{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "from scipy import stats\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "def r_scatter(r):\n",
    "    plt.figure(figsize=(5,5))\n",
    "    \"Generate a scatter plot with a correlation approximately r\"\n",
    "    x = np.random.normal(0, 1, 1000)\n",
    "    z = np.random.normal(0, 1, 1000)\n",
    "    y = r*x + (np.sqrt(1-r**2))*z\n",
    "    plt.scatter(x, y)\n",
    "    plt.xlim(-4, 4)\n",
    "    plt.ylim(-4, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation\n",
    "\n",
    "In this section we will develop a measure of how tightly clustered a scatter diagram is about a straight line. Formally, this is called measuring *linear association*."
   ]
  },
  {
   "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 adapted from the online data archive of [Prof. Larry Winner](http://www.stat.ufl.edu/%7Ewinner/) of the University of Florida. The columns:\n",
    "\n",
    "- `vehicle`: model of the car\n",
    "- `year`: year of manufacture\n",
    "- `msrp`: manufacturer's suggested retail price in 2013 dollars\n",
    "- `acceleration`: acceleration rate in km per hour per second\n",
    "- `mpg`: fuel econonmy in miles per gallon\n",
    "- `class`: the model's class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "hybrid = pd.read_csv(path_data + 'hybrid.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>vehicle</th>\n",
       "      <th>year</th>\n",
       "      <th>msrp</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>mpg</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Prius (1st Gen)</td>\n",
       "      <td>1997</td>\n",
       "      <td>24509.74</td>\n",
       "      <td>7.46</td>\n",
       "      <td>41.26</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Tino</td>\n",
       "      <td>2000</td>\n",
       "      <td>35354.97</td>\n",
       "      <td>8.20</td>\n",
       "      <td>54.10</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Prius (2nd Gen)</td>\n",
       "      <td>2000</td>\n",
       "      <td>26832.25</td>\n",
       "      <td>7.97</td>\n",
       "      <td>45.23</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Insight</td>\n",
       "      <td>2000</td>\n",
       "      <td>18936.41</td>\n",
       "      <td>9.52</td>\n",
       "      <td>53.00</td>\n",
       "      <td>Two Seater</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Civic (1st Gen)</td>\n",
       "      <td>2001</td>\n",
       "      <td>25833.38</td>\n",
       "      <td>7.04</td>\n",
       "      <td>47.04</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>S400</td>\n",
       "      <td>2013</td>\n",
       "      <td>92350.00</td>\n",
       "      <td>13.89</td>\n",
       "      <td>21.00</td>\n",
       "      <td>Large</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>Prius Plug-in</td>\n",
       "      <td>2013</td>\n",
       "      <td>32000.00</td>\n",
       "      <td>9.17</td>\n",
       "      <td>50.00</td>\n",
       "      <td>Midsize</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>C-Max Energi Plug-in</td>\n",
       "      <td>2013</td>\n",
       "      <td>32950.00</td>\n",
       "      <td>11.76</td>\n",
       "      <td>43.00</td>\n",
       "      <td>Midsize</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>151</th>\n",
       "      <td>Fusion Energi Plug-in</td>\n",
       "      <td>2013</td>\n",
       "      <td>38700.00</td>\n",
       "      <td>11.76</td>\n",
       "      <td>43.00</td>\n",
       "      <td>Midsize</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>152</th>\n",
       "      <td>Chevrolet Volt</td>\n",
       "      <td>2013</td>\n",
       "      <td>39145.00</td>\n",
       "      <td>11.11</td>\n",
       "      <td>37.00</td>\n",
       "      <td>Compact</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>153 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   vehicle  year      msrp  acceleration    mpg       class\n",
       "0          Prius (1st Gen)  1997  24509.74          7.46  41.26     Compact\n",
       "1                     Tino  2000  35354.97          8.20  54.10     Compact\n",
       "2          Prius (2nd Gen)  2000  26832.25          7.97  45.23     Compact\n",
       "3                  Insight  2000  18936.41          9.52  53.00  Two Seater\n",
       "4          Civic (1st Gen)  2001  25833.38          7.04  47.04     Compact\n",
       "..                     ...   ...       ...           ...    ...         ...\n",
       "148                   S400  2013  92350.00         13.89  21.00       Large\n",
       "149          Prius Plug-in  2013  32000.00          9.17  50.00     Midsize\n",
       "150   C-Max Energi Plug-in  2013  32950.00         11.76  43.00     Midsize\n",
       "151  Fusion Energi Plug-in  2013  38700.00         11.76  43.00     Midsize\n",
       "152         Chevrolet Volt  2013  39145.00         11.11  37.00     Compact\n",
       "\n",
       "[153 rows x 6 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hybrid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph below is a scatter plot of `msrp` *versus* `acceleration`. That means `msrp` is plotted on the vertical axis and `accelaration` on the horizontal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.plot.scatter('acceleration', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the positive association. 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",
    "The scatter diagram of MSRP versus mileage shows a negative association. 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 plot showed, those were also the cars that tended to cost more. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.plot.scatter('mpg', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "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, not around a straight line. \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": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv = hybrid[hybrid['class'] == 'SUV']\n",
    "suv.plot.scatter('mpg', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv.plot.scatter('acceleration', 'msrp')\n",
    "plt.show()"
   ]
  },
  {
   "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",
    "Recall that in an earlier section we defined the function `standard_units` to convert an array of numbers to standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "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": [
    "We can use this function to re-draw the two scatter diagrams for SUVs, with all the variables measured in standard units.  \n",
    "\n",
    "(*employing Pandas plotting function instead of matplotlib*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SUVs = pd.DataFrame(\n",
    "    {'mpg (standard units)':standard_units(suv['mpg']), \n",
    "    'msrp (standard units)':standard_units(suv['msrp'])}\n",
    ").plot.scatter(0, 1)\n",
    "\n",
    "plt.xlim(-3, 3)\n",
    "\n",
    "plt.ylim(-3, 3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(\n",
    "    {'acceleration (standard units)':standard_units(suv['acceleration']), \n",
    "    'msrp (standard units)':standard_units(suv['msrp'])}).plot.scatter(0, 1)\n",
    "\n",
    "plt.xlim(-3, 3)\n",
    "\n",
    "plt.ylim(-3, 3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "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 now 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",
    "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 just 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 scatter plot changes. \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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(-0.55)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating $r$\n",
    "\n",
    "The formula for $r$ is not apparent from our observations so far. It has a mathematical basis that is outside the scope of this class. However, as you will see, 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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x  y\n",
       "0  1  2\n",
       "1  2  3\n",
       "2  3  1\n",
       "3  4  5\n",
       "4  5  2\n",
       "5  6  7"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 7, 1)\n",
    "y = np.array([2, 3, 1, 5, 2, 7])\n",
    "t = pd.DataFrame({'x':x,\n",
    "        'y':y})\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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.plot.scatter(0, 1, s=30, color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Step 1.** Convert each variable to standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x (standard units)</th>\n",
       "      <th>y (standard units)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.46385</td>\n",
       "      <td>-0.648886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.87831</td>\n",
       "      <td>-0.162221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.29277</td>\n",
       "      <td>-1.135550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0.29277</td>\n",
       "      <td>0.811107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>0.87831</td>\n",
       "      <td>-0.648886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1.46385</td>\n",
       "      <td>1.784436</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x  y  x (standard units)  y (standard units)\n",
       "0  1  2            -1.46385           -0.648886\n",
       "1  2  3            -0.87831           -0.162221\n",
       "2  3  1            -0.29277           -1.135550\n",
       "3  4  5             0.29277            0.811107\n",
       "4  5  2             0.87831           -0.648886\n",
       "5  6  7             1.46385            1.784436"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_su = t.copy()\n",
    "\n",
    "t_su['x (standard units)'] = standard_units(x)\n",
    "\n",
    "t_su['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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>x (standard units)</th>\n",
       "      <th>y (standard units)</th>\n",
       "      <th>product of standard units</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.46385</td>\n",
       "      <td>-0.648886</td>\n",
       "      <td>0.949871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.87831</td>\n",
       "      <td>-0.162221</td>\n",
       "      <td>0.142481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.29277</td>\n",
       "      <td>-1.135550</td>\n",
       "      <td>0.332455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0.29277</td>\n",
       "      <td>0.811107</td>\n",
       "      <td>0.237468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>0.87831</td>\n",
       "      <td>-0.648886</td>\n",
       "      <td>-0.569923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1.46385</td>\n",
       "      <td>1.784436</td>\n",
       "      <td>2.612146</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x  y  x (standard units)  y (standard units)  product of standard units\n",
       "0  1  2            -1.46385           -0.648886                   0.949871\n",
       "1  2  3            -0.87831           -0.162221                   0.142481\n",
       "2  3  1            -0.29277           -1.135550                   0.332455\n",
       "3  4  5             0.29277            0.811107                   0.237468\n",
       "4  5  2             0.87831           -0.648886                  -0.569923\n",
       "5  6  7             1.46385            1.784436                   2.612146"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_product = t_su.copy()\n",
    "\n",
    "t_product['product of standard units'] = t_su.iloc[:,2] * t_su.iloc[:,3]\n",
    "\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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# r is the average of the products of standard units\n",
    "\n",
    "r = np.mean(t_product.iloc[:,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",
    "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.plot.scatter('y', 'x', s=30, color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The `correlation` function\n",
    "We are going to be calculating correlations repeatedly, so it will help to define a function that computes it by performing all the steps described above. Let's define a function ``correlation`` that takes a table and the labels of two columns in the table. The function returns $r$, the mean of the products of those column values in standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def correlation(t, x, y):\n",
    "    return np.mean(standard_units(t[x])*standard_units(t[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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(t, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we noticed, the order in which the variables are specified doesn't matter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(t, 'y', 'x')"
   ]
  },
  {
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6667143635709919"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(suv, 'mpg', 'msrp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4869979927995918"
      ]
     },
     "execution_count": 26,
     "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": {},
   "source": [
    "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Association is not Causation\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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation Measures *Linear* Association\n",
    "Correlation measures only one kind of association – linear. 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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_x = np.arange(-4, 4.1, 0.5)\n",
    "nonlinear = pd.DataFrame(\n",
    "        {'x':new_x,\n",
    "        'y':new_x**2}\n",
    "    )\n",
    "nonlinear.plot.scatter('x', 'y', s=30, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(nonlinear, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation is Affected by Outliers\n",
    "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": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbUAAAEfCAYAAADGLVhVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAdnklEQVR4nO3dfVBU1/3H8Q+4WhbSuOqIT4PaIJmyaBq0Q6M1MfxIsFGBGI0ErX9kMjEJ4DSdkKrp2EjSqbHR1FSHjYrp2EaMIjqsxoeMo5kRweqkabUw1e3IEG2FHU3Qgm4MLr8/UqhEnlYeLnt8v2b44957Dvf75agf7tkVQmpraxsFAIABQq0uAACA7kKoAQCMQagBAIxBqAEAjEGoAQCMQagBAIxBqAEAjEGoAQCMQah1wOPxWF1Cj6NHM9CjGeixawg1AIAxCDUAgDEINQCAMfpMqK1Zs0YOh0Ovvvpqu+PKy8s1Y8YMDR8+XLGxsVq1apUaG/mZzAAAyWZ1AZJ08uRJbdmyRXFxce2Ou3r1qmbPnq0pU6bo8OHD8ng8ysrKUnh4uBYvXtxL1QIA+irLn9SuXLmi559/XuvWrZPD4Wh3bGFhoa5fvy6XyyWn06m0tDT97Gc/U15eHk9rANDX+f2yFRdr9MqVshUXS35/t9/C8lB7+eWXlZaWpmnTpnU49sSJE5o8ebLsdnvzuaSkJF28eFFVVVU9WSYAoCv8foXPm6fwF15Q5K5dCn/hBYXPm9ftwWZpqG3ZskXnzp3TL3/5y06N93q9Gjp0aItzTcder7fb6wMAdA/bnj2ylZQoxOeTJIX4fLKVlMi2d2/33qdbP1sAPB6P3njjDe3fv18DBgzo9LyQkJAWx03bjt8+/+17dQX/GdIM9GgGegxOo4uLFfHfQGsS4vOpvrhYn8fGBvS5YmJi2rxmWaidOHFCly9f1uTJk5vP3bx5U6WlpXr//ff173//W9/5zndazImMjLztiezSpUuSdNsT3K3a+wJ0xOPxdGl+MKBHM9CjGUzt0ZaWpsZ9+5qf1CSpMSxMEWlp3dqvZduPM2fOVGlpqY4ePdr8ER8frzlz5ujo0aOtPr0lJCSorKxMvlu+KEeOHNGIESM0ZsyY3iwfABCAhpQUNUydqsawMEnfBFrD1KlqmDWrW+9jWag5HA45nc4WH+Hh4Ro0aJCcTqdCQkKUm5ur1NTU5jlz586V3W5XZmamKioq5Ha7tXbtWmVmZra7/QgAsFhoqK7t2KFrGzfKO2eOrm3cqGs7dkih3RtDfeL/qbWlurpalZWVzccDBw7U7t27lZOTo8TERDkcDmVlZSk7O9vCKgEAnRIaqobUVH0eG9tjW6x9KtQ++uijFscul+u2MXFxcdq/f39vlQQACCKW/z81AAC6C6EGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwhmWhtmnTJk2ZMkVRUVGKiorS448/roMHD7Y5vqqqSg6H47aPQ4cO9WLVAIC+zGbVjUeOHKnc3FxFR0fL7/dr27ZtWrBggT755BONHz++zXlFRUUtrg8aNKg3ygUABAHLQm3mzJktjpcvX67Nmzfr5MmT7Yba4MGDNWzYsJ4uDwAQhPrEa2o3b95UUVGR6uvrlZCQ0O7YhQsXaty4cZo+fbqKi4t7qUIAQDAIqa2tbbTq5uXl5UpOTpbP51NERIQ2bdqk6dOntzr28uXLKigo0EMPPSSbzaZ9+/ZpzZo1crlcSk9Pb/c+Ho+nJ8oHAFggJiamzWuWhtqNGzd04cIFXblyRW63W1u2bNHevXvldDo7Nf+VV15RWVmZSktLe6xGj8fT7hfQBPRoBno0Az12jaXbjwMGDNB9992n+Ph4vf7665owYYLy8vI6PX/SpEk6d+5cD1YIAAgmfeI1tSZ+v183btzo9PjTp0/zphEAQDPL3v24YsUKJScna9SoUaqrq9POnTtVUlKiHTt2SJJyc3P16aefyu12S5IKCgrUv39/PfDAAwoNDdWBAweUn5+vFStWWNUCAKCPsSzUampqtGjRInm9Xt17772Ki4vTzp07lZSUJEmqrq5WZWVlizmrV6/W+fPn1a9fP0VHR2v9+vUdvkkEAHD3sCzUXC5XQNfnz5+v+fPn92RJAIAg16deUwMAoCsINQCAMQg1AIAxCDUAgDEINQCAMQg1AIAxCDUAgDEINQCAMQg1AIAxCDUAgDEINQCAMQg1AIAxCDUAgDEINQCAMQg1AIAxCDUAgDEINQCAMQg1AIAxCDUAgDEINQCAMQg1AIAxCDUAgDEINQCAMQg1AIAxLAu1TZs2acqUKYqKilJUVJQef/xxHTx4sN055eXlmjFjhoYPH67Y2FitWrVKjY2NvVQxAKCvs1l145EjRyo3N1fR0dHy+/3atm2bFixYoE8++UTjx4+/bfzVq1c1e/ZsTZkyRYcPH5bH41FWVpbCw8O1ePFiCzoA0Gv8ftn27NHo4mLZ0tLUkJIihbLRhNtZFmozZ85scbx8+XJt3rxZJ0+ebDXUCgsLdf36dblcLtntdjmdTp09e1Z5eXnKzs5WSEhIb5UOoDf5/QqfN0+2khJF+Hxq3LdPDX/6k67t2EGw4TZ94k/EzZs3VVRUpPr6eiUkJLQ65sSJE5o8ebLsdnvzuaSkJF28eFFVVVW9VSqAXmbbs0e2khKF+HySpBCfT7aSEtn27rW4MvRFlj2pSd+8RpacnCyfz6eIiAh98MEHiouLa3Ws1+vVyJEjW5wbOnRo87WxY8e2eR+Px9OlOrs6PxjQoxlM7HF0cbEi/htoTUJ8PtUXF+vz2FiLqupZJq7jt3Wlx5iYmDavWRpqMTExOnr0qK5cuSK3262XXnpJe/fuldPpbHX8t7cYm94k0tHWY3tfgI54PJ4uzQ8G9GgGU3u0paWpcd++5ic1SWoMC1NEWpqR/Zq6jrfqyR4t3X4cMGCA7rvvPsXHx+v111/XhAkTlJeX1+rYyMhIeb3eFucuXbok6X9PbADM05CSooapU9UYFibpm0BrmDpVDbNmWVwZ+qI+8ZpaE7/frxs3brR6LSEhQWVlZfLd8t3akSNHNGLECI0ZM6a3SgTQ20JDdW3HDl3buFHeOXN0beNG3iSCNln2p2LFihUqLS1VVVWVysvLlZubq5KSEj399NOSpNzcXKWmpjaPnzt3rux2uzIzM1VRUSG32621a9cqMzOTdz4CpgsNVUNqqj5fulQNqakEGtpk2WtqNTU1WrRokbxer+69917FxcVp586dSkpKkiRVV1ersrKyefzAgQO1e/du5eTkKDExUQ6HQ1lZWcrOzraqBQBAH2NZqLlcroCvx8XFaf/+/T1VEgAgyPEMDwAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMIZlofbOO+8oMTFRUVFRio6OVnp6uioqKtqdU1VVJYfDcdvHoUOHeqlqAEBfFlCoffzxx/L7/d1y45KSEj333HM6ePCg3G63bDabnnzySX355Zcdzi0qKtKZM2eaPx555JFuqQkAENxsgQxOT0/X0KFDNWfOHKWnp+vBBx+84xvv2rWrxfGGDRs0evRoHT9+XE888US7cwcPHqxhw4bd8b0BAGYK6Entww8/1MMPP6w//vGP+r//+z/96Ec/0u9+9ztduHChy4XU1dXJ7/fL4XB0OHbhwoUaN26cpk+fruLi4i7fGwBghoBCbfr06dq8ebPOnDmjdevWacSIEfr1r3+tH/zgB0pJSdHWrVv1n//8544KWbp0qSZMmKCEhIQ2x9xzzz1688039Yc//EGFhYV65JFH9Oyzz2r79u13dE8AgFlCamtrG7vyCaqrq1VYWKjt27eroqJCYWFhmjFjhjIyMpSUlNSpz/Haa69p165dOnDggMaOHRvQ/V955RWVlZWptLS0zTEejyegzwkA6LtiYmLavBbQa2qt+frrr3Xjxg3duHFDjY2N+u53v6uysjIVFRUpNjZWGzdu1Pjx49ucv2zZMu3atUt79uwJONAkadKkSdq6dWu7Y9r7AnTE4/F0aX4woEcz0KMZ6LFr7ugt/VeuXNGWLVs0Y8YMPfjgg3r77bfldDr14YcfqqKiQn//+9+1bds21dfXa/HixW1+niVLlmjnzp1yu926//7776iB06dP86YRAICkAJ/UPvroI23fvl0ff/yxvvrqK/3whz/U22+/raeeeuq2N3j85Cc/kdfr1SuvvNLq58rJydH27dv1wQcfyOFwqKamRpIUERGhe+65R5KUm5urTz/9VG63W5JUUFCg/v3764EHHlBoaKgOHDig/Px8rVixIsC2AQAmCijUfvrTn2rUqFHKyspSRkaGxo0b1+74uLg4Pf30061ey8/PlySlpaW1OL9kyRItW7ZM0jev11VWVra4vnr1ap0/f179+vVTdHS01q9fr/T09EDaAAAYKqBQ2717t6ZNm6aQkJBOjZ80aZImTZrU6rXa2toO57tcrhbH8+fP1/z58zt1bwDA3SegUHv00Ud7qAwAALqOH2gMADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwhmWh9s477ygxMVFRUVGKjo5Wenq6KioqOpxXXl6uGTNmaPjw4YqNjdWqVavU2NjYCxUDAPo6y0KtpKREzz33nA4ePCi32y2bzaYnn3xSX375ZZtzrl69qtmzZysyMlKHDx/WW2+9pXXr1mn9+vW9WDmCit8vW3GxRq9cKVtxseT3W10RgB5ks+rGu3btanG8YcMGjR49WsePH9cTTzzR6pzCwkJdv35dLpdLdrtdTqdTZ8+eVV5enrKzsxUSEtIbpSNY+P0KnzdPtpISRfh8aty3Tw1/+pOu7dghhbLzDpioz/zNrqurk9/vl8PhaHPMiRMnNHnyZNnt9uZzSUlJunjxoqqqqnqhSgQT2549spWUKMTnkySF+HyylZTItnevxZUB6CmWPal929KlSzVhwgQlJCS0Ocbr9WrkyJEtzg0dOrT52tixY1ud5/F4ulRbV+cHAxN7HF1crIj/BlqTEJ9P9cXF+jw21qKqepaJ6/ht9GiGrvQYExPT5rU+EWqvvfaajh8/rgMHDqhfv37tjv32FmPTm0Ta23ps7wvQEY/H06X5wcDUHm1paWrct6/5SU2SGsPCFJGWZmS/pq7jrejRDD3Zo+Xbj8uWLVNRUZHcbnebT1pNIiMj5fV6W5y7dOmSpP89sQFNGlJS1DB1qhrDwiR9E2gNU6eqYdYsiysD0FMsDbUlS5Zo586dcrvduv/++zscn5CQoLKyMvlu+c77yJEjGjFihMaMGdOTpSIYhYbq2o4durZxo7xz5ujaxo28SQQwnGV/u3NyclRQUKD8/Hw5HA7V1NSopqZGdXV1zWNyc3OVmprafDx37lzZ7XZlZmaqoqJCbrdba9euVWZmJu98ROtCQ9WQmqrPly5VQ2oqgQYYzrLX1PLz8yVJaWlpLc4vWbJEy5YtkyRVV1ersrKy+drAgQO1e/du5eTkKDExUQ6HQ1lZWcrOzu69wgEAfZZloVZbW9vhGJfLddu5uLg47d+/vwcqAgAEO/ZiAADGINQAAMYg1AAAxiDUAADGINQAAMYg1AAAxiDUAADGINQAAMYg1AAAxiDUAADGINQAAMYg1AAAxiDUAADGINQAAMYg1AAAxiDUAADGINQAAMYg1AAAxiDUAADGINQAAMYg1AAAxiDUAADGINQAAMYg1AAAxrA01I4dO6ZnnnlGsbGxcjgc2rp1a7vjq6qq5HA4bvs4dOhQL1UMAOjLbFbevL6+Xk6nUxkZGXrxxRc7Pa+oqEjjx49vPh40aFBPlAcACDKWhlpycrKSk5MlSZmZmZ2eN3jwYA0bNqynygIABKmgfE1t4cKFGjdunKZPn67i4mKrywEA9BEhtbW1jVYXIUmjRo3Sb3/7Wy1YsKDNMZcvX1ZBQYEeeugh2Ww27du3T2vWrJHL5VJ6enqb8zweT0+UDACwQExMTJvXLN1+DNSQIUO0ePHi5uP4+Hh98cUXevfdd9sNtfa+AB3xeDxdmh8M6NEM9GgGeuyaoNx+vNWkSZN07tw5q8sAAPQBQR9qp0+f5k0jAABJFm8/1tXVNT9l+f1+XbhwQadOndKgQYMUFRWl3Nxcffrpp3K73ZKkgoIC9e/fXw888IBCQ0N14MAB5efna8WKFRZ2AQDoKywNtc8++0wpKSnNxytXrtTKlSuVkZEhl8ul6upqVVZWtpizevVqnT9/Xv369VN0dLTWr1/f7utpAIC7h6Wh9vDDD6u2trbN6y6Xq8Xx/PnzNX/+/B6uCgAQrIL+NTUAAJoQagAAYxBqAABjEGoAAGMQagAAYxBqAABjEGoAAGMQagAAYxBqAABjEGoAAGMQagAAYxBqAABjEGoAAGMQagAAYxBqAABjEGoAAGMQagAAYxBqAABjEGoAAGMQagAAYxBqAABjEGoAAGMQagAAYxBqAABjWBpqx44d0zPPPKPY2Fg5HA5t3bq1wznl5eWaMWOGhg8frtjYWK1atUqNjY29UC0AoK+zNNTq6+vldDr11ltvyW63dzj+6tWrmj17tiIjI3X48GG99dZbWrdundavX98L1QIA+jqblTdPTk5WcnKyJCkzM7PD8YWFhbp+/bpcLpfsdrucTqfOnj2rvLw8ZWdnKyQkpPuK8/tl27NHo4uLZUtLU0NKihTKbi0A9GVB9a/0iRMnNHny5BZPdUlJSbp48aKqqqq670Z+v8LnzVP4Cy8octcuhb/wgsLnzZP8/u67BwCg2wVVqHm9Xg0dOrTFuaZjr9fbbfex7dkjW0mJQnw+SVKIzydbSYlse/d22z0AAN3P0u3HO/HtLcamN4m0t/Xo8XgCusfo4mJF/DfQmu/r86m+uFifx8YG9LmCRaBfo2BEj2agRzN0pceYmJg2rwVVqEVGRt72RHbp0iVJuu0J7lbtfQFaY0tLU+O+fc1PapLUGBamiLS0gD9XMPB4PEb2dSt6NAM9mqEnewyq7ceEhASVlZXJd0vYHDlyRCNGjNCYMWO67T4NKSlqmDpVjWFhkr4JtIapU9Uwa1a33QMA0P0sDbW6ujqdOnVKp06dkt/v14ULF3Tq1CmdP39ekpSbm6vU1NTm8XPnzpXdbldmZqYqKirkdru1du1aZWZmdu87H0NDdW3HDl3buFHeOXN0beNGXduxg3c/AkAfZ+n242effaaUlJTm45UrV2rlypXKyMiQy+VSdXW1Kisrm68PHDhQu3fvVk5OjhITE+VwOJSVlaXs7OzuLy40VA2pqfo8Ntb4rQAAMIWlofbwww+rtra2zesul+u2c3Fxcdq/f38PVgUACFbspwEAjEGoAQCMQagBAIwRUltby4+4BwAYgSc1AIAxCDUAgDEINQCAMQg1AIAxCDUAgDHu2lA7duyYnnnmGcXGxsrhcGjr1q0dzikvL9eMGTM0fPhwxcbGatWqVc2/+qYvCrTHqqoqORyO2z4OHTrUSxUH7p133lFiYqKioqIUHR2t9PR0VVRUdDgvmNbyTnoMtrXctGmTpkyZoqioKEVFRenxxx/XwYMH250TTGsoBd5jsK3ht61Zs0YOh0Ovvvpqu+O6ex2D6lfPdKf6+no5nU5lZGToxRdf7HD81atXNXv2bE2ZMkWHDx+Wx+NRVlaWwsPDtXjx4l6oOHCB9tikqKhI48ePbz4eNGhQT5TXLUpKSvTcc89p4sSJamxs1G9+8xs9+eST+vOf/9xm3cG2lnfSY5NgWcuRI0cqNzdX0dHR8vv92rZtmxYsWKBPPvmkRf1Ngm0NpcB7bBIsa3irkydPasuWLYqLi2t3XE+s410basnJyUpOTpYkZWZmdji+sLBQ169fl8vlkt1ul9Pp1NmzZ5WXl6fs7Ozu/S0B3STQHpsMHjxYw4YN66myutWuXbtaHG/YsEGjR4/W8ePH9cQTT7Q6J9jW8k56bBIsazlz5swWx8uXL9fmzZt18uTJVv/BD7Y1lALvsUmwrGGTK1eu6Pnnn9e6dev029/+tt2xPbGOd+32Y6BOnDihyZMny263N59LSkrSxYsXVVVVZWFl3W/hwoUaN26cpk+fruLiYqvLCUhdXZ38fr8cDkebY4J9LTvTY5NgXMubN2+qqKhI9fX1SkhIaHVMsK9hZ3psEmxr+PLLLystLU3Tpk3rcGxPrONd+6QWKK/Xq5EjR7Y41/Tbtr1er8aOHWtBVd3rnnvu0ZtvvqmHHnpINptN+/bt07PPPiuXy6X09HSry+uUpUuXasKECe3+QxHsa9mZHoNxLcvLy5WcnCyfz6eIiAh98MEHbW5fBesaBtJjMK7hli1bdO7cOW3YsKFT43tiHQm1AHz7Ubjpxcy+uNVxJ4YMGdJiHzs+Pl5ffPGF3n333T77l+hWr732mo4fP64DBw6oX79+7Y4N1rXsbI/BuJYxMTE6evSorly5IrfbrZdeekl79+6V0+lsdXwwrmEgPQbbGno8Hr3xxhvav3+/BgwY0Ol53b2ObD92UmRkpLxeb4tzly5dkvS/7yxMNGnSJJ07d87qMjq0bNkyFRUVye12d/jdXbCuZSA9tqavr+WAAQN03333KT4+Xq+//romTJigvLy8VscG6xoG0mNr+vIanjhxQpcvX9bkyZM1ZMgQDRkyRMeOHVN+fr6GDBmir7766rY5PbGOhFonJSQkqKysTD6fr/nckSNHNGLECI0ZM8bCynrW6dOn+/yL1EuWLNHOnTvldrt1//33dzg+GNcy0B5bEwxreSu/368bN260ei0Y17A17fXYmr68hjNnzlRpaamOHj3a/BEfH685c+bo6NGjrT699cQ63rWhVldXp1OnTunUqVPy+/26cOGCTp06pfPnz0uScnNzlZqa2jx+7ty5stvtyszMVEVFhdxut9auXavMzMw+u90RaI8FBQUqLCzUmTNn5PF4tG7dOuXn52vRokVWtdChnJwcFRQUKD8/Xw6HQzU1NaqpqVFdXV3zmGBfyzvpMdjWcsWKFSotLVVVVZXKy8uVm5urkpISPf3005KCfw2lwHsMtjV0OBxyOp0tPsLDwzVo0CA5nU6FhIT0yjreta+pffbZZ0pJSWk+XrlypVauXKmMjAy5XC5VV1ersrKy+frAgQO1e/du5eTkKDExUQ6HQ1lZWcrOzrai/E4JtEdJWr16tc6fP69+/fopOjpa69ev75P7903y8/MlSWlpaS3OL1myRMuWLZOkoF/LO+lRCq61rKmp0aJFi+T1enXvvfcqLi5OO3fuVFJSkqTgX0Mp8B6l4FrDzuiNdeT3qQEAjHHXbj8CAMxDqAEAjEGoAQCMQagBAIxBqAEAjEGoAQCMQagBAIxBqAEAjEGoAQCMQagBAIxBqAFB6Pr160pISNDEiRNVX1/ffL6+vl7x8fFKSEho8ZPPgbsFoQYEIbvdrvfee0+ff/65fvWrXzWfX758uc6fP6/33ntPYWFhFlYIWOOu/Sn9QLCbOHGifv7zn+vtt9/WzJkzJUnvv/++fvGLX2jixIkWVwdYg5/SDwSxr7/+Wo899pguXbqkxsZGDR06VIcOHVL//v2tLg2wBKEGBLny8nL9+Mc/ls1mU0lJib7//e9bXRJgGV5TA4Lc4cOHJUkNDQ06c+aMxdUA1uJJDQhi//jHPzRt2jTNmjVL//rXv/TPf/5TZWVlGjp0qNWlAZYg1IAg1dDQoMcee0w1NTUqLS1VbW2tpk6dqkcffVRbt261ujzAEmw/AkFq9erV+utf/6p3331XgwYN0ve+9z3l5ubqo48+0rZt26wuD7AET2pAEPrb3/6mxx57TBkZGfr973/ffL6xsVFPPfWU/vKXv6i0tFSjRo2ysEqg9xFqAABjsP0IADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADAGoQYAMAahBgAwBqEGADDG/wPtaUMuw77kEQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line = pd.DataFrame(\n",
    "        {'x':np.array([1, 2, 3, 4]),\n",
    "        'y':np.array([1, 2, 3, 4])}\n",
    "    )\n",
    "line.plot.scatter('x', 'y', s=30, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(line, 'x', 'y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outlier = pd.DataFrame(\n",
    "        {'x':np.array([1, 2, 3, 4, 5]),\n",
    "        'y':np.array([1, 2, 3, 4, 0])}\n",
    "    )\n",
    "outlier.plot.scatter('x', 'y', s=30, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(outlier, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ecological Correlations Should be Interpreted with Care\n",
    "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": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>State</th>\n",
       "      <th>Participation Rate</th>\n",
       "      <th>Critical Reading</th>\n",
       "      <th>Math</th>\n",
       "      <th>Writing</th>\n",
       "      <th>Combined</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Alabama</td>\n",
       "      <td>6.7</td>\n",
       "      <td>547</td>\n",
       "      <td>538</td>\n",
       "      <td>532</td>\n",
       "      <td>1617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>Alaska</td>\n",
       "      <td>54.2</td>\n",
       "      <td>507</td>\n",
       "      <td>503</td>\n",
       "      <td>475</td>\n",
       "      <td>1485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Arizona</td>\n",
       "      <td>36.4</td>\n",
       "      <td>522</td>\n",
       "      <td>525</td>\n",
       "      <td>500</td>\n",
       "      <td>1547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Arkansas</td>\n",
       "      <td>4.2</td>\n",
       "      <td>573</td>\n",
       "      <td>571</td>\n",
       "      <td>554</td>\n",
       "      <td>1698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>California</td>\n",
       "      <td>60.3</td>\n",
       "      <td>498</td>\n",
       "      <td>510</td>\n",
       "      <td>496</td>\n",
       "      <td>1504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Colorado</td>\n",
       "      <td>14.3</td>\n",
       "      <td>582</td>\n",
       "      <td>586</td>\n",
       "      <td>567</td>\n",
       "      <td>1735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>Connecticut</td>\n",
       "      <td>88.4</td>\n",
       "      <td>507</td>\n",
       "      <td>510</td>\n",
       "      <td>508</td>\n",
       "      <td>1525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>Delaware</td>\n",
       "      <td>100.0</td>\n",
       "      <td>456</td>\n",
       "      <td>459</td>\n",
       "      <td>444</td>\n",
       "      <td>1359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>District of Columbia</td>\n",
       "      <td>100.0</td>\n",
       "      <td>440</td>\n",
       "      <td>438</td>\n",
       "      <td>431</td>\n",
       "      <td>1309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>Florida</td>\n",
       "      <td>72.2</td>\n",
       "      <td>491</td>\n",
       "      <td>485</td>\n",
       "      <td>472</td>\n",
       "      <td>1448</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   State  Participation Rate  Critical Reading  Math  Writing  \\\n",
       "21               Alabama                 6.7               547   538      532   \n",
       "34                Alaska                54.2               507   503      475   \n",
       "26               Arizona                36.4               522   525      500   \n",
       "15              Arkansas                 4.2               573   571      554   \n",
       "33            California                60.3               498   510      496   \n",
       "12              Colorado                14.3               582   586      567   \n",
       "30           Connecticut                88.4               507   510      508   \n",
       "49              Delaware               100.0               456   459      444   \n",
       "50  District of Columbia               100.0               440   438      431   \n",
       "43               Florida                72.2               491   485      472   \n",
       "\n",
       "    Combined  \n",
       "21      1617  \n",
       "34      1485  \n",
       "26      1547  \n",
       "15      1698  \n",
       "33      1504  \n",
       "12      1735  \n",
       "30      1525  \n",
       "49      1359  \n",
       "50      1309  \n",
       "43      1448  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sat2014 = pd.read_csv(path_data + 'sat2014.csv').sort_values(by=['State'])\n",
    "sat2014.head(10)"
   ]
  },
  {
   "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": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sat2014.plot.scatter('Critical Reading', 'Math')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9847558411067431"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "correlation(sat2014, 'Critical Reading', 'Math')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's an extremely high correlation. But it's important to note that this does not reflect the strength of the relation between the Math and Critical Reading scores of *students*. \n",
    "\n",
    "The data consist of average scores in each state. But 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",
    "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 whereas\n",
    "[others](http://www.reuters.com/article/2012/10/10/us-eat-chocolate-win-the-nobel-prize-idUSBRE8991MS20121010#vFdfFkbPVlilSjsB.97) were more relaxed. You are welcome to make your own decision! The following graph, provided in the paper, should motivate you to go and take a look."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "source": [
    "![Choco-Nobel](../../images/chocoNobel.png)"
   ]
  }
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