{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8501b536",
   "metadata": {},
   "source": [
    "# Covariance and Correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06a3540a",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "We will look at a dataset containing of measurements of heights and middle finger lengths for 3000 men (this is adapted from a dataset bizarrely recorded for jail inmates 1902 - W. R. MacDonell (Biometrika, Vol. I., p. 219)). \n",
    "\n",
    "\n",
    "### Set up Python libraries\n",
    "\n",
    "As usual, run the code cell below to import the relevant Python libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7f1d34e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set-up Python libraries - you need to run this but you don't need to change it\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import pandas \n",
    "import seaborn as sns\n",
    "sns.set_theme() # use pretty defaults"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36ec0b2a",
   "metadata": {},
   "source": [
    "### Load and inspect the data\n",
    "\n",
    "Load the data from the file HeightFinger.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5bf8d8ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>FingerLength</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>56</td>\n",
       "      <td>3.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>57</td>\n",
       "      <td>4.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>58</td>\n",
       "      <td>3.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>58</td>\n",
       "      <td>4.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>58</td>\n",
       "      <td>4.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2995</th>\n",
       "      <td>74</td>\n",
       "      <td>4.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2996</th>\n",
       "      <td>74</td>\n",
       "      <td>5.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2997</th>\n",
       "      <td>74</td>\n",
       "      <td>5.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2998</th>\n",
       "      <td>74</td>\n",
       "      <td>5.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2999</th>\n",
       "      <td>77</td>\n",
       "      <td>4.375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Height  FingerLength\n",
       "0         56         3.875\n",
       "1         57         4.000\n",
       "2         58         3.875\n",
       "3         58         4.000\n",
       "4         58         4.000\n",
       "...      ...           ...\n",
       "2995      74         4.875\n",
       "2996      74         5.000\n",
       "2997      74         5.000\n",
       "2998      74         5.250\n",
       "2999      77         4.375\n",
       "\n",
       "[3000 rows x 2 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "heightFinger = pandas.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/data/HeightFingerInches.csv')\n",
    "display(heightFinger)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9c1eaba",
   "metadata": {},
   "source": [
    "The height data are in inches and are rounded to the nearest inch. \n",
    "\n",
    "Finger lengths are in inches and rounded to the nearest 1/8 of an inch.\n",
    "\n",
    "### Plot the data\n",
    "\n",
    "Let's plot the data. A scatterplot is usually a good choice for bivariate data such as these."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "7dd85335",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Height', ylabel='FingerLength'>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=heightFinger, x='Height', y='FingerLength')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a41e12d",
   "metadata": {},
   "source": [
    "Hm, that looks strange. Because data were rounded to the nearest inch or 1/8th inch, the data points appear to be on a regular grid. \n",
    "\n",
    "One consequence of this is that some datapoints will fall exactly on top of each other! You can see this if I make the data points a bit transparent (by using the alpha parameter) so that the dots appear darker where several fall on top of eachother"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "47bac5dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Height', ylabel='FingerLength'>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=heightFinger, x='Height', y='FingerLength', alpha=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed73b14d",
   "metadata": {},
   "source": [
    "Alternatively, we can visualise the data using another type of plot such as a 2D KDE plot - this is a good solution if the dataset is very large"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "f5268cf5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Height', ylabel='FingerLength'>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(data=heightFinger, x='Height', y='FingerLength')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad8cde74",
   "metadata": {},
   "source": [
    "## Covariance\n",
    "\n",
    "We can see there is probably some covariance between height and middle finger length, as tall people tend to have long fingers.\n",
    "\n",
    "We can calculate the covariance using a built in function from <tt>pandas</tt>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "e6ddcfdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>FingerLength</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Height</th>\n",
       "      <td>6.542118</td>\n",
       "      <td>0.359824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FingerLength</th>\n",
       "      <td>0.359824</td>\n",
       "      <td>0.046754</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Height  FingerLength\n",
       "Height        6.542118      0.359824\n",
       "FingerLength  0.359824      0.046754"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heightFinger.cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d662c0a",
   "metadata": {},
   "source": [
    "This calculates the <b>covariance matrix</b>\n",
    "\n",
    "<ul>\n",
    "<li>The entry for height vs height (top left) is simply the variance of the distribution of heights\n",
    "<li>The entry for FingerLength vs FingerLength (bottom right) is simply the variance of the distribution of finger lengths\n",
    "<li>The (identical) entries for height vs finger length are the covariance between the two. \n",
    "</ul>\n",
    "\n",
    "You can check that the Height-Height and FingerLength-FingerLength entries are indeed the relevant variances, using the function <tt>std</tt> to obtain the standard deviation $s$ - the variance is then $s^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "11949307",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.542118372790553"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heightFinger['Height'].std()**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cc50118",
   "metadata": {},
   "source": [
    "### Use the formula\n",
    "\n",
    "Just for our own understanding, let's calculate the covariance ourselves using the formula:\n",
    "\n",
    "$$ s_{xy} = \\sum{\\frac{(x_i - \\bar{x})(y_i - \\bar{y})}{n-1}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "f23a462a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean height = 65.473 inches\n",
      "mean finger length = 4.547666666666666 mm\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>FingerLength</th>\n",
       "      <th>devHeight</th>\n",
       "      <th>devFinger</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>56</td>\n",
       "      <td>3.875</td>\n",
       "      <td>-9.473</td>\n",
       "      <td>-0.672667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>57</td>\n",
       "      <td>4.000</td>\n",
       "      <td>-8.473</td>\n",
       "      <td>-0.547667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>58</td>\n",
       "      <td>3.875</td>\n",
       "      <td>-7.473</td>\n",
       "      <td>-0.672667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>58</td>\n",
       "      <td>4.000</td>\n",
       "      <td>-7.473</td>\n",
       "      <td>-0.547667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>58</td>\n",
       "      <td>4.000</td>\n",
       "      <td>-7.473</td>\n",
       "      <td>-0.547667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2995</th>\n",
       "      <td>74</td>\n",
       "      <td>4.875</td>\n",
       "      <td>8.527</td>\n",
       "      <td>0.327333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2996</th>\n",
       "      <td>74</td>\n",
       "      <td>5.000</td>\n",
       "      <td>8.527</td>\n",
       "      <td>0.452333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2997</th>\n",
       "      <td>74</td>\n",
       "      <td>5.000</td>\n",
       "      <td>8.527</td>\n",
       "      <td>0.452333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2998</th>\n",
       "      <td>74</td>\n",
       "      <td>5.250</td>\n",
       "      <td>8.527</td>\n",
       "      <td>0.702333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2999</th>\n",
       "      <td>77</td>\n",
       "      <td>4.375</td>\n",
       "      <td>11.527</td>\n",
       "      <td>-0.172667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Height  FingerLength  devHeight  devFinger\n",
       "0         56         3.875     -9.473  -0.672667\n",
       "1         57         4.000     -8.473  -0.547667\n",
       "2         58         3.875     -7.473  -0.672667\n",
       "3         58         4.000     -7.473  -0.547667\n",
       "4         58         4.000     -7.473  -0.547667\n",
       "...      ...           ...        ...        ...\n",
       "2995      74         4.875      8.527   0.327333\n",
       "2996      74         5.000      8.527   0.452333\n",
       "2997      74         5.000      8.527   0.452333\n",
       "2998      74         5.250      8.527   0.702333\n",
       "2999      77         4.375     11.527  -0.172667\n",
       "\n",
       "[3000 rows x 4 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Work out the mean in x and y\n",
    "mx = heightFinger['Height'].mean()\n",
    "my = heightFinger['FingerLength'].mean()\n",
    "\n",
    "print('mean height = ' + str(mx) + ' inches')\n",
    "print('mean finger length = ' + str(my) + ' mm')\n",
    "\n",
    "# Make new columns in the data frame for the deviations in x and y\n",
    "heightFinger['devHeight'] = heightFinger['Height']-mx\n",
    "heightFinger['devFinger'] = heightFinger['FingerLength']-my\n",
    "\n",
    "display(heightFinger)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc53a275",
   "metadata": {},
   "source": [
    "Check you understand what the deviations are. For example:\n",
    "<ul>\n",
    "    <li>the person in row 1 has height 57 inches, which is below the mean of 65.473 inches, so his deviation in height is -8.473\n",
    "    <li>the person in row 2999 has height 77 inches, which is above the mean of 65.473 inches, so his deviation in height is 11.527\n",
    "</ul>\n",
    "\n",
    "Now we can apply the equation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "5952136d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "covariance = 0.3598236078692932\n"
     ]
    }
   ],
   "source": [
    "# get n\n",
    "n = len(heightFinger)\n",
    "\n",
    "# Equation for covariance\n",
    "s_xy =  sum(heightFinger['devHeight']*heightFinger['devFinger'])/(n-1)\n",
    "print('covariance = ' + str(s_xy))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece7408a",
   "metadata": {},
   "source": [
    "Ta-daa! This should match what you got with the built in function <tt>df.covariance</tt> above"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f5c7822",
   "metadata": {},
   "source": [
    "## Correlation\n",
    "\n",
    "Correlation is a scaled or normalized form of covariance, that does not change if the units of the variables $x$ and $y$ changes\n",
    "\n",
    "We can calulate the correlation using a built in function of <tt>pandas</tt>:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "c467ffa6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>FingerLength</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Height</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.650611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FingerLength</th>\n",
       "      <td>0.650611</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Height  FingerLength\n",
       "Height        1.000000      0.650611\n",
       "FingerLength  0.650611      1.000000"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reload the data to get rid of the extra columns we added just now\n",
    "heightFinger = pandas.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/data/HeightFingerInches.csv')\n",
    "heightFinger.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a36e5635",
   "metadata": {},
   "source": [
    "The correlation between height and finger length is $r$=0.65 (We usually use the symbol $r$ for correlation)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7453cb05",
   "metadata": {},
   "source": [
    "Once again we can check that this matches what we should get with the formula:\n",
    "\n",
    "$$ r = \\frac{s_{xy}}{s_x s_y} $$\n",
    "\n",
    "where $s_{xy}$ is the covariance as above:\n",
    "    \n",
    "$$ s_{xy} = \\sum{\\frac{(x_i - \\bar{x})(y_i - \\bar{y})}{n-1}} $$\n",
    "\n",
    "... and $s_x$, $s_y$ are the standard deviations of the two datasets (height and finger length)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "0d47f0be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The correlation is 0.6506112650191417\n"
     ]
    }
   ],
   "source": [
    "s_x = heightFinger['Height'].std()\n",
    "s_y = heightFinger['FingerLength'].std()\n",
    "# s_xy, the covariance, was calculated above\n",
    "\n",
    "r = s_xy/(s_x * s_y)\n",
    "print('The correlation is ' + str(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02c71de3",
   "metadata": {},
   "source": [
    "Ta-daa, hopefully this matches the output of the built in function above."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "347bba3e",
   "metadata": {},
   "source": [
    "# Corr vs Cov\n",
    "\n",
    "When should you use the correlation, when would you use the covariance?\n",
    "\n",
    "### Changing units\n",
    "\n",
    "If we change the units of one of our variables, this changes the covariance but not the correlation.\n",
    "\n",
    "Let's convert the finger length data to cm using the conversion 1 inch = 2.54 cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "91f0e297",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
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       "      <td>9.8425</td>\n",
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       "      <th>1</th>\n",
       "      <td>57</td>\n",
       "      <td>10.1600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>58</td>\n",
       "      <td>9.8425</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>58</td>\n",
       "      <td>10.1600</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>58</td>\n",
       "      <td>10.1600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2995</th>\n",
       "      <td>74</td>\n",
       "      <td>12.3825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2996</th>\n",
       "      <td>74</td>\n",
       "      <td>12.7000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2997</th>\n",
       "      <td>74</td>\n",
       "      <td>12.7000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2998</th>\n",
       "      <td>74</td>\n",
       "      <td>13.3350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2999</th>\n",
       "      <td>77</td>\n",
       "      <td>11.1125</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Height  FingerLength\n",
       "0         56        9.8425\n",
       "1         57       10.1600\n",
       "2         58        9.8425\n",
       "3         58       10.1600\n",
       "4         58       10.1600\n",
       "...      ...           ...\n",
       "2995      74       12.3825\n",
       "2996      74       12.7000\n",
       "2997      74       12.7000\n",
       "2998      74       13.3350\n",
       "2999      77       11.1125\n",
       "\n",
       "[3000 rows x 2 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "heightFinger['FingerLength'] = heightFinger['FingerLength']*2.54 \n",
    "display(heightFinger)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93542c43",
   "metadata": {},
   "source": [
    "Now we recalculate the covariance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "d06abc62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>FingerLength</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Height</th>\n",
       "      <td>6.542118</td>\n",
       "      <td>0.913952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FingerLength</th>\n",
       "      <td>0.913952</td>\n",
       "      <td>0.301637</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Height  FingerLength\n",
       "Height        6.542118      0.913952\n",
       "FingerLength  0.913952      0.301637"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heightFinger.cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c2d8379",
   "metadata": {},
   "source": [
    "... and the correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "9312743f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Height</th>\n",
       "      <th>FingerLength</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Height</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.650611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FingerLength</th>\n",
       "      <td>0.650611</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Height  FingerLength\n",
       "Height        1.000000      0.650611\n",
       "FingerLength  0.650611      1.000000"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heightFinger.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c62a190a",
   "metadata": {},
   "source": [
    "We can see that the covariance changes when we change the units, but correlation doesn't change. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01f4ad00",
   "metadata": {},
   "source": [
    "### Interpreting covariance - the slope\n",
    "\n",
    "You may be asking, why would we ever use covariance?\n",
    "\n",
    "The answer is that the covariance tells us something about how much $y$ increases with $x$ and vice versa.\n",
    "\n",
    "If we apply the equation\n",
    "\n",
    "$$ b = s_{xy}/s^2_{x} $$\n",
    "\n",
    "we get a coefficient $b$ which tells us how many units $y$ increases, for one unit increase in $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "0b145b8f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.055001084872729034\n"
     ]
    }
   ],
   "source": [
    "b = s_xy/(s_x**2)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc004651",
   "metadata": {},
   "source": [
    "For every extra 1 inch of height, finger length increases by 0.055 inches.\n",
    "\n",
    "This is actually a regression coefficient (there will be much more detail on this later in the course) and we can see if we plot a regression line that b is its slope:\n",
    "\n",
    "<img src= \"https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/images/regFingerHeight.png\" width=\"70%\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1f72ae2",
   "metadata": {},
   "source": [
    "Conversely:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "b349978c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.6961212519589495\n"
     ]
    }
   ],
   "source": [
    "b = s_xy/(s_y**2)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b947f8dc",
   "metadata": {},
   "source": [
    "for every extra inch in finger length, height increases by 7.70 inches.\n",
    "\n",
    "<img src= \"https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/images/regHeightFinger.png\" width=\"70%\"  />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bc1500e",
   "metadata": {},
   "source": [
    "Now, if we were to convert our finger measurements to cm instead of inches, the coviariance would change, and so would our slop - because a one cm increase in finger length is assocated with a smaller increase in height, than a 1 inch increase in finger length would be.\n",
    "\n",
    "There will be a whole block on regression later in the course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a280f64",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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