{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def calculate_ss(x_values, y_values):\n",
    "    \"\"\"\n",
    "    Calculate the residual and total sums of squares.\n",
    "    @param x_values the independent x values.\n",
    "    @param y_values the dependent y values.\n",
    "    @return a list of the residual and total sums of squares.\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",
    "    mean_x = np.mean(x)\n",
    "    mean_y = np.mean(y)\n",
    "    \n",
    "    numerator = sum_xy - (sum_x*sum_y)/n\n",
    "    denominator = sum_xx - ((sum_x*sum_x)/n)\n",
    "    \n",
    "    m = numerator/denominator\n",
    "    b = mean_y - m*mean_x\n",
    "    \n",
    "    ss_residual = sum_yy - b*sum_y - m*sum_xy\n",
    "    ss_total    = sum_yy - (sum_y*sum_y)/n\n",
    "    \n",
    "    return ss_residual, ss_total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_r2(ss_residual, ss_total):\n",
    "    \"\"\"\n",
    "    Calculate the coefficient of determination.\n",
    "    @param ss_residual the residual sum of squares.\n",
    "    @param ss_total the total sum of squares.\n",
    "    @return the coefficient of determination.\n",
    "    \"\"\"\n",
    "    cofd = 1 - ss_residual/ss_total\n",
    "    return cofd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = [35.43, 36.10, 35.74, 35.30, 35.40, 35.91, 35.48, 36.28]\n",
    "ys = [30.0,  24.2,  25.4,  29.8,  30.7,  24.0,  28.5,  22.7]\n",
    "\n",
    "show_scatter_plot('Scatter Plot', 'Dependent variable', \n",
    "                  'Independent variable', xs, ys )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ss_residual =  6.11253\n",
      "ss_total    = 70.60875\n"
     ]
    }
   ],
   "source": [
    "ss_residual, ss_total = calculate_ss(xs, ys)\n",
    "\n",
    "print(f'ss_residual = {ss_residual:8.5f}')\n",
    "print(f'ss_total    = {ss_total:8.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coefficient of determination = 0.913\n"
     ]
    }
   ],
   "source": [
    "r2 = calculate_r2(ss_residual, ss_total)\n",
    "\n",
    "print(f'coefficient of determination = {r2:.3f}')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}