{
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   "source": [
    "import numpy as np\n",
    "\n",
    "def calculate_slope_intercept(x_values, y_values):\n",
    "    \"\"\"\n",
    "    Calculate the slope and intercept of a regression line.\n",
    "    @param x_values the independent x values.\n",
    "    @param y_values the dependent y values.\n",
    "    @return a list of the slope and y-intercept of the line.\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_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",
    "    return m, b  # slope and intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def show_least_squares_line(title, 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",
    "    # First show the scatter plot.\n",
    "    plt.scatter(x_values, y_values)\n",
    "    \n",
    "    # Now show the least squares line.\n",
    "    m, b = calculate_slope_intercept(x_values, y_values)\n",
    "    reg_line = [m*x + b for x in x_values]  # regression line\n",
    "    plt.plot(xs, reg_line, color='red')\n",
    "\n",
    "    plt.title(f'{title}, m = {m:.2f}, b = {b:.2f}')\n",
    "    plt.ylabel(x_label)\n",
    "    plt.xlabel(y_label)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = [32, 37, 38, 40, 45, 50, 50, 54, 54, 55, \n",
    "      61, 63, 63, 64, 64, 70, 70, 75, 76]\n",
    "ys = [18.3, 18.9, 19.0, 20.9, 21.4, 20.5, 20.1, 20.1, 20.8, 20.5, \n",
    "      19.9, 20.5, 20.6, 22.1, 21.9, 21.2, 20.5, 22.7, 22.8]\n",
    "\n",
    "show_least_squares_line('Linear Regression Line', 'Dependent variable', \n",
    "                        'Independent variable', xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = range(2, 26)\n",
    "ys = [10,12,20,22,21,25,30,21,32,34,35,30,50,45,55,60,66,64,67,72,74,80,79,84]\n",
    "\n",
    "show_least_squares_line('Linear Regression Line', 'Dependent variable', \n",
    "                        'Independent variable', xs, ys)"
   ]
  }
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