{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "from datascience import *\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "import math\n",
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "hybrid = Table.read_table('hybrid_reg.csv') # http://www.stat.ufl.edu/~winner/data/hybrid_reg.csv\n",
    "hybrid = hybrid.drop(['carid', 'mpgmpge'])\n",
    "hybrid = hybrid.relabel('accelrate', 'acceleration')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "def hybrid_class(s):\n",
    "    if s == 'C':\n",
    "        return 'Compact'\n",
    "    elif s == 'M':\n",
    "        return 'Midsize'\n",
    "    elif s == 'TS':\n",
    "        return 'Two Seater'\n",
    "    elif s == 'L':\n",
    "        return 'Large'\n",
    "    elif s == 'PT':\n",
    "        return 'Pickup Truck'\n",
    "    elif s == 'MV':\n",
    "        return 'Minivan'\n",
    "    else:\n",
    "        return 'SUV'\n",
    "\n",
    "hybrid.append_column('class', hybrid.apply(hybrid_class, 'class'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "def r_scatter(r):\n",
    "    \"Generate a scatter plot with a correlation approximately r\"\n",
    "    x = np.random.normal(0, 1, 700)\n",
    "    z = np.random.normal(0, 1, 700)\n",
    "    y = r*x + (np.sqrt(1-r**2))*z\n",
    "    plots.scatter(x, y)\n",
    "    plots.xlim(-4, 4)\n",
    "    plots.ylim(-4, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# HIDDEN\n",
    "def standard_units(any_numbers):\n",
    "    \"Convert any array of numbers to standard units.\"\n",
    "    return (any_numbers - np.mean(any_numbers))/np.std(any_numbers)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The relation between two variables\n",
    "\n",
    "In the previous sections, we developed several tools that help us describe the distribution of a single variable. Data science also helps us understand how multiple variables are related to each other. This allows us to predict the value of one variable given the values of others, and to get a sense of the amount of error in the prediction.\n",
    "\n",
    "A good way to start exploring the relation between two variables is by visualization. A graph called a *scatter diagram* can be used to plot the value of one variable against values of another. Let us start by looking at some scatter diagrams and then move on to quantifying some of the features that we see."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table ``hybrid`` contains data on hybrid passenger cars sold in the United States from 1997 to 2013. The data were obtained from the online data archive of [Prof. Larry Winner](http://www.stat.ufl.edu/%7Ewinner/) of the University of Florida. The columns include the model of the car, year of manufacture, the MSRP (manufacturer's suggested retail price) in 2013 dollars, the acceleration rate in km per hour per second, fuel econonmy in miles per gallon, and the model's class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>vehicle</th> <th>year</th> <th>msrp</th> <th>acceleration</th> <th>mpg</th> <th>class</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>Prius (1st Gen)</td> <td>1997</td> <td>24509.7</td> <td>7.46        </td> <td>41.26</td> <td>Compact   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Tino           </td> <td>2000</td> <td>35355  </td> <td>8.2         </td> <td>54.1 </td> <td>Compact   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Prius (2nd Gen)</td> <td>2000</td> <td>26832.2</td> <td>7.97        </td> <td>45.23</td> <td>Compact   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Insight        </td> <td>2000</td> <td>18936.4</td> <td>9.52        </td> <td>53   </td> <td>Two Seater</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Civic (1st Gen)</td> <td>2001</td> <td>25833.4</td> <td>7.04        </td> <td>47.04</td> <td>Compact   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Insight        </td> <td>2001</td> <td>19036.7</td> <td>9.52        </td> <td>53   </td> <td>Two Seater</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Insight        </td> <td>2002</td> <td>19137  </td> <td>9.71        </td> <td>53   </td> <td>Two Seater</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Alphard        </td> <td>2003</td> <td>38084.8</td> <td>8.33        </td> <td>40.46</td> <td>Minivan   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Insight        </td> <td>2003</td> <td>19137  </td> <td>9.52        </td> <td>53   </td> <td>Two Seater</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Civic          </td> <td>2003</td> <td>14071.9</td> <td>8.62        </td> <td>41   </td> <td>Compact   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (143 rows omitted)</p"
      ],
      "text/plain": [
       "vehicle         | year | msrp    | acceleration | mpg   | class\n",
       "Prius (1st Gen) | 1997 | 24509.7 | 7.46         | 41.26 | Compact\n",
       "Tino            | 2000 | 35355   | 8.2          | 54.1  | Compact\n",
       "Prius (2nd Gen) | 2000 | 26832.2 | 7.97         | 45.23 | Compact\n",
       "Insight         | 2000 | 18936.4 | 9.52         | 53    | Two Seater\n",
       "Civic (1st Gen) | 2001 | 25833.4 | 7.04         | 47.04 | Compact\n",
       "Insight         | 2001 | 19036.7 | 9.52         | 53    | Two Seater\n",
       "Insight         | 2002 | 19137   | 9.71         | 53    | Two Seater\n",
       "Alphard         | 2003 | 38084.8 | 8.33         | 40.46 | Minivan\n",
       "Insight         | 2003 | 19137   | 9.52         | 53    | Two Seater\n",
       "Civic           | 2003 | 14071.9 | 8.62         | 41    | Compact\n",
       "... (143 rows omitted)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hybrid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Table method ``scatter`` can be used to plot ``acceleration`` on the horizontal axis (the first argument) and ``msrp`` on the vertical (the second argument). There are 153 points in the scatter, one for each car in the table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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CAvLz84mIiABg5cqVLFiwgJdeegl/f3927txJbW0t6enpeHl5ER0dzd///nfefvtt5s+f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\nXyYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10afb5cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.scatter('acceleration', 'msrp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter of points is sloping upwards, indicating that cars with greater acceleration tended to cost more, on average; conversely, the cars that cost more tended to have greater acceleration on average. \n",
    "\n",
    "This is an example of *positive association*: above-average values of one variable tend to be associated with above-average values of the other.\n",
    "\n",
    "The scatter diagram of MSRP (vertical axis) versus mileage (horizontal axis) shows a *negative association*. The scatter has a clear downward trend. Hybrid cars with higher mileage tended to cost less, on average. This seems surprising till you consider that cars that accelerate fast tend to be less fuel efficient and have lower mileage. As the previous scatter showed, those were also the cars that tended to cost more. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j0XDs2DEKCgrIz88nNDQUgDVr1rB48WJef/11fH192bdvHzdv3iQlJQVPT08iIiL46quv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\ndDpCgdGbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cb70080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.scatter('mpg', 'msrp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Along with the negative association, the scatter diagram of price versus efficiency shows a non-linear relation between the two variables. The points appear to be clustered around a curve. \n",
    "\n",
    "If we restrict the data just to the SUV class, however, the association between price and efficiency is still negative but the relation appears to be more linear. The relation between the price and acceleration of SUV's also shows a linear trend, but with a positive slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TJ08WaoKDg+Hk5GRR4+vrCy8vL6Fm+vTpMJlMOH/+vPU/NNEA1P5MSUFxOefk\npn5Jsg333XffxeXLl7Fhw4ZO63Q6HWQyGZRKpcVypVIJnU4HANDr9XB0dMTw4cPvWqPT6bqcu9Pd\n3d2ipuP7uLm5wdHRUagZyDiIiayBt9vQQCDJiS++++47bN68GX/961/h4CDZvwl+VmVlpa0jdMta\nGVctniE8azU85BFUX7ti1Xl77WFbAvaRU6oZq6urYTQacVvuCAAwGo2orq6WbN42Us/Xhjl7z9vb\nu9evIcmGW1paitraWkyZMkVY1tLSgjNnzuA///M/cfbsWZjNZuj1eqhUKqFGr9fDw8MDAODh4YGW\nlhbU1tZaHOXq9XqEhIQINTU1NZ3e/8aNGxavU1paarG+pqYGLS0tQk1XrPHD6UuVlZVWzfjrif5W\ne632rJ2zr9hDTilnjPVSoeK7a8IMTiNHKBG76FlJD0qS8vZsjzmlQ5KHj1FRUThz5gyKi4uF/379\n61/jueeeQ3FxMcaOHQtPT08UFRUJ32MymXD27FkEB985nRkQEAC5XG5Rc+XKFWi1WqEmKCgIDQ0N\nKCsrE2pKSkpgNBqFZh8UFAStVotr164JNSdOnIBCoUBAQECfbgeigYK329BAIMkjXBcXF7i4uFgs\nGzJkCFxdXeHr6wsAWLFiBdLT0zF27FhoNBrs2LEDzs7OmD9/vvAaixYtQnJyMtzd3eHq6ooNGzYI\nI40BwMfHB9OnT8fq1auRkZEBs9mMhIQEzJw5ExqNBgAQHh4OPz8/xMXFYfPmzaitrUVycjJiYmLg\n7Ows4lYh6t/4OLn+iQ8b+X+SbLhdkclkFl/Hx8fDZDIhMTERBoMBgYGByM3NhZOTk1CzdetWyOVy\nLFmyBCaTCaGhocjOzrZ4rb179yIxMVFo1LNmzcL27duF9Q4ODjh48CDWrFmDyMhIKBQKREdHY9Om\nTX38iYmI7BsfNmJJZjAYzN2XUX9jL9dLmNN67CEjwJzWYvEYQRtdD9+XewKHj5/G4EF3ju2abjdj\nfuS0Lp8uJvXtaQ12c4RLRET3ho8RlCZJDpoiIqJfTir3NfM+fUs8wiUioj7RNvqcg6buYMMlIupn\nZkcEo/D0eRjqGnG7uQVKd9sdWbaNPic2XCKifqf9kaU1Bk3x1h7rYMMlIuqHrHVfM2/tsR4OmiIi\norviIzithw2XiIhIBGy4RER0V7y1x3p4DZeIiO6Kt/ZYDxsuERH9LN7aYx08pUxERCQCNlwiIiIR\n8JQyEVGAdGrwAAAS60lEQVQ/ZPG0IC8Vr7tKABsuEVE/w6cFSRNPKRMR9TN5BV+gprYO+hsG1P6r\nHjW1dZysQgJ4hEtE1M+YfmrCxe9+REurGS0tLbhZfwumn5psHWvAY8MlogGrv07KbzYDZhkAmGE2\nm2GW3VlGtsWGS0QDUn+elP8+xWD4aUaj1lCPpp9+wghPd9ynGGzrWAMer+ES0YDUnyflnx0RDPfh\nLvBwd8XwYUPhPtyF0zFKAI9wiajf6q+njLtj7efhknWw4RJRv9TdKePZEcEoPH1eWN/fJuW31vNw\nyXrYcImoX2p/yhiAcMq4bU5gTspPYmPDJaIBi5Pyk5g4aIqIJKGuwYh9uSeQ9+mXqGsw9vr1Bvpz\nXK29Pan3eIRLRDbXF1MRDuRTxpzaUZp4hEtENtf+eusguaPVbtFpO2X84rzwAdVs+mp7Uu/wCJeI\nyM51vP2JpIkNl4hsrv0tOrebW6B0H1jXW3ujq9uftqyN4faUIDZcIrI5TtTwy3V1+1PRma+4PSWI\nDZeIJIETNVgXt6f0cNAUEZEdG+i3P9kTHuES9XNtA2qqq6sR66Xi0U4/M5Bvf7I3bLhE/RjvxxwY\nOGOWfeApZaJ+jPdjEkkHGy4REZEIJNlw09PTER4eDrVajbFjx+KFF17At99+26kuNTUV48aNg5eX\nF6KionDx4kWL9U1NTVi7di00Gg1UKhUWLlyIq1evWtQYDAYsW7YMarUaarUay5cvx82bNy1qqqqq\nsGDBAqhUKmg0GiQlJaG5udn6H5zIytoPqLnd3MIBNUQ2JMmGe+bMGcTGxqKgoACffPIJ5HI55syZ\nA4PBINRkZGQgMzMTaWlpKCoqglKpxNy5c9HY2CjUrFu3DseOHUNOTg6OHz+O+vp6LFiwAGazWahZ\nunQpKioqcOTIEeTm5qK8vBxxcXHC+tbWVkRHR8NoNCI/Px85OTnIy8vD+vXrxdkYRL3QNqBmfuQ0\nRDw2gddviWxIkoOmDh06ZPF1dnY21Go1SkpK8NRTTwEAsrKykJCQgKioKABAZmYmvL29cejQIcTE\nxKCurg779u1DZmYmQkNDhdfx9/fHyZMnERYWBq1Wi8LCQhQUFCAwMBAAsHPnTkRGRuLSpUvQaDQo\nLCyEVqtFRUUFvLy8AAApKSmIj4/Hxo0b4ezsLNZmIfpFeD8mkTRI8gi3o/r6erS2tsLV1RUAcPny\nZVRXVyMsLEyoUSgUCAkJQUlJCQDg3LlzaG5utqhRqVTw9fUVasrKyjB06FBMnjxZqAkODoaTk5NF\nja+vr9BsAWD69OkwmUw4f/58331oIiLqV+yi4a5btw4TJ05EUFAQAECn00Emk0GpVFrUKZVK6HQ6\nAIBer4ejoyOGDx9+1xqdTgc3N7dO7+fu7m5R0/F93Nzc4OjoKNQQERF1R5KnlNt77bXXUFpaivz8\nfMhkMlvHISI70vEpOjylTrYk6Yb76quv4qOPPsLRo0ehVquF5R4eHjCbzdDr9VCpVMJyvV4PDw8P\noaalpQW1tbUWR7l6vR4hISFCTU1NTaf3vXHjhsXrlJaWWqyvqalBS0uLUNOVysrKX/CJxWUPGQHm\ntCZ7yAhYJ2eD0YQ/7s5FfaMJAPBR/ims/908OA9R9Pq12wyk7SkGKef09vbu9WtItuEmJSXh448/\nxtGjR6HRaCzWjRkzBp6enigqKkJAQAAAwGQy4ezZs9iyZQsAICAgAHK5HEVFRZg/fz4A4MqVK9Bq\ntQgOvnNbRFBQEBoaGlBWViZcxy0pKYHRaMSUKVOEmjfeeAPXrl0TruOeOHECCoVCeO+uWOOH05cq\nKyslnxFgTmuyh4yA9XLuyz2BFrMDXO93AQA03W7G15f0VpuRaaBtz75mLzl7Q5IN95VXXsHBgwex\nf/9+uLi4CNdKnZyc4OTkBABYsWIF0tPTMXbsWGg0GuzYsQPOzs5Cc3VxccGiRYuQnJwMd3d3uLq6\nYsOGDfD39xdGLfv4+GD69OlYvXo1MjIyYDabkZCQgJkzZwpNPjw8HH5+foiLi8PmzZtRW1uL5ORk\nxMTEcIQyERHdM0k23LfffhsymQzPPvusxfKkpCQkJSUBAOLj42EymZCYmAiDwYDAwEDk5uYKDRkA\ntm7dCrlcjiVLlsBkMiE0NBTZ2dkW14L37t2LxMREoVHPmjUL27dvF9Y7ODjg4MGDWLNmDSIjI6FQ\nKBAdHY1Nmzb15SYgol5q/1B7AJz0g2xOZjAYzN2XUX9jL6dvmNN67CEjYN2c3Q2a6s2gqoG4PfuS\nveTsDUke4RIRWcPPPUWn/ZOUAKDw9HnOxEV9yi7uwyUisrb2T1IaPEjOJylRn2PDJSIiEgEbLhEN\nSO2fpNR0u5mDqqjP8RouEQ1IbU9S4kxUJBY2XCIasH5uUBWRtfGUMhERkQjYcImIiETAhktERCQC\nNlwiIiIRsOESERGJgA2XiIhIBGy4REREImDDJSIiEgEbLhERkQjYcImIiETAhktERCQCNlwiIiIR\nyAwGg9nWIYiIiPo7HuESERGJgA2XiIhIBGy4REREImDDJSIiEgEbLhERkQjYcH+BM2fOYOHChXj4\n4YcxbNgwHDhwwGJ9Y2Mj1q5di/Hjx8PLywuTJ0/Gnj17RM2Ynp6O8PBwqNVqjB07Fi+88AK+/fbb\nTnWpqakYN24cvLy8EBUVhYsXL0oqZ3NzM5KTkzFt2jSoVCr4+fkhNjYWVVVVksrZ0erVqzFs2DD8\nx3/8h4gp7z3nd999h0WLFuGBBx7AyJEj8cQTT6CyslIyGaWwD+3duxfTpk2DWq2GWq1GREQECgoK\nLGpsvf90l1Mq+093OTuy1f5zLxl7s++w4f4CjY2NGD9+PLZu3YohQ4Z0Wv/aa6/h008/xVtvvYXS\n0lK88sorSElJwcGDB0XLeObMGcTGxqKgoACffPIJ5HI55syZA4PBINRkZGQgMzMTaWlpKCoqglKp\nxNy5c9HY2CiZnEajERcuXEBiYiI+//xzHDhwAFVVVXj++efR2toqmZztffzxx/j73/+OkSNHipav\nJzm///57zJw5Ew8++CCOHj2Ks2fPYsOGDXBycpJMRinsQyqVCps2bcLnn3+OkydP4vHHH8e//du/\n4ZtvvgEgjf2nu5xS2X+6y9meLfef7jJevny5V/sO78PtpVGjRiEtLQ0LFy4UloWEhGD27NlYt26d\nsOzpp5/G+PHjsX37dlvERGNjI9RqNf7yl7/gqaeeAgD4+flh+fLlSEhIAACYTCZ4e3tjy5YtiImJ\nkUzOjrRaLYKDg3HmzBmMGzdO5IR33C3nDz/8gMjISHz00UeYP38+li1bht///vc2yXi3nLGxsZDJ\nZHjrrbdslqu9rjJKcR8CgAcffBCvv/46YmJiJLn/dJWzIynsP2065pTa/tMx49KlS+Hg4PCL9x0e\n4faB4OBg5Ofn48qVKwCAkpISVFRUYMaMGTbLVF9fj9bWVri6ugK485dadXU1wsLChBqFQoGQkBCU\nlJTYKmannF2pq6uDTCb72Zq+1lXOlpYWxMbGYu3atfD29rZZtvY65jSbzcjPz4efnx+ee+45jB07\nFuHh4Thy5IhkMgLS24daW1tx+PBhGI1GTJkyRbL7T/ucQUFBXdZIYf/pKqfU9p+OP3Oz2Yy//vWv\nvdp35H2Yd8Datm0bVq9ejUceeQRyuRwymQzbt2+3acNdt24dJk6cKPxy63Q6yGQyKJVKizqlUonr\n16/bIiKAzjk7un37NjZs2IDIyEh4eXmJnO7/dZXzT3/6E9zd3fHSSy/ZLFdHHXPq9Xo0NDQgPT0d\n69evx+uvv47PPvsMsbGxcHZ2tsnvaFfbUir70DfffIOIiAiYTCY4Oztj37598PPzQ2lpqaT2n65y\ndnX0auv95+dySmX/udvPXKfT9XrfYcPtA1lZWSgrK8MHH3yAUaNG4cyZM9iwYQPUajXCw8NFz/Pa\na6+htLQU+fn5kMlkor//veouZ9tfwPX19fjggw9skPCOrnKeOnUKBw4cQHFxsc1yddRVzrbrdrNm\nzcKKFSsAAI888gjOnz+PP//5z6I3tLv9zKWyD/n4+KC4uBg3b95EXl4e4uLicOzYMdHe/17dLaef\nn59QI4X952459Xq9ZPafu2VsOyPQm32HDdfKTCYTNm/ejPfeew8REREAgIcffhjl5eV48803RW+4\nr776Kj766CMcPXoUarVaWO7h4QGz2Qy9Xg+VSiUs1+v18PDwEDXjz+Vs09LSgiVLluDixYsWv/xi\nu1vO06dPo7q6Gj4+PsKylpYWJCcnIysrCxUVFZLI6ebmBrlcDl9fX4t6Hx8f0U8r3y2jlPYhuVyO\nMWPGAAAmTpyIv/3tb9izZw9efvllSe0/d8v57//+7wCks//cLefIkSMls//cLeMbb7zR632HDdfK\nbt++jdu3b8PBwfLyuKOjo+ijApOSkvDxxx/j6NGj0Gg0FuvGjBkDT09PFBUVISAgAMCdf+jOnj2L\nLVu2SCYncOfWht/+9rfQarU4duwY3N3dRc3X5udyxsbGYs6cORbL5s2bh+eee070ATQ/l3PQoEF4\n9NFHO93G8N1332H06NGSyCilfaij1tZW/PTTT5Laf7rSlhOQzv7TlbacUtp/OmrLaI19hw33F2hs\nbMQ//vEPmM1mtLa2oqqqChcuXMCwYcMwatQoTJs2Da+//jqGDBmC0aNHo7i4GO+//z42b94sWsZX\nXnkFBw8exP79++Hi4gKdTgcAcHJyEoawr1ixAunp6Rg7diw0Gg127NgBZ2dnzJ8/XzI5W1pasHjx\nYnz11Vc4cOAAzGazUOPi4gKFQiGJnG5ubnBzc7P4HrlcDg8Pjy7/iLBVTgBYtWoVlixZgqlTp+Lx\nxx/H559/jiNHjuAvf/mLJDIOHTpUEvtQSkoKIiIioFKp0NDQgA8//BCnT5/Ghx9+CEAa+093OaWy\n/3SXUyr7T3c/897uO7wt6BcoLi7GM8880+k648KFC7F7927o9XqkpKSgqKgI//rXvzB69GgsXrwY\nv/vd70TLOGzYsC6vgyYlJSEpKUn4etu2bXjnnXdgMBgQGBiIHTt2WFz3sXXOH374QTiC6Gj37t0W\nt2P1pXvdnu1NnDgRsbGxot7WcK85Dxw4gDfeeANXr17FQw89hDVr1mDu3LmSySiFfWjlypUoLi6G\nTqeDi4sLxo8fj/j4eDzxxBNCja33n+5ySmX/6S5nV2yx/9xLxt7sO2y4REREIuB9uERERCJgwyUi\nIhIBGy4REZEI2HCJiIhEwIZLREQkAjZcIiIiEbDhEhERiYANl4iISARsuERERCJgwyUiIhIBGy7R\nAJaamophw4ahsrIS8+fPh0qlwiOPPIL9+/cDAN5//30EBQVh1KhReOaZZ3D58mXheydMmIBly5bh\nvffew6OPPooRI0YgNDQUp06d6vQ+e/bswYQJEzBixAg8+eSTKC0txYQJE0SdG5nI1vi0IKIBrO0h\nAi+99BJiYmKwatUq7N27F7///e/xj3/8A6dPn0ZKSgqampqwbt06xMbG4r//+7+F7z99+jTKy8uR\nnJyMQYMGYdeuXYiOjkZxcbHwlJf33nsP69evR0xMDJ599ln885//xNKlS1FXV2eTz0xkK2y4RAOc\nTCZDfHw8oqOjAdx5Ssvx48fxzjvvoLy8XHis3/Xr1/Hqq6+iqqoKo0aNAgDcuHEDn376Kby8vAAA\njz/+OPz9/ZGWloasrCyYzWZs374dERERyMjIAACEhYVBqVRi8eLFNvi0RLbDU8pEhCeffFL4f1dX\nVyiVSkyaNElotgDg4+MDALhy5YqwbNKkSUKzBQBnZ2dERESgrKxMqL1y5QqeffZZi/d7+umnIZfz\n730aWNhwiQiurq4WXw8aNKjLZWazGSaTSVjm4eHR6bU8PDxw7do1AEB1dTUAQKlUWtQ4ODh0euA4\nUX/HhktEv5hOp+tyWdtRr6enJ4A7D5Rvr7W1FTU1NX0fkEhC2HCJ6J61DbJq8+WXX+Lq1avC1/X1\n9SgoKEBQUBAAQKVSQaVS4eOPP7b4vk8++QTNzc19H5hIQngRhYjumdlstvhaqVRi3rx5SEpKEkYp\n37p1C2vXrgVwp0EnJiYiPj4eq1atwpw5c/DPf/4TGRkZuP/+++HgwL/5aeBgwyUa4DoetbYtu5fl\n06ZNw2OPPYZNmzbh2rVr8PPzw6FDh/DQQw8JNYsXL4bRaMSePXvw4YcfYty4cfjzn/+MF154AS4u\nLn3zoYgkSGYwGMzdlxERWZowYQKmTp2K7OzsHn/vuXPnEB4ejrfeegvPP/98H6Qjkh4e4RJRn/r+\n+++xd+9eTJ06FUOHDoVWq8XOnTvx4IMP4plnnrF1PCLRsOES0S9yt9POHd1333349ttv8cEHH8Bg\nMMDV1RVPPPEEkpOToVAoREhKJA08pUxERCQCDhEkIiISARsuERGRCNhwiYiIRMCGS0REJAI2XCIi\nIhGw4RIREYngfwGx3gSXBDsnoQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ca718d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv = hybrid.where('class', 'SUV')\n",
    "suv.scatter('mpg', 'msrp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jVVVVHDx4kP/5n//h0KFD2Gw2LBYLoaGhRozFYiEoKAiAoKAgqqqquHz5sl0v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\nwRUREXECFVwREREnUMEVERFxgv8f4qU0enBTkDkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cf547f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv.scatter('acceleration', 'msrp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will have noticed that we can derive useful information from the general orientation and shape of a scatter diagram even without paying attention to the units in which the variables were measured.\n",
    "\n",
    "Indeed, we could plot all the variables in standard units and the plots would look the same. This gives us a way to compare the degree of linearity in two scatter diagrams.\n",
    "\n",
    "Here are the two scatter diagrams for SUVs, with all the variables measured in standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZYePGjXjw4EF91ENERPSPCRot6ePjg8zMTLFrISIJqZyLl7DzIOfiUb0T1Oc2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\ncCMiIslhuBERkeQw3IiISHL+HxnbGRhrmktDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3b9b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Table().with_columns([\n",
    "    'mpg (standard units)',  standard_units(suv.column('mpg')), \n",
    "    'msrp (standard units)', standard_units(suv.column('msrp'))\n",
    "]).scatter(0, 1)\n",
    "plots.xlim([-3, 3])\n",
    "plots.ylim([-3, 3])\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Yvbz8Qr4uRBomKLlt3rwZjx49wscffwwA+PXXXzFs2DDcu3cP7du3x44dO+Sr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\nNyIiEh0mNyIiEh0mNyIiEp3/B/GSDMIaVTOQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d4ed828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Table().with_columns([\n",
    "    'acceleration (standard units)', standard_units(suv.column('acceleration')), \n",
    "    'msrp (standard units)',         standard_units(suv.column('msrp'))\n",
    "]).scatter(0, 1)\n",
    "plots.xlim([-3, 3])\n",
    "plots.ylim([-3, 3])\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The associations that we see in these figures are the same as those we saw before. Also, because the two scatter diagrams are drawn on exactly the same scale, we can see that the linear relation in the second diagram is a little more fuzzy than in the first.\n",
    "\n",
    "We will now define a measure that uses standard units to quantify the kinds of association that we have seen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The correlation coefficient\n",
    "\n",
    "The *correlation coefficient* measures the strength of the linear relationship between two variables. Graphically, it measures how clustered the scatter diagram is around a straight line.\n",
    "\n",
    "The term *correlation coefficient* isn't easy to say, so it is usually shortened to *correlation* and denoted by $r$.\n",
    "\n",
    "Here are some mathematical facts about $r$ that we will observe by simulation.\n",
    "\n",
    "- The correlation coefficient $r$ is a number between $-1$ and 1.\n",
    "- $r$ measures the extent to which the scatter plot clusters around a straight line.\n",
    "- $r = 1$ if the scatter diagram is a perfect straight line sloping upwards, and $r = -1$ if the scatter diagram is a perfect straight line sloping downwards."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function ``r_scatter`` takes a value of $r$ as its argument and simulates a scatter plot with a correlation very close to $r$. Because of randomness in the simulation, the correlation is not expected to be exactly equal to $r$.\n",
    "\n",
    "Call ``r_scatter`` a few times, with different values of $r$ as the argument, and see how the football changes. Positive $r$ corresponds to positive association: above-average values of one variable are associated with above-average values of the other, and the scatter plot slopes upwards.\n",
    "\n",
    "When $r=1$ the scatter plot is perfectly linear and slopes upward. When $r=-1$, the scatter plot is perfectly linear and slopes downward. When $r=0$, the scatter plot is a formless cloud around the horizontal axis, and the variables are said to be *uncorrelated*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UirRagW+/BXJyXNDpRBgMAm66CZg3j8nQ/S2B9uxR44orBHg8yUHnnGbNYoo7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\nh6xYdJzSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d18d2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rKx246SafsXj3XR0WLkxGY6MBZWUWFBS48MtfOrFliwnl5XbU17dj+HCPJLk3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d9cd7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uRvAYfPBBO/LyXMI5YnOUnFu7XJxTY6MF99/PedaVldmwYwcnmJcty1RkdlLD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\nOSpGhBBCmKNiRAghhLl/AFMdkox2IKolAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dad1b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gtTLYtUtQFJ82zQ27nYHJxOOZZ1z4f//PXy338ssOrF+vxenTqpD1W1qYkEq/\nDz6wYupUE/LzhYq9YIkgcUSFuDe1mg9RURCbbwNDkkePCn1dOh2PrVt1steK5fTi+PRAAtUy9uzR\nhJUaKipyYcyY0DBe8Ch2MeTZlcIG8TPTGwsYUvXfaipBOSMihI4UHMxmJ1paIjvVsfSziNdOTxcO\n80GDeJw6xWDsWKEPqrbWjsGDfRg92oe//lXwwNLTOdx6qw9LlgjGJz/fI6uWe+45Az74wIq+fUPX\nN5l4mQqD2exERgYvyf0EM3myVwqVAX7pHiX1ij17NBg0yB2iRffqqzZs3aqTvfb8eaHCb/Jkb0he\nLXDPOTk+yeNZu1Yna4B94AEv7ryTkz3r4MrAigo9ysqcKC3Vh/RidYbeZISI3gOF6QhFIik4VFTo\npQO9q3mKwGs3NalRWGiEzQYUFRllYbSmJhXKygzYuVOL5cud2LDBIY0XP3eOxcmToR9lrTacNBEL\nnU7IDxUUuJGTI4zJyM31YfZsFx54QD4u46GHlKfP7tqlkeVqSktd2LtXrfjMfvELA1av9lfVvfKK\nHWVlylV1gc/GYmEwZowQ4hs3ziuNxBCfuWjAOqqU/OILQRdQbP4liGSDjBHRKSZO9KK1lUFRkQvb\nt9ukfhgRsQRYTLKHy1nYbEBBgX+AXXo6pzgD6dNP/aXcr7yixdVX87L31dZqsX69/7APlDUKxGIR\nckNLlhgkzyY72++RZGYC997LYexYLz74QCh2uPNOTjYLaeNGQbpHGD6owZtv2lBU5EJtrQaVlU5F\no9DezuLYMZWU19HrOdxzjy/suPLgEuqsLF4ymIcOXUJDgxWjRoUfmx6439JSF7Zt06KiQi9NzCWI\nZIPCdESHKMkO3X47h+uu80iKAIHjsEWvwO0Gios9stHe4cZNrFzpgMXC4Ac/8GH+fLmY6erVDqlJ\nVCwEmDpVmOUjloA/+qgXb7yhwQcfWKHVhsoaAUJe6vRp4TAWNfL69+cuywL5X3/ggDx3BQjNt/n5\ngodUVqZHfb1NJqGUne3Bz37mkZ7BqVOM7B6WLHFi2TJ/rue223wYM8aHurrQ592RunbgqA2lfJzF\nwmDpUh3Kypz44guhuEFcV2kt8XdMED0JeUZEVCiNrM7KEmYQhauoe+QRj+ybf2CZeOCB63YDLheD\nmho9fvYzIx591IuNG7WSmOmgQT6UlLgVm0wrKvRYsEDwSubPdyMnh1c0RI2NKlRX61BWpsfKlX6v\nYfVqhySQ2Dv8AAAgAElEQVSC2tLC4NgxNqSU+uxZ9vIgPh1ee00wiv/7vyrk5ZmQl+f3XAKNcVGR\nEeXlekkw9ZZbvMjMFNasrHTA7QbWrdPKQnfRhDqjKb232QRPrKxMjwEDeGi1UKx+owZWIpkgY0RE\nTXBeItzBKHpSJhOP9HQOM2e6MHOmK+xU1GDF7spKHSZM8KGuTgujEbjzTh55eR40NFgVS8DvuMOH\n3bvlHoLFwqClRShrFsd2cxxQUODBr36lQ0GBG1VVdpw4weK55wz47/8WjMvu3ZqQ63/4oVqWG/qP\n/3CEGKxwYchBg3iUlRnw+OMmrFzpxJo1dixbpoPZbMA99/jwve95sWOHUMptNuslw9aVEmoxnyeG\nEauq7GhosIY8n+5QbSCIaKEwHRE1sYR0cnN9uPFGH+6+2ycTJxXfGxj6U1LsNpl42SGcmQlkZgr/\nvXlzO+bMEUZyi9JDgQRX/g0b5kN6OgeDgcfp04Lm3bZtgrTQY4+5MXmyF3PnCgfztm1a2SyhV1+1\n4ZNP1PjqK0YSek1Li3zv4r0FD+J75pk0bNtmhc3GIjNTKIzgOAZz5hgkpYdIM6mCnxsgKEUEFyVk\nZvor8ADgqquUvcWuEs3ngcKARLRQn1EX6M31/7HuPVzfUKR+omhGoLe0MHjvPQ2uvZaXxktUV9tx\n002+kN4bkZMnT8JkGg4g9JBTWrOgwI377vPiu+8YLFokGMbSUiG0N3myF5Mne/DTn/qH9Ykq3F9/\nzWDUKA4//7lfkFWlAux2HgMHAgsWCD9fu9aBu+7y4tpr5ftsamIwdap8L++/fx7XXKOT9VStWeOA\nxwN8/rkK+/eroyq/tlgYaVhgezuLrVttkj5f8DiMcNfq6HcX/N7Az0w0fWTdKd7aEVfSv9XeCnlG\nRIdESqh3dT6O0Qi88YZONgF22LDwhggAOI6Lea3z5xksXervQ6qs1OGtt2wYOpRDZqbgtYkeXEmJ\nGxs3avHSS07JYwKEfp3HHnPj+9/3YcUKf0HDihU67Njhw7XX8rJDPCeHl123qsoBvf4seD5b1re0\ncKEBBQVu7NypxcaN0YfkCguN0pTcpiYVior8s6JycyOrmAPhe8HERt29e9WKjbLRjC+nEedErFDO\nKIXoqkp1ZwnX4xJN7kN8jVYL1NdrMGQIh8cfN3Y6oZ6VxWPLFvmU1jFjvIpNukOG+JUPJk70oqHB\nit27rRg/3oMdO+w4ejR0DyqVMMIisKChvV24dmBBwB/+wKKlhcHttwvXbWiwYuJEL7zeUHkfALBa\nGZw7x+LZZ+W5m2h+p8E5t1jyP8G/uwMHVCgsNEpyQ6WlerS0CHtgg8fpRiBW8dae+uwSyQMZoxQh\nkZVRXUmoK1XhiYgHUG6uMGm2oMCN8nJBKTvaAzVQe018/ahRPhQVuVBW5sS5cwyamlg88ohbZqSU\nci1nz7KYMsWEH/6wD775hsEPf+iRVbtt2GDH1KluXH89J2uKNZsFZfHSUj3y8z147DE3vvqKRV6e\nCWPH9sHZs6wsZxPcB2Q2O/HxxyrMnClo7Yn7ivQ7DfydKOXcbLaofj0hz1L02Nxu4OuvGSxY4MJ7\n7wkahKdPDw1ZO5xQbSzirVTVRwBkjFKC7qiMimRUOkLJcwo+gEQ9uECpm3CwrNBEe/Qoi5/+1BAi\n2Co2h27cqEX//jyqq/XIz+8DnY7HwYNWbN9ug9msx9ixfaTDL7jUvLlZhccfN2HNGh1efdWGn/7U\nhWXL9Ni3T4MzZ4CBAzlJwWHIEA4mkxDeq6/XYOdOLfR6QTtP6LUK9XaWLtXhscfc2LTJjj59ODz7\nrPDeujotTpxQSRWAkX6nosq4wcBj40a5kOz06WmdPtjFcR51dVqUlRlw7bU83G5gzpx0aQ/iF4jg\nKj2RcOKtwVBVHyGSMGNUW1uL2267Df3798f48ePx6aefJmopIkEEh05iGc7X0XWDD6DAgXQdeV+n\nTw/FuHEmFBYa8fTTbtTUaCUj8tFHarS0CN7Wjh121NRopQF5zz1ngM0m5FqamtSy1wd6SYFhr6Ym\nNZ5+2gink0F7O4sbb/Th22+FGUVWKwOrlUFFhQ7nzzM4fVrYw7lzLBYtMuDmm4UZSiUlzhBPpb2d\nRVWVHk8/nQaVigkJsynp3gU/w6IiI9av12PVKgPKyoQZT2IFXWtr7Ad7uHEea9bo8cgjckmkxkZ5\nn5XSdTIzBa/toYc8EXOABAEkyBj99re/xaJFi1BaWorDhw/jrrvuwqOPPoqvv/46Ectd8XS1L0WJ\n7g6dnDnDROV9WSwM5sxJlw7KJUsEodHAb/PiAdmnDy95K/X1GpSUuMGywnMJfv2JEyq8/rotbNgr\nN9eLZcscGDqUx7FjKkyeLOR+Pv5YhYICD6ZONaGuTovFi12SRNHJkyy++opFTY1e2hPLsrLfl1Yr\neFnBXLyImH+nDAMMH87h668ZqR+LYXi0tAg9Vx1hsTAYMYJT7OUymXhs3tweIsQazpvJzfWhosIZ\nVnfPv+fw86CIK4uElHY/8MADuOWWW7B+/XrpZ3fccQemTp2KsrKyeC/XYyRbyWUsPR2R9h5NSXZX\n9xQouSOWWXdU0iyOsAge/1BVZcenn6pDxjk0NFhDXnvwoBV//zuLgweVX19fr8aYMT5cusTgxRf1\naG9nsXChE1u2aLFjh9DIu2+fBitXCpVrmzbZZRV3Yin5kCEcTp1i8ZvfyNfYtes8brpJF/JsDh5U\nYdYsf29Unz4c7rhDMMgcx8BoDH2GgWrny5c78c03rNQftWaNAwMG+HDhglAUAQjVfBMnKhdQBF5r\n82YHOA5S2XhNjR2jR/tw6dJJ3HDDDVF9PpReEzxeI3DNTZscGDQoPp63Esn2bzUWevPeYyHunpHH\n48GxY8cwfvx42c8nTJiAP/7xj/FejgggXmG0aIim+imSdzV6tNCUmZ/vwapV/oq0jq41fXoaNmyw\nyRLjOTk+3Hpr9Hms0aN9ijkMk4nHqFE8ZswwYu7cNCxd6kJRkQsrVghGyWgUpreuXOkPqf3hD6Hd\nEf/+7x7U1Ghht4c+n/feuwoHDgg5ocDf15Ah/uexcaMWbjeDd94R8kfTp6dJzzBwUN6IEYIBfecd\nG44cUctCfQsXGtCnD/Dss34PZt48g6KHFKwlOH26EYWFRlRUOHH48CWMGsWB5xn4fNfIFDZi9Wb2\n7NGEyEG53cB99/mwZ4+GFMWvcOJujL799lv4fD5kBgWJr732WrS2tsZ7OSIBdHTYRBPC6yiUk5kJ\n3H+/F/X1msuyNeEPtOAxE8uWGdDQIITzxo/3QadjsGaNLqR6Kztb+T4yM4FBg+QVcbW1dvA8I81E\nOneOxQsvGOByMdBqIVWDBauM792rlmndbdpkx9ChHFavduLwYZVsDVE9u6QkDdXVOlnxBMcxqKvT\nYtcuDZYtc+Lqq4GtW3WYNy8NxcUeqRCiulqHKVPSsH+/GuPGCTmbL79UQacLfXaiMczI4KRKPTFM\nqUSwlqDZrMf//q//d/3JJ9diyhShMKKjkKrSCHVxvIZIeroQKhULN44fp0q6K5m4h+nOnTuHUaNG\noaGhAXfffbf08//4j//Ae++9hz/96U+K72tubo7nNoguwrIs3O4MAMK4aY4TDl+vtx8efnhwkKrA\nV1Crz8veH83rwq0RTEfXYlkWp08PxeLFV2HyZC9++EMnMjO/hNfrVVyDZVl4PNcAMIDnAYZxQKP5\nFm53Rsg6NTU29OnjQ79+X+HkyYGSDJE4PVVskJ0wwQeTiYfBwGPKlFa0tvbBxx+nwWDg8W//5sFH\nH2nw6qt+9ez8fA/q6zV4992LaGrSQK0G+vf34ssv1bjmGh7z5slDf+LrxUbb4Cm7v/71Jfz1r/6J\nsJs3X8KaNWkoLPTA54P08+rq7zB48CnZsxaf3+HDabLQ5fPPO0NCmeI+lH7nwajVarS2DsWHH+qx\nd68aq1ZdxJAhX0q/g/PnszFjxlUdfpaI3kmsocW4KzBcc801UKlUIV7Qv/71rxBvKZDeGBPtzbHc\n2PbeV/ovpdBcRkYGsrL6hvw8eOzEqFF9ZdcKt4YSgdfavLk95Fo33ADs3m0HAGRlMbBYsi//d+B3\nLeH1oTI1OgB+rbtAXTuz2YDKSif0+qGYM8efA6mo0KO83AGDgYfNxqK+npVyXxMnZmDmTL+80Btv\n6LB9uzDptX9/DkuXOtDUpMLs2U6cPatBWZmg0LBhgwNnzrA4cSL0GYvip+XloZVtAPBf/6XFgw96\n8NvfWnHNNUIxw+nTKjQ3+7Bzp9+gzJ59NQ4eHB7ihd5wA3DzzS6MG+eF2azH5Mle/OhHwuC/QAwG\noZxcp8tAdnbk3xkADBsGDB3qRkmJG1lZKgA3BNxT9J+lWAnOVV45/1Z7L3EP02k0Gtx+++04cOCA\n7Oe///3vMWbMmHgvR3QzseQLutKbFOlaQ4Z8GXZvWVk8jhxh8eabGhw6pMKxY/IDr6PwYbgGXKUm\n0r//XYVNm3R4801Bdbu2VoPiYg/27w/9jseyQnjvySddSE8Hdu7Uor2dxfz5/rDg/PkG3HWXF3v3\nylXCq6rs0Ol4qFTC9NrDh1X41a/kw/NefVWHn/zEhHff1eIvfxF6rWpr7VApRL6C76W1VdAItFoZ\n3HKLDy+9JHhEs2cb8PLL/nXWrHHg5pt9sorFwBxWuDxiVxQ6OgM10fZOEqJN98wzz6CkpATf+973\nMGbMGLz++uuwWCwoKipKxHJENxOLHl08CyrEa128qBzOA4SDtblZha1bhYo1s9kJm82He+8N/55g\njEaENODabMKAPLGKrqzMgXvv9aKkhAHL8ti/X0jEr1qlQ2Ymhy1b7FJ1XHW1XVLmnjnThRdeEPIy\nSr1Ex46pUFIi9E4VFLgxYYIHTU0sHA4GOh2HX/3Kjmuu4bB+vR5vvmnD/v0aaXheTo4Xw4dz+PRT\nFUaO9GLkSB8++USF1asdkkCs2ezEN98wkiLE0aMMvv5ahYULhb9/9VWbVB147hyL9et5bNtmw4cf\navCPf7B44w2/CnlxcRqKilzYulWHjRuFMert7WxMoqhd1TYMJpwmHpH8JMQYPfzww7hw4QLWrl0L\ni8WCUaNG4d1338XAgQMTsRzRAyRrL4jV6q92A4RwWkGBG9dd55bKo4PDh0p6eTU1dlnp+YEDavTr\nx0tNpSwLXLoEGAxC6fWkSR4UFRmh1QIvv+wAAOm1dnvoPjMyOKSl8VizxiEZArPZiWuu4fDyyzpM\nnerBPfd40bcvhxEjAI1GEHoFgF/+0oFp0zx4/nkDZs1yQ6sVlMaXLHFJCuP33efFLbf48MYbOkyb\nJihFWK0Mysv10GqBgwetYBgebW1C5Z34vH7/e/k8p3vu8WHGDCHkOHOmK+Q+vvc9Dq++KlTtPfaY\nG1VV+phFUZP1s0R0LwlT7X7yySfx5JNPJuryRIrS1fk3RqPyz99+W5hfJH5r7+jbuFh6brUyWLVK\nh6efduGVV/xGLifHi2XLgJkzdZg82YuHHvLg8OFL4Dhh/8E9Nhs2ODB/PovDh1Worrbj9GmhJ8ho\ndIUYik2b7PjmGxZPPy3czOrVDkllAgB++UsDVqxwoL2dvazE4MLYsV48+aQ/TzVnTtrlPJUN+/Zp\nQgoRAMFwf/qp/AjYu1eNqio75s0TDPHEif680a5dGqxd65CN4Vi2TIdHHhGKGm68MXrvMxZi+UyE\n+7Jx8WJCtkbEEdKmI5KGeMT6g/MQZrMTI0cKw/SCp9FGKiXnecHbEUvPH3hA3iw6ebIXy5frUFzs\nkVQGjh9XgWGE8u/gqbbffQc8+aQLr7/ehtGjOakn6F//YlFXp8Vrr+mksOCFC/JepkWLDJLig8gd\nd/hQU2PHDTdw2LpVhwMHQr9X/vd/qzFsGI/Zs12KKgdGo2B8AsVgi4s9WLtWhw8+EHTn7r6bk6lF\nDBsW2h8mFld8/TWD/v05bN1qk55juOcbrUxRZz4T8cxVEt0HGSMiKYinYKZYhLBihQMmE48NG/wH\nfXo6B5st/EEZePh5vQwOHbp02YviZT1Dd9/txeTJXllfzqxZQh9QXp4J5eUu5OR4JYO4bp0Ot9/O\nIS3trGy9Xbs0Ib1Ip06F/rO8+26vzJhkZ/MYP96H//N/vDCbnVCroaAkLrw3MxMYP15+QFssgh5f\nZaUTzc2szMCcPq1C376Q8kri4f7++1/h9tt5WX/Y6tVCRWFOjg9FRW4cOnQJXi8T1oDEYly68pno\nzgZwIj7QcD0iJTEagbIyA9xuYPFiFyorWaSncygvdyEvzwQgdPpoSwuDjz4SBFTb2lhZ8ruw0CQb\nAPjZZyqMGeNDXZ18XXEu0bx5BnzwgRW/+Y0W5eVC0cOnn6owYMD1MBoFwyb2/uh0PN56y4YDB9Q4\nfx646y4vfvADL2bNEsJ0ZWUOfPaZCmVlTpw5w2DkSP+ehw4VRowbjSzWrvUP/Kup0aKy0iFrchUP\n5yNHWOzbJ+SGpk51A1Dh5pt9WLLEgMxMDlVVQs6rtVVQnBCVEbTaNgB9ZWFOhuFxzz2MbLpsuKF6\nNHCPiAR5RkRSEO8y38ChfbW1GmzfbsOOHXaZwkLgN+0DBwQV6mCx03AwDLBunVZW+mw2O7Frl78A\nQKuFlG8RRVkfeaTfZfFUv5r4hg2C6veIEULIbc4cI2w2Fk8+KeST0tN57NypwTPPpGHrVh2sVnmY\na8wYDuPGebFqlVMShf35zwUZo0uXGFlYrLUVaGpSSWoIdjuD3/5Wg5//3ICiIheWLnXhpz81Ytw4\nExoaNJgyJU36f3Gekfh8RTWLeBsTcb+JKv0mkhPyjIikId5lvsHXUwrxMAyPo0dZ2RjwykodZsxw\n4/77vdI+tm61oalJJRMitdl8WLJEh6IiF6ZM8eDYMRW0WkiGyWQSDtOPPlJL4TxAECCtqHBK1Xpm\nsxMDB3J47DF/0cMLLxiQn+/Ba6/ppF6jpUv1WL7chenT00JKqDMzgZtvlhdd/OhHXly8yGD6dKHg\nYNMmB/r04VFXJ/RDVVbqUFenxYYNDqxbp8X3v++TKT9UVAjDAisq9Cgrc+Lw4TTcfLMr4jiISNWK\n0VQyhjYkx/czQSQvZIyIpCLeB07g9ZQOQ55nsGePJuR9Tzzhlk1nHTaMR1GRXgrVHTumgtHIQ6MB\nvv99Djt3arF3r1oWJps82YvcXB+uv55DXZ0WGRmcFOa76SbhkLXZBHUFno+cC/n0UzVeecWBZ54R\n+pWA0DBXZiYwaZIHhw6p8eKLXixaZEBdnRYLFwo5pcJCIewnVsuJRmf+fAN27bLivfe0yosD+OIL\nodBi3DgvMjMjFwVEMiAjR/rw4YeXJCXyQCiMd2VDYTqi24mlmipe1w4ccR5caRWseCCKrAZey2YT\nquFeeskhzTsaM8Yrhf62bdOiuNgjhckqK53SIdraymDZMgeWLnVKoqD/+IcKWVk8srP9oa7AkNSG\nDQ4cPqySiYxeugRpdlM4XC4GDgeDRYv84cgtW7TQ63nk5wuCq59+qkZ6uiCeOnOmC+npHI4fV4U8\nB7PZL/YqViOWlERXRBBuuu+PfmTE4cMa5OWRQgIhhzwjoltRCsNEi3gIsqzyd6hw1460ZlaWUFFW\nWio0xz70kAd33snJ3lNV5cDSpTr83//rgdvNSHmgIUM4DB4seEJtbSyqqzVYscKBW27xISfHn9Av\nKjLiscfcMo244MQ+IHgUb71lw969Gqxbp8W6dQ4cOqRGba0Gv/ylC2azMF9o6VJBpLWiwik78C0W\nBrNmpUneGSA015aUuCX9u8WLXdi3T4Xly12YP1/42a9+5cDLL2sl5YeiIhcmT/ZAr+eRmcmhvFwf\ncRx8SwsDtxvIyOAVQ3jiHKrSUj0mTvTKmpKLi9PQ0GCNuiG5q31oRPKSkOF6Vwq9WcCwJ/belaF9\ngcZh8+Z2TJgg/0Yd7tpAaAOq0pqBh5zStfLzPbj9dh9WrNDLft7QYMXZsyxKS/UoKXFLOaWtW20Y\nNkzoOZo+PQ333ecLUdo+eNCK5mZWuq8337ThZz8zyl5TVuYEAGzcqJXCc/37c3jnHRtuv13uIYn7\n9lcQ6lBQ4A5peP3Nb2yYNs0Ycn+HD6vwzjs2fPGFCnPnCnvasMEOi4XFqlXCfW3ZYseoUT7wvFBg\n8F//pZKG95nNTuTk+DBmjH9fgUMUzWYnjEYeZWUG2driHsUvCuEMTle+yNC/1eSHwnRE0hPcbzJn\nTnrcw3wd9aUYDDz+8Y/Qfy5Go+DRvPOODadPs8jP98Bo5NDUpJLmDZWXu/D552zI/CSG4WX3tX9/\naO7q2DEVjh1ThQwfvO46ZeHR11+3YcYMN9raBCUHpaGDvMJtmkyCh8hxjEybbv78NFx9tWAwtm+/\nCJ2Ox9ixfTBunAm//70KZWX+5tyKCj327fMP0AssDBH/XqvlQ/qhomlIjmcfGpGckDEiuo1EluoG\nX1schif+PCfHi+efd2L7dluHazocoQemycRj/341Nm5U3v+XX6pQV6dFfb0Gq1a5ZFNX580zoLra\ngbw8Dz744IyUrwouWgge1FdVJeSNRJVu8R7eest/DxYLg5YWBuLEFq9XCCO+8YYOly4x2LFDg+pq\n+XNZuFAvyw1VV9sxe7YLubk+sKygvzdzpr+8ffhwDrNnu3D11Rexb59Gyj3Nnp0WogwhYrEoF4bc\neiuHESOEqr8VKwSZo0ghwESSyNwlETuUMyK6lc6U6gbnEjZvbr88Gyf02tu327BnjwZmsx6VlU7k\n5vqQm+uTSqkDw0Hh4DgGNTVaTJvmxsiRHM6cYXDffR5MmODFnXdyIfu3WBhZafiRI6F7a2sTlLK/\n++5fyMpKV7yv8nIX1q7VynJXw4f78PbbWrzxhgZlZS4sWCBUyNXU2GEycSgsFBp4zWYnbr3Vh4UL\n9VLOaM0aHSorHdiwQZinNGgQD4bhcfq0CqtWqWSVfWKu5/x54R4OH1Zh6VIndDoeTz2VhpdfdsBu\nv1rWN1Vbq8GkSX7tOjFMJ4Y69+5VY+FCJ9as0Ut/b7EwuPdeDsOHu8EwPK67jlfMEQWH6qLJJ8VC\nV0J+RGKgnFEX6M2x3GTbezSJafE1VusXuOGGGxT/vit5o0B+/3uVJGYKhOZKIq2bk+PFypVOPPOM\nX/W7tlaD3bvtuHjxRMhzD85XBT+HI0dYXLzIhEx/raryK4vPmCGMm/jnP1ksX+5XAW9tFeYUqVT+\ncvXGRhVKS/WSwOuddwoeUGB+xz8o0IuqKr3i1NeqKjsyMjjodMC33zL4y19U+MEP/DmjxkYVPvlE\nBYdD2MOuXRpJMTy48AKApPTwz3+yqK/XYO9etfSFQulZxULg570rucueINn+rSYKCtMRPU60emVi\n2C3cePJ4EihmGqg7p7RHceSEGPZauNCF48fZEEHRcAR6A0r5kmHD+BB1bUAo0X7iCTfKygRDMXOm\nEV6vUNkm5mg4Drj3XvlAPNFTFAVeGxtVMu/u3DkWlZW6sCE4kcZGNQoLTfjtb7WYOrUPli1LQ1GR\nUVYd+OMfe0KEYJXuv7mZxY9+ZERDgwbTpxtRVyeUypeW6mWhNNKcS13IGBE9SjwT0+FyUvHKVYm6\nc8F7bGxUwWwWSsM3bHDgH/9g8etfazFgAC8Jir7+uqBk7fX2C7luNMY4uAdo5UoHPvlEhQce8GDN\nGr/RXLlSj8JCt/S+e+7xYtkynez5trTIDU9xcRouXAhd8+67vRg1yoecHC8mTfKgurpdJui6fXv4\nJlmR7OyOn734GbjvPp/sC0A0BrEzkMxQckI5IyKlCJeTijVXFZyjWL3agRMnWMyb54RK5Q8pBRrT\npiY1+vfnMG2aWzatdcoUN6xWFuPGGQGYZDmKjlQHRKP38ssOPPecAQUFbtx9txevvabFggVu6X2B\n3HKLTypWGDqUi+iVifznf2pQVeXAvHlCiG/lSgcWLdLDZmPR0GBFdjaPkye/xMGDw3HmDIO5cw2X\ndf/sUKt5KW+kdLB3RdLnoYc8CTEUJDOUfJAxInqUeCemxWvG8vNwiAfWmTMMlizRo6DAg4oKYZz5\n/feHl8VhWUFJe/du/4jXceNil7kRk+zp6Rw2bXJgxw67pP6wZo0TeXkmTJvmlimAm81O3HKLVzIg\ngPBMxRxRfr4HbW2QvWfhQidWrNAjM5OTlMZ//nMD2tpY9O/PSbI9HMdJnqZ4b+I9dHSwR7pX8TNQ\nWqqX7aumxi7lsxIBGaHkgowR0eMk+7fUwkKjJBiqZFACjWlNjR2jR/tkSgSRwo7hjLHoMbndQHGx\nR9KVE70qsVfo7be1WL7cKY041+l4FBUZUVLiRmurUEwQXE1oNjuxcaOgGm4y8fjySxZtbSy0WkFF\n4f77vair00pl7adOhRZtdPTn4Hvv6PeamysYb4bhpdBcuIIOIjUhY0T0KKlw2Iwc6ZNJ2gTTkfcX\nyRg/8ohHpvgdaARraoRqulde0WLNGgc+/VSNJUsEj6aiQiigGDZMMFKBpeeiGreoCF5Q4JZyJ5mZ\ngNXKYcUKB1paWLS0sDh9mkV2tivm5xJr+bT/3vlOvZ/o3cS9gGHbtm3Iz8/HkCFD0LdvX5w5cybe\nSxApQmOjClOmpKGmRoujR7u/liaapkfRkIiCocFJ78ZGFcaO7YO8PBOam8PfQ+C0VKVDVQx/iU2s\nLMtjyxZ/WE6J0aOF5tH77vPh44812Lo1fMVaMNdc47+P2bNdUiNuY6Mw12ntWh1GjxbUyOvqtDh+\nXCVpAkbz3LpamEKKC1cecT8B7HY77r//fixatAgMQx8eQhmLhUFpqR7FxR6pxPjAge5TcI5l/LUY\nQsrL84SM7o7lwMzK4qFWn+9wT3l5Jnz4oQY+Hw+DgUdFhXyA36lTwhqZmZBGgO/bJ1eHMJudmDTJ\no1hNaDY7cd99Xnz44SWMHOmTVMMD7+e++3z4+c/9yt8lJWnweK6J6blFIhqDFqwsTqQ2cQ/TzZ49\nGxt1RNAAABvdSURBVABw7NixeF+aSDEmT/bKQlAlJd0zv6Yzc3OCQ0iJ3tPKlUKp+Pr1esyf75SG\n5pWX66HVAocOXQLPM7j+eg4ffngJaWmCcQqckZSZ6VfMHjzYh6IiF779lpWu8eSTLjgcjKzxNRI+\nnyHq56YUmmQYweCdOiUomYs/D+cplpe7pOq+qipHrw7lEh1DfUZEj5CVxeOhhzwdvzABnDkTH489\n1n4Vi4VR7DPqCLudkTWOivOHRC/qwAENWlpYaU/ijKRAT+vjjzW45RYf0tKE/Q0Z4sMPfiAUCsyd\na8CBAyqwrF+T7/BhFSorHbJ702gcMe07cHaUWu0XWP3mGxZGI6foTYoeU2srZCPi580zUJguxSFj\nRPQYd97JyZQLuqP50GIRemSCh+l1dl21WhAWLShwQ60Ofw3RMDz88GDF8FZWFi8Lsy1Z4sSYMV7J\nMAT+XXm5M0QNO1AtW7zPwBBiRYUeR4+qwbJCD9ELL7gwa5Zf6cBs1uPSJUGTr6zMicmThWbZ/HwP\nCgrcGDnSB5Xq24jGVyn0Jv59UZFR2suiRQasWiUIsaanc7DZgNZWeej0+HGVFJrLyBCKLGy2Tv2K\niF5CVNp0L730EtauXRv+IgyD+vp63HvvvdLPjh07hgkTJuAvf/kLBg0a1OFGmpubo9wykUqwLAu3\nOwMAoNW2JVzqx+vth4cfHiyNDzeZeBQUWMAw/+r0tQI1zt5//6uQvFA0r/N6++FnPxuIBQuEqrWT\nJ1kwDJCdzeG222zw+YC//c2Iv/1NBZ6HbFCfWBH32GPnpGsqrSmG+kwmPkRnrqDAjWnTLDh7tg8O\nH04L+fv33muHWu0Fy7rg8eig0znh9fLgeR5paRfxxRdD8MwzfQAIQrZDhnwp/S7D7cVg4HHbbV7M\nn29UnLu0bdtFzJ9vks2JCr52NHT3Z4wQiFVPL6qc0TPPPIPHH3884msGDhwY08LB9EYhwN4sYJic\ne+8b1au6uncxl1Ffr0FtrR0jR6YDSJe9Jhbh1kAyMjKQldU35tdZLAza21ksXGjA4sUubN0qNNdu\n3WpDa2ualHspLXWhrk6N1asdWLRIyKcI4TQfRo3qi8BnGJizMZsF5Yhly/SYMcMvFyTy0EMe5OSk\nIycHuPlmF8aN80qiqS+/7MCCBX0uN/32Q3o6J8vnbNpkx4sv+nuw5sxJx8GDw2XPTixDF++htlaD\nrVvtmDpVECy1WkOf0dChLHbssCMvzxTx2h0hLxHv1+tKxJPz32r8icoY9e3bF337RndQEESy01GT\nbaT+lkAjFa16RDSvC3xNba1GGvkAAOPG+aeyVlbqUFVlx9KlQoHDmDE+rFunxVtvheZzxPs8d45B\nWxuwaJEg4TNqlA9LljixcqWy0kFmJpCZKbz3wgWgqEiuG5ef75HyOQAwd24aCgrc0iRaJcaP94/3\nqK3VoLLSicAjZdcuDZYu9asvBDb/doXOFKsQPUPcq+laW1thsVjQ3NwMnufR1NSE9vZ2DBo0COnp\n6R1fgCC6gUiKAeEOLyUjJeaMAETMGYmGoa2t7bIHo/yaQ4cuwWplpAZapcP400/VaGpSS1p44vri\n/gPvT/z/q6/msWOHHUajX1dv4kSv7DVKz8hmYy5r20X2JsaMEfTwAITNwd15J4dBgwTdPnEPgUY6\nJyf0S0IsclHxbKBOhWbs3kbcCxjeeOMNjB07FrNmzQLDMJg2bRrGjRuHvXv3xnspgug2lHqKWlqE\nEuX16/VYv14vG58Q+L7Ag02pzyjwNSdOCE2nYh+P0gTbvXvl3yFFMVGlHiDxZz/8YR+cPcsiK4u/\n7PlEN44hO5uXJs4GVtpVVckn0q5bp708mtyG8ePDGy5xXMTYsX0wdmwfqNW8VHE3ZgynuKfAqrxw\nIbZw/U+nTjGKzcqRiFcvFREbNFyvC/TmWC7tPTxKHpDSQLaGBqssnxE8pE3pOsF7P3KExb59wnju\nBx7woLxcj1tvFTyMw4dV2L1bHq4K9tBqauwYP75z+4sWi4XBhQuASuXEVVcJYTSW5XHpUqgH19G1\nLRYGU6YIYb/ge+wsHQ1VDCxWmT3bJdMNjPZaPekh9eZ/q7FA2nREryVRoRSlnJJSuEic1RNubLZS\nuC+Q1lagqUkljV8YMkRQR5g9W2gINZudUjgrGi279HROGjl++HB8vtEHGr7qai9uuonHV1+xmDs3\nDe3t7OV79kVV6JGVJYw9D6yOW73aAYcjsQd9Wxsr6fCVlLiRqMZlomtQnxHR62BZNuGhFKVwkSiI\nGhguiiaEFA6rlZENk6uo0OP8eVb2Z55XTuCLB3tLCyNNiC0vd6G+XoP6eg3Ky11hB9tFI8UDhIYm\nZ89OR3W1DoWFRhQXey4rikeWQFL6PQXe86JFBuzcKWgTtrQIza6xEs+hijR4r+cgz4jodbjdGd1e\nIRUccsvK8hueWCroLl70v0acExTIyZPy74fhGj2PHGHR1KSSPIwtW+xYutQvrTRvnkEykIFeVFeV\nsMVpt5WVOqxY4cQXX7CS9xaMknfY0CD3DtPTOdxwAyeNyDCbncjJEUZfhEPJI+5oqGKkwpFgOqq2\npOKGxECeEUF0QGcVpDvymoK/hW/ZYseIET48/7wTzz/vxLJlDkXVbouFwb59GpmHMWtWWtgR3YGK\n4LEKuwYLrO7apZH+/osvWNTVaXHiRGyeaeA1ly93YckSg8wb3LdPg5YW5X1F8oiDvVnRA8zK4qHV\ntkXtESpdK5r1ia5BxojodWi1bb0mlNJRxVqgwRo3zoerrgLq6oSxDf368RGT7cE89JAn7s8kcH83\n3OCEVgvJMG3bppWMWmsr0NLCyIyIkjGbPduAtDQeDQ1WvPOOFZ99pnwEvf22NuSwj8WYBhuNs2eH\ndtmI0FiLxELGiOh1cBzXpVxNrCQ6jxDouTz7rP+we/ZZ5cMuK4vHpEmekJLlO+/kYvLEYr2PgQO/\nwsGDVjQ0WFFTo5VmJ6Wnc/j8c6EkPS/PhP37/dH/3Fwhz1ZQ4MbGjVo8+qgX06cbkZdngtXK4qmn\n3DJ9QrPZiexsDtu2aTt92CsZjY8/JiOS7FDOiOi1dKc3lGyj0ceM4ZCdzWHsWK9swmxHe4t0H0q5\nkMAc02uvDcbIkUKu6+WXHdIYiKoqB376U6MsX9XQYEV2tnAdo1Hw9vLzlafWjh/vV3v4z//UoKZG\nUCcXm2hFwuXhuiuHE0sDbjCUZ+oY8owIIkqiaRLt6vVj8VwyM4Wm1Fj3FOiJiYekUi4k0MNwu4GT\nJ/XSa7xeBocOXcLBg1b06xe6PsvyspxNbW3kqbVZWTxycnjcc49PCgUq3X+wR6y0b6XnOGFCfDzb\nznjklGeKDmp67QK9uRmN9t4zRLP37vgWHejxbN9uQ2Gh37MJbho9d47FzJlC2XhwU63ole3fr5aE\nU6ur7dBoEFK119oKHD+ukgRTw1XzRXv/LS1MxKbewOucPHkSJtNw6c/d5anEo4m2N3/eY4HCdASR\nZCRaey245HrPHo3i67KyeEltW8mrefttodCittaOiRO9Utm20QjZARxYei8KsCrdRyz319iowkcf\nRT6+Aq/DcVxEZQyi56EwHUH0MNGUHCcy1LN3rzrskMPRo30oKHCD44CFC52yQoPAajqLhUF2Ni/l\niSLdp1K4M9r7a2lh0NTEYMUKHbZt06K01IWcHC+ef96J7dttUckRdWdFHDXRRg8ZI4LoQaI5hON9\ngAYfkJWVTqmIIDgXkpkJ3H+/F7/5jRZbtmixfbstpJquo+vX1tpx6hQT9j6jvb/9+9XIyzNh6lQT\nnn3Wjb59OVRXa7BwoQt1dVoUFhoVn2E0495j6UGKle6s/OzNUJiOIHqInpy1E05/L9JrA1UMKiud\nEavKxPfYbEIxw+OPG7t0ny0tjGyGUmmpAStWOHD8uAqLFhnCXtsfkjOhttYOvV7w6gLnJp06xUiV\ngYkK25E31DHkGRFEktPVUE/wt/5I4bJIewgcfxHNt/3mZhZ5ecL4ipISNzIylCV+Ont/t9ziw7Rp\noVNrRZQ8rj17tCgv1yM/34OCAjcGDvShqMhIPUhJABkjgughYjmEOxvqCQ4DHjnCxi33FMmYBRuC\nigo91qxxICfHG1XJdjDiXCUxP/TmmzY4nTyKitJinlckqnjX1WnBcWR4kgUK0xFEDxJLM21n5hAF\nhwELCtw9NoL7+HEVKiqcYY1pR1WEEyd6odHwmD07DXV1WpjNTrS2sigv12PGDDeeeMItK6BQalJV\nq3lpZEdHY0C6myu9MZaMEUH0MIk+fDIyOGm4nMHQ+bVYlo36wAw2BKWlLqxaJXgjsRjA4H6o2bP9\nxrWiQo9HHvFIXo4wq0iOUr4r2Pgng7oGlZuTMSKIlCUri8fWrTbZqIlNm+xYvNgBh4PBpEmemA7f\n06eHYs4cE4DoDkxRl+7tt7VYtUpZ4icS0fRDmUx8h+E5YXTHeQB9pT8rvaan6MlClmQirjmj9vZ2\n/OIXv8Bdd92F6667DjfffDMWLFiACxcuxHMZgiCiZNgwXjZqYu7cNDgcDOrqtPB6o8+XWCwM5sxJ\njznRn53N4/77vRElfqJFqR9q9mwXlUynCHH1jL755hucO3cOK1aswI033oizZ89iwYIFKC4uxq5d\nu+K5FEEQnUQckNfRN/B45TA6GwYLDvVVVPj7oeTX6t0eRFcEWFOJuHpGo0aNwltvvYVJkyZh6NCh\nuOeee1BeXo4DBw7AarV2fAGCIOJKRwPywhFchZeVxWPz5vZOl5fHUkYeWIqem+vD9u02FBS4YTbr\npb2k2mFNjbHdkDO6ePEidDod0tLSEr0UQRAKBHomp04xHYbMwuUwhgz5EgcP+sVGE0FwIn/kSJ9M\nxDWcN5cKlWi9ee/xIKHGqL29HatWrcKMGTPAstTSRBDdTfAhnZXFd7pyLFBstDNrR/P6YCMoiq9G\ngirRUoOoLMRLL72Evn37hv1fRkYG/vCHP8jeY7PZUFBQgAEDBmD58uUJ2TxBEOEJp3vXUZhLKbR3\n5gzg810btTpBvIRdjUZEbAymUeCpQ1TzjC5cuIBvv/024msGDhwIvV4oH7XZbPjxj38MlmXx7rvv\nRhWia25ujnLLBEFEgmVZOJ0D8cgj/WRzdN5//yuZpE8keP5a1NVlwWpl8PHHKjz7rFsqD9+8uR1D\nhnwJjlMu0/Z6++HhhwfHvDbLspfLx9Nl6wCA250BANBq22TrdnYtIvHEOoMp7sP1rFYrHn30UQDA\nrl27UjpX1JuHXtHee4bu2Ls466euTtvpoW6BQ+GUBut1VIXXlYFysYb3ognT0Wcm+YlrzshqteLh\nhx+GzWbDr3/9a1itVqmKrm/fvtBoOq7iIQii84hhK7cbWLzYhcpKHYDYyoUtFgYM4y83jjQuXMlw\ndLVUOdZcVjIoKBBdJ67G6NixY/if//kfAMAdd9wBAOB5HgzDoL6+Hvfee288lyMIIgxtbSxWrdKF\naLZ15HUEehlbt9pw8KAVDCM0rgYbl0geSWcNRGer4sgI9X7iaoxyc3PR1tYWz0sSBBEDwV7J/fd7\nJUPUUTgruJqtqMiIgwetyMwEMjN9eP/9r5CRkYGsLD4qCZtYDQRVxV3ZkDYdQaQYSl5JPPTP1Orz\nyMrqG/8Nx2l/RO+Gmn8IIgXpjEpBLPOVujrwjyCCIc+IIK4Aoi0qiCXXE8/CAdJnI8gYEcQVQrTG\nI5GVb5GgqrgrGzJGBHEFkeyHfLLvj0gclDMiCIIgehwyRgRBpCSBoyiI5IeMEUEQKUewUCtNDUh+\n6DdEEISM7vYo4r2ekpK3KLRKJC9kjAiCkIjX6IdkXS9aKMTX/ZAxIggCQPfPBlJar6Wl6+spNeRq\ntdHLlCWrgUx1yBj9//buPybK+oED+PswwIljHnkNuuOkOGiKzqCNBbJkVARbJLcJebqBW7lctWyD\nRFr+4EdiNb0Nx1yNa7sCTG8yQUebTIP4NbGUlqmDljSjhI045I7Bl93d9w8ni4jj7rzz89zxfm1s\n7vG5e94yfN73fJ6Hz4eIJOPrr0O8UgAPfmepvd2CtDTbgmsv/RsX6xOHZUREAB79FD//Pl5x8TSM\nxhCvFYAnUyJJwVIdImQZEdGsf19RPIrjtbRYoNP9D4cPh+Lvv8WekkTPubeUhwg5AwMRzfGoryae\nfvr+ekknT4Z4XACeroP0X0RNS7TQzOVLBcuIiIR7mALwxTpI/ji85+84TEdEkuDJPZ5AeuBA9BCh\naLwyIiKSiKU8czmvjIjIbwXi1YS/PgX4sLxeRnv27EFiYiKioqKg0Wiwfft29Pf3e/swREQAHv0T\ngOQbXi+jpKQknDhxAr29vWhsbITD4YBWq4XNxh8SIvKNpXo1EUi8fs+osLBw9s/R0dH46KOPkJaW\nhsHBQcTGxnr7cEREFAB8es/IarWirq4OarUaarXal4ciIiI/5pMyMhgMUKlUUKlUuHTpEpqamhAc\nHOyLQxERUQBwqYwqKyshl8sX/IqIiEBXV9fs/vn5+ejo6EBLSwtiY2NRUFCAqakpn/0jiIjIv8nM\nZvOid/3GxsYwOjrqdB+VSoXly5fP2z4zM4OYmBjo9Xrk5+cv+PqBgQEX4hIRkT+Ii4tza3+XHmB4\ncAXkCbvdDofDgenpaaf7uRtcCgYGBvwyN8DsojC7GMwufV59mu727dtobm7G5s2bsXr1agwNDUGv\n1yM0NBRZWVnePBQREQUQr5ZRSEgIOjs7UVNTg/HxcSgUCqSmpqK1tRUKhcKbhyIiogDi1TJSKpUw\nmUzefEsiIloCODcdEZGHluqqrL7AMiIi8sBSXpXVF1hGRERuCqR1lKSCZURERMKxjIiI3BSI6yiJ\nxpVeiYg8sJRXZfUFlhERkYdYQt7DYToiIhKOZURERMKxjIiISDiWERERCccyIiIi4VhGREQkHMuI\niIiEYxkREZFwLCMiIhKOZURERMKxjIiISDiWERERCefTMtq6dSvkcjmam5t9eRgiIvJzPiuj48eP\nY9myZZDJuPohERE555MlJK5evYrPP/8c7e3t0Gg0vjgEEREFEK9fGU1MTGDXrl2orq7G448/7u23\nJyKiAOT1MioqKsLLL7+MjIwMb781EREFKJeG6SorK3H06NEF/14mk+HcuXO4c+cOrl+/jra2Nm/l\nk7S4uDjRETzG7GIwuxjMLn0ys9m86Lq5Y2NjGB0ddbqPUqlEUVERTp06NeehBZvNhqCgICQnJ+Pb\nb799+MRERBRwXCojV929exdms3nOtpSUFFRVVSE7Oxtr1qzx1qGIiCiAePVpusjISERGRs7b/uST\nT7KIiIhoQT6fgYG/Z0RERIvx6jAdERGRJyQ5N52/TSO0Z88eJCYmIioqChqNBtu3b0d/f7/oWIsy\nm83Yu3cvkpOTERUVhfXr16OoqAhjY2Oio7nEaDQiJycHa9asgVwux507d0RHWlBtbS02btyIyMhI\npKeno6enR3Qkl3R3d0On02HdunWQy+U4efKk6EguOXbsGDIyMqBWq6HRaLBt2zbcvHlTdCyX1NbW\nYtOmTVCr1VCr1cjMzMSFCxdEx/LIsWPHIJfLsXfv3kX3lVwZ+eM0QklJSThx4gR6e3vR2NgIh8MB\nrVYLm80mOppTf/31F+7evYuKigr09PTgiy++QHd3N958803R0VwyOTmJF198EaWlpZL+eWlsbERp\naSmKi4vR0dGB5ORk5OXlYWhoSHS0RVmtViQkJODIkSNYsWKF6Dgu6+7uxq5du3DhwgWcO3cOjz32\nGHJzc+c9YCVFSqUS5eXl+P7779HW1oYXXngBO3bswI0bN0RHc8uVK1dgNBqxfv16l/aX1DDd1atX\nUVBQMDuNkNFoxGuvvSY6ltt++eUXpKWl4YcffkBsbKzoOG5pbW3Ftm3b8Pvvv2PlypWi47ikr68P\nGRkZ+OmnnxAdHS06zjwvvfQSNmzYAL1eP7vtueeeQ25uLvbv3y8wmXtUKhU+++wz6HQ60VHcZrVa\noVar0dDQgFdeeUV0HLc99dRTOHToEAoLC0VHccn4+DjS09Nx/PhxHDlyBOvWrcOnn37q9DWSuTIK\nlGmErFYr6urqZi+x/c29e/cQGhrqV5+CpWxmZgZ9fX1IT0+fsz0jIwOXL18WE2oJmpiYgN1ux6pV\nq0RHcYvdbseZM2cwOTmJ5ORk0XFc9v7770Or1SItLc3l1/hkolRP+Ps0QgaDAQcPHoTVakV8fDya\nmpoQHBwsOpZbzGYzDh8+jMLCQgQFSeZzil8bHR2FzWbDE088MWe7QqFAe3u7oFRLz759+7Bx40a/\nOaHfuHEDmZmZmJqawsqVK1FXV4e1a9eKjuUSo9GIwcFBGAwGt17n0zNOZWUl5HL5gl8RERHo6urC\nN998g+vXr6O8vNyXcdziavYH8vPz0dHRgZaWFsTGxqKgoABTU1N+kR24f0Wn0+mgVCpRVlYmJDfg\nWXYiZz788EP09vbiq6++kvS9xX+Kj49HZ2cnLl68iDfeeAO7d+/GrVu3RMda1K+//oqKigrU1ta6\n/YHWp/eM/HkaIVeyq1QqLF++fN72mZkZxMTEQK/XIz8/31cRF+RudqvViq1btyIoKAgmk0noEJ0n\n33cp3zOamZlBVFQUDAYDtmzZMrv9gw8+wM2bN3H+/HmB6dzjj/eMSktLcfbsWZw/f97v7t/+U25u\nLtRqNaqrq0VHcaqhoQHvvvvunCKy2WyQyWRYtmwZ/vzzzwVHjHw6TPfg0+xiDhw4gPfee2/OtpSU\nFHz88cfIzs72VTynXM3+X+x2OxwOB6anp72cyjXuZLdYLMjLywMA4UUEPNz3XYqCg4Px7LPPoq2t\nbU4Zfffdd8jNzRWYLPCVlJSgqanJ74sIuH9OEXU+ccerr76KpKSkOdvefvttaDQaFBUVOb11IYl7\nRv48jdDt27fR3NyMzZs3Y/Xq1RgaGoJer0doaCiysrJEx3PKYrFAq9XCarWivr4eFosFFosFwP1S\nkPo9r5GREQwPD2NgYAAOhwO3bt2C2WxGdHS0pG5Uv/POO9i9ezcSExPx/PPPw2AwYHh4GDt37hQd\nbVFWqxW//fYbHA4H7HY7/vjjD/z888+Qy+VQqVSi4y2ouLgYp0+fRn19PcLDwzEyMgIACAsLQ1hY\nmOB0zpWVlSEzMxNKpRIWiwUmkwldXV0wmUyioy0qPDwc4eHhc7atWLECq1atwjPPPOP0tZIoo//i\nL2O7ISEh6OzsRE1NDcbHx6FQKJCamorW1lYoFArR8Zzq6+vDjz/+COD+o8YA4HA4ZpcE2bRpk8h4\ni/ryyy/xySefQCaTQSaT4fXXXwcA1NTUSGooSavVYmxsDEePHsXw8DDWrl0Lk8kk6ZP5A9euXUNO\nTs7s/8eqqipUVVVBp9OhpqZGcLqFGQwGyGSyOVejwP2rpZKSEkGpXDM8PIy33noLIyMjCA8PR0JC\nAs6cOTPviUx/4eq5XFK/Z0REREsTn98lIiLhWEZERCQcy4iIiIRjGRERkXAsIyIiEo5lREREwrGM\niIhIOJYREREJxzIiIiLh/g+iE4qtei8t9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd1e390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(-0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating $r$\n",
    "\n",
    "The formula for $r$ is not apparent from our observations so far, and it has a mathematical basis that is outside the scope of this class. However, the calculation is straightforward and helps us understand several of the properties of $r$.\n",
    "\n",
    "**Formula for $r$**:\n",
    "\n",
    "- $r$ is the average of the products of the two variables, when both variables are measured in standard units.\n",
    "\n",
    "Here are the steps in the calculation. We will apply the steps to a simple table of values of $x$ and $y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>x</th> <th>y</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1   </td> <td>2   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2   </td> <td>3   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3   </td> <td>1   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4   </td> <td>5   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>6   </td> <td>7   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "x    | y\n",
       "1    | 2\n",
       "2    | 3\n",
       "3    | 1\n",
       "4    | 5\n",
       "5    | 2\n",
       "6    | 7"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 7, 1)\n",
    "y = [2, 3, 1, 5, 2, 7]\n",
    "t = Table().with_columns([\n",
    "        'x', x,\n",
    "        'y', y\n",
    "    ])\n",
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the scatter diagram, we expect that $r$ will be positive but not equal to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OnXrttdcUHx//g9v7/X4HUl1bPWtqFF5X1/w6EAgo2NioihCY7ZJQ+Jy+C3PZje+W+yQk\nJLRqeyNllZeXpz//+c967bXX1KtXrxa9p7WD2cibmqrIkhLJ61UgEFC0x6MLaWkhMZt08csUKrP8\nL+ayH9+t0Od4Wc2aNUubN2/W+vXrFRMTo1OnTkmSoqOjFR0d7XQcR9Xn5kq6eMoi2NioC2lpqs/J\nMZwKcD++W6EvrLq6usnJHfp8vu+8PpWXl6e8vDwnoxgVir8pheJMEnO5TSjOFYoztZbjR1Zffvml\n07sEALic8VvXAQD4IZQVAMB6lBUAwHqUFQDAepQVAMB6lBUAwHqUFQDAepQVAMB6lBUAwHqUFQDA\nepQVAMB6lBUAwHqUFQDAepQVAMB6lBUAwHqUFQDAepQVAMB6lBUAwHqUFQDAekbKqqysTFlZWUpO\nTpbP59PGjRtNxAAAuISRsgoEAurXr5/y8/MVFRVlIgIAwEUiTex01KhRGjVqlCQpJyfHRAQAgIsY\nKSvAeg0N8hYUKKK8XD1rauRNTVV9bq7k8ZhOBlyXuMEC+A7eggJFlpQo7Nw5hdfVKbKkRN6CAtOx\ngOsWZQV8h4jycsnr/XrB6724BsAI15wG9Pv9piO0O2ayV8+aGoXX1TW/DgQCCjY2qiJE5rskVD6v\nbwrFuUJtpoSEhFZt75qyau1gtvP7/cxkMW9qqiJLSiSvV4FAQNEejy6kpYXMfFJofV7/KxTnCsWZ\nWstIWQUCAVVUVKipqUnBYFAnT57U0aNH5fP5FBcXZyIScJn63FxJF08HBhsbdSEtTfXcuQoYY6Ss\n/vGPf2js2LEKCwuTJC1ZskRLlixRVlaWCriIDRt4PKqfOVOSVMFvtYBxRsoqNTVVX375pYldAwBc\niLsBAQDWo6wAANajrAAA1qOsAADWo6wAANajrAAA1qOsAADWo6wAANajrAAA1qOsAADWo6wAANaj\nrAAA1qOsAADWo6wAANajrAAA1qOsAADWo6wAANajrAAA1qOsAADWM1ZWRUVFSklJUbdu3ZSenq6D\nBw+aigIAsJyRstq+fbvmzp2rWbNm6cCBAxo6dKgefPBB/fe//zURBwBgOSNlVVhYqIcffli//OUv\nlZCQoKVLlyo2NlZr1qwxEQcAYDnHy6qhoUHl5eVKT0+/bH3kyJE6dOiQ03EAAC7geFl9/vnnamxs\n1E033XTZeteuXXXq1Cmn4wAAXIC7AQ1JSEgwHaHdheJMEnO5TSjOFYoztZbjZXXjjTcqIiLiW0dR\np0+f/tbRFgAAkoGy8ng8GjhwoPbv33/Z+t/+9jcNGzbM6TgAABeINLHT3NxczZgxQ4MGDdKwYcO0\nevVqVVVVacqUKSbiAAAsZ6Ssxo8fry+//FLLly9XVVWVkpKStGXLFsXFxZmIAwCwXFh1dXWT6RAA\nAFyJ1XcDhtojmcrKypSVlaXk5GT5fD5t3LjRdKQ2W7FihUaOHKn4+Hj17t1bDz30kD788EPTsdqs\nqKhId911l+Lj4xUfH6+MjAzt3bvXdKx2tWLFCvl8Ps2ePdt0lDbJz8+Xz+e77Kdv376mY7WLqqoq\nZWdnq3fv3urWrZuGDx+usrIy07Ha5LbbbvvW5+Xz+TRp0qQrvs/IacCWuPRIphUrVmjYsGFatWqV\nHnzwQR06dEjdu3c3He+qBAIB9evXT1lZWcrOzjYdp12UlZVp+vTpGjRokJqamrR48WKNGzdOhw4d\nUqdOnUzHu2rdu3fXokWL1KtXLwWDQW3YsEGTJ09WSUmJkpOTTcdrsyNHjqi4uFj9+/c3HaVdJCYm\nas+ePWpquniiKCIiwnCitjt79qwyMzM1YsQIbd26VZ07d1ZlZaW6du1qOlqb7N+/X42Njc2vP/vs\nM6Wnp2vChAlXfJ+1pwHvvfdeDRgwQM8991zz2uDBgzVu3DgtWLDAYLL2ERcXp2XLlikrK8t0lHYV\nCAQUHx+vDRs2KDMz03ScdnXrrbfqqaee0iOPPGI6SpucPXtW6enpevHFF5Wfn6/k5GQtXbrUdKyr\nlp+fr127drn+iOObFi1apIMHD+qNN94wHeWaevbZZ/WnP/1J//znP9WhQ4fv3c7K04A8ksm9vvrq\nKwWDQVcfVX1TMBjUtm3bVFtbq6FDh5qO02YzZ87U+PHjlZqaajpKu/nkk0+UlJSklJQUTZs2TZWV\nlaYjtdnrr7+uwYMHa+rUqUpISFBaWppWrVplOla7W7dunSZNmnTFopIsPQ14pUcylZSUGEqFlpgz\nZ45SUlJC4l/qx44dU0ZGhurq6nTDDTdo3bp1SkpKMh2rTYqLi1VZWanVq1ebjtJuhgwZosLCQiUk\nJOj06dNatmyZMjMzXX8q+tLnlJOToyeeeEJHjx7V7NmzFRYWpkcffdR0vHaxb98+nThxokVnK6ws\nK7jTvHnzdPjwYb355psKCwszHafNEhMTVVpaqrNnz2rXrl2aMWOG9uzZ49qL9x9//LH++Mc/6q23\n3lJ4uJUnVa7KPffcc9nrIUOGKCUlRRs2bFBOTo6hVG0XDAY1ePDg5sseAwYM0PHjx1VUVBQyZVVc\nXKzbb7+9RdeBrfwnlkcyuc/cuXO1Y8cO7d69W/Hx8abjtIvIyEjdcsstSklJ0YIFCzRgwAAVFhaa\njnXVDh8+rC+++EJ33nmnunTpoi5duuidd95RUVGRunbtqoaGBtMR20VUVJT69u2riooK01HaJDY2\nVomJiZetJSYm6uTJk4YSta8zZ87ojTfeaPE1YCvLikcyuUteXl5zUfXq1ct0nGsmGAzq/PnzpmNc\ntTFjxqisrEylpaXNP4MGDdIDDzyg0tJSeTwe0xHbRV1dnfx+v2JjY01HaZNhw4bJ7/dftub3+9Wj\nRw9DidrX+vXr1bFjR02cOLFF21t7GjAUH8kUCARUUVGhpqYmBYNBnTx5UkePHpXP53Pt0ztmzZql\nzZs3a/369YqJiWk+Go6OjlZ0dLThdFdv4cKFysjIUPfu3VVTU6MtW7bonXfe0ZYtW0xHu2oxMTGK\niYm5bC0qKkqdOnVSnz59DKVquwULFmj06NGKi4trvmZVW1vr+jttc3JylJmZqeXLl2vChAl67733\n9Morr+ipp54yHa1drF27VhMnTlRUVFSLtrf21nVJWrNmjV544YXmRzItWbLE1UdWpaWlGjt27Leu\n52RlZamgoMBQqrbx+XzfeX0qLy9PeXl5BhK1j5ycHJWWlurUqVOKiYlRv3799Pjjj3/rDlW3Gzt2\nrJKSklx96/q0adN08OBBff755+rSpYvuuOMOzZ8//1un0NzoL3/5ixYuXKjjx48rLi5Ojz32mKZP\nn246VpsdOHBAP//5z7Vv3z4NHDiwRe+xuqwAAJAsvWYFAMD/oqwAANajrAAA1qOsAADWo6wAANaj\nrAAA1qOsAADWo6wAANajrAAA1qOsAADWo6wAgy7934fvueceNTY2Nq/v27dPnTt3Dqn/SSLQFpQV\nYFBUVJSKior0/vvva/HixZKkU6dOKTs7W/fdd5+mTZtmOCFgBx5kC1igsLBQf/jDH7Rt2zatXLlS\nH330kUpLS+Xz+UxHA6xAWQGW+MUvfqG3335bDQ0N2rlzp9LS0kxHAqzBaUDAEpMmTdL58+fVv39/\nigr4BsoKsEBVVZXmzJmjgQMH6v3339dLL71kOhJgFcoKsEB2drY6duyonTt3asaMGVq4cKGOHTtm\nOhZgDa5ZAYa9+OKLWrhwoXbv3q3hw4eroaFB9957r+rr67V//3516NDBdETAOI6sAIPee+89LV68\nWL/73e80fPhwSZLH49Hq1av1n//8R/PnzzecELADR1YAAOtxZAUAsB5lBQCwHmUFALAeZQUAsB5l\nBQCwHmUFALAeZQUAsB5lBQCwHmUFALDe/wO3RYhHtjpj2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd8b9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.scatter(0, 1, s=30, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 1.** Convert each variable to standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>x</th> <th>y</th> <th>x (standard units)</th> <th>y (standard units)</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1   </td> <td>2   </td> <td>-1.46385          </td> <td>-0.648886         </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2   </td> <td>3   </td> <td>-0.87831          </td> <td>-0.162221         </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3   </td> <td>1   </td> <td>-0.29277          </td> <td>-1.13555          </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4   </td> <td>5   </td> <td>0.29277           </td> <td>0.811107          </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2   </td> <td>0.87831           </td> <td>-0.648886         </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>6   </td> <td>7   </td> <td>1.46385           </td> <td>1.78444           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "x    | y    | x (standard units) | y (standard units)\n",
       "1    | 2    | -1.46385           | -0.648886\n",
       "2    | 3    | -0.87831           | -0.162221\n",
       "3    | 1    | -0.29277           | -1.13555\n",
       "4    | 5    | 0.29277            | 0.811107\n",
       "5    | 2    | 0.87831            | -0.648886\n",
       "6    | 7    | 1.46385            | 1.78444"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_su = t.with_columns([\n",
    "        'x (standard units)', standard_units(x),\n",
    "        'y (standard units)', standard_units(y)\n",
    "    ])\n",
    "t_su"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 2.** Multiply each pair of standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>x</th> <th>y</th> <th>x (standard units)</th> <th>y (standard units)</th> <th>product of standard units</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1   </td> <td>2   </td> <td>-1.46385          </td> <td>-0.648886         </td> <td>0.949871                 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>2   </td> <td>3   </td> <td>-0.87831          </td> <td>-0.162221         </td> <td>0.142481                 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>3   </td> <td>1   </td> <td>-0.29277          </td> <td>-1.13555          </td> <td>0.332455                 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>4   </td> <td>5   </td> <td>0.29277           </td> <td>0.811107          </td> <td>0.237468                 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2   </td> <td>0.87831           </td> <td>-0.648886         </td> <td>-0.569923                </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>6   </td> <td>7   </td> <td>1.46385           </td> <td>1.78444           </td> <td>2.61215                  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "x    | y    | x (standard units) | y (standard units) | product of standard units\n",
       "1    | 2    | -1.46385           | -0.648886          | 0.949871\n",
       "2    | 3    | -0.87831           | -0.162221          | 0.142481\n",
       "3    | 1    | -0.29277           | -1.13555           | 0.332455\n",
       "4    | 5    | 0.29277            | 0.811107           | 0.237468\n",
       "5    | 2    | 0.87831            | -0.648886          | -0.569923\n",
       "6    | 7    | 1.46385            | 1.78444            | 2.61215"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_product = t_su.with_column('product of standard units', t_su.column(2) * t_su.column(3))\n",
    "t_product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 3.** $r$ is the average of the products computed in Step 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61741639718977093"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# r is the average of the products of standard units\n",
    "\n",
    "r = np.mean(t_product.column(4))\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, $r$ is positive but not equal to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties of $r$\n",
    "\n",
    "The calculation shows that:\n",
    "\n",
    "- $r$ is a pure number. It has no units. This is because $r$ is based on standard units.\n",
    "- $r$ is unaffected by changing the units on either axis. This too is because $r$ is based on standard units.\n",
    "- $r$ is unaffected by switching the axes. Algebraically, this is because the product of standard units does not depend on which variable is called $x$ and which $y$. Geometrically, switching axes reflects the scatter plot about the line $y=x$, but does not change the amount of clustering nor the sign of the association."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10decaeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.scatter('y', 'x', s=30, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can define a function ``correlation`` to compute $r$, based on the formula that we used above. The arguments are a table and two labels of columns in the table. The function returns the mean of the products of those column values in standard units, which is $r$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def correlation(t, x, y):\n",
    "    return np.mean(standard_units(t.column(x))*standard_units(t.column(y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's call the function on the ``x`` and ``y`` columns of ``t``. The function returns the same answer to the correlation between $x$ and $y$ as we got by direct application of the formula for $r$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61741639718977093"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(t, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calling ``correlation`` on columns of the table ``suv`` gives us the correlation between price and mileage as well as the correlation between price and acceleration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6667143635709919"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(suv, 'mpg', 'msrp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48699799279959155"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(suv, 'acceleration', 'msrp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These values confirm what we had observed: \n",
    "\n",
    "- There is a negative association between price and efficiency, whereas the association between price and acceleration is positive.\n",
    "- The linear relation between price and acceleration is a little weaker (correlation about 0.5) than between price and mileage (correlation about -0.67). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "###  Care in Using Correlation\n",
    "\n",
    "Correlation is a simple and powerful concept, but it is sometimes misused. Before using $r$, it is important to be aware of what correlation does and does not measure.\n",
    "\n",
    "- Correlation only measures association. Correlation does not imply causation. Though the correlation between the weight and the math ability of children in a school district may be positive, that does not mean that doing math makes children heavier or that putting on weight improves the children's math skills. Age is a confounding variable: older children are both heavier and better at math than younger children, on average.\n",
    "\n",
    "- Correlation measures **linear** association. Variables that have strong non-linear association might have very low correlation. Here is an example of variables that have a perfect quadratic relation $y = x^2$ but have correlation equal to 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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af6FjrGASS4vALXDNv9AxVjCJIgMAOI0iA26Ba/6FjrGCSRwjA26Ba/6FjrGCSRQZcCtc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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10deceac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nonlinear = Table().with_columns([\n",
    "        'x', np.arange(-4, 4.1, 0.5),\n",
    "        'y', np.arange(-4, 4.1, 0.5)**2\n",
    "    ])\n",
    "nonlinear.scatter('x', 'y', s=30, color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(nonlinear, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Outliers can have a big effect on correlation. Here is an example where a scatter plot for which $r$ is equal to 1 is turned into a plot for which $r$ is equal to 0, by the addition of just one outlying point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5RHFxcfL5fJKk2NhYxcbGSpIKCwt18uTJ4IdaysvLZbfbNW7cOEVFRenQoUPatm2bCgsL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\nijAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e1075f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line = Table().with_columns([\n",
    "        'x', [1, 2, 3, 4],\n",
    "        'y', [1, 2, 3, 4]\n",
    "    ])\n",
    "line.scatter('x', 'y', s=30, color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(line, 'x', 'y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AYPi5XOopK5MktcbYVesXFRVxk6SVK1dq5cqVpmcAAKIAr5YEAFiHuAEArEPcAADWIW4A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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dfc4eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outlier = Table().with_columns([\n",
    "        'x', [1, 2, 3, 4, 5],\n",
    "        'y', [1, 2, 3, 4, 0]\n",
    "    ])\n",
    "outlier.scatter('x', 'y', s=30, color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(outlier, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Correlations based on aggregated data can be misleading. As an example, here are data on the Critical Reading and Math SAT scores in 2014. There is one point for each of the 50 states and one for Washington, D.C. The column ``Participation Rate`` contains the percent of high school seniors who took the test. The next three columns show the average score in the state on each portion of the test, and the final column is the average of the total scores on the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>State</th> <th>Participation Rate</th> <th>Critical Reading</th> <th>Math</th> <th>Writing</th> <th>Combined</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>Alabama             </td> <td>6.7               </td> <td>547             </td> <td>538 </td> <td>532    </td> <td>1617    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Alaska              </td> <td>54.2              </td> <td>507             </td> <td>503 </td> <td>475    </td> <td>1485    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Arizona             </td> <td>36.4              </td> <td>522             </td> <td>525 </td> <td>500    </td> <td>1547    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Arkansas            </td> <td>4.2               </td> <td>573             </td> <td>571 </td> <td>554    </td> <td>1698    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>California          </td> <td>60.3              </td> <td>498             </td> <td>510 </td> <td>496    </td> <td>1504    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Colorado            </td> <td>14.3              </td> <td>582             </td> <td>586 </td> <td>567    </td> <td>1735    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Connecticut         </td> <td>88.4              </td> <td>507             </td> <td>510 </td> <td>508    </td> <td>1525    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Delaware            </td> <td>100               </td> <td>456             </td> <td>459 </td> <td>444    </td> <td>1359    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>District of Columbia</td> <td>100               </td> <td>440             </td> <td>438 </td> <td>431    </td> <td>1309    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "        <tr>\n",
       "            <td>Florida             </td> <td>72.2              </td> <td>491             </td> <td>485 </td> <td>472    </td> <td>1448    </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (41 rows omitted)</p"
      ],
      "text/plain": [
       "State                | Participation Rate | Critical Reading | Math | Writing | Combined\n",
       "Alabama              | 6.7                | 547              | 538  | 532     | 1617\n",
       "Alaska               | 54.2               | 507              | 503  | 475     | 1485\n",
       "Arizona              | 36.4               | 522              | 525  | 500     | 1547\n",
       "Arkansas             | 4.2                | 573              | 571  | 554     | 1698\n",
       "California           | 60.3               | 498              | 510  | 496     | 1504\n",
       "Colorado             | 14.3               | 582              | 586  | 567     | 1735\n",
       "Connecticut          | 88.4               | 507              | 510  | 508     | 1525\n",
       "Delaware             | 100                | 456              | 459  | 444     | 1359\n",
       "District of Columbia | 100                | 440              | 438  | 431     | 1309\n",
       "Florida              | 72.2               | 491              | 485  | 472     | 1448\n",
       "... (41 rows omitted)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sat2014 = Table.read_table('sat2014.csv').sort('State')\n",
    "sat2014"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter diagram of Math scores versus Critical Reading scores is very tightly clustered around a straight line; the correlation is close to 0.985. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DfT2AOne/kyZNYvPmzTzyyCMMGTKEAwcO8PTTT/PLL7+wYsUKW7nj\nx4+TkpJC9+7dqaio4J133uHOO+9k27ZtREdHA1BcXExSUhJhYWFkZWXh5eXFX/7yF3755Zcm61fb\nbuPHj+c3v/kNqampfPTRR6SlpdG9e3ceeOAB22fcfffdhIeHs2TJEry8vFi8eDF5eXketZG2uJeC\nUTzSyZMnOXPmTKPPcKvPPffcw5///OcGj19xxRX07dsXq9VKVFRUk12CzzzzDJWVlezatcvhAam/\n/vWvbX++++67Hd5T2/WZkpLCggUL8PPza9Z3gPPdvdXV1VRVVfHDDz8we/Zsrr/+eu644w5bmZ07\nd/Lee++RlZXF/fffD0B8fDx+fn48/PDDfP/99wwYMACAF1980fa+mpoabrnlFr755htef/11Wzf1\nyy+/jMVi4b333iMsLAyA//zP/3S6e9lgMPDHP/7R9ui4+Ph4tm/fzrvvvmsLxpdeeomzZ8+ydu1a\nQkNDARg+fLjtjl6kJagrVeT/GAwG7rzzzhY957Zt2xg5cmSjTw0/deoUs2fPZvDgwQQHBxMYGMjD\nDz+M1Wrlp59+uqjPXbhwIYGBgYSGhnLLLbdQUVHBqlWrMBqNtjJbtmyhY8eOJCUlUV1dbftJSEjA\narWyc+dOh+9x1113cc0113DVVVcRGBjITz/9xMGDB21lvvzyS2JjY22hCODj48OoUaOcrveIESMc\nfv/Vr37l0P27Z88eYmNjbaEI0KlTpzrvE7kUumMUjxQQEEDnzp2d6sazZ/8XbksoLi5ucvZlamoq\nn332GU899RQDBgzAx8eHr776imnTpl30OOP48eNJTk7m7NmzbN++nfnz55OcnMy6detsZQoLCzl7\n9qxDkNUyGAwUFxcD58f07r//fm699VZeeuklQkND6dChA3/84x8d6pefn28bs7XX2D8KLnThOKG3\nt3eLf4ZIUxSM4pGMRiM33XQTW7du5dy5c3h5eTn1PmfHqZwtd9VVV3H8+PEGj589e5aNGzfy5JNP\n8tBDD9le//777506f0NqJ/nA+a7Zmpoann32Wf7+97/bum5r//GwcePGeifI1Abm+++/j5eXFytX\nrqRDh393MpWUlDh084aEhFBQUFDnPPn5+Zf0XS78XoWFha36GSLqShWP9cgjj1BcXMysWbPqPZ6X\nl8cPP/zQ7PN27NgRq9Xq1N1cQkICmzZtqjcw4HwwVldXYzI5/ht11apVza5XYx555BFCQ0MdZnne\ncsstWCwWSktLGTRoUJ2fkJAQAM6cOePQBQuwffv2OjNcr7vuOvbs2cOxY8dsr5WXl7Np06YW+x5D\nhgzhyy+/dPjHxpkzZ/j4449b7DNEFIzisYYOHcrTTz/Nq6++yujRo/nb3/7Grl272LhxI48//jhD\nhw7l8OHDzT5vZGQkJpOJlStXsnv3bvbu3dvgesgnnniCjh07ctttt/H666/zj3/8g9WrV9vuDn19\nfRkyZAgvvfQSb7/9Nh9//DETJ05s8TugTp068ac//Yl9+/bx/vvvA3DTTTcxZswYJk6cSEZGBlu2\nbGHbtm2sWLGC8ePHc+jQIQBuvfVWTp8+zeTJk9m+fTvLli1j8uTJhIeHO3xGamoqnTt3ZvTo0bz3\n3nt88MEHjBkzhs6dO7fY95gyZQqdO3fm3nvvZd26dWzYsIH77ruPjh07alaqtBgFo3i0lJQUPvro\nI/z8/Pif//kf7r77bqZMmcLBgwdZtGhRk7ve1LL/S9ff358FCxbw/fffk5iYyPDhw9m7d6+tnH3Z\nnj178vHHH3Pdddfxv//7v9x///3Mnz/fdjcGsGzZMgYNGsT06dOZMmUKoaGhpKenN1mPxupaX7mJ\nEyfSs2dPFixYYHvt1VdfZcaMGaxfv57f/OY3TJw4kaVLlxIZGUlQUBBwftbn/Pnz+eKLLxg3bhyr\nVq1iyZIlXH311Q6fExAQwPr167nqqqtITU3l8ccf59Zbb2X8+PFO1bGh71bfZ/j5+ZGSksL06dNJ\nSEjgzjvvdPmOPuK5DCUlJXUHF0RE2oiamhqGDRtGYGCgw+QikYulyTci0qbMmzePa665hh49enDy\n5EneeOMN9u3bx5o1a9xdNfEQCkYRaVMMBgMZGRmcOHECg8FA//79WbVqFcOHD3d31cRDqCtVRETE\njibfiIiI2FEwioiI2FEwioiI2FEwioiI2FEwioiI2FEwioiI2Pl/U3yHNkRYm44AAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e0330f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sat2014.scatter('Critical Reading', 'Math')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98475584110674341"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(sat2014, 'Critical Reading', 'Math')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "It is important to note that this does not reflect the strength of the relation between the Math and Critical Reading scores of students. States don't take tests – students do. The data in the table have been created by lumping all the students in each state into a single point at the average values of the two variables in that state. But not all students in the state will be at that point, as students vary in their performance. If you plot a point for each student instead of just one for each state, there will be a cloud of points around each point in the figure above. The overall picture will be more fuzzy. The correlation between the Math and Critical Reading scores of the students will be lower than the value calculated based on state averages.\n",
    "\n",
    "Correlations based on aggregates and averages are called *ecological correlations* and are frequently reported. As we have just seen, they must be interpreted with care."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Serious or tongue-in-cheek?\n",
    "\n",
    "In 2012, a [paper](http://www.biostat.jhsph.edu/courses/bio621/misc/Chocolate%20consumption%20cognitive%20function%20and%20nobel%20laurates%20%28NEJM%29.pdf) in the respected New England Journal of Medicine examined the relation between chocolate consumption and Nobel Prizes in a group of countries. The [Scientific American](http://blogs.scientificamerican.com/the-curious-wavefunction/chocolate-consumption-and-nobel-prizes-a-bizarre-juxtaposition-if-there-ever-was-one/) responded seriously;\n",
    "[others](http://www.reuters.com/article/2012/10/10/us-eat-chocolate-win-the-nobel-prize-idUSBRE8991MS20121010#vFdfFkbPVlilSjsB.97) were more relaxed. The paper included the following graph:\n",
    "\n",
    "![choc_Nobel](../images/chocoNobel.png)"
   ]
  }
 ],
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