{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "%matplotlib inline\n",
    "path_data = '../../../assets/data/'\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": "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": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "def r_scatter(r):\n",
    "    plots.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",
    "    plots.scatter(x, y)\n",
    "    plots.xlim(-4, 4)\n",
    "    plots.ylim(-4, 4)"
   ]
  },
  {
   "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 = Table.read_table(path_data + 'hybrid.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "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",
       "        <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",
       "        <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",
       "        <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",
       "        <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",
       "        <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",
       "        <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",
       "        <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",
       "        <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",
       "        <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": 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 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.scatter('acceleration', 'msrp')"
   ]
  },
  {
   "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 360x360 with 1 Axes>"
      ]
     },
     "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, 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 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv = hybrid.where('class', 'SUV')\n",
    "suv.scatter('mpg', 'msrp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "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",
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "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);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "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);"
   ]
  },
  {
   "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",
    "\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": [
       "<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",
       "        <tr>\n",
       "            <td>2   </td> <td>3   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>3   </td> <td>1   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>4   </td> <td>5   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2   </td>\n",
       "        </tr>\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": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(1, 7, 1)\n",
    "y = make_array(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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "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": 18,
   "metadata": {},
   "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",
       "        <tr>\n",
       "            <td>2   </td> <td>3   </td> <td>-0.87831          </td> <td>-0.162221         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>3   </td> <td>1   </td> <td>-0.29277          </td> <td>-1.13555          </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>4   </td> <td>5   </td> <td>0.29277           </td> <td>0.811107          </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2   </td> <td>0.87831           </td> <td>-0.648886         </td>\n",
       "        </tr>\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": 18,
     "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": 19,
   "metadata": {},
   "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",
       "        <tr>\n",
       "            <td>2   </td> <td>3   </td> <td>-0.87831          </td> <td>-0.162221         </td> <td>0.142481                 </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>3   </td> <td>1   </td> <td>-0.29277          </td> <td>-1.13555          </td> <td>0.332455                 </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>4   </td> <td>5   </td> <td>0.29277           </td> <td>0.811107          </td> <td>0.237468                 </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>5   </td> <td>2   </td> <td>0.87831           </td> <td>-0.648886         </td> <td>-0.569923                </td>\n",
       "        </tr>\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": 19,
     "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": 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.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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.scatter('y', 'x', s=30, color='red')"
   ]
  },
  {
   "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.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": 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": [
       "0.48699799279959155"
      ]
     },
     "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",
    "\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 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_x = np.arange(-4, 4.1, 0.5)\n",
    "nonlinear = Table().with_columns(\n",
    "        'x', new_x,\n",
    "        'y', new_x**2\n",
    "    )\n",
    "nonlinear.scatter('x', 'y', s=30, color='r')"
   ]
  },
  {
   "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": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line = Table().with_columns(\n",
    "        'x', make_array(1, 2, 3, 4),\n",
    "        'y', make_array(1, 2, 3, 4)\n",
    "    )\n",
    "line.scatter('x', 'y', s=30, color='r')"
   ]
  },
  {
   "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 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outlier = Table().with_columns(\n",
    "        'x', make_array(1, 2, 3, 4, 5),\n",
    "        'y', make_array(1, 2, 3, 4, 0)\n",
    "    )\n",
    "outlier.scatter('x', 'y', s=30, color='r')"
   ]
  },
  {
   "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": [
       "<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",
       "        <tr>\n",
       "            <td>Alaska              </td> <td>54.2              </td> <td>507             </td> <td>503 </td> <td>475    </td> <td>1485    </td>\n",
       "        </tr>\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",
       "        <tr>\n",
       "            <td>Arkansas            </td> <td>4.2               </td> <td>573             </td> <td>571 </td> <td>554    </td> <td>1698    </td>\n",
       "        </tr>\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",
       "        <tr>\n",
       "            <td>Colorado            </td> <td>14.3              </td> <td>582             </td> <td>586 </td> <td>567    </td> <td>1735    </td>\n",
       "        </tr>\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",
       "        <tr>\n",
       "            <td>Delaware            </td> <td>100               </td> <td>456             </td> <td>459 </td> <td>444    </td> <td>1359    </td>\n",
       "        </tr>\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",
       "        <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": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sat2014 = Table.read_table(path_data + '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": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sat2014.scatter('Critical Reading', 'Math')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9847558411067434"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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",
    "\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": "code",
   "execution_count": 36,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(\"../../../images/chocoNobel.png\")"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}