.222587639001\n"
     ]
    }
   ],
   "source": [
    "from matplotlib import pyplot\n",
    "\n",
    "x = log_df_inst['InstagramFollowers']\n",
    "y = log_df_inst['InstagramLikes']\n",
    "\n",
    "(m, b) = np.polyfit(x, y, 1)\n",
    "print('the slope and y-intercept of the best fit line are %s and %s' % (m, b))\n",
    "\n",
    "(C2, C1, C0) = np.polyfit(x, y, 2)\n",
    "print('the coefficients of the second order polynomial are %s, %s, and %s' % (C0, C1, C2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lVLXs2gqCIAhlgq0JFcjdtqjIX855Aw0b1fSjX2QoK2MSXD7xWP/exLkxT1Nr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\nfJFASTfRxqtTXu5xJs9fyfyfv9njPeccf/7hY37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QdqkqxS+OxEPMzdu7d8N//gN33gkr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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a1e8b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create dummy points along the x-axis to plot our fit curves against\n",
    "xi = np.linspace(min(x), max(x), 100)\n",
    "\n",
    "# define functions that map the the linear (f1) and 2nd order (f2) curves to values along the y-axis\n",
    "def f1(xi):\n",
    "    return b + m*xi\n",
    "\n",
    "def f2(xi):\n",
    "    return C0 + C1*xi + C2*xi*xi\n",
    "\n",
    "pyplot.scatter(x, y, s=11, label=None)  # plot the data\n",
    "pyplot.plot(xi, f1(xi), c='r', label='linear fit')  # plot the linear fit\n",
    "pyplot.plot(xi, f2(xi), c='g', label='2nd order fit')  # plot the 2nd order fit\n",
    "\n",
    "pyplot.legend(loc='upper left')\n",
    "pyplot.xlabel('log10(Instagram Followers)')\n",
    "pyplot.ylabel('log10(Instagram Likes)')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both the linear and the 2nd order fits go right through the middle of our data points, but the 2nd order fit does a little better at the ends. We can measure the \"goodness\" of the fit with the [Coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination) (more commonly referred to as the \"r-squared\" value). r-squared varies between 0 and 1, 1 meaning the fit line passes through every data point (perfect fit) and values close to 0 meaning the line does a very poor job fitting the data. There are built in python functions to compute r-squared, but it's [definition](https://en.wikipedia.org/wiki/Coefficient_of_determination#Definitions) is short so let's write our own function to calculate it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-squared for linear fit: 0.724575905639\n",
      "r-squared for 2nd order fit: 0.755966152427\n"
     ]
    }
   ],
   "source": [
    "def rsquared(f, x, y):\n",
    "    yhat = f(x)\n",
    "    ybar = np.sum(y)/len(y)          # or sum(y)/len(y)\n",
    "    ssreg = np.sum((yhat-ybar)**2)   # or sum([ (yihat - ybar)**2 for yihat in yhat])\n",
    "    sstot = np.sum((y - ybar)**2)    # or sum([ (yi - ybar)**2 for yi in y])\n",
    "    return ssreg / sstot\n",
    "\n",
    "rsq_linear = rsquared(f1, x, y)\n",
    "rsq_2nd = rsquared(f2, x, y)\n",
    "\n",
    "print('r-squared for linear fit: %s' % rsq_linear)\n",
    "print('r-squared for 2nd order fit: %s' % rsq_2nd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The r-square gives us a way to quantify our intuition that the second order polynomial fits the data a little better than the straight line. This is to be expected. The extra coefficient in the 2nd order equation gives the function an extra degree of freedom. In fact, polynomials can have any number of degrees of freedom and it can be tempting to keep increasing the order of the polynomial until the curve fits the data perfectly. But look what happens when we fit the data to a 30th order polynomial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r-squared for 30th order fit: 0.774511728656\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/numpy/lib/polynomial.py:595: RankWarning: Polyfit may be poorly conditioned\n",
      "  warnings.warn(msg, RankWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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dvjGlOoAVVBkREZGCr4wkHUaAF/DWF4k1v9S/P+76IxNgETALeMS/wzl3zMyeBlYRJ4yY\nWRlQFnVXVcZamE5lRJvliYiIpvYOWpSxVgRjVuR65O7BjVGPxXILcFtGWjRSOpURddOIiEiBD2BN\nOow45/ZksiFZdDtwR9Sfq4D9GXml8VRG1E0jIlK8CrybJt8GsCZyOHLdMOL+hqjHRnHO9Tjn2v0L\n0JGpBo6rMtLUlFdL+4qISIAKvDJSSGFkF17ouMK/w8yq8WbVrM1Wo4ZJpzJSV+eNjHYODsfNVCIi\nUsgKfG+avAojZlZpZmeZ2VmRuxZF/rzAOeeArwL/ZmavNrMzgB8AB8mV/XTSqYyEQho3IiJS7Aq8\nMpLKANZccC7weNSf/bEe3wduBL6AtxbJt4Fa4I/ANc65ExPYxvjSqYyAF0b27NG4ERGRYlXgY0by\nKow4554g9tRi/3EHfCJyyT3pVEZA03tFRIqZc+lP7c2THd9TDiNmNgP4NHA53i69w7p6nHPTg2la\nARpPZQRUGRERKUYnTkA47N1OpZsGoL9/aEXWHJZOZeSHwCnA3XhreGRzobP8ks7eNKDKiIhIMfO7\naCD1MNLbW7Bh5BLgYufcuqAbU/DS2bUXNIBVRKSY+V00U6ZAScnYx48MI8kEmCxLZzbNFiDFr/YC\njL8yom4aEZHik8rgVfACiz9OJE8GsaYTRv4R+JyZXWpmM8ysOvoSdAMLigawiohIqlKZ1gteEMmz\nnXvT6aZpA6qBx0bc72+Ul0QNqUiNdwBrR4d3qcrcXn4iIpJjUq2MgNdV09tb0GHkx0Af8DY0gDU1\n6VZGKiuhpgaOHYN9+2DZsuDbJiIiuSmVab2+PFtrJJ0wsgJ4mXNua9CNKWgDA0O/FKlWRgAWLYIX\nXoBduxRGRESKSardNJB3YSSdMSPPAPODbkjB6+kZup1qZQRg8WLveufOYNojIiL5Id1uGsibMJJO\nZeS/gK+Z2ReBDXhdNoOcc+uDaFjB8ceLQHqVEYUREZHiNJ7KSJ5slpdOGLkncv3dqPscGsCamD9e\npLTUu6RKYUREpDipMhLTosBbUQzSnUnjUxgRESlORTBmJOUw4pzbk4mGFLx0Z9L4Tj7Zu965M282\nPhIRkQBoNk18ZrYMWABMjr7fOfeb8TaqII23MrJgAYRC0N0NTU3Q0BBc20REJHepm2Y0M1sM/C9w\nBkNjRWBovRGNGYkl3aXgfZMnw/z5sGePVx1RGBERKQ5F0E2TztTerwG7gJlAN7AceAXelN/LAmtZ\noUl3k7xo/riRHTvG3x4REckPRVAZSSeMrAI+4Zw7AoSBsHPuj8AtwH8G2biCMt7KCGgQq4hIMVJl\nJKYSoCNy+wgQ2TiFPcCSIBpVkIKsjCiMiIgUj3QqI0WwUd5GYCVeV83TwEfNrBd4N6CzZDyqjIiI\nSDqKoDKSThj5LOD/jXwC+C3wB6AFeHNA7So8453aCwojIiLFSFN7R3POPRh1ezuw1MymA0edc9rB\nN57xTu2FoTBy4IAXbsbzXCIikh80gHU4M5tkZv1mtiL6fudcq4LIGIKojMyYAVVV3u3du8fdJBER\nyXHOFUU3TUphxDnXB+xFa4mkLojKiJm6akREiklvLwwMeLfTqYzkyUZ56cym+Rzw75GuGUlWEJUR\nUBgRESkmflUECroyks4A1vcDpwAHzWwP0BX9oHPu7CAaVnCCqIyAwoiIyDiFw441Gw+zu6WLk2ZU\ncO2KWYRCObrflz9epKwstR3fiyCM/DrwVhSDoCsjWoVVRCRl4bDjvT96loc2NVISMgbCjquXN/DN\nvz0nNwNJOuNFoPDDiHPuU5loSMELqjISvXuviIikZM3Gwzy0qRGAgbA37+LBFxtZs/Ew1585O5tN\niy2dab2QMIzkYmUo7V17JUVBLHoGw7tpnPMGtYqISFJ2t3QNVkR8JSFjd0tXgp/KonSm9QLhSZMI\nAdv2tfDS+kODgSNXK0MpD2A1s6Nm1hrj0mJmB8zsSTN7ZyYam9eCWA4eYOFCL4B0d0NT0/jbJSKS\nI8Jhx/3rD3Hn49u5f/0hwuHgV4w4aUbFsCACXoXkpBkpdoNMlDS6acJhx09fOAzA9gOt3PST53jf\nj58drIg89OJhPvfg17n1oW8xtffEYGUom9KpjHwauBVYA/wlct/5wDXAncAi4JtmVuqc+04grSwE\nQVVGJk+G+fNh716vOtLQMP62iYhkUTjsuH/DIb726Da2N3Vl9Bv7tStmcdWyhlGVgWtXzArsNQKV\nRhhZs/Ew65uO87fApP5+YKgrandLF+XhPv72hQcA+PIlb8+JylA6YeRi4N+cc3dF32lm7wGucs69\n3szWAzcDCiO+oCoj4HXV+GFk1arxP5+ISBpSHXsQ63hgsNvAF8RYjnhtC4WMu95+Ts6NmYjLDyP+\ngpdJ2N3SxUCpt1HepAEvjPiB46QZFZT2DY0j6SmdnBOVoXTCyNXAv8S4/1Hgy5HbvwM+n26j0mVm\nnwRuG3H3Vufc0oluyyhBVUbACyNPPKFBrCKSNWONPRgZBq5e1sA//uS5UcffcOacYUEkWrrf2Mdq\nWyhkwwKO3z2Uk+Gko8O7TiGMnDSjgq3mrU06KewteuYHjmtXzOKJxTXefRaiP1SSE5WhdMJIK3AD\n8JUR998QeQy8jfQ6xtGu8XgRuDLqz/1ZasdwQVdGQGFEJMNycdZBrrQr0ayUa1fM4j0/fIaHNzdh\n5o21P3NuNesPtI86vqWzd9SAUl+639jHnDHT1QX79sG0aYTrZ+bkgM5BaYSRa1fMYt/COgAmR1Zv\n9QNHKGT8x/WnwQchXFbGnX97Tk78XqcTRj6DNybkcobGjJwHXAe8N/Ln1cCT429eWvqdc9kdiRNL\n0JURUBgRGYfoE/qC6eUYsKe1O2b3QaZPUqmEi1RnQ2QquCSalXL/hkM8vNkbYO/vWuYHkZGe2XM0\n7muM/MYe/V4WTi/HAXujPjP/fUW3bXr3Ma7Y/hcu3/UM5/+iBY42wtHIa5aWsudN/4en666EqVU5\nN9U3HHbs3nmIxcCOE8aisEvqswuFjHdfuRS+DgsqS7jzbWcP+/sJ9fYAMKl8atbfoy+ddUa+Y2ab\n8FZifV3k7q3Apc65pyLHfDnez0+AU83sIHACWAvc4pzbG+9gMysDyqLuSj5+pkKVEZGcEX1CDxn4\n59N43QeZPEklChfhsOP2B7awrbGD0xqquOWapTy4qTFhRSKZrpEgAtXC6eVxZ6U8+KL3fXB2ezNn\nH9jCwrZDzDvWyLxjTcw71khVbzcOw5nhgBOlZTRWzeBAdT2HquronTOXC69ZxQWXzwbnuH/9YXYd\n6eShTY2s339sWAjyP7/B99Xfx8qD23jX2v/hyu1Pc86BLZS48Og3UFkJnZ0s+sndPDnlHr728rfy\nw5ddT39JaU4M6PR/Ly5bt4fFwL07Otj642eT/uxCU7zTWsOU0Ojf16AW4QxQWuuMOOf+BPwp4LYE\n4WngRrxwNBtv/MgfzGyFcy5et9EtjB5nErxMVEYOHPB+qYIIOCI5YiK6IKLL+NHn0+iTe1lpyYSs\nRxGvS+G36w/ymd9uprnT+xb7h5eOcN+6g/zdhQtitmvXkc5RoWblvBrW7T826rmTCVTxBpuu2egF\nAz9wRHtrfT/X/uleZv74N3x0w7PMa09++YGT2g4Nv+NXXwXg+NQK5tbOxdU08OrK6VxQOYPGqhkc\nn1TG1L4TlPeeoLyvh4bHW2i7Yx/Tt2zg4hMnuDjqqV6cuZidF13BdX//Gv7YU87WyTXMXTCLaw9v\npPP9H6T2pc3c9uh3ePvza/i7N3+ag9Uzsz6g0/+9uL7XO3d0TZqSWhhOtFFekF+OAzKuRc/MbAow\nOfo+51zsWtwEcM6tifrjejN7GtgDvAm4O86P3Q7cEfXnKmB/4I0LMonW1Q2menbvhqXZH58rEoQg\nF2TyT6a7jnRytLuPaeWTWFRXybUrZsXsYohWEnmtWN/8W7t6ufPx7SkFpUQBK153xw/W7hkMIr6m\njh6e33csZrue29vGY1uahrV73f5jwyo//nPHClQju61+s+4AD29qGmzbVcsacM7x8OamwecMhQc4\n++AWrtj+V1654y8sOeIVoc+LPGe/hdjUsJitdSexv2Ym+2sa2F8zk/Yp3oneHBiOqX0nmNN+hNkd\nzcxuP8K8Y41c2NdCxf7dTD3exVnHt3HWoW1j/j37emumcXDpSjafdRGNl15F/fLTuHZZA+8brBJ1\nM/DHg1y9vIE7N6zjB+/9JNf+/Buc3Lqff338e/zmli9nfUCn/3tR3hcJI5OnphaGEy0HH9SK4AFK\nOYyYWTnwBbwT/IwYh5SMt1FBcc61mdk2vI394h3TAwz+i7dMrGg6MDD0CxHEh2/mVUfWr/e6ahRG\npEDEqxLcv+EQN6ycM+bPRwcQv6RvQPSp++rlDVx/xuy4QcR/7StOn8naHUdo7hz6z3xyiXH3H3el\nFJTCYcd7fvQMD28aGsx5yswKPnjFaVx/xuy4i3B19cQee9/XHx5cJyOaH0SijQwi/nOP/NYfKwRG\nHw8Mvl5lTzev2PUcV2x/mlfueIZpJ4aKzuFQCaGXX4S77DK+0tPA/+tr4HjZ1MFxI6n4yNVLsJ4e\nfv2LJ1ncup857UeY2dnCrM4WZnW0UNbfR/fkMronTeH4pCm0TanijNdcwa/K5vPD1imUlIS8z6i/\ngm9Guq9i/W49sKWZP1z+Gn4cmsOa736AV235A+t2bQbOTb3RAfJ/Lyp7h8JISgN6E4WRAqmMfBG4\nHHgf8EPgJmAu8B7gY8E1bfzMrBI4Ga+d2dMT9e0mqD66U07xwsjmzXDddcE8p0gKEn3bT7erZXdL\nV8wT6Nce3cb1Z8we9hyJpo5GP8fI8+CDLzbS2x9jDAEMBperlzdAmGFBBKB3wHu2RF0e4bDjdxsO\n8eCLhzl07ARh51UtYGgw5/amLj7w0+e5b90BvvG2c2IuwjW7ZiqbD4/uXT5tVhW3Xnc6n71/E9/9\n0+74f5l4fwdnzqsZNs4i1jTOWCdqX+lAP2cefolVezewas86zt/3IpPDQ0GpbUolTyw+h8dOPp/r\nP/pOrr74dAz4p7BjSdRg03tfOMDDm5uGdSHNnzaV326IPd/gpBkVPLe3l231C9lWv3DYY9EBM3rM\nyPQz5/DDnz4PNvozileBemhTIw9vaoL6k/jfFZfz+o2Pcen37mDNa1dndXCnvzhbRSSMdJaVpzYF\ntwjCyA3AO5xzT5jZ94A/OOe2m9ke4G+BHwfawhSY2ZeA+/C6ZuYAnwIGgJ9mq03AUEkMgvvwzzsP\nfvUr+POfg3k+kRQk6k6BsWehxOtCWTC9fFQQAe/k/bsNh3hVpDoS/fr+ial26iTajnv942OtIv74\n1uaY91eUlfLGc+Yyo7KMrz3+0ph/DyPL5tFVEICS8AD1nUc5s6uVmZ1HmdnVyszOVqYdb6f2eCe1\nP++g4wthvtXXzfGOLjhxgkl9vZT29dLr4MOEGAiV0B8q4fikKXSWlbPkqXmEvl3L1cdg5olJtJTX\n0lJRw5HyWloqamkur6Wtahq9hLxuiLeezYObGhMGQ/9EXdLbyykt+zjtyB6WNu/m9KZdnHNg8+C3\nc9+O6XN59OTzeeTUC3h+3un0mbdWxeqLhqq0I9fyuO6M2THHoJzo+yuPbBn+eVy1zDvp7jrSGfPv\n/eJT6njzefNHzab55pM74o7ziVeB8o8ZCDvuuPjtvGrz77l4zzruffBBOPPGRB9/RvmLs3V/wgvO\n775uJRek0l1ZBGFkOuBP42iP/Bngj8A3g2jUOMzDCx4zgGa8Nl3onIv9P89E8cNIaal3CcKFF3rX\nCiOSQKYGgyZaxwGI+djnfreZW687HWBUkPCdMrOSmqmlHDs+uovioU2Ng2Ek+vX9n/eDyHh09vTz\nvaf2xKzORCvr72V69zGmdx/jvC1thHc8yUsvbKNp6y7euGcf7+/wuhPqutpiz+SIoXzkazB8mh94\nA1Fp2gXABZFLPL2105hUX4f9Vy3X19ZCbS2URT2jmXdSam7mHfsO8aZDjUw/3h6zvUenVLF2wRms\nXXgmf1p4FrtmzMMBK+fV8MFlDYNjcRL9bo0MJ75vv+M8bypw5PO8alkD10WqYIvqYm8O95bzF8R8\nrkT7zsTN106LAAAgAElEQVRbBn71sgZ+s+4gAAdqZvKjl13Pu565l8u+dwd8+B0QSnkLt8CEQjYY\nBFeddZJXBkpWEYSRnXj7z+wFtuCNHfkLXsWkLbimpc4595Zsvn5cmfjgzzvP+0eyf793mTcvuOeW\ngpDuYNBkul9+9te9cQdGOudGhQyAu/+4i/1Hu4dNmR15zPam2N+EAZwbWiVzy6H26Aeo6D1ORe9x\npvb3MKW/lyl9PZQN9DFpoN+7hPspHeinNDxAiQtTEg5TEh7w7g8PUDrQz+Swd+yU/h6m9vVQ1t/L\n1L4eKnu7qe7ppqqni+oTXdSc6KAqulLwfe9qSeQyUl+ohOaKaTRVTqO5YjrNFdM4Ul5D29Rq2qZW\n0jalitJptXzjXS+ntLIcpkzh+88c5NtP7qAkPOC1L9xPRe8Jqnq6uHx2Ge9cMZ3NG3fxx7WbmdF9\njLquNuq7jlLX3Ubd8XYsHGZy21Foi7+GR7QqhtY0aJtSydb6k9hat5Ct9Qt5bu5SttSfhLPhJ+V3\nXbyIW687fdzhNhQyblg5J+aYoFT3kUl0fLxl4AHuW3dw8Ge+vupNvG3jI9Rs3gC/+AW8+c3jen/j\n5i96luKuvUmFkTyf2vs9YCXeomafB+4zs/cDk4APBdi2whHktF5fRQWceSa88AI8/bTCyATIhVUv\nU2nPWKtQjrVPSKw1L15311MxB4X6r7Fgejkv7Gsb9ZjPX3FzrMpDRU83szpbaOgYGrC45M/d9DU3\nc2Z3O5d1H+NfTnRQ3dNNRe/xpKsPQRooKSU0s5726mk81zeVxsoZNFVMo6lqBocrZ3C4agaNlTM4\nUlEz6kQey+1HKvn4hcsAqOuu4MALsVcjqF05h3e+9WUsCTvuGDEw9qplDdz11rOwo63Q2Ahtbd7l\n2DFvoa++Pu9Af/DK5MlQXw/19YRn1PHYUWOLm8pDm5tGrecRrSRkTK+YPObv/3j/zaS6j8xYx8er\nzoz8mbK6j8Jtt8Gtt8LrXgeTJiXd5kCFw95qsZDSCqzA8DDinFcJ8xVCZcQ595Wo24+Y2VLgHGC7\nc259kI0rGJn64C+80Asjf/4zvP71wT63DBPklNOJak+iFTJjLfpVWVbCuQun8cS2I8DwAPPBnz3P\n+v3H2NPaDYwOIr4vPbiVebWJf8+f2XOUsr4e5h9rZP6xRha0HWZB22HmHWtkbnsz8441UnsifoUk\nnn4LcWJSGSdKJ3OidDI9pWX0lpTSHyqhP1RKX4l33R8qYSDk7ckRthB9JZPoC5XQV1JKf6iU45Hn\n8K87J5fTUVZBR5l33Ta1ipbyGm5/5yVcv3IOP3p8O3c8vC3h7JxkbGscCh/Xrpg1bPn0aFct83bq\nDoWMb7393Ngn3pkzvUsc8ULClXh7afzj5acOPt7a1cvdf9w17OeTmdUR1L+ZeAEiqONj/sziD8E3\nvgE7dsDdd8N73xv/hzOpu3soOKYbRpzzZnRGDxEokKm97wDuiUyJxTm3B9hjZpPN7B3OuR8E3ci8\nl4nKCHhh5K67YO3aYJ9XRhlzr4scac/1//kHLjqljluuWRq3/3zh9HJ+t+HQqEW/OnsGBoPISPet\nPxTz/pH2tHazp7WbUHiAhs5W5kUCx/y2RhYcO8z8SPCY1dk65nO1Ty6nMVJlaKyaQXPFNFrKq2kt\nr6F1ag1Hp1ZFhYRyTpSWDf/2l0FXL2/g2jO8zz3W3zPAOQtrwcH+o8dp7OgZDH1VU0rpODF6TMxp\nDUMnm1DI+NX7Xs5rv/kUGw4MVaL88RTRx6X6+5dMSIh+3nDYsa+1O+muEl+u/ZtJSWUlfOxj8M//\nDD/+cfbCiN9FEwpB+chRRWOYHLUEWG/v8DBSCJURvG6aB4CRk9qrIo8pjIyUycoIwLPPer9skycn\nPl7SlqjKMF7plLLjLdq1+XAHmw93cN+6g/zxI5ezetnMwZkdvntfOMCuI+m3OxQeYEb3MRo6vZkh\nszpbmNPezOz2ZuZ0HGF2+xHmtDcPm/4Zy/GplRyZOZeNZTPYV9PAvtoGDlTPZH/NTA5Uz6SrLMX/\nfFOwYk4VGw+O7gZZML2cvZHqTzQ/DJw6s5IPXnHq4ABLGD5OwQ8cK+fVcM8/rOLBTY3c9JPngKHQ\n13Gin+oppbRHBZKZVWXccs3w9YJKS0Pce9PLA+8ajBcSPve7zUyvmByzayOVrhJfJv/NTIjXvMYL\nI3/+sxcKUq1MBCF6vEiqQTu6a6m3d3iYKZAwEqu7GLyZLMfG15wClanKyGmnwbRpXl/w+vVwbnYX\n6SlkiUbppxMm/J/Z2dzBL549wN7W7tF7bCR4jnjfxn1NHT28+0fPxHzM38DMZy5M9Ykuph9vZ3r3\nMWZEZolMP94+eLuuq4267jZmRB5PZoxGX6iEA9UzOVBTz96aWeyrncWe2tnsrZ3FvtoGPvvOV/DZ\n323mcHvPmM8VS33lZJo7ewfHS8Ry1bKZhJ3jkc3NUeMqZnL9mXP44M9eGHX83tbuUetyrJxXw+oE\nM0ZCIeMbbzt7cDxNyLyVT2/66XOcMbcm5gn5Hy5ZTNvxvmF7zpSWjh5Xkk7lYyzxgmyixdzSaUei\nfzN54aST4OSTva6aJ5+EV71q4tuQxo69g0aGkWj5HEbM7Hm8EOKAR80s+mtPCd4MmweCbV6ByNQH\nb+ZVR9as8dK7wkjGXLtiFqtPnzlsS/Srls3k6mUNo0reVy1r4IaVc2LuJhoOO+5bf5DbY5yE/f+3\nE5Wyh0JMJwumT2Vv6/FRx/ie3rifWZ0tXBgZCNrQ2erNuOhqGwwXdd1tTOtupzTFAaADFqK5opam\nyuk0Vk7nUFU9h6rrBjc621/TQGPldMKh4QsyRy8q5szSCiJmsGhGBTsj1Z3oIHLDmbOZWT1l2NLv\nwKiw+M0nd8QMMWZeV8h7XnFySuHywchqrzD8c5w3LfZmcovrK7PWVZEoyAbZnZLqTJicdOWVXhh5\n5JHshJHOyNipVGfSgPfLPGmSN2i5kMII8OvI9VnAg0D0CLNeYDfwy2CaVWAyVRmB4WHk/e8P/vlz\n3ITOcBn1tMaaF0eXvB+K7KoaazGw9/zwmVGViVgefPHwqPcycqGv0oE+Fh1rYuHRgywcMQh07rGm\nYct0J6N9cjlHy6tpnVoTNTajmpbyWo5U1NJSXsORimk0R26PDBrJuPiUOt5y/oKhQED8wbDxOMdg\nEIlWEjKWzq7mpstH7/4w8qR60oyKmNUU52BRXepBIV6XxLTySRNyQk7l30GskDDycwiiOyXd7p2c\ncuWV8K1veWEkG8ZTGQGv676vb/Rmefk8tdc59ykAM9sN/MwfwCpJyGQK9ceNFOEg1omc4bJm4+HB\nsRf+SeyhTY1MmTR6Z1dfrMXAkgkiAL9Zd5A9LV388j2rKD3SBFu28OKjT3PhA2t5W+sBFrfuZ257\n85jdJR2Tp9JUOYPDVdMHp556waJ28LqlvJqjU2voLR0q655cX8HO5q6Ug8JYoherOmlGRUrPn2hj\nO0itCyC60hXNX/lzpLFO9vG6JBbVVfKPl52S0RNyqv8ORoaEdGfLJCMT3UwT6pWv9CoML74IBw/C\nnLH3RwpUEGGkq2t0ZaQQZtMAjwH1RHa2NbPzgbcBm5xz3w6wbYUjk5WR88/3rnfuhKamhNP5Cs1E\njtaP983XOTfmlE5/e/dtjfGnq5YO9LOg7TAnt+7n5BbvckrLPk589ACVx72fOyNyidY9qYw9tbPZ\nM202e2tmDe6MeiAyCLQzzUGgl55Wz47mYAYaRo+FiT7Rxxr4eea8GmZWTeaRzc1R3V4zefXKuexp\n7Wbr4Q5+u/5gzDVKUqk4hELGt/7u3Lgrf0ZL5mQ/1mJbmTwhp/PvIIjZMkVh+nQ45xx45hl49FH4\nu7+b2NcPIoxAwXXT+H4CfBv4oZnNAh4BNgJ/a2aznHOfDrKBBSGTH3xtLSxbBps2eYuf3XBD8K+R\noyZytH68b757Wsd+rYGw46FNjWzec4SF7c3Mb2tkYdshFrUe4KSjB1l09CDz2xrjzj5xoRAsXsxL\n0+byBNPZNX0uOyOX5oppgU9n9Re08gdyJnJKfQWXnFrP957aPeqxGy86iXMXTmNPjLEzEL+MD6PH\nePg/d//6Q4NLd0dLZzXQRCt/RkvmZJ/NLonx/jsoiO6UTLrySi+MPPKIwkgGpRNGVuAt/w7eUvAb\nnHMvN7OrgLsAhZGRMlkZAa+rZtMmb9xIEYWReAGhtauXcNgF+p9prG++K+fVsC5ysi4JDzCjq42G\nzlYaOluZ3dHMnPYjzO5oZtHxVuqOHGZWZ0vCbpXuSWXsmD6PHTPmsXP6PLbPmM/Ounn8zRsu5fmm\nE6O2jE/W0llVzK6ZQvmkEH/a0TrmHi5+98Kv3nvyqBVXF04v54y51YRCIVYva+D6yJoX+9u6R60E\n+olXLRvzM4hXNYj3jT5eBSKIZcnjSfZkn60uiSBmreR9d0omrV4Nn/+8F0ZGrmSaaQojCU0C/PEi\nVwK/idzeAui3OZaJCCPf/W7RbZoXfWKKHoDn74ESyNgR5+DIEdi7j3cde5ErmrdR09rEMusi/MRB\nOvfsp77zaNIboh0vLWNfTQN7axvYPW0Ou6bPZde0OeyePodDVXUxlw1/eX8o7SBSEvn27w/q/Ppj\nL3HHw9tidnPE6l749T8mt85F3JVAA5aNb/G5PkW1IGat5LKLLvJO2gcPwubNXiV6ooxnNg0UfBh5\nEXivmd0PrAY+Hrl/DtASVMMKSqY/eH8Q61/+4i37W5L6LIdEcm1PFp9/Yvrc7zaPGoCX0tgR57x9\nPDZu9Aaq7dw5/HLiBCHG3iU1errr4ao6DlbVcai6jiXnLuNHh4x9tbNorqiN+c3q3IXTOLhn9KZm\nK+fVMK180piDNwFWzKlm48Hhy4ePPGkuqquMGUTedfGiuAteJfN3OJHfrCf6W3yun+zVzZJhU6bA\nJZfAww971ZGJDCOqjCT0L8D/Ah8Bvu+cWxe5/9UMdd9ItExXRpYt835ZOzq8k+mZZwb21Lm2J8tI\nocj4hqT7zJ2D3bu94Pb00/Dcc14IaUmco5srajlUVUdjZAO0poppNFVOj+zG6q21EWu669XLG/jI\nW8/mgZ88x3NRAzUBSswYcN7f5xlza3h+X9uw9xAyBhfbSmbfk6uXNzCndmrCk+bVyxqoryyjuXNo\nMpy/+mesRbfyVZABOh9O9upmybArrxwKIzffPHGvm+kwko9Te33OuSfMrA6ods5Ff5X7NjB6HWXJ\nfAotKfFm1Tz6qNdVE2AYyYf9JRKW0cNh2LABnngCHn8cnnoKmptHP0ko5K22uHy5t7Lt4sWDl2/u\n6OFLT+xOGAhqp5YSPt4fd9nw6JPZgunlGAwb2Llm4+FRzx+OrHkR/c08kcX1VdwUtcFZrJPmg5sa\nhwUR8FZrfXBTY858nuOViQCtk32RW70a/uVfvP9H+vombhffTIWRApnai3NuADg64r7dQTSoIGW6\nMgJeV82jj3rJ/d3vDuxp82F/iZFl9Dmth3hPzw6u++R34cknoHXEpmyTJsHKlXDBBXDeeV54W7o0\n7uezoOsQA+FdMR/zrZhbw1vPXxg3BIx1Mhtrauhdbz+H+zcc4muPbmN70+i/+2SnkebD5zle+RCg\nJc+sXAkzZngV1L/8BV7+8ol5XXXTxGdmDcCXgCuAmYxYl9I5F+yAhUIwER/8618Pn/sc/PKXsH07\nnDJ6Fcp0RFcd6juPcumuZznlyF6u3jsdfjEJenoiy1Yu8ioKS5bAqadCxcQN7gsda+Ou8j3s23Uf\ntX98nJqDe4cfUFHh9fledpl3ffbZKX0W8QbKRtvXejyjXQH+NNTrz5jNmo2H2XWkk6PdfcOWPU/m\ntXN9MGYQiiFwyQQLheCKK+DnP/e+8OVLGPErOIUYRoD/BhYAnwEOkfpqzsVnIiojL3uZt3fCb38L\n//7v3uyaAFzbf5ivb/4VC59+kjMadww9MNbooCVLvGrNBRd412ecMXwL6/FoafHGe/zhD95/DM8+\nS8g5FvqPl5bCqlVw1VXefyDnnjuusmp0UNjZ3ME3ntjB8b7hM2f2tHaP+5t3Ml0B4+0uyPXBmEEo\nhsAlWbB6tRdGHn4YbrttYl4zE7NpnCuYMHIxcIlzbvSWlxLbRH3wH/+4F0Z+8APv9qJF6T/Xzp1w\nyy2Efv5zoreHalu+kporLsUqK71f9MmTvRk8O3bA1q2wbZsXFrZu9S7f/773g2VlXiA56ywvOC1f\nDnPnwqxZMf+hhcOOh57eTtuLWzmlo4mzB1oJrVvnjYnZvn10e08/3QseV13lVUAytN13KBTiiqUz\nuX/D4cD38pgI+TAYc7yKIXBJFlx6qXf97LMZmbUYUya6afr7vbF0kPdhZB8xtgyTBCaiMgLeINZr\nroEHHoDbb4dvx16dP+FMg6NHve6e//ov7xfYDF77Wnj1q+Gaa6htaBi7Hc3N8Ne/esHhz3/2qhjt\n7d4qhs/E2Na+shLq673E3tuL6+ujp7Oba44nOLn7lZcrroBXvpLw7DlD72lXJ9euqAzsBBtrQORI\n+fTNu9AHYxZD4JIsOPlk7//w48e9L2unnpr51wwqjERvlOd/OYa8DyP/BHzezN6jQatJmsiS2Cc+\n4YWR//5vuPVWWLhw2MNxZxq87WxCP78HPvCBoWmuq1fDl76U+uyc+nq47jrv4r2o94/3hReGLlu2\nwKFD0N3tlSI7h/ZtMcCPba1Tq9lb28C+mlksufx8Tnv1lV7omj597PcU0PTjWAMiffrmnZsKPXBJ\nFoRC3jIKzz7rLQeQ6TASDg/9vxhkZaSAwsg9QDmww8y6gWFrSzvnpsf8qWI2UZURgFWrcFdciT36\nCBtu/lf2fuZLw74VxjqxPv3MSxz+0aeZ89B93nMsX+6FkKuvDmbp41DIG1B7yinwhjcMf6yjwwsl\nR454Zc9Jk/jpC4e5++n9NJbX0lHmVRtKQsaHVp/GaTG2h8/07IlYAyJDBq86cw5LZlXpm7dIsVix\nYiiMvPa1mX2trqjKcJBhxD8flZVN7NL2Y0i3MiJJCocdvZ3dTAF+v7eDi88Lds+UWK/35fPfyEce\nfYTT7v85/zD3Kn6zavlglWDkifWyHX/lC2v+k5ldR72Bnx//OPzrvwY32HQsVVXe5bTTBu+qLj3E\n9m3JD0DM9OyJWAMivV1oZ+nbt0gxWb7cu37xxcy/ll8VCYXS/yKbqDKSQ1URSG/Rs+9noiGFyO8+\n+FJHF1OA2x7eyWknajO6eumajYe5MzyXS+av4MJ9G7n18bv5ZMl7WLNyLtefOXvwxPqyA1t479P/\nw9UvefvZdCw+lap7fuLNPMmicNgRdo5TZlawvalr2Cql8bpBMj17QgMiRQTwKiPgVUYyzR8vUlmZ\nfgWjEMOImVUnc5xzrn3so4qD330wpd/7RegpnZTxxZf8KsHXXv5WLvzZrdyw5Q9cs+0p9j97KXzo\nfVw7uYyH/vc2Ttv2PABhjMeufiuv/OV3oKI8I21KVvTYDz+rLa6vGLaSaSyZDguJtrq/f/0hDZIU\nKRZ+GNm61TvB+yf7TBjv4FUozDACtJF4TRF/PSgtehaxu6WLSYSZHO4H4ERpWcangPpVgrULV3Lz\nDR/h/z5zL2cd2saitY/BGx8jBJwGhEsnseXKv+HJV7+DgSVL6dlxjGtXTM3qyTR67Idf6HipqRMz\nS9iuiZg9MXJAZK7v2SMiGTBvHlRXe7MDX3ppqNsmExRG4ro8Y60oUH4w+LfV72NKfw+dk8szPgU0\nukpw/4rL+M2yS/k/td18su1Z7Mc/9voh/+Ef4AM389XHvZN/yb6XcuJkOp6xHxM9e0JLjosUITMv\ngKxd63XVKIwEJukw4px7MpMNKUTXrpjFlSvm8KPQ9RM21iBelcBCb4TPf37wuDXrD+XcyTSfVs7U\nkuMiRcoPI5kexJrpMJJDO/ZCkmHEzCqcc0n/L5vq8YUqW4svJVMlyMWTaT4NFM2n4CQiAZqoQazj\nXWMEEk/tzdPKyHYz+xrwfefcoVgHmJkBVwIfAn4P3B5ME/Nbri6+lIsn03xaOTOfgpOIBMgPIxNV\nGUl3XxooyG6ay4B/Bz5pZuuAZ4CDwAlgGrAMWAX044WQbwXeUglUrp5MczW8jZRPwUlEAuSPE9m+\n3asyZKq7I4humli79uZzGHHObQVeb2YLgDcClwAX4a3afQR4HvgHYI1zbiBDbZUA6WQ6fvkSnEQk\nQA0NMGOGt23Gli3exp+ZoAGs8Tnn9gJfjlxylpndBHwEmAWsAz7gnBtr0/uio5OpiEiK/Bk1v/+9\n11WTD2Ek1kZ5ORZGQtluQNDM7M3AHcCngLPxwsiDZjYzqw0TEZHCMBGDWIusMpJSGDGzZWb2DTN7\n3swORS7PR+5blqlGpuhDwHecc99zzm0C3gt0A/831sFmVmZm1f4FGMcnLyIiBW8i9qjxZ9NkagBr\nPk7tBTCza4FfA88B9wKNkYcagNXAc2b2N865BwNvZZLMbDJwDlEzeZxzYTN7BG+AbSy3ALdNQPNE\nRKQQ5HNlJM+n9gJ8HvgP59wnYjz2STP7JPBFIGthBKjDW46+ccT9jcDSOD9zO163jq8K2B9800RE\npCD4lZHdu70KxniqF/Gomyau04AfJ3j8p8Cp42vOxHPO9Tjn2v0L0JHtNomISA6bMQNmRZZB2LQp\nM6+hMBLXbuD6BI9fD+wZV2vG7wgwgNd1FK0BODzxzRERkYKU6a6aIgsjqXTTfAL4iZldBjzC8DEj\nVwDXAG8LtHUpcs71mtmzkfb8GsDMQpE/fz2bbRMRkQKyfDk88kjmBrEqjMTmnPuFmR0AbgY+jLeG\nB3gVh7XAZc65tcE3MWV3AN83s2eAvwD/BFQA38tqq0REpHBksjISDkNXZJ8wLQc/mnPuKeCpDLUl\nEM65e8ysHvg0XmB6AbjGOTdyUKuIiEh6MhlGuqI2LNWuvfnLOfd11C0jIiKZsiyytNbBg3D0KEyb\nFtxz+100odD4QkMeTe0NbAVWMzvdzHYG9XwiIiI5q7oa5s3zbm/dGuxzR48XsXHsF5ZH3TRBLgc/\nGVgY4POJiIjkrpNP9q53Bvw9PIjBqzC0a284DAORPWxzNIyksgLrHWMcUj/OtoiIiOSPxYvhySeD\nDyP+UvDjDSN+ZQS8zfJKSvI/jAAfxBsM2h7n8QwsQSciIpKjFi/2rjNVGRnvyq7RYaS31wsgBRBG\ntgNfcc79KNaDZnYW8GwgrRIREcl1mQ4jQXXTwNC4kRwNI6mMGXkGbxO6eBwwjpE2IiIieSTXw0go\nBKWRmsPIMJLHU3s/DJTFe9A5t45gB8SKiIjkLj+M7N8PPT1QFvcUmZqgwgh4XTX9/V4YGRgYCiX5\nWhlxzh12zmV77xkREZHcUF/vjetwztvBNyhBhxHwQkhPz9D9+RpGREREJIpZZrpqgppNA8PDiN9F\nA/kfRszsqJm1xri0mNkBM3vSzN6ZicaKiIjklEyEkaBm00DsMFJSMjSWJEek05pPA7cCa/A2ogM4\nH2/X3juBRcA3zazUOfedQFopIiKSizIZRjJVGcmxqgikF0YuBv7NOXdX9J1m9h7gKufc681sPd7u\nvgojIiJSuBRGApHOmJGrgUdi3P9o5DGA3wGL022UiIhIXsjHMJJj03ohvTDSCtwQ4/4bIo8BVAAd\n6TZKREQkL/j70+zY4c2qCUKmwkiO7tgL6XXTfAZvTMjlDI0ZOQ+4Dnhv5M+rgSfH3zwREZEctnCh\nN6umqwuam2HmzPE/Z5CzafxVWHO8myblMOKc+46ZbQLeD7wucvdW4FLn3FORY74cXBNFRERyVFkZ\nzJsH+/Z5XTVBhJFMzKbp6yusMALgnPsT8KeA2yIiIpJ/Fi8eCiMXXjj+58tUN00oMjKjUMKImZUA\nrwFOj9z1IvAb59xAUA0TERHJC4sXw5NPBjOINRz2unwg+DDiK4QwYman4M2WmYvXPQNwC7DPzK53\nzu0IsH0iIiK5zZ9RsyOA058/XgSCDyPhsHc7B8NIOrNp/hPYAcx3zp3tnDsbWADsijwmIiJSPPwZ\nNUFURvwumpKSYEJDnqwzkk43zaXAhc45fxovzrkWM/sYGkciIiLFJsi1RqJn0piN//miw4g/9bhA\n1hnpAWLVjiqB3hj3i4iIFC4/jBw4MHwzunQEOZMG8qYykk4Y+S3wbTO7wIZcCNwF/CbY5omIiOS4\nujovPDgHe/aM77mCnEkDBR1GbsYbM7IWOBG5/AnYDnwwuKaJiIjkAbPgumqKNIyks+hZG/A3ZnYq\nsDRy92bn3PZAWyYiIpIvFi+G9evHP6NGYSQ1zrmXgJcCbIuIiEh+CqoyEuRS8FBYYcTM7kj2CZ1z\nH0q/OSIiInkoqOm9qowk9LIkjwtoy0IREZE8EvSYkUzMpvF37c3Bqb1JhRHn3OWZboiIiEjeig4j\nzqW/RkjQlRF/194c3ygvndk0IiIiEm3hQi+AdHVBU1P6z9Pe7l0XWTeNwoiIiMh4lZXBvHne7fF0\n1fhBZubM8bcJFEaywcx2m5kbcflYttslIiJFIIgN8xobveuGhvG3BxRGsugTwOyoy39ltzkiIlIU\n/Bk1u3al/xxFGkbSXmckh3U45w5nuxEiIlJkxjujxrmiDSOFWBn5mJm1mNnzZvYRM0sYuMyszMyq\n/QuxNwEUERFJbLxhpL19KDBkIozk+9TePPKfwHNAK3ARcDteV02ihdhuAW7LfNNERKSgjXfMiF8V\nqaqC8vJg2qTKSDDM7PMxBqWOvCwFcM7d4Zx7wjm33jl3F/Bh4ANmVpbgJW4HaqIu8zL+pkREpPD4\nYeTAgaETfyqC7qKBvAkj+VAZ+TLw32McE68m9jTeezwJ2BrrAOdcD9Dj/9nSXahGRESKW12dt3Jq\nZyfs3g1Ll475I8NkMoz09CiMjIdzrhloTvPHzwLCwDhWoBEREUmC2dDuvTt35lYY6eryBsiCwkgm\nmUMOcdYAABRiSURBVNkq4ALgcaADWAV8BfiRc+5oNtsmIiJF4uSTh8JIqg5HJoJmIoz4K7uCwkiG\n9QBvAT4JlAG78MJI0jsOi4iIjMt4ZtT4lZFZs4Jrjx9GOjuH7itLNIwyOwomjDjnngMuzHY7RESk\niAURRoKsjPgb5UV30eTg2Micn00jIiKSN8YzvTeTY0Z8OdhFAwojIiIiwYmujPjViGQpjIiIiMi4\nLVzodYN0dw/twJsM5zI7gNWnMCIiIlLgyspg/nzvdirjRjo6gl8KHhRGREREilI6g1j9LprKSqio\nCK4tCiMiIiJFaDxhJMiqCAzNpvEpjIiIiBSBXAojJSXexZeDO/aCwoiIiEiw0pnem4nBq77orhpV\nRkRERIrAeCojQa6+6lMYERERKTJ+GDlwYGiGzFgy1U0DCiMiIiJFp64Oqqq827t3J/czCiMiIiIS\nGLPUu2oURkRERCRQqYYRDWAVERGRQKUyo8a5zA5gjV5rRFN7RUREikQqlZHOTjh+3LutyoiIiIgE\nIpUw4ldFKiqCXQrepzAiIiJShE4+2bveudPrhkkkk4NXQWFERESkKC1c6M2q6e6GpqbEx2Zy8Coo\njIiIiBSlyZNh/nzv9lhdNZkcvOq3xacwIiIiUkSSHTeibhqFERERkYxIdnrvRIYRTe0VEREpIrkY\nRlQZERERKSJLl3rXGzYkPk4DWBVGREREMuL8873r9eu9WTXxqDKiMCIiIpIR8+bB7NkwMADPPRf/\nOM2mURgRERHJCLOh6sjTT8c+prNzqGqiyoiIiIgE7oILvOt4YcSvipSXQ2VlZtqgMCIiIlLExgoj\nmR68Ctq1V0REpKide67XXbN371DwiJbpwaugyoiIiEhRq66G00/3bv/lL6Mfz/TgVRgeRsrKMvc6\n46AwIiIikkmJumomsjJSWupdclDehBEzu9XMnjKzbjNri3PMAjO7P3JMk5l90cxy829eRESKQ66E\nkRztooE8CiPAZOAXwDdjPWhmJcD9keMuAv4PcCPw6Qlqn4iIyGh+GPnrXyEcHv7YRAxgVRgJjnPu\nNufcV4B46+peBSwD3u6ce8E5twb4OHCTmU2O8zMiIiKZtWKFN4ulvR22bBn+mCojQB6FkSSsAjY4\n5xqj7nsQqAaWx/shMyszs2r/AlRluJ0iIlJMSkvhnHO829GDWI8dg82bvdtz5mTu9f0wkqPTeqGw\nwsgsoHHEfY1Rj8VzC3As6rI/+KaJiEhRizVu5DOfgbY2b0O9c8/N3GurMpKYmX3ezNwYl6UZbsbt\nQE3UZV6GX09ERIrNyDCybRt87Wve7a98ZfjCZEGrr/euM9kVNE7ZnmnyZeC/xzhmZ5LPdRg4f8R9\nDVGPxeSc6wF6/D+bWZIvJyIikiQ/jPg7+H74w9DfD9dfD9dck9nXvugiuOeezFZfximrYcQ51ww0\nB/R0a4FbzWymc64pct9qoB3YFNBriIiIpG7+fG9hs8OH4fbb4be/9caSfPnLmX9tM3jTmzL/OuOQ\nN2NGImuInAUsAErM7KzIxd9Z6CG80PFDM1tpZlcDnwXujFQ/REREsiN6B9/Pfta7vvlmWLIke23K\nIXkTRvDWC3ke+BRQGbn9PHAugHNuAHgVMIBXJfkR8APgE9lorIiIyDB+Vw1AXR18/OPZa0uOyfaY\nkaQ5527EW8Qs0TF7gOsmoj0iIiIpiQ4jn/0s1NZmry05Jm/CiIiISF5btQrOPNOb1fL3f5/t1uQU\nhREREZGJUF4O69aBc94YEhmUT2NGRERE8p+CyCgKIyIiIpJVCiMiIiKSVQojIiIiklUKIyIiIpJV\nCiMiIiKSVQojIiIiklUKIyIiIpJVCiMiIiKSVQojIiIiklUKIyIiIpJV2psmjvb29mw3QUREJK+k\ne+4051zATclvZjYX2J/tdoiIiOSxec65A8kerDAygpkZMAfoyPBLVeGFnnkT8FoTRe8pP+g95Qe9\np/yg9xT75w+6FAKGumlGiPzlJZ3m0mVDuzZ2OOcKok9I7yk/6D3lB72n/KD3FFPKP6MBrCIiIpJV\nCiMiIiKSVQoj2dMDfCpyXSj0nvKD3lN+0HvKD3pPAdAAVhEREckqVUZEREQkqxRGREREJKsURkRE\nRCSrFEZEREQkqxRGMsDMXmFm95nZQTNzZvaaJH7mMjN7zsx6zGy7md04AU1NSarvK/KeXIzLrIlq\ncyJmdouZ/dXMOsysycx+bWZLkvi5N5rZFjM7YWYbzOy6iWhvMtJ5T2Z2Y4zP6MREtXksZvY+M1tv\nZu2Ry1ozu3aMn8nZzwhSf0+5/hnFYmYfi7Tzq2Mcl9OfVbRk3lOuf1Zm9skY7dsyxs9k/DNSGMmM\nCmAdcFMyB5vZIuB+4HHgLOCrwP8zs6sz1sL0pPS+oiwBZkddmgJuV7ouBe4ELgRWA5OAh8ysIt4P\nmNlFwE+Bu4GXAb8Gfm1mKzLf3KSk/J4i2hn+GS3MZCNTtB/4GHAOcC7wGHCvmS2PdXAefEaQ4nuK\nyOXPaBgzOw94D7B+jOPy4bMCkn9PEbn+Wb3I8PZdHO/ACfuMnHO6ZPACOOA1YxzzH8DGEff9DHgg\n2+0f5/u6LHJcbbbbm+R7qo+09xUJjrkH+O2I+/4M3JXt9o/jPd0ItGW7rSm+r1bgXYXwGSX5nvLm\nMwIqgW3AlcATwFcTHJsXn1WK7ymnPyvgk8ALKRw/IZ+RKiO5YRXwyIj7HozcXwheMLNDZvawmb08\n241JoCZy3ZrgmHz7rJJ5TwCVZrbHzPaZ2Vjf0LPGzErM7C14Vbq1cQ7Lq88oyfcEefIZ8f/bO/Mg\nq4orDn8/3I0EXFETEEVcUcE1oAhBQUJZ7hqNGjEucceoMUkZE2KRImWiRlFLY1lFcLdihBK3qMmg\nEXdxQVncMLiAik5EQEA5+eP0gzs384Y3b2a4b/B8VV3zum9333P6vHl93um+rz0yd7+Z5W3QGO3F\nVs3RCWrfVj3Tcvvbkm6T1K2JuqvERnFQXm2wOTA3VzYX+Lak9cxsUQEytQYfAmcAzwPrAKcCdZL2\nMbMXC5Ush6QO+PLYk2Y2tYmq5WxVE/tgsjRDpxnAT/DwcyfgImCypJ3N7L22l3TlSNoFn6jXBb4A\nDjez18tUbxc2aqZONW8jgORU7Q7sVWGTmrdVFTrVuq2ewaM3M/Almt8CT0jqZWaNndC7SmwUzkjQ\nZpjZDPwNX2KypB7Az4ATi5GqLNcBvWhi7bQdUpFOZvYUmW/kkiYD0/D18UvbUsBmMAPfT9UJOAr4\nq6QBTUze7YGKdWoPNpLUFbgaGGxmNbNhsyVUo1Ot28rMHsxkX5H0DPAucAy+L6QQwhmpDeYAXXJl\nXYDP23FUpBzPUmMTvqRrgYPxfRUr++ZSzlZz2kK2ammmTg0ws6WSpgDbtolwVWBmS4A3U/aFtJlw\nBP4Bn6dd2KiZOuXb1pyN8M24mwEvasUR9GsA+0s6B1jHzL7Otal1W1WjUwNq1FbLMbN6STMpL98q\nsVHsGakNngIOyJUNpun14/ZKb3z5pnDkXAscDgwys3cqaFbTtqpSp3wfawC7UCN2KkMHfOmvMWra\nRk3QlE4NqFEbPYbL1DuTngduA3qXmbRr3VbV6NSAGrXVciRtAPSgvHyrxkZF7+xdHRO+87r0xjV8\nWaI30C1dHw2My9TfGlgAXA7sAJwFfAUcVLQuLdTrfOBQ3OPuhe9f+Bo4oGhdknzXA/X447CbZ9J6\nmTrjgNGZfD9gKXBhstVIYAnQq2h9WqDTb4AhwDb42vgdwCJgp6L1ybyv9ge64x/qo4FleOi83dmo\nSp1q2kZN6FlH5smT9mirKnSqaVsBf0qfD93T+D8CfAxsWqSNCh+Y1TGx4pHWfBqbro8F6hppMwU/\nsvktYHjRerRUL+BiPAy9CJiH/47K94vWIyNfY7pYduzTB8/YXLuj8fX+xcBUYFjRurREJ+AqfM14\nMR56vR/oU7QuGfluBmYl+T7Cd/YPbq82qkanWrdRE3rW0XDibne2aq5OtW4r/GcjPkjyvZfyPYq2\nkdKNgiAIgiAICiH2jARBEARBUCjhjARBEARBUCjhjARBEARBUCjhjARBEARBUCjhjARBEARBUCjh\njARBEARBUCjhjARBEARBUCjhjARBEARBUCjhjARBlUiqk/TnouUoh6TtJc2R1LFoWb6J5N8fkmZJ\nOr9ImZqLpDslXVi0HMHqTzgjQVBDSNpC0u2SZkpaVs7ZkXS0pOmSvpT0qqRhjVQbDYwxs/mpzUBJ\nJqlzK8k6UtJLrdFXrSGpexqrfLq1aNlWMaOASyR1KlqQYPUmnJEgqC3WwQ+tGgW83FgFSf3ww7du\nBvoA44Hxknpl6nQDDsbPC2r3SFq7oFsfCGyRSWcXJEerU8mYmtlU/KysE9peouCbTDgjQdBKSNpQ\n0jhJn0laKOlBST1zdU6TNDtdv1fSBZLqS9fNbJaZjTCzccB/y9xqBPCQmf3RzKaZ2aXAi8A5mTrH\nAC+b2ftNyDtcUr2kgyRNk/SFpIckbZGpM1DSs5IWpLpPStpK0nDgt8BumajB8NTmghStWZB0vT4d\nU17xOJSiLpJOlfQO8GUqHyrp30mWeZImSuqRaVeKaBwj6QlJiyQ9J2k7SXtJej7p+aCkTcuNTYZ5\nZjYnk5bbRNKANDaLJX0o6Q+S1qygz1L7bpImJHk+l3S3pC7pWidJX0vaM+U7SPpU0tOZ9idImp3J\nd0191Ke6EyR1z1wfK2m8pEskfYAffIaksyS9kaJscyX9LSfqfcCxleoVBNUQzkgQtB5jgT2BQ4C+\ngIAHJK0FIGlf4AbgaqA3fnT3JVXcpy9+ymuWh1N5if7A8xX0tT5wEXAifqR9N/yIcdLEOh6YBOya\n+v8LfgrwXcAVwGusiBrclfpcBpwH7AycBAwCLi/dsBnjsC1wJHBEqgfwLeBKfJwPSPe6V1L+s+x3\neHRpd+Ar4PYkw4g0NtsCl1UwPo0i6TvAA8BzwG7AmcApwK8rbN8BmABshB/nPhg/cv4ugOT0vISf\nlA2wCz7ufTKO3QDcNqT32MPA/KTfvsAXwEO5CMgBwPbpfgcnZ+ca/Nj77YGhwOM5cZ8F9pa0TiW6\nBUFVFH2ccaRI7TWROUoc6IlPFv0y1zcGFgJHp/ydwMRcH7cC9SvrP1e+BDguV3YWMDeTfwm4NFdn\nYJKxc8oPT/keuX7mpNcbpesDysg3EnipgnE6Cvgkk1/pOKS+lwCbrqTvTZKMvVK+e8qfkqlzbCob\nlCn7JTC9iX5L/SzEJ/VS6pOu/x6YDn7yeWbs5gMdGrMfMAs4P70ejDtJXTPXd0r33CvlryiNE+5E\n3ZnsOjSVvQGcll6f0Ig8ayf5h6T8WPxI+7UzdY7AI3AdmxiLXZNcWxX9Pxdp9U0RGQmC1mFHfHJ5\nplRgZvPwUPiOqWh7/Ftmlny+tViPtLSxEhaa2VuZ/IfAZgBm9ik+gT0s6T5JI7JLOOWQdKCkxyS9\nL2k+cAuwsaT1U5VKx+FdM/s413dPSXdIelvS5/gEDx7RyfJK5vXc9PfVXNlmK9MF+CEelSml11P5\njsBTZmaZuk8CGwDfraDfHYHZZrZ8mcXMXgfqWfF+mQTsJ2kNPApSl9JASVvi0Z26VHe3lJ+fln2+\nAD4F1gWWL2MBr5rZkkz+EeBd4G1Jt0g6PmOnEovS33x5ELQa4YwEQftjDtAlV9YllZf4BNiwgr6W\n5vKGLy95xuxkfHlmMj4xz5T0vXKdpT0KE3Fn4EhgD1Zs+mzuJtQFjZTdh0dsTgP2SamxvrN6WZmy\nSj7/ZpvZm5m0uII2rcXjQEd8qWl/Ms4I7px8YGZvpLobAC/Q0HHqDWyHL1GVaDCm5k9a7Q4chzui\nlwEvq+ETVxulvw0cwyBoTcIZCYLWYRqwJismRyRtjEcBSt+mZwB75drl85XwFL72n2VwKi8xBQ/7\ntxgzm2Jmo82sHzAV+FG6tARYI1d9D/xz5UIze9rMZgJb5upUNQ6Z8RxlZo+Z2TQqc7jagmlAX0nK\nlO2LL9O8V2H7rpK6lgok7QR0Jr1fzKwed+rOAZaa2XTcQemDPyk1KdPfi/hS4Uc55+lNy2y6bQwz\n+8rMHjWzi/Elme74Pp8SvYD3zOyTCvQKgqoIZyQIWoH0DXUCcJOk/STthu+DeD+VA4wBhqUnR3pK\n+inwA1Z8cwdAUm9JvfFvu5umfNaxuBoYKulCSTtIGolv6Lw2U+dhfLLMOwsVI2lrSaMl9ZU/QTME\nn/CmpSqzgK2TfJukDY5vAmsB50raRtKJwBm5risah0b4DJgHnC5pW0mD8M2sRXA90BUYk2xwKL5p\n9kozW1ZB+0fxZaPbJO0uaW9gHDDJzLIbj+uA40mOR1o6m4ZHqbLOyG14NGyCpP7JdgMlXSOp7LKR\npIMlnZdsuBXwY3xemJGp1h/4RwU6BUHVhDMSBK3HyXiofCIepRAwzMyWApjZk/jEfAH+GyJDgav4\n/70dU1LaA49CTMGf3CD1MzmVn576OQo4zPw3IUo8iO9hObAF+iwEdgDuAWbiT9JcB9yYrt8DPAT8\nCw/hH2dmLyf9foFHUY4HfpXttBnjQK7dMnwz6h6p76uAn7dAv6oxf2R6GLA3rsMN+O++jKqwvQGH\n4g7W47hz8jbuZGSZhEef6jJldfkyM1uIL+X8B/g77rDcjO8Z+bwJUerxTaz/TG3OwO34GoCkdYHD\ngJsq0SsIqkUN918FQbAqkXQTsIOZ9W+Dvs8GDjGzg1q779amLcchqB5JZwKHm9mQomUJVm8q/oGe\nIAhajqSL8CcYFuBLEyfhj4S2BTcCnSV1TBsVa4ZVPA5B9SwFzi1aiGD1JyIjQbAKkXQ3/jRERzws\nP8bMbihUqAKIcQiCIEs4I0EQBEEQFEpsYA2CIAiCoFDCGQmCIAiCoFDCGQmCIAiCoFDCGQmCIAiC\noFDCGQmCIAiCoFDCGQmCIAiCoFDCGQmCIAiCoFDCGQmCIAiCoFD+B/U1IfSFVk8dAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a62d610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C30 = np.polyfit(x, y, 30)\n",
    "def fN(xi, C):\n",
    "    \"\"\"function to calculate y values for polynomial of arbitrary degree\"\"\"\n",
    "    yi = np.zeros(len(xi))\n",
    "    N = len(C)\n",
    "    for i in range(N):\n",
    "        yi += C[(N-1)-i] * xi**i\n",
    "    return yi\n",
    "\n",
    "def f30(xi):\n",
    "    return fN(xi, C=C30)\n",
    "\n",
    "pyplot.scatter(x, y, s=11, label=None)  # plot the data\n",
    "pyplot.plot(xi, f30(xi), c='r')  # plot the 30th order polynomial\n",
    "pyplot.xlabel('log10(Instagram Followers)')\n",
    "pyplot.ylabel('log10(Instagram Likes)')\n",
    "\n",
    "print('r-squared for 30th order fit: %s' % rsquared(f30, x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The r-squared value for the 30th degree polynomial is slightly better than that of the 2nd degree polynomial. It also passes right through the points on the end, but it's obvious that this function is a poor representation of the relationship between the two variables. As a rule of thumb, if increasing the degrees of freedom of a fitting curve only marginally improves r-squared, go with a lower degree fit. In our case either the linear or 2nd degree fit would be a good choice.\n",
    "\n",
    "   **Note:** Choosing a function with too many degrees of freedom is called over fitting. There's a systematic way to avoid over fitting by splitting your data into two sets, a training set and a testing set. You can fit various models to the trainig set and then calculate the r-squared value on the test set. The best fitting function will generally be the one that fits the test set best. This method of avoiding overfitting is known as [cross validation](https://medium.com/towards-data-science/train-test-split-and-cross-validation-in-python-80b61beca4b6) and is applicable for many other machine learning problems.\n",
    "   \n",
    "A best fit curve allows us to put data in context or make predictions about what to expect with new data. For instance, let's say we know that an artist has 1000 Instagram followers and 100 likes. How is that artist doing relative to other artists?\n",
    "\n",
    "Using the linear fit we can calculate the expected number of Instagram likes given the number of followers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7042.86628183\n"
     ]
    }
   ],
   "source": [
    "follower_count = 1000\n",
    "\n",
    "# since our fits were performed on log-transformed data, we have to log-transform this data point as well\n",
    "log_follower_count = np.log10(follower_count)\n",
    "expected_log_like_count = f1(log_follower_count)\n",
    "\n",
    "# now we have to undo the log transform\n",
    "expected_like_count = 10**expected_log_like_count\n",
    "print(expected_like_count)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "We'd expect an artist with 1000 Instagram followers to have around 7,000 likes. Since this artist has many fewer, we might conclude that the artist has relatively low engagement on instagram. We might use a similar approach to flag artists they may have bought followers.\n",
    "\n",
    "If we knew the number of followers and not the number of likes, we could also use our fit curves to predict the number of likes. In the case of an artist with 1000 followers our best guess for number of likes would be around 7,000. While that guess won't be exactly right all of the time, we assume that using this method to guess a value for likes will *on average* be closer than any other guess."
   ]
  }
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