{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Covariance and Correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Covariance measures how two variables vary in tandem from their means.\n",
    "\n",
    "For example, let's say we work for an e-commerce company, and they are interested in finding a correlation between page speed (how fast each web page renders for a customer) and how much a customer spends.\n",
    "\n",
    "numpy offers covariance methods, but we'll do it the \"hard way\" to show what happens under the hood. Basically we treat each variable as a vector of deviations from the mean, and compute the \"dot product\" of both vectors. Geometrically this can be thought of as the angle between the two vectors in a high-dimensional space, but you can just think of it as a measure of similarity between the two variables.\n",
    "\n",
    "First, let's just make page speed and purchase amount totally random and independent of each other; a very small covariance will result as there is no real correlation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "from pylab import *\n",
    "\n",
    "def de_mean(x):\n",
    "    xmean = mean(x)\n",
    "    return [xi - xmean for xi in x]\n",
    "\n",
    "def covariance(x, y):\n",
    "    n = len(x)\n",
    "    return dot(de_mean(x), de_mean(y)) / (n-1)\n",
    "\n",
    "pageSpeeds = np.random.normal(3.0, 1.0, 1000)\n",
    "purchaseAmount = np.random.normal(50.0, 10.0, 1000)\n",
    "\n",
    "scatter(pageSpeeds, purchaseAmount)\n",
    "\n",
    "covariance (pageSpeeds, purchaseAmount)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll make our fabricated purchase amounts an actual function of page speed, making a very real correlation. The negative value indicates an inverse relationship; pages that render in less time result in more money spent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "purchaseAmount = np.random.normal(50.0, 10.0, 1000) / pageSpeeds\n",
    "\n",
    "scatter(pageSpeeds, purchaseAmount)\n",
    "\n",
    "covariance (pageSpeeds, purchaseAmount)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But, what does this value mean? Covariance is sensitive to the units used in the variables, which makes it difficult to interpret. Correlation normalizes everything by their standard deviations, giving you an easier to understand value that ranges from -1 (for a perfect inverse correlation) to 1 (for a perfect positive correlation):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.01964600590705939"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def correlation(x, y):\n",
    "    stddevx = x.std()\n",
    "    stddevy = y.std()\n",
    "    return covariance(x,y) / stddevx / stddevy  #In real life you'd check for divide by zero here\n",
    "\n",
    "correlation(pageSpeeds, purchaseAmount)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "numpy can do all this for you with numpy.corrcoef. It returns a matrix of the correlation coefficients between every combination of the arrays passed in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.01962636],\n",
       "       [-0.01962636,  1.        ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(pageSpeeds, purchaseAmount)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(It doesn't match exactly just due to the math precision available on a computer.)\n",
    "\n",
    "We can force a perfect correlation by fabricating a totally linear relationship (again, it's not exactly -1 just due to precision errors, but it's close enough to tell us there's a really good correlation here):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "purchaseAmount = 100 - pageSpeeds * 3\n",
    "\n",
    "scatter(pageSpeeds, purchaseAmount)\n",
    "\n",
    "correlation (pageSpeeds, purchaseAmount)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember, correlation does not imply causality!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "numpy also has a numpy.cov function that can compute Covariance for you. Try using it for the pageSpeeds and purchaseAmounts data above. Interpret its results, and compare it to the results from our own covariance function above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:base] *",
   "language": "python",
   "name": "conda-base-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}