{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def show_scatter_plot(title, \n",
    "                      x_label, y_label, \n",
    "                      x_values, y_values):\n",
    "    \"\"\"\n",
    "    @param title the chart title.\n",
    "    @param x_label the x-axis label.\n",
    "    @param y_label the y-axis label.\n",
    "    @param x_values the independent x values to plot.\n",
    "    @param y_values the dependent y values to plot.\n",
    "    \"\"\"\n",
    "    plt.scatter(x_values, y_values)\n",
    "    plt.title(title)\n",
    "    plt.ylabel(x_label)\n",
    "    plt.xlabel(y_label)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "\n",
    "def calculate_r(x_values, y_values):\n",
    "    \"\"\"\n",
    "    Calculate the correlation coefficient.\n",
    "    @param x_values the x values.\n",
    "    @param y_values the y values.\n",
    "    @return the correlation coefficient.\n",
    "    \"\"\"\n",
    "    x = np.array(x_values)\n",
    "    y = np.array(y_values)\n",
    "    \n",
    "    n = len(x)\n",
    "    sum_x  = np.sum(x)\n",
    "    sum_y  = np.sum(y)\n",
    "    sum_xx = np.sum(x*x)\n",
    "    sum_yy = np.sum(y*y)\n",
    "    sum_xy = np.sum(x*y)\n",
    "    \n",
    "    numerator = sum_xy - (sum_x*sum_y)/n\n",
    "    denominator = math.sqrt(sum_xx - (sum_x*sum_x)/n)*math.sqrt(sum_yy - (sum_y*sum_y)/n)\n",
    "    \n",
    "    r = numerator/denominator\n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = [ 11,  13,  18,  30,  36,  40,  50,  58,  67,  82,  91, 102]\n",
    "ys = [1.1, 0.5, 2.4, 1.2, 2.1, 1.2, 4.0, 2.3, 1.7, 3.7, 3.0, 3.9]\n",
    "\n",
    "show_scatter_plot('Scatter Plot', 'Dependent variable', \n",
    "                  'Independent variable', xs, ys )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = calculate_r(xs, ys)\n",
    "\n",
    "print(f'r = {r:.3f}')"
   ]
  }
 ],
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