{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "aacf3566",
   "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": 1,
   "id": "81e8694c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:04.250018Z",
     "iopub.status.busy": "2026-08-31T06:02:04.249826Z",
     "iopub.status.idle": "2026-08-31T06:02:04.997424Z",
     "shell.execute_reply": "2026-08-31T06:02:04.997114Z"
    },
    "tags": [
     "hide-input",
     "thebe-init",
     "runnable"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy import stats\n",
    "import math\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f777ce4b",
   "metadata": {},
   "source": [
    "```{contents}\n",
    ":local:\n",
    ":depth: 2\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d4158a8",
   "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": 2,
   "id": "bbc6794a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:04.998854Z",
     "iopub.status.busy": "2026-08-31T06:02:04.998742Z",
     "iopub.status.idle": "2026-08-31T06:02:05.006305Z",
     "shell.execute_reply": "2026-08-31T06:02:05.006077Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "hybrid = pd.read_csv(path_data + 'hybrid.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bdb79575",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.007504Z",
     "iopub.status.busy": "2026-08-31T06:02:05.007443Z",
     "iopub.status.idle": "2026-08-31T06:02:05.012270Z",
     "shell.execute_reply": "2026-08-31T06:02:05.012082Z"
    },
    "tags": []
   },
   "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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hybrid"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1595d5b",
   "metadata": {},
   "source": [
    "The graph below is a scatter plot of `msrp` *versus* `acceleration` (the higher the better). That means `msrp` is plotted on the vertical axis and `acceleration` on the horizontal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "aae8bb6a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.013301Z",
     "iopub.status.busy": "2026-08-31T06:02:05.013243Z",
     "iopub.status.idle": "2026-08-31T06:02:05.058078Z",
     "shell.execute_reply": "2026-08-31T06:02:05.057862Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='acceleration', ylabel='msrp'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.plot.scatter('acceleration', 'msrp', figsize=(4,3), s = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e23d3db5",
   "metadata": {},
   "source": [
    "Notice the **positive association**. The scatter of points is sloping upwards, indicating that cars with greater acceleration tend to cost more, on average; conversely, cars that cost more tend to have greater acceleration on average. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7e56769",
   "metadata": {},
   "source": [
    "The scatter diagram below of MSRP versus mileage (mpg) 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": 5,
   "id": "022e7166",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.059348Z",
     "iopub.status.busy": "2026-08-31T06:02:05.059278Z",
     "iopub.status.idle": "2026-08-31T06:02:05.088072Z",
     "shell.execute_reply": "2026-08-31T06:02:05.087848Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='mpg', ylabel='msrp'>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hybrid.plot.scatter('mpg', 'msrp', figsize=(4,3), s=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ee76356",
   "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. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79daa3bc",
   "metadata": {},
   "source": [
    "If we restrict the data just to the SUV class below, however, the association between price and efficiency is still negative, but the relation appears to be more **linear**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "381d9822",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.089227Z",
     "iopub.status.busy": "2026-08-31T06:02:05.089147Z",
     "iopub.status.idle": "2026-08-31T06:02:05.114741Z",
     "shell.execute_reply": "2026-08-31T06:02:05.114544Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='mpg', ylabel='msrp'>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv = hybrid[hybrid['class'] == 'SUV']\n",
    "suv.plot.scatter('mpg', 'msrp', figsize=(4,3), s=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c72cab2d",
   "metadata": {},
   "source": [
    "The relation between the price and acceleration of SUVs also shows a **linear** trend, but with a positive slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6ae501b6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.115836Z",
     "iopub.status.busy": "2026-08-31T06:02:05.115771Z",
     "iopub.status.idle": "2026-08-31T06:02:05.142032Z",
     "shell.execute_reply": "2026-08-31T06:02:05.141828Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='acceleration', ylabel='msrp'>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suv.plot.scatter('acceleration', 'msrp', figsize=(4,3), s=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6747a4af",
   "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",
    "We can define the function `standard_units` to convert an array of numbers to standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "39ac92d9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.143167Z",
     "iopub.status.busy": "2026-08-31T06:02:05.143092Z",
     "iopub.status.idle": "2026-08-31T06:02:05.144536Z",
     "shell.execute_reply": "2026-08-31T06:02:05.144334Z"
    },
    "tags": []
   },
   "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",
   "id": "02890a36",
   "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": 9,
   "id": "20e72815",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.145551Z",
     "iopub.status.busy": "2026-08-31T06:02:05.145486Z",
     "iopub.status.idle": "2026-08-31T06:02:05.174244Z",
     "shell.execute_reply": "2026-08-31T06:02:05.174049Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3.0, 3.0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 300x300 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3,3))\n",
    "\n",
    "SUVs = pd.DataFrame(\n",
    "    {'mpg (standard units)':standard_units(suv['mpg']), \n",
    "    'msrp (standard units)':standard_units(suv['msrp'])}\n",
    ").plot.scatter(0, 1, figsize=(4,3), s=10)\n",
    "\n",
    "plt.xlim(-3, 3)\n",
    "plt.ylim(-3, 3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ed18301b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.175335Z",
     "iopub.status.busy": "2026-08-31T06:02:05.175262Z",
     "iopub.status.idle": "2026-08-31T06:02:05.203038Z",
     "shell.execute_reply": "2026-08-31T06:02:05.202823Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3.0, 3.0)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 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, figsize=(4,3), s=10)\n",
    "\n",
    "plt.xlim(-3, 3)\n",
    "plt.ylim(-3, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8641166",
   "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",
   "id": "df56b07f",
   "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",
   "id": "76a64826",
   "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 $r$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f1b057b8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.204247Z",
     "iopub.status.busy": "2026-08-31T06:02:05.204182Z",
     "iopub.status.idle": "2026-08-31T06:02:05.205888Z",
     "shell.execute_reply": "2026-08-31T06:02:05.205694Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def r_scatter(r):\n",
    "    plt.figure(figsize=(4,3))\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, s=10)\n",
    "    plt.xlim(-4, 4)\n",
    "    plt.ylim(-4, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27b31dfc",
   "metadata": {},
   "source": [
    "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,
   "id": "8bad89a4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.206860Z",
     "iopub.status.busy": "2026-08-31T06:02:05.206800Z",
     "iopub.status.idle": "2026-08-31T06:02:05.229992Z",
     "shell.execute_reply": "2026-08-31T06:02:05.229806Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b2193b76",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.230994Z",
     "iopub.status.busy": "2026-08-31T06:02:05.230934Z",
     "iopub.status.idle": "2026-08-31T06:02:05.253003Z",
     "shell.execute_reply": "2026-08-31T06:02:05.252819Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fe2ee63e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.253963Z",
     "iopub.status.busy": "2026-08-31T06:02:05.253905Z",
     "iopub.status.idle": "2026-08-31T06:02:05.278108Z",
     "shell.execute_reply": "2026-08-31T06:02:05.277896Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4cc9790d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.279162Z",
     "iopub.status.busy": "2026-08-31T06:02:05.279100Z",
     "iopub.status.idle": "2026-08-31T06:02:05.301625Z",
     "shell.execute_reply": "2026-08-31T06:02:05.301433Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_scatter(-0.55)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23bb5efd",
   "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",
    "$\n",
    "r = \\frac{1}{n}\\sum_{i=1}^{n} \\left(\\frac{x_i-\\bar{x}}{\\mathrm{SD}(x)}\\right)\\left(\\frac{y_i-\\bar{y}}{\\mathrm{SD}(y)}\\right)\n",
    "$\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,
   "id": "3cb05fc5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.302689Z",
     "iopub.status.busy": "2026-08-31T06:02:05.302627Z",
     "iopub.status.idle": "2026-08-31T06:02:05.305126Z",
     "shell.execute_reply": "2026-08-31T06:02:05.304942Z"
    },
    "tags": []
   },
   "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({\n",
    "        'x': x,\n",
    "        'y': y\n",
    "})\n",
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91adb84a",
   "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,
   "id": "7047b793",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.306138Z",
     "iopub.status.busy": "2026-08-31T06:02:05.306078Z",
     "iopub.status.idle": "2026-08-31T06:02:05.327348Z",
     "shell.execute_reply": "2026-08-31T06:02:05.327160Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x', ylabel='y'>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.plot.scatter(0, 1, s=30, color='red', figsize=(4,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c570dd9",
   "metadata": {},
   "source": [
    "**Step 1.** Convert each variable to standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "90d6bf0f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.328332Z",
     "iopub.status.busy": "2026-08-31T06:02:05.328275Z",
     "iopub.status.idle": "2026-08-31T06:02:05.331123Z",
     "shell.execute_reply": "2026-08-31T06:02:05.330938Z"
    },
    "tags": []
   },
   "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",
    "t_su['y (standard units)'] = standard_units(y)\n",
    "\n",
    "t_su"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaa955e6",
   "metadata": {},
   "source": [
    "**Step 2.** Multiply each pair of standard units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f8a273ae",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.332089Z",
     "iopub.status.busy": "2026-08-31T06:02:05.332035Z",
     "iopub.status.idle": "2026-08-31T06:02:05.334788Z",
     "shell.execute_reply": "2026-08-31T06:02:05.334608Z"
    },
    "tags": []
   },
   "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",
    "t_product['product of standard units'] = t_su.iloc[:,2] * t_su.iloc[:,3]\n",
    "\n",
    "t_product"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "084a3c83",
   "metadata": {},
   "source": [
    "**Step 3.** $r$ is the average of the products computed in Step 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e2a918fe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.335711Z",
     "iopub.status.busy": "2026-08-31T06:02:05.335659Z",
     "iopub.status.idle": "2026-08-31T06:02:05.337276Z",
     "shell.execute_reply": "2026-08-31T06:02:05.337087Z"
    },
    "tags": []
   },
   "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]).item()\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3ff6577",
   "metadata": {},
   "source": [
    "As expected, $r$ is positive but not equal to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22699753",
   "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,
   "id": "b13a9367",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.338263Z",
     "iopub.status.busy": "2026-08-31T06:02:05.338210Z",
     "iopub.status.idle": "2026-08-31T06:02:05.361734Z",
     "shell.execute_reply": "2026-08-31T06:02:05.361529Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='y', ylabel='x'>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.plot.scatter('y', 'x', s=10, color='red', figsize=(4,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4baec0d",
   "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,
   "id": "65996308",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.362794Z",
     "iopub.status.busy": "2026-08-31T06:02:05.362735Z",
     "iopub.status.idle": "2026-08-31T06:02:05.364121Z",
     "shell.execute_reply": "2026-08-31T06:02:05.363952Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def correlation(t, x, y):\n",
    "    return np.mean(standard_units(t[x])*standard_units(t[y])).item()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8489fb77",
   "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,
   "id": "e69f6dc2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.365059Z",
     "iopub.status.busy": "2026-08-31T06:02:05.365006Z",
     "iopub.status.idle": "2026-08-31T06:02:05.366780Z",
     "shell.execute_reply": "2026-08-31T06:02:05.366630Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(t, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b79202d",
   "metadata": {},
   "source": [
    "As we noticed, the order in which the variables are specified doesn't matter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ccff5900",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.367668Z",
     "iopub.status.busy": "2026-08-31T06:02:05.367602Z",
     "iopub.status.idle": "2026-08-31T06:02:05.369244Z",
     "shell.execute_reply": "2026-08-31T06:02:05.369083Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6174163971897709"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(t, 'y', 'x')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a43a0e0c",
   "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,
   "id": "6e1ba73b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.370108Z",
     "iopub.status.busy": "2026-08-31T06:02:05.370055Z",
     "iopub.status.idle": "2026-08-31T06:02:05.371818Z",
     "shell.execute_reply": "2026-08-31T06:02:05.371658Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.666714363570992"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(suv, 'mpg', 'msrp')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c6ccf5ac",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.372684Z",
     "iopub.status.busy": "2026-08-31T06:02:05.372633Z",
     "iopub.status.idle": "2026-08-31T06:02:05.374346Z",
     "shell.execute_reply": "2026-08-31T06:02:05.374137Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4869979927995918"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(suv, 'acceleration', 'msrp')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78a7106c",
   "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",
   "id": "577144c5",
   "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",
   "id": "c7344fd7",
   "metadata": {},
   "source": [
    "### Association vs. Causation\n",
    "\n",
    "Correlation only measures **association**. Correlation does not imply **causation**. \n",
    "\n",
    "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",
   "id": "91fd7fed",
   "metadata": {},
   "source": [
    "### *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,
   "id": "4c4c7426",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.375427Z",
     "iopub.status.busy": "2026-08-31T06:02:05.375370Z",
     "iopub.status.idle": "2026-08-31T06:02:05.400835Z",
     "shell.execute_reply": "2026-08-31T06:02:05.400624Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 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=10, color='r', figsize=(4,4))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "13748200",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.401988Z",
     "iopub.status.busy": "2026-08-31T06:02:05.401926Z",
     "iopub.status.idle": "2026-08-31T06:02:05.403854Z",
     "shell.execute_reply": "2026-08-31T06:02:05.403669Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(nonlinear, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6898df2",
   "metadata": {},
   "source": [
    "### Correlation and 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,
   "id": "0b20d5a6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.404790Z",
     "iopub.status.busy": "2026-08-31T06:02:05.404734Z",
     "iopub.status.idle": "2026-08-31T06:02:05.428964Z",
     "shell.execute_reply": "2026-08-31T06:02:05.428757Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x', ylabel='y'>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 400x300 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=10, color='r', figsize=(4,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "9a5c742e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.429992Z",
     "iopub.status.busy": "2026-08-31T06:02:05.429934Z",
     "iopub.status.idle": "2026-08-31T06:02:05.431885Z",
     "shell.execute_reply": "2026-08-31T06:02:05.431711Z"
    },
    "tags": []
   },
   "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,
   "id": "397a69e1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.432768Z",
     "iopub.status.busy": "2026-08-31T06:02:05.432709Z",
     "iopub.status.idle": "2026-08-31T06:02:05.455343Z",
     "shell.execute_reply": "2026-08-31T06:02:05.455136Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 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=10, color='r', figsize=(4,3))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7a6d810d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.456487Z",
     "iopub.status.busy": "2026-08-31T06:02:05.456423Z",
     "iopub.status.idle": "2026-08-31T06:02:05.458369Z",
     "shell.execute_reply": "2026-08-31T06:02:05.458208Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(outlier, 'x', 'y')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e424efc",
   "metadata": {},
   "source": [
    "### Ecological Correlations\n",
    "\n",
    "An [ecological correlation](https://en.wikipedia.org/wiki/Ecological_correlation) is a correlation computed using group-level (aggregate) data rather than individual-level data. \n",
    "\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,
   "id": "cee9bc5e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.459276Z",
     "iopub.status.busy": "2026-08-31T06:02:05.459215Z",
     "iopub.status.idle": "2026-08-31T06:02:05.463011Z",
     "shell.execute_reply": "2026-08-31T06:02:05.462847Z"
    },
    "tags": []
   },
   "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",
   "id": "c5a54a2b",
   "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,
   "id": "e923d713",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.463906Z",
     "iopub.status.busy": "2026-08-31T06:02:05.463843Z",
     "iopub.status.idle": "2026-08-31T06:02:05.491751Z",
     "shell.execute_reply": "2026-08-31T06:02:05.491579Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Critical Reading', ylabel='Math'>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sat2014.plot.scatter('Critical Reading', 'Math', figsize=(4,3), s=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "33f63d92",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.492787Z",
     "iopub.status.busy": "2026-08-31T06:02:05.492725Z",
     "iopub.status.idle": "2026-08-31T06:02:05.494737Z",
     "shell.execute_reply": "2026-08-31T06:02:05.494556Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9847558411067434"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(sat2014, 'Critical Reading', 'Math')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7a5a03a",
   "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",
   "id": "5b297e10",
   "metadata": {},
   "source": [
    "## Serious or Sarcastic?\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,
   "id": "8b323713",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.495652Z",
     "iopub.status.busy": "2026-08-31T06:02:05.495594Z",
     "iopub.status.idle": "2026-08-31T06:02:05.498734Z",
     "shell.execute_reply": "2026-08-31T06:02:05.498562Z"
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 36,
     "metadata": {
      "image/png": {
       "width": 500
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(\"../../figures/chocoNobel.png\", width=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3609b84",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "cell-88c223b7",
   "metadata": {},
   "source": [
    "\n",
    "## Section Practice\n",
    "\n",
    "Use this short exercise to check the main workflow from this section.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "cell-444051cb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.499785Z",
     "iopub.status.busy": "2026-08-31T06:02:05.499711Z",
     "iopub.status.idle": "2026-08-31T06:02:05.501017Z",
     "shell.execute_reply": "2026-08-31T06:02:05.500852Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Practice Correlation\n",
    "# A coffee chain recorded daily temperature (F) and iced-drink sales at one store.\n",
    "#   1. Convert both variables to standard units (np.mean, np.std).\n",
    "#   2. Compute r as the mean of the products of the standard units.\n",
    "#   3. Check your answer with np.corrcoef(x, y)[0, 1]. Print both, rounded to 3 decimals.\n",
    "import numpy as np\n",
    "\n",
    "temperature = np.array([58, 62, 66, 70, 75, 79, 83, 88])\n",
    "iced_sales = np.array([120, 135, 150, 148, 180, 205, 210, 240])\n",
    "### Your code starts here\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "cell-f1b31259",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:05.501899Z",
     "iopub.status.busy": "2026-08-31T06:02:05.501845Z",
     "iopub.status.idle": "2026-08-31T06:02:05.503346Z",
     "shell.execute_reply": "2026-08-31T06:02:05.503181Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "r: 0.985\nnp.corrcoef: 0.985\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "\n",
    "temperature = np.array([58, 62, 66, 70, 75, 79, 83, 88])\n",
    "iced_sales = np.array([120, 135, 150, 148, 180, 205, 210, 240])\n",
    "\n",
    "def standard_units(x):\n",
    "    return (x - np.mean(x)) / np.std(x)\n",
    "\n",
    "r = np.mean(standard_units(temperature) * standard_units(iced_sales))\n",
    "\n",
    "print('r:', round(r, 3))\n",
    "print('np.corrcoef:', round(np.corrcoef(temperature, iced_sales)[0, 1], 3))\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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