{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a3bef3f1",
   "metadata": {},
   "source": [
    "---\n",
    "title: \"Correlation, Bivariate, and Regression Analysis\"\n",
    "date: \"12/18/2024\"\n",
    "author: Rafiq Islam\n",
    "categories: [Data Science, Machine Learning, Artificial Intelligence, Statistics]\n",
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    "image: corr.png\n",
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    "---   \n",
    "\n",
    "## Introduction  \n",
    "\n",
    "<p style=\"text-align: justify\">\n",
    "Correlation and regression are two fundamental concepts in statistics, often used to study relationships between variables. While correlation measures the strength and direction of a linear relationship between two variables, regression goes further by modeling the relationship to predict or explain one variable based on another. This blog explores the mathematical underpinnings of both concepts, illustrating their significance in data analysis.</p>\n",
    "\n",
    "\n",
    "## Correlation Analysis\n",
    "\n",
    "To better explain, we will use the following hypothetical stock data of 10 companies with stock price and their corresponding proportion in the portfolio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ab222889",
   "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>Stock</th>\n",
       "      <th>Apple</th>\n",
       "      <th>Citi</th>\n",
       "      <th>MS</th>\n",
       "      <th>WF</th>\n",
       "      <th>GS</th>\n",
       "      <th>Google</th>\n",
       "      <th>Amazon</th>\n",
       "      <th>Tesla</th>\n",
       "      <th>Toyota</th>\n",
       "      <th>SPY</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>StockPrice</th>\n",
       "      <td>2.11</td>\n",
       "      <td>2.42</td>\n",
       "      <td>2.52</td>\n",
       "      <td>3.21</td>\n",
       "      <td>3.62</td>\n",
       "      <td>3.86</td>\n",
       "      <td>4.13</td>\n",
       "      <td>4.27</td>\n",
       "      <td>4.51</td>\n",
       "      <td>5.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Portfolio</th>\n",
       "      <td>2.12</td>\n",
       "      <td>2.16</td>\n",
       "      <td>2.51</td>\n",
       "      <td>2.65</td>\n",
       "      <td>3.62</td>\n",
       "      <td>3.15</td>\n",
       "      <td>4.32</td>\n",
       "      <td>3.31</td>\n",
       "      <td>4.18</td>\n",
       "      <td>4.45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Stock       Apple  Citi    MS    WF    GS  Google  Amazon  Tesla  Toyota   SPY\n",
       "StockPrice   2.11  2.42  2.52  3.21  3.62    3.86    4.13   4.27    4.51  5.01\n",
       "Portfolio    2.12  2.16  2.51  2.65  3.62    3.15    4.32   3.31    4.18  4.45"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame({\n",
    "    'Stock': ['Apple', 'Citi', 'MS', 'WF', 'GS', 'Google', 'Amazon', 'Tesla', 'Toyota', 'SPY'],\n",
    "    'StockPrice': [2.11, 2.42, 2.52, 3.21, 3.62, 3.86, 4.13, 4.27, 4.51, 5.01], \n",
    "    'Portfolio': [2.12, 2.16, 2.51, 2.65, 3.62, 3.15, 4.32, 3.31, 4.18, 4.45]\n",
    "})\n",
    "\n",
    "df.set_index('Stock', inplace=True)\n",
    "\n",
    "df.T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9f7f7ca",
   "metadata": {},
   "source": [
    "The scatterplot of the data looks like this  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6c7129e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1650x1050 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "#| fig-align: center\n",
    "from mywebstyle import plot_style\n",
    "plot_style('#f4f4f4')\n",
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(df.StockPrice, df.Portfolio, color='red')\n",
    "plt.xlabel('Stock Price')\n",
    "plt.ylabel('Portfolio')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd8a87ed",
   "metadata": {},
   "source": [
    "We can see from the graph that there appears to be a linear relationship between the $x$ and $y$ values in this case. To find the relationship mathematically we define the followings  \n",
    "\n",
    "\\begin{align*}\n",
    "S_{xx}& = \\sum (x_i-\\bar{x})^2 = \\sum (x_i^2-2x_i\\bar{x}+\\bar{x}^2)\\\\\n",
    "& = \\sum x_i^2 - 2\\bar{x}\\sum x_i + \\sum \\bar{x}^2= \\sum x_i^2 - 2\\bar{x} n \\bar{x} + n \\bar{x}^2 = \\sum x_i ^2 - n \\bar{x}^2\n",
    "\\end{align*}  \n",
    "\n",
    "Similarly, \n",
    "\\begin{align*}\n",
    "S_{yy}& = \\sum (y_i-\\bar{y})^2=\\sum y_i ^2 - n \\bar{y}^2\\\\\n",
    "S_{xy} & = \\sum (x_i-\\bar{x})^2 \\sum (y_i-\\bar{y})^2 = \\sum x_iy_i -n \\bar{xy}\n",
    "\\end{align*}  \n",
    "\n",
    "The sample correlation coefficient $r$ is then given as \n",
    "\n",
    "$$\n",
    "r = \\frac{S_{xy}}{\\sqrt{S_{xx}S_{yy}}} = \\frac{\\sum x_i ^2 - n \\bar{x}^2}{\\sqrt{\\left(\\sum x_i ^2 - n \\bar{x}^2\\right)\\left(\\sum y_i ^2 - n \\bar{y}^2\\right)}}\n",
    "$$  \n",
    "\n",
    "You may have seen a different formula to calculate this quantity which often looks a bit different \n",
    "\n",
    "$$\n",
    "\\rho = Corr(X,Y)=\\frac{Cov(X,Y)}{\\sqrt{var(X)var(Y)}}\n",
    "$$  \n",
    "The sample correlation coefficient, $r$, is an estimator of the population correlation coefficient, $\\rho$, in the same way as $\\bar{X}$ is an estimator of $\\mu$ or $S^2$ is an estimator of $\\sigma^2$ . Now the question is what does this $r$ values mean?  \n",
    "\n",
    "| Value | Meaning |  \n",
    "|-------| ---------------- |  \n",
    "| $r=1$ | The two variables move together in the same direction in a perfect linear relationship. |  \n",
    "| $0 < r < 1$ | The two variables tend to move together in the same direction but there is NOT a direct relationship. |  \n",
    "| $r= 0$ | The two variables can move in either direction and show no linear relationship. |  \n",
    "| $-1 < r < 0$ | The two variables tend to move together in opposite directions but there is not a direct relationship. |  \n",
    "| $r =-1$ | The two variables move together in opposite directions in a perfect linear relationship. |  \n",
    "\n",
    "\n",
    "Let's calculate the correlation of our stock data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9a60c49f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum x: 35.66\n",
      "Sum y: 32.47\n",
      "Sₓₓ: 8.53\n",
      "Sᵧᵧ: 6.97\n",
      "Sₓᵧ: 7.13\n",
      " \n",
      "r : 0.92\n"
     ]
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "import math\n",
    "x = df.StockPrice.values\n",
    "y = df.Portfolio.values\n",
    "\n",
    "n = len(x)\n",
    "\n",
    "x_sum, y_sum =0,0\n",
    "s_xx, s_yy, s_xy = 0,0,0\n",
    "for i in range(n):\n",
    "    x_sum += x[i]\n",
    "    s_xx += x[i]**2\n",
    "    y_sum += y[i]\n",
    "    s_yy += y[i]**2\n",
    "    s_xy += x[i]*y[i]    \n",
    "\n",
    "s_xx = s_xx - (x_sum)**2/n\n",
    "s_yy = s_yy - (y_sum)**2/n\n",
    "s_xy = s_xy - (x_sum * y_sum)/n\n",
    "\n",
    "r = s_xy/math.sqrt(s_xx * s_yy)\n",
    "\n",
    "# Print with formatted labels\n",
    "print(f\"Sum x: {x_sum:.2f}\")\n",
    "print(f\"Sum y: {y_sum:.2f}\")\n",
    "print(f\"Sₓₓ: {s_xx:.2f}\")\n",
    "print(f\"Sᵧᵧ: {s_yy:.2f}\")\n",
    "print(f\"Sₓᵧ: {s_xy:.2f}\")\n",
    "print(' ')\n",
    "print(f\"r : {r:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5b1f307",
   "metadata": {},
   "source": [
    "## Bivariate Analysis  \n",
    "\n",
    "The joint probability density function for $X$ and $Y$ in the bivariate normal distribution is given by:\n",
    "\n",
    "$$\n",
    "f_{X,Y}(x, y) = \\frac{1}{2\\pi \\sigma_X \\sigma_Y \\sqrt{1-\\rho^2}} \n",
    "\\exp\\left( -\\frac{1}{2(1-\\rho^2)} \\left[ \\frac{(x-\\mu_X)^2}{\\sigma_X^2} - 2\\rho\\frac{(x-\\mu_X)(y-\\mu_Y)}{\\sigma_X \\sigma_Y} + \\frac{(y-\\mu_Y)^2}{\\sigma_Y^2} \\right] \\right)\n",
    "$$\n",
    "\n",
    "<p style=\"text-align: justify\">\n",
    "When $|\\rho| = 1$, the denominator $\\sqrt{1-\\rho^2}$ in the PDF becomes zero, which might appear problematic. However, what happens in this case is that the joint distribution degenerates into a **one-dimensional structure** (a line) rather than being a two-dimensional probability density.</p>\n",
    "\n",
    "To see why, consider the quadratic term inside the exponential:\n",
    "\n",
    "$$\n",
    "Q = \\frac{(x-\\mu_X)^2}{\\sigma_X^2} - 2\\rho \\frac{(x-\\mu_X)(y-\\mu_Y)}{\\sigma_X \\sigma_Y} + \\frac{(y-\\mu_Y)^2}{\\sigma_Y^2}\n",
    "$$\n",
    "\n",
    "When $|\\rho| = 1$, this quadratic expression simplifies, as shown next.\n",
    "\n",
    "Start with the simplified $Q$ when $|\\rho| = 1$:\n",
    "\n",
    "\\begin{align*}\n",
    "Q &= \\left( \\frac{x-\\mu_X}{\\sigma_X} \\right)^2 - 2\\rho \\left( \\frac{x-\\mu_X}{\\sigma_X} \\cdot \\frac{y-\\mu_Y}{\\sigma_Y} \\right) + \\left( \\frac{y-\\mu_Y}{\\sigma_Y} \\right)^2\\\\\n",
    "&=\\left( \\frac{x-\\mu_X}{\\sigma_X} - \\rho \\frac{y-\\mu_Y}{\\sigma_Y} \\right)^2\n",
    "\\end{align*}\n",
    "\n",
    "This is a **perfect square** because the \"cross term\" cancels out all independent variability of $X$ and $Y$ when $|\\rho| = 1$.\n",
    "\n",
    "For the quadratic term $Q$ to have any non-zero probability density (since it appears in the exponent of the PDF), it must be equal to zero:\n",
    "$$\n",
    "\\frac{x-\\mu_X}{\\sigma_X} - \\rho \\frac{y-\\mu_Y}{\\sigma_Y} = 0\n",
    "$$\n",
    "\n",
    "Rearranging this equation:\n",
    "$$\n",
    "\\frac{y-\\mu_Y}{\\sigma_Y} = \\rho \\frac{x-\\mu_X}{\\sigma_X}\n",
    "$$\n",
    "\n",
    "Multiply through by $\\sigma_Y$:\n",
    "$$\n",
    "y - \\mu_Y = \\rho \\frac{\\sigma_Y}{\\sigma_X} (x - \\mu_X)\n",
    "$$\n",
    "\n",
    "Thus:\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbb{E}(Y| X=x)&= \\mu_Y + \\rho\\frac{\\sigma_Y}{\\sigma_X}(x-\\mu_X)\\\\\n",
    "& = \\mu_Y + \\rho \\frac{\\sigma_Y}{\\sigma_X} (x - \\mu_X)\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "This is the equation of a straight line in the $(X, Y)$-plane. The slope of the line is $\\rho \\frac{\\sigma_Y}{\\sigma_X}$, and the line passes through the point $(\\mu_X, \\mu_Y)$. When $|\\rho| = 1$, all the joint probability mass collapses onto this line, meaning $X$ and $Y$ are perfectly linearly dependent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "194bf25c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
      "text/plain": [
       "<Figure size 2400x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "import numpy as np\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# Define the bivariate normal PDF\n",
    "def bivariate_normal_pdf(x, y, mu_x, mu_y, sigma_x, sigma_y, rho):\n",
    "    z = (\n",
    "        ((x - mu_x) ** 2) / sigma_x**2\n",
    "        - 2 * rho * (x - mu_x) * (y - mu_y) / (sigma_x * sigma_y)\n",
    "        + ((y - mu_y) ** 2) / sigma_y**2\n",
    "    )\n",
    "    denominator = 2 * np.pi * sigma_x * sigma_y * np.sqrt(1 - rho**2)\n",
    "    return np.exp(-z / (2 * (1 - rho**2))) / denominator\n",
    "\n",
    "# Parameters\n",
    "x = np.linspace(-3, 3, 100)\n",
    "y = np.linspace(-3, 3, 100)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "# Function to plot the bivariate normal distribution and a line for rho = 1 or -1\n",
    "def plot_bivariate_and_line_side_by_side(rho1, rho2):\n",
    "    fig = plt.figure(figsize=(8, 4))\n",
    "\n",
    "    # Plot for the first rho\n",
    "    ax1 = fig.add_subplot(121, projection='3d')\n",
    "    if abs(rho1) == 1:\n",
    "        # Degenerate case: Straight line\n",
    "        line_x = np.linspace(-3, 3, 100)\n",
    "        line_y = line_x  # Since rho = 1 implies y = x (perfect correlation)\n",
    "        ax1.plot(line_x, line_y, np.zeros_like(line_x), label=f'Degenerate Line (ρ = {rho1})', color='red')\n",
    "    else:\n",
    "        # General bivariate normal distribution\n",
    "        Z = bivariate_normal_pdf(X, Y, 0, 0, 1, 1, rho1)\n",
    "        ax1.plot_surface(X, Y, Z, cmap='viridis', edgecolor='none', alpha=0.8)\n",
    "\n",
    "    ax1.set_title(f'Bivariate Normal (ρ = {rho1:.2f})')\n",
    "    ax1.set_xlabel('X')\n",
    "    ax1.set_ylabel('Y')\n",
    "    ax1.set_zlabel('PDF')\n",
    "\n",
    "    # Plot for the second rho\n",
    "    ax2 = fig.add_subplot(122, projection='3d')\n",
    "    if abs(rho2) == 1:\n",
    "        # Degenerate case: Straight line\n",
    "        line_x = np.linspace(-3, 3, 100)\n",
    "        line_y = line_x  # Since rho = 1 implies y = x (perfect correlation)\n",
    "        ax2.plot(line_x, line_y, np.zeros_like(line_x), label=f'Degenerate Line (ρ = {rho2})', color='red')\n",
    "    else:\n",
    "        # General bivariate normal distribution\n",
    "        Z = bivariate_normal_pdf(X, Y, 0, 0, 1, 1, rho2)\n",
    "        ax2.plot_surface(X, Y, Z, cmap='viridis', edgecolor='none', alpha=0.8)\n",
    "\n",
    "    ax2.set_title(f'Bivariate Normal (ρ = {rho2:.2f})')\n",
    "    ax2.set_xlabel('X')\n",
    "    ax2.set_ylabel('Y')\n",
    "    ax2.set_zlabel('PDF')\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "# Plot examples side by side\n",
    "plot_bivariate_and_line_side_by_side(0.5, 1)  # Example with rho = 0.5 and rho = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23767229",
   "metadata": {},
   "source": [
    "### $t-$Statistic  \n",
    "\n",
    "Under the null hypothesis, where $H_0: \\rho =0, \\frac{r\\sqrt{n-2}}{\\sqrt{1-r^2}}$ has a $t-$ distribution \n",
    "with $\\nu=n-2$ degree of freedom.\n",
    "\n",
    "\n",
    "### Fisher's Transformation of $r$  \n",
    "\n",
    "If $W = \\frac{1}{2}\\ln{\\frac{1+r}{1-r}}=\\tanh^{-1}r$, then $W$ has approximately a normal distribution with \n",
    "mean $\\frac{1}{2}\\ln{\\frac{1+\\rho}{1-\\rho}}$ and standard deviation $\\frac{1}{\\sqrt{n-3}}$.  \n",
    "\n",
    "For our stock data:  \n",
    "\n",
    "**Null Hypothesis $H_0$:** There is no association between stock prices and the portfolio values, i.e., $\\rho =0$  \n",
    "**Alternative Hypothesis $H_1$:** There is some association between the stock price and portfolio values, i.e., $\\rho > 0$  \n",
    "\n",
    "If $H_0$ is true, then the test statistic \n",
    "$\\frac{r\\sqrt{n-2}}{\\sqrt{1-r^2}}=\\frac{0.92\\sqrt{8}}{\\sqrt{1-0.92^2}}=6.64$ has a $t_8$ distribution. The\n",
    "observed value $6.64$ is much greater than the critical value of $t_8$ at $0.5\\%$ level which is $3.36$.  \n",
    "\n",
    "So, we reject the null hypothesis $H_0$ at the $0.5\\%$ level and conclude that there is a very strong \n",
    "evidence that $\\rho>0$.  \n",
    "\n",
    "Alternatively, if we want to use the Fisher's test:  \n",
    "\n",
    "If $H_0$ is true, then the test statistic $Z_r=\\tanh^{-1}r=\\tanh^{-1}(0.92)$ has a $N\\left(0,\\frac{1}{7}\\right)$\n",
    "distribution.  \n",
    "\n",
    "The observed value of this statistic is $\\frac{1}{2}\\log{\\frac{1+0.92}{1-0.92}}=1.589$, which corresponds to\n",
    "a value of $\\frac{1.589}{\\sqrt{\\frac{1}{7}}}=4.204$ on the $N(0,1)$ distribution. This is much greater than\n",
    "$3.090$, the upper $0.1\\%$ point of the standard normal distribution.  \n",
    "\n",
    "So, we reject $H_0$ at the $0.1\\%$ level and conclude that there is very strong evidence that\n",
    "$\\rho > 0$ ie that there is a positive linear correlation between the stock price and portfolio value.  \n",
    "\n",
    "## Regression Analysis  \n",
    "\n",
    "Given a set of points $(x_i,y_i)_{i=0}^{n}$ for a simple linear regression of the form  \n",
    "\n",
    "$$\n",
    "Y_i = \\alpha +\\beta x_i + \\epsilon_i; \\hspace{4mm} i=1,2,\\cdots,n\n",
    "$$  \n",
    "\n",
    "with $\\mathbb{\\epsilon_i}=0$ and $var[\\epsilon_i]=\\sigma^2$.  \n",
    "\n",
    "### Model Fitting  \n",
    "We can estimate the parameters from the method of least squares but that's not the goal in this\n",
    "case. Fitting the model involves finding $\\alpha$ and $\\beta$ and the estimating the variance $\\sigma^2$.  \n",
    "\n",
    "$$\n",
    "\\hat{y} = \\hat{\\alpha}+\\hat{\\beta}x\n",
    "$$  \n",
    "\n",
    "where, $\\hat{\\beta}= \\frac{S_{xy}}{S_{xx}}$ and $\\hat{\\alpha} = \\bar{y}-\\hat{\\beta}\\bar{x}$  \n",
    "\n",
    "$\\hat{\\beta}$ is the observed value of a statistic $\\hat{B}$ whose sampling distribution has the \n",
    "following properties  \n",
    "\n",
    "$$\n",
    "\\mathbb{E}[\\hat{B}]=\\beta, \\hspace{4mm} var[\\hat{B}]=\\frac{\\sigma^2}{S_{xx}}\n",
    "$$  \n",
    "\n",
    "And the estimate of the error variance \n",
    "\n",
    "\\begin{align*}\n",
    "\\hat{\\sigma}^2 & =\\frac{1}{n-2}\\sum (y_i -\\hat{y_i})^2\\\\\n",
    "& = \\frac{1}{n-2} \\left(S_{yy}-\\frac{S_{xy}^2}{S_{xx}}\\right)\n",
    "\\end{align*}  \n",
    "\n",
    "### Goodness of fit  \n",
    "\n",
    "To better understand the goodness of fit of the model for the data at hand, we can study the \n",
    "total variation in the responses, as given by \n",
    "\n",
    "$$\n",
    "S_{yy} = \\sum (y_i-\\bar{y})^2\n",
    "$$  \n",
    "\n",
    "Let's see how: \n",
    "\n",
    "\\begin{align*}\n",
    "y_i - \\bar{y} &= (y_i - \\hat{y_i}) + (\\hat{y_i}-\\bar{y}) \\\\\n",
    "\\implies (y_i - \\bar{y})^2 & = \\left((y_i - \\hat{y_i}) + (\\hat{y_i}-\\bar{y})\\right)^2\\\\\n",
    "& = (y_i - \\hat{y_i})^2 + 2(y_i - \\hat{y_i})(\\hat{y_i}-\\bar{y})+(\\hat{y_i}-\\bar{y})^2\\\\\n",
    "& = (y_i - \\hat{y_i})^2 + 2 [y_i -(\\hat{\\alpha}+\\hat{\\beta}x_i)][\\hat{\\alpha}+\\hat{\\beta}x_i-(\\hat{\\alpha}+\\hat{\\beta}\\bar{x})]+(\\hat{y_i}-\\bar{y})^2\\\\\n",
    "& = (y_i - \\hat{y_i})^2 + 2 \\hat{\\beta}\\left(y_i -\\hat{\\alpha}-\\hat{\\beta}x_i\\right)(x_i-\\bar{x})+(\\hat{y_i}-\\bar{y})^2\\\\\n",
    "\\implies \\sum (y_i - \\bar{y})^2 & =\\sum (y_i - \\hat{y_i})^2 + 2 \\hat{\\beta}\\sum\\left(y_i -\\hat{\\alpha}-\\hat{\\beta}x_i\\right)(x_i-\\bar{x})+\\sum(\\hat{y_i}-\\bar{y})^2\\\\\n",
    "& =\\sum (y_i - \\hat{y_i})^2 + 2 \\hat{\\beta}\\left[\\sum x_iy_i-\\bar{x}\\sum y_i -\\hat{\\alpha}\\sum x_i + n\\hat{\\alpha}\\bar{x}-\\hat{\\beta}\\sum x_i^2\\right.\\\\\n",
    "&\\left.\\hspace{4mm}+\\hat{\\beta}\\bar{x}\\sum x_i\\right]+\\sum(\\hat{y_i}-\\bar{y})^2\\\\\n",
    "& =\\sum (y_i - \\hat{y_i})^2 + 2 \\hat{\\beta}\\left(\\sum x_iy_i-n\\bar{x}\\bar{y}\\right)-2\\hat{\\beta}^2\\left(\\sum x_i^2 - n\\bar{x}^2\\right)+\\sum(\\hat{y_i}-\\bar{y})^2\\\\ \n",
    "& = \\sum (y_i - \\hat{y_i})^2 + 2 \\hat{\\beta}S_{xy}-2\\hat{\\beta}^2S_{xx}+\\sum(\\hat{y_i}-\\bar{y})^2\\\\ \n",
    "& = \\sum (y_i - \\hat{y_i})^2 + 2 \\frac{S_{xy}}{S_{xx}}S_{xy}-2\\left(\\frac{S_{xy}}{S_{xx}}\\right)^2S_{xx}+\\sum(\\hat{y_i}-\\bar{y})^2\\\\ \n",
    "\\implies \\sum (y_i - \\bar{y})^2 & =\\sum (y_i - \\hat{y_i})^2 +\\sum(\\hat{y_i}-\\bar{y})^2\\\\ \n",
    "SS_{TOT} & = SS_{RES}+ SS_{REG}\n",
    "\\end{align*}  \n",
    "\n",
    "In the case that the data are “close” to a line ( $|r|$ high- a strong linear relationship) the model \n",
    "fits well, the fitted responses (the values on the fitted line) are close to the observed responses, \n",
    "and so $SS_{REG}$ is relatively high with $SS_{RES}$ relatively low.  \n",
    "\n",
    "In the case that the data are not “close” to a line ( $|r|$ low - a weak linear relationship) the model\n",
    "does not fit so well, the fitted responses are not so close to the observed responses, and so $SS_{REG}$ \n",
    "is relatively low and $SS_{RES}$ relatively high.  \n",
    "\n",
    "The proportion of the total variability of the responses “explained” by a model is\n",
    "called the coefficient of determination, denoted $R^2$ . \n",
    "\n",
    "$$\n",
    "R^2 = \\frac{SS_{REG}}{SS_{TOT}} =\\frac{S_{xy}^2}{S_{xx}S_{yy}}\n",
    "$$  \n",
    "\n",
    "which takes value between 0 to 1, inclusive. The higher $R^2$, the better fitting.  \n",
    "\n",
    "For our data, we have: \n",
    "\n",
    "\\begin{align*}\n",
    "n & = 10, \\hspace{4mm} \\sum x = 35.66, \\hspace{4mm} \\sum y = 32.47\\\\\n",
    "S_{xx} &= 8.53 \\hspace{4mm} S_{yy}=6.97, \\hspace{4mm} S_{xy}=7.13\\\\\n",
    "\\implies \\hat{\\beta} &=\\frac{S_{xy}}{S_{xx}}= \\frac{7.13}{8.53} = 0.836\\\\\n",
    "\\hat{\\alpha} &= \\frac{\\sum y}{n} - \\hat{\\beta} \\frac{\\sum x}{n} = \\bar{y}-\\hat{\\beta}\\bar{x}\\\\\n",
    "& = 3.247 - 0.836 \\times 3.566 = 0.266\n",
    "\\end{align*}  \n",
    "\n",
    "Therefore, the fitted line would be $\\hat{y}=0.266 + 0.836x$. Now we see the other metrics  \n",
    "\n",
    "\\begin{align*}\n",
    "SS_{TOT} &= 6.97 \\\\\n",
    "SS_{REG} & = \\frac{S_{yy}^2}{S_{xx}} = \\frac{6.97^2}{8.53}=5.695\\\\\n",
    "SS_{RES} & = 6.97 - 5.695 = 1.275 \\\\\n",
    "\\implies \\hat{\\sigma}^2 & = \\frac{1.275}{8}=0.1594\\\\\n",
    "R^2 & = \\frac{5.695}{6.97}=0.817\n",
    "\\end{align*} "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c3ecb817",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1650x1050 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "#| fig-align: center\n",
    "# Parameters for the line\n",
    "alpha = 0.266  \n",
    "beta = 0.836   \n",
    "\n",
    "# Line values\n",
    "line_x = np.linspace(min(df.StockPrice), max(df.StockPrice), 100)  \n",
    "line_y = alpha + beta * line_x             \n",
    "\n",
    "# Plot\n",
    "plt.scatter(df.StockPrice, df.Portfolio, color='blue', label='Data Points')\n",
    "plt.plot(line_x, line_y, color='red', label=f'Line: y = {alpha} + {beta}x')\n",
    "\n",
    "# Labels and title\n",
    "plt.xlabel('Stock Price')\n",
    "plt.ylabel('Portfolio')\n",
    "plt.title('Scatter Plot with Regression Line')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "108a887e",
   "metadata": {},
   "source": [
    "### Inference on $\\beta$  \n",
    "\n",
    "We can rewrite $\\hat{\\beta}= \\frac{S_{xy}}{S_{xx}}$, as \n",
    "\n",
    "\\begin{align*}\n",
    "\\hat{\\beta}&= \\frac{S_{xy}}{S_{xx}}=\\frac{\\sum (x_i-\\bar{x})(y_i-\\bar{y})}{S_{xx}}\\\\\n",
    "& = \\frac{\\sum (x_i-\\bar{x})y_i-\\bar{y}\\sum (x_i-\\bar{x})}{S_{xx}}\\\\\n",
    "& = \\frac{\\sum (x_i-\\bar{x}y_i)-\\bar{y}\\left(\\sum x_i -n\\bar{x}\\right)}{S_{xx}}\\\\\n",
    "& = \\frac{\\sum (x_i-\\bar{x})y_i}{S_{xx}}\n",
    "\\end{align*}  \n",
    "\n",
    "Now we recall that $\\hat{B}$ is the random variable that has $\\hat{\\beta}$ as its realization. Therefore, \n",
    "$\\hat{B}=\\frac{\\sum (x_i-\\bar{x})Y_i}{S_{xx}}$. We also recall that $\\mathbb{E}(Y_i)=\\alpha +\\beta x$. Putting these together we obtain,\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbb{E}[\\hat{B}] &= \\mathbb{E}\\left[\\frac{\\sum (x_i-\\bar{x})Y_i}{S_{xx}}\\right] = \\frac{\\sum (x_i -\\bar{x})\\mathbb{E}[Y_i]}{S_{xx}}\\\\\n",
    "& = \\frac{\\sum (x_i-\\bar{x})(\\alpha + \\beta x_i)}{S_{xx}}\\\\\n",
    "& = \\frac{\\alpha \\sum (x_i-\\bar{x})+\\beta \\sum x_i (x_i-\\bar{x})}{S_{xx}}\\\\\n",
    "& = \\frac{\\alpha \\left(\\sum x_i -n\\bar{x}\\right)+\\beta \\left(\\sum x_i^2-\\bar{x}\\sum x_i\\right)}{S_{xx}} \\\\\n",
    "& = \\frac{\\alpha (n\\bar{x}-n\\bar{x})+\\beta\\left(\\sum x_i^2-n\\bar{x}^2\\right)}{S_{xx}}\\\\\n",
    "& = \\frac{0+\\beta S_{xx}}{S_{xx}} = \\beta\n",
    "\\end{align*}  \n",
    "\n",
    "Now the fact that $Y_i'$s are uncorrelated. Therefore,  $var\\left(\\sum (Y_i)\\right)=\\sum var(Y_i)$ and we have $var(Y_i)=\\sigma^2$. Therefore,\n",
    "\n",
    "\\begin{align*}\n",
    "var[\\hat{B}]& = var\\left[\\frac{\\sum (x_i-\\bar{x})Y_i}{S_{xx}}\\right]= \\frac{\\sum (x_i-\\bar{x})^2var[Y_i]}{S_{xx}^2}\\\\\n",
    "& = \\frac{\\sum (x_i-\\bar{x})^2\\sigma^2}{S_{xx}^2} = \\frac{\\sigma^2}{S_{xx}^2}\\sum (x_i-\\bar{x})^2 = \\frac{\\sigma^2}{S_{xx}^2}S_{xx}\\\\\n",
    "& = \\frac{\\sigma^2}{S_{xx}}\n",
    "\\end{align*}\n",
    "\n",
    "Since $\\mathbb{E}(\\hat{\\beta})=\\beta$ and $var(\\hat{\\beta})=\\frac{\\sigma^2}{S_{xx}}$ so \n",
    "\n",
    "$$\n",
    "M = \\frac{\\hat{\\beta}-\\beta}{\\sqrt{\\frac{\\sigma^2}{S_{xx}}}}\\sim N(0,1)\n",
    "$$ \n",
    "\n",
    "and the observed variance $\\hat{\\sigma}^2$ has the property \n",
    "\n",
    "$$\n",
    "N = \\frac{(n-2)\\hat{\\sigma}^2}{\\sigma^2} \\sim \\chi_{n-2}^2\n",
    "$$\n",
    "\n",
    "Since $\\hat{\\beta}$ and $\\hat{\\sigma}^2$ are independent, it follows that \n",
    "\n",
    "$$\n",
    "\\frac{M}{\\sqrt{\\frac{N}{n-2}}} \\sim t_{n-2}\n",
    "$$  \n",
    "\n",
    "In other words: \n",
    "$$\n",
    "\\frac{\\hat{\\beta}-\\beta}{se(\\hat{\\beta})} = \\frac{\\hat{\\beta}-\\beta}{\\sqrt{\\frac{\\hat{\\sigma}^2}{S_{xx}}}} \\sim t_{n-2}\n",
    "$$  \n",
    "\n",
    "Now the big question is what's the use of this mathematical jargon that we have learned so far? Let's use\n",
    "our regression problem on stock data to explain. \n",
    "\n",
    "**$H_0: \\beta =0$, there is no linear relationship**  \n",
    "vs  \n",
    "**$H_1: \\beta> 0$, there is a linear relationship**  \n",
    "\n",
    "Based on our data we have $\\hat{\\beta} = 0.836$ and $\\hat{\\sigma}^2=0.1594$, and $S_{xx}=8.53$. Therefore, \n",
    "under $H_0$, the test statistic \n",
    "\n",
    "$$\n",
    "\\frac{\\hat{\\beta}-0}{\\sqrt{\\frac{\\hat{\\sigma}^2}{S_{xx}}}} \\text{ has a } t_{10-2} \\text{ or } t_8 \\text{ distribution}\n",
    "$$  \n",
    "\n",
    "But the observed value of this statistic \n",
    "$$\n",
    "\\frac{0.836-0}{\\sqrt{0.1594/8.53}}=6.1156\n",
    "$$  \n",
    "\n",
    "which is way higher than the critical value at $5\\%$ significance level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "46b7a5af",
   "metadata": {},
   "outputs": [
    {
     "data": {
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UooUTE1QUx0qEwgnwqQyPq0MUTECugNgQpKwW7DBk7CvOkg3ydD1ckSOz7ESDJGFUI0SqPjz1x783H9GeOEm9+bjz1JHkiXPDmw/3Tp20nTj3uvEY6tSZ0ImjmJuPQE6dMNzcrD/V3r659Xuiz3lbD/DA2o2Jj0sC1gTg+xlLZoMtbv6BXODHab1/MPcZgaQgeNCI/TjxfEi03kFoWCKKjrE6pE+aU01MKA1LYjLmJJ900cvIoIvx1+6kHEY8XrC76bI/I17/Y4HLm/9YgGf/5N8a7E8eBjg9qiraOXFXZPumuxJTLC97r6z4QbkKTnmOx5Ss4PSdFgJPOF5oaTdwTt68wUEkuRhn5HJWnfCJwctFwIdPLt5dvb347/urizev5z8urn6Z0/zk/Oe3D3DajLT+N39xfv5ufvPT/PWD6j6cT+2Ltw+ma4/++OaSSU/rpB89dvX20PW/M8G6rv2VSYn+uFI5JJNUR/Is0iu5b5nLndkDZA96fKLcgohHbjFCUx5F7YqNoA8Iz16fOps2iONK8s7iATbopZUscff4liBt0/LoNqEdnXWz33nNdXzR3JETRjG79vT2uo5uM5Oxd76L8arnm8THN+6quVm7Z7V+ubUsGTasJGOmDVTOkG1dJslnrvOaQdzE237aLpfderEsbHOXwx9Xr7uevll29R/s+WDjx7003vlSZR+Pe7gT00pBXQ6MLztxdt6L6ST6N34c58iPej9csPtTOtjee5sO/vnrr+dvCSzqb/Nj2djUZEqKIfmf3friqJObw9B8IgwdRTIikvwxxWABO+9Vc+RiAfvqf99e+qc0YKTOr3/DcVoDX729uLo4e/Fqvnr4QK5Y+1V8M3/x+4tX78/nv8+jp302/R8/1EHiCmVuZHN0cmVhbQplbmRvYmoKMTIgMCBvYmoKNDAxOAplbmRvYmoKMTAgMCBvYmoKWyBdCmVuZG9iagoxNyAwIG9iago8PCAvTGVuZ3RoIDkxIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDWMuw3AMAhEe6a4Efg4gPeJohT2/m2ILRfcPemJ82xgZJ2HI7TjFrKmcFNMUk6odwxqpTcdO+glzf00yXouGvQPcfUVtpsDklEkkYdEl8uVZ+VffD4MbxxiCmVuZHN0cmVhbQplbmRvYmoKMTggMCBvYmoKPDwgL0xlbmd0aCAyMzUgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNVFJbgAxCLvnFf5ApbAn75mq6qH9/7WGUS8DA9jYJO/BRiQ+xJDuKFd8yuo0y/A7WeTFz0rh5L2ICqQqwgppB89yVjMMnhuZApcz8VlmPpkWOxZQTcRxduQ0g0GIaVxHy+kw0zzoCbk+GHFjp1muYkjr3VK9vtfynyrKR9bdLLdO2dRK3aJn7Elcdl5PbWlfGHUUNwWRDh87vAf5IuYsLjqRbvabKYeVpCE4LYAfiaFUzw6vESZ+ZiR4yp5O76M0vPZB0/W9e0FHbiZkKrdQRiqerDTGjKH6jWgmqe//gZ71vb7+AENNVLkKZW5kc3RyZWFtCmVuZG9iagoxOSAwIG9iago8PCAvTGVuZ3RoIDE2NCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw9kMERQyEIRO9WsSWAgEA9yWRy+L//a0CTXGQdYPepO4GQUYczw2fiyYPTsTRwbxWMawivI/QITQKTwMTBmngMCwGnYZFjLt9VllWnla6ajZ7XvWNB1WmXNQ1t2oHyrY8/wjXeo/Aa7B5CB7EodG5lWguZWDxrnDvMo8znfk7bdz0YrabUrDdy2dc9OsvUUF5a+4TOaLT9J9cvuzFeH4UUOQgKZW5kc3RyZWFtCmVuZG9iagoyMCAwIG9iago8PCAvTGVuZ3RoIDc2IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDM1N1UwULC0ABKmhuYK5kaWCimGXEA+iJXLBRPLAbPMTMyALENLZJaJsSGQZWJhhsQyNrGAyiJYBkAabE0OzPQcrgyuNAA1FxkFCmVuZHN0cmVhbQplbmRvYmoKMjEgMCBvYmoKPDwgL0xlbmd0aCAxNTYgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNY9LDsMwCET3PsVcoBJfQ86Tquoivf+2YCeSEU/2zBhCBYQMvFgxzRFy4M2jbpp+g3MuuhZJ1U2UVQR2hkiCOXAO8YlUKAnmhFbVOYdVQIGF96uT3nJXXgFuO3D1bEfT/vYZapOE3cSRmFJ+Cnjd+tE2iYqGea6FeoDuNVgpmoSsBeyxDcy0EmrfDqzWyvPZ/xrf8fkDYBM2+AplbmRzdHJlYW0KZW5kb2JqCjIyIDAgb2JqCjw8IC9MZW5ndGggMzA3IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nD2SS24DMQxD9z6FLhDA+tme86Qoupjef9snJemKHNkWRWqWukxZUx6QNJOEf+nwcLGd8jtsz2Zm4Fqil4nllOfQFWLuonzZzEZdWSfF6oRmOrfoUTkXBzZNqp+rLKXdLngO1yaeW/YRP7zQoB7UNS4JN3RXo2UpNGOq+3/Se/yMMuBqTF1sUqt7HzxeRFXo6AdHiSJjlxfn40EJ6UrCaFqIlXdFA0Hu8rTKewnu295qyLIHqZjOOylmsOt0Ui5uF4chHsjyqPDlo9hrQs/4sCsl9EjYhjNyJ+5oxubUyOKQ/t6NBEuPrmgh8+CvbtYuYLxTOkViZE5yrGmLVU73UBTTucO9DBD1bEVDKXOR1epfw84La5ZsFnhK+gUeo90mSw5W2duoTu+tPNnQ9x9a13QfCmVuZHN0cmVhbQplbmRvYmoKMjMgMCBvYmoKPDwgL0xlbmd0aCAyNDQgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicRZFNcgUhCIT3nqIv8KrkVz3PpFJZTO6/Dc28JCtaheYD0wITR/ASQ+yJlRMfMnwv6DJ8tzI78DrZmXBPuG5cw2XDM2Fb4DsqyzteQ3e2Uj+doarvGjneLlI1dGVkn3qhmgvMkIiuEVl0K5d1QNOU7lLhGmxbghT1SqwnnaA06BHK8HeUa3x1E0+vseRUzSFaza0TGoqwbHhB1MkkEbUNiyeWcyFR+aobqzouYJMl4vSA3KCVZnx6UkkRMIN8rMlozAI20JO7ZxfGmkseRY5XNJiwO0k18ID34ra+9zZxj/MX+IV33/8rDn3XAj5/AEv+XQYKZW5kc3RyZWFtCmVuZG9iagoyNCAwIG9iago8PCAvTGVuZ3RoIDIzMiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw1UUluxDAMu/sV/MAA1u68J8Wgh/b/11LKFAhAJba4JWJjIwIvMfg5iNz4kjWjJn5nclf8LE+FR8Kt4EkUgZfhXnaCyxvGZT8OMx+8l1bOpMaTDMhFNj08ETLYJRA6MLsGddhm2om+IeGzI1LNRpbT1xL00ioEylO23+mCEm2r+nP7rAtt+9oTTnZ76knlE4jnlqzAZeMVk8VYBj1RuUsxfZDqbKEnobwon4NsPmqIRJcoZ+CJwcEo0A7sue1n4lUhaF3dp21jqEZKx9O/DU1Nkgj5RAlntjTuFv5/z72+1/sPTiFUEQplbmRzdHJlYW0KZW5kb2JqCjI1IDAgb2JqCjw8IC9MZW5ndGggMjMxIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDVPOZIEIQzLeYU+MFUY20C/p6e2Ntj5f7qSmU6Q8CHJ0xMdmXiZIyOwZsfbWmQgZuBTTMW/9rQPE6r34B4ilIsLYYaRcNas426ejhf/dpXPWAfvNviKWV4Q2MJM1lcWZy7bBWNpnMQ5yW6MXROxjXWtp1NYRzChDIR0tsOUIHNUpPTJjjLm6DiRJ56L7/bbLHY5fg7rCzaNIRXn+Cp6gjaDoux57wIackH/Xd34HkW76CUgGwkW1lFi7pzlhF+9dnQetSgSc0KaQS4TIc3pKqYQmlCss6OgUlFwqT6n6Kyff+VfXC0KZW5kc3RyZWFtCmVuZG9iagoyNiAwIG9iago8PCAvTGVuZ3RoIDI0OSAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw9UDuORCEM6zmFL/Ak8iNwHkarLWbv364DmilQTH62MyTQEYFHDDGUr+MlraCugb+LQvFu4uuDwiCrQ1IgznoPiHTspjaREzodnDM/YTdjjsBFMQac6XSmPQcmOfvCCoRzG2XsVkgniaoijuozjimeKnufeBYs7cg2WyeSPeQg4VJSicmln5TKP23KlAo6ZtEELBK54GQTTTjLu0lSjBmUMuoepnYifaw8yKM66GRNzqwjmdnTT9uZ+Bxwt1/aZE6Vx3QezPictM6DORW69+OJNgdNjdro7PcTaSovUrsdWp1+dRKV3RjnGBKXZ38Z32T/+Qf+h1oiCmVuZHN0cmVhbQplbmRvYmoKMjcgMCBvYmoKPDwgL0xlbmd0aCAzOTUgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicPVJLbsVACNvnFFyg0vCbz3lSVd28+29rQ1KpKryJMcYwfcqQueVLXRJxhcm3Xq5bPKZ8LltamXmIu4uNJT623JfuIbZddC6xOB1H8gsynSpEqM2q0aH4QpaFB5BO8KELwn05/uMvgMHXsA244T0yQbAk5ilCxm5RGZoSQRFh55EVqKRQn1nC31Hu6/cyBWpvjKULYxz0CbQFQm1IxALqQABE7JRUrZCOZyQTvxXdZ2IcYOfRsgGuGVRElnvsx4ipzqiMvETEPk9N+iiWTC1Wxm5TGV/8lIzUfHQFKqk08pTy0FWz0AtYiXkS9jn8SPjn1mwhhjpu1vKJ5R8zxTISzmBLOWChl+NH4NtZdRGuHbm4znSBH5XWcEy0637I9U/+dNtazXW8cgiiQOVNQfC7Dq5GscTEMj6djSl6oiywGpq8RjPBYRAR1vfDyAMa/XK8EDSnayK0WCKbtWJEjYpscz29BNZM78U51sMTwmzvndahsjMzKiGC2rqGautAdrO+83C2nz8z6KJtCmVuZHN0cmVhbQplbmRvYmoKMjggMCBvYmoKPDwgL0xlbmd0aCA3NCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJyzMLZQMFAwNDBTMDQ3UjA3NlIwMTVRSDHkAgmBmLlcMMEcMMsYqCwHLItgQWQzwGwjU1OoHhALoscQrhLBgshmcKUBAFG+GRYKZW5kc3RyZWFtCmVuZG9iagoyOSAwIG9iago8PCAvTGVuZ3RoIDEzNiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxNj0EOAzEIA+95hZ9AIEB4z1ZVD9v/X0vYdtMLHsmAbFEGgSWHeIcb4dHbD99FNhVn45xfUiliIZhPcJ8wUxyNKXfyY4+AcZRqLKdoeF5Lzk3DFy13Ey2lrZeTGW+47pf3R5VtkQ1Fzy0LQtdskvkygQd8GJhHdeNppcfd9myv9vwAzmw0SQplbmRzdHJlYW0KZW5kb2JqCjMwIDAgb2JqCjw8IC9MZW5ndGggMjQ5IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nE1RSYoDMAy75xX6QCFek7ynQ5lD5//Xyg6FOQQJr5KTlphYCw8xhB8sPfiRIXM3/Rt+otm7WXqSydn/mOciU1H4UqguYkJdiBvPoRHwPaFrElmxvfE5LKOZc74HH4W4BDOhAWN9STK5qOaVIRNODHUcDlqkwrhrYsPiWtE8jdxu+0ZmZSaEDY9kQtwYgIgg6wKyGCyUNjYTMlnOA+0NyQ1aYNepG1GLgiuU1gl0olbEqszgs+bWdjdDLfLgqH3x+mhWl2CF0Uv1WHhfhT6YqZl27pJCeuFNOyLMHgqkMjstK7V7xOpugfo/y1Lw/cn3+B2vD838XJwKZW5kc3RyZWFtCmVuZG9iagozMSAwIG9iago8PCAvTGVuZ3RoIDk0IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nEWNwRHAIAgE/1RBCQoK2k8mk4f2/40QMnxg5w7uhAULtnlGHwWVJl4VWAdKY9xQj0C94XItydwFD3Anf9rQVJyW03dpkUlVKdykEnn/DmcmkKh50WOd9wtj+yM8CmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0xlbmd0aCAzNDEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicRVJLbkQxCNu/U3CBSOGXkPO0qrqY3n9bm0zVzeAJYGx4y1OmZMqwuSUjJNeUT30iQ6ym/DRyJCKm+EkJBXaVj8drS6yN7JGoFJ/a8eOx9Eam2RVa9e7Rpc2iUc3KyDnIEKGeFbqye9QO2fB6XEi675TNIRzL/1CBLGXdcgolQVvQd+wR3w8droIrgmGway6D7WUy1P/6hxZc7333YscugBas577BDgCopxO0BcgZ2u42KWgAVbqLScKj8npudqJso1Xp+RwAMw4wcsCIJVsdvtHeAJZ9XehFjYr9K0BRWUD8yNV2wd4xyUhwFuYGjr1wPMWZcEs4xgJAir3iGHrwJdjmL1euiJrwCXW6ZC+8wp7a5udCkwh3rQAOXmTDraujqJbt6TyC9mdFckaM1Is4OiGSWtI5guLSoB5a41w3seJtI7G5V9/uH+GcL1z26xdL7ITECmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0xlbmd0aCAxNjQgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicRZDHcQUxDEPvqgIlMIAK9azH8w/r/q+G9NNBehhCDGJPwrBcV3FhdMOPty0zDX9HGe7G+jJjvNVYICfoAwyRiavRpPp2xRmq9OTVYq6jolwvOiISzJLjq0AjfDqyx5O2tjP9dF4f7CHvE/8qKuduYQEuqu5A+VIf8dSP2VHqmqGPKitrHmraV4RdEUrbPi6nMk7dvQNa4b2Vqz3a7z8edjryCmVuZHN0cmVhbQplbmRvYmoKMzQgMCBvYmoKPDwgL0xlbmd0aCA1NCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJwzNjNUMFAwsVQwMjZRMDY0AmIThRRDLqAIiJXLBRPLAbNAqnK4oMpzYKpyuDK40gAFGA4yCmVuZHN0cmVhbQplbmRvYmoKMzUgMCBvYmoKPDwgL0xlbmd0aCA3MiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJwzMrdQMFCwNAEShhYmCuZmBgophlxAvqmJuUIuF0gMxMoBswyAtCWcgohngJggbRDFIBZEsZmJGUQdnAGRy+BKAwAl2xbJCmVuZHN0cmVhbQplbmRvYmoKMzYgMCBvYmoKPDwgL0xlbmd0aCA0NyAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJwzMrdQMFCwNAEShhYmCuZmBgophlyWEFYuF0wsB8wC0ZZwCiKewZUGALlnDScKZW5kc3RyZWFtCmVuZG9iagozNyAwIG9iago8PCAvTGVuZ3RoIDI1OCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxFkUtyBCAIRPeegiOA/OQ8k0plMbn/Ng3OZDZ2l6j9hEojphIs5xR5MH3J8s1ktul3OVY7GwUURSiYyVXosQKrO1PEmWuJautjZeS40zsGxRvOXTmpZHGjjHVUdSpwTM+V9VHd+XZZlH1HDmUK2KxzHGzgym3DGCdGm63uDveJIE8nU0fF7SDZ8AcnjX2VqytwnWz20UswDgT9QhOY5ItA6wyBxs1T9OQS7OPjdueBYG95EUjZEMiRIRgdgnadXP/i1vm9/3GGO8+1Ga4c7+J3mNZ2x19ikhVzAYvcKajnay5a1xk63pMzx+Sm+4bOuWCXu4NM7/k/1s/6/gMeKWb6CmVuZHN0cmVhbQplbmRvYmoKMzggMCBvYmoKPDwgL1R5cGUgL1hPYmplY3QgL1N1YnR5cGUgL0Zvcm0gL0JCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9MZW5ndGggMzkKL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnic4zI0MFMwNjVVyOUyNzYCs3LALCNzIyALJItgQWQzuNIAFfMKfAplbmRzdHJlYW0KZW5kb2JqCjM5IDAgb2JqCjw8IC9MZW5ndGggMTYzIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nEWQOxIDIQxDe06hI/gjAz7PZjIpNvdvY9hsUsDTWCCDuxOC1NqCieiCh7Yl3QXvrQRnY/zpNm41EuQEdYBWpONolFJ9ucVplXTxaDZzKwutEx1mDnqUoxmgEDoV3u2i5HKm7s75Q3D1X/W/Yt05m4mBycodCM3qU9z5NjuiurrJ/qTH3KzXfivsVWFpWUvLCbedu2ZACdxTOdqrPT8fCjr2CmVuZHN0cmVhbQplbmRvYmoKNDAgMCBvYmoKPDwgL0xlbmd0aCAyMTggL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicPVC5jQQxDMtdhRpYwHrtqWcWi0um//RI+fYi0RZFUio1mZIpL3WUJVlT3jp8lsQOeYblbmQ2JSpFL5OwJffQCvF9ieYU993VlrNDNJdoOX4LMyqqGx3TSzaacCoTuqDcwzP6DW10A1aHHrFbINCkYNe2IHLHDxgMwZkTiyIMSk0G/65yj59eixs+w/FDFJGSDuY1/1j98nMNr1OPJ5Fub77iXpypDgMRHJKavCNdWLEuEhFpNUFNz8BaLYC7t17+G7QjugxA9onEcZpSjqG/a3Clzy/lJ1PYCmVuZHN0cmVhbQplbmRvYmoKNDEgMCBvYmoKPDwgL0xlbmd0aCA4MyAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxFjLsNwDAIRHumYAR+JvY+UZTC3r8NECVuuCfdPVwdCZkpbjPDQwaeDCyGXXGB9JYwC1xHUI6d7KNh1b7qBI31plLz7w+Unuys4obrAQJCGmYKZW5kc3RyZWFtCmVuZG9iago0MiAwIG9iago8PCAvTGVuZ3RoIDIzOSAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxNUMltBDEM+7sKNTDA6By7HgeLPLL9f0PKCZKXaEviofKUW5bKZfcjOW/JuuVDh06VafJu0M2vsf6jDAJ2/1BUEK0lsUrMXNJusTRJL9nDOI2Xa7WO56l7hFmjePDj2NMpgek9MsFms705MKs9zg6QTrjGr+rTO5UkA4m6kPNCpQrrHtQloo8r25hSnU4t5RiXn+h7fI4APcXejdzRx8sXjEa1LajRapU4DzATU9GVcauRgZQTBkNnR1c0C6XIynpCNcKNOaGZvcNwYAPLs4Skpa1SvA9lAegCXdo64zRKgo4Awt8ojPX6Bqr8XjcKZW5kc3RyZWFtCmVuZG9iago0MyAwIG9iago8PCAvTGVuZ3RoIDQwNiAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw1UkuyIzEI2/cpuMBUmY8xPk+mXr1F5v7bkbB7kaAEJARmzyFD5pQ/6lJ7ygqTv/osW+Km8u/JvRvlSvGxJXOI1ZTPkxFiiYynGOoZtYIZIgixQkc15yQgAkzNKGEThM+zYIC/12J2bT/VhXakl66W63gyQGYprLBLsc5Qw8GhJG2/g3ye3zNUOYZaqxqVYricaMchN5UXFPfZhcE+4+1JZMigYh1KjPYCIFTkDtmDkbOeraY78jn8lM/lpM9Zrdax9YkskEEBHZBxPFGBLqlI1+8cnMmgkTUwk8IfkYKfiU1NbDNYpYFHgkuFzqw8Mdiz0QAHFXE5cThQCXKgGoPb9o6fx6aef1Z0he1xOT6yVVyjVTt2n0bFA5rtxGpfb3bdUpXu33k4W2b0PeK98M3P9zGocKtAoy566753H4dDf0SuuGoL8cDtFc/NeYUTmY0THdHx+gSKQgYV4YfjuzkKlIap8QZ4JfZh5Ka0kfroCuXkzVmjRfq4jeE0AWBXZGmC5ccWBWiUgjT+jsJV/PwHEemvxgplbmRzdHJlYW0KZW5kb2JqCjQ0IDAgb2JqCjw8IC9MZW5ndGggNTEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicMza0UDBQMDQwB5JGhkCWkYlCiiEXSADEzOWCCeaAWQZAGqI4B64mhyuDKw0A4bQNmAplbmRzdHJlYW0KZW5kb2JqCjQ1IDAgb2JqCjw8IC9MZW5ndGggMTYwIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nEWQORIDMQgEc72CJ0hcgvesy7XB+v+pB9ZHoukCNBy6Fk3KehRoPumxRqG60GvoLEqSRMEWkh1Qp2OIOyhITEhjkki2HoMjmlizXZiZVCqzUuG0acXCv9la1chEjXCN/InpBlT8T+pclPBNg6+SMfoYVLw7g4xJ+F5F3Fox7f5EMLEZ9glvRSYFhImxqdm+z2CGzPcK1zjH8w1MgjfrCmVuZHN0cmVhbQplbmRvYmoKNDYgMCBvYmoKPDwgL0xlbmd0aCAzMzQgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicLVJLcsUgDNtzCl2gM/gH5DzpdLp4vf+2kpNFRg5g9DHlholKfFkgt6PWxLeNzECF4a+rzIXPSNvIOojLkIu4ki2Fe0Qs5DHEPMSC76vxHh75rMzJswfGL9l3Dyv21IRlIePFGdphFcdhFeRYsHUhqnt4U6TDqSTY44v/PsVzLQQtfEbQgF/kn6+O4PmSFmn3mG3TrnqwTDuqpLAcbE9zXiZfWme5Oh7PB8n2rtgRUrsCFIW5M85z4SjTVka0FnY2SGpcbG+O/VhK0IVuXEaKI5CfqSI8oKTJzCYK4o+cHnIqA2Hqmq50chtVcaeezDWbi7czSWbrvkixmcJ5XTiz/gxTZrV5J89yotSpCO+xZ0vQ0Dmunr2WWWh0mxO8pITPxk5PTr5XM+shORUJqWJaV8FpFJliCdsSX1NRU5p6Gf778u7xO37+ASxzfHMKZW5kc3RyZWFtCmVuZG9iago0NyAwIG9iago8PCAvTGVuZ3RoIDMyMCAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJw1UktuBTEI288puECl8E/O86qqi777b2sTvRVMMGDjKS9Z0ku+1CXbpcPkWx/3JbFC3o/tmsxSxfcWsxTPLa9HzxG3LQoEURM9WJkvFSLUz/ToOqhwSp+BVwi3FBu8g0kAg2r4Bx6lMyBQ50DGu2IyUgOCJNhzaXEIiXImiX+kvJ7fJ62kofQ9WZnL35NLpdAdTU7oAcXKxUmgXUn5oJmYSkSSl+t9sUL0hsCSPD5HMcmA7DaJbaIFJucepSXMxBQ6sMcCvGaa1VXoYMIehymMVwuzqB5s8lsTlaQdreMZ2TDeyzBTYqHhsAXU5mJlgu7l4zWvwojtUZNdw3Duls13CNFo/hsWyuBjFZKAR6exEg1pOMCIwJ5eOMVe8xM5DsCIY52aLAxjaCaneo6JwNCes6VhxsceWvXzD1TpfIcKZW5kc3RyZWFtCmVuZG9iago0OCAwIG9iago8PCAvTGVuZ3RoIDE4IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDM2tFAwgMMUQ640AB3mA1IKZW5kc3RyZWFtCmVuZG9iago0OSAwIG9iago8PCAvTGVuZ3RoIDEzMyAvRmlsdGVyIC9GbGF0ZURlY29kZSA+PgpzdHJlYW0KeJxFj0sOBCEIRPecoo7Axx/ncTLphXP/7YCdbhNjPYVUgbmCoT0uawOdFR8hGbbxt6mWjkVZPlR6UlYPyeCHrMbLIdygLPCCSSqGIVCLmBqRLWVut4DbNg2yspVTpY6wi6Mwj/a0bBUeX6JbInWSP4PEKi/c47odyKXWu96ii75/pAExCQplbmRzdHJlYW0KZW5kb2JqCjUwIDAgb2JqCjw8IC9MZW5ndGggMzQwIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDVSOW4EMQzr/Qp9IIBu2+/ZIEiR/L8NqdkUA3F0UpQ7WlR2y4eFVLXsdPm0ldoSN+R3ZYXECcmrEu1ShkiovFYh1e+ZMq+3NWcEyFKlwuSk5HHJgj/DpacLx/m2sa/lyB2PHlgVI6FEwDLFxOgals7usGZbfpZpwI94hJwr1i3HWAVSG9047Yr3oXktsgaIvZmWigodVokWfkHxoEeNffYYVFgg0e0cSXCMiVCRgHaB2kgMOXssdlEf9DMoMRPo2htF3EGBJZKYOcW6dPTf+NCxoP7YjDe/OirpW1pZY9I+G+2Uxiwy6XpY9HTz1seDCzTvovzn1QwSNGWNksYHrdo5hqKZUVZ4t0OTDc0xxyHzDp7DGQlK+jwUv48lEx2UyN8ODaF/Xx6jjJw23gLmoj9tFQcO4rPDXrmBFUoXa5L3AalM6IHp/6/xtb7X1x8d7YDGCmVuZHN0cmVhbQplbmRvYmoKNTEgMCBvYmoKPDwgL0xlbmd0aCAyNTEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicLVFJcgNBCLvPK/SEZqffY5crh+T/1wjKBwYNi0B0WuKgjJ8gLFe85ZGraMPfMzGC3wWHfivXbVjkQFQgSWNQNaF28Xr0HthxmAnMk9awDGasD/yMKdzoxeExGWe312XUEOxdrz2ZQcmsXMQlExdM1WEjZw4/mTIutHM9NyDnRliXYZBuVhozEo40hUghhaqbpM4EQRKMrkaNNnIU+6Uvj3SGVY2oMexzLW1fz004a9DsWKzy5JQeXXEuJxcvrBz09TYDF1FprPJASMD9bg/1c7KT33hL584W0+N7zcnywlRgxZvXbkA21eLfvIjj+4yv5+f5/ANfYFuICmVuZHN0cmVhbQplbmRvYmoKNTIgMCBvYmoKPDwgL0xlbmd0aCAxNzQgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicTZBJDkMhDEP3nMIXqIQzwOc8v6q6aO+/rUMHdYH85CBwPDzQcSQudGTojI4rmxzjwLMgY+LROP/JuD7EMUHdoi1Yl3bH2cwSc8IyMQK2RsnZPKLAD8dcCBJklx++wCAiXY/5VvNZk/TPtzvdj7q0Zl89osCJ7AjFsAFXgP26x4FLwvle0+SXKiVjE4fygeoiUjY7oRC1VOxyqoqz3ZsrcBX0/NFD7u0FtSM83wplbmRzdHJlYW0KZW5kb2JqCjUzIDAgb2JqCjw8IC9MZW5ndGggNTQgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicMzUwUDBQ0LVU0DUyNlUwNQSyDc1MFVIMueDsXAgTJJ/DBVMJYYGkcxAqc7gyuNIAc1EPjwplbmRzdHJlYW0KZW5kb2JqCjU0IDAgb2JqCjw8IC9MZW5ndGggNzUgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicM7U0UjBQMDYAEqZmRgqmJuYKKYZcQD6IlctlaGQKZuVwGVmaKVhYABkmZuZQIZiGHC5jU3OgAUBFxqZgGqo/hyuDKw0AlZAS7wplbmRzdHJlYW0KZW5kb2JqCjU1IDAgb2JqCjw8IC9MZW5ndGggODkgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicNYy7DYAwDER7T+ER4r/ZByEK2L/FSXBj392TXlLiQOU6EY6mgSdB9ZleINnpAVZF4lFJzP9NvalFU8+m7atNBCczjvV1HKia03rQWihtkxbecH0AnB3tCmVuZHN0cmVhbQplbmRvYmoKNTYgMCBvYmoKPDwgL0xlbmd0aCAxNDEgL0ZpbHRlciAvRmxhdGVEZWNvZGUgPj4Kc3RyZWFtCnicPY/BDsMwCEPv+Qr/QKTYKaF8T6dqh+7/ryNLuwt6AmOMhdDQG6qaw4Zgm+PF0iVUa/gUxUAlN8iZYA6lpNIdR5F6YjgYXB60G47isej6EbuSZn3QxkK6JWiAe6xTadymcRPEHTUF6inqnKO8ELmfqWfYNJLdNLOSc7gNv3vPU9f/p6u8y/kFvXcu/gplbmRzdHJlYW0KZW5kb2JqCjU3IDAgb2JqCjw8IC9MZW5ndGggMjE1IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlID4+CnN0cmVhbQp4nDVROQ4DIQzs9xX+QCSML3hPoijN/r/NjNFWHsFchrSUIZnyUpOoIeVTPnqZLpy63NfMajTnlrQtc4C4trwvrZLAiWaIg8FpmLgBmjwBQ9fRqFFDFx7Q1KVTKLDcBD6Kt24P3WO1gZe2IeeJIGIoGSxBzalFExZtzyekNb9eixvel+3dyFOlxpYYgQYBVjgc1+jX8JU9TybRdBUy1Ks1yxgJE0UiPPmOptUT61o00jIS1MYRrGoDvDv9ME4AABNxywJkn0qUs+TEb7H0swZX+v4Bn0dUlgplbmRzdHJlYW0KZW5kb2JqCjE1IDAgb2JqCjw8IC9UeXBlIC9Gb250IC9CYXNlRm9udCAvQk1RUURWK0RlamFWdVNhbnMgL0ZpcnN0Q2hhciAwIC9MYXN0Q2hhciAyNTUKL0ZvbnREZXNjcmlwdG9yIDE0IDAgUiAvU3VidHlwZSAvVHlwZTMgL05hbWUgL0JNUVFEVitEZWphVnVTYW5zCi9Gb250QkJveCBbIC0xMDIxIC00NjMgMTc5NCAxMjMzIF0gL0ZvbnRNYXRyaXggWyAwLjAwMSAwIDAgMC4wMDEgMCAwIF0KL0NoYXJQcm9jcyAxNiAwIFIKL0VuY29kaW5nIDw8IC9UeXBlIC9FbmNvZGluZwovRGlmZmVyZW5jZXMgWyAzMiAvc3BhY2UgMzcgL3BlcmNlbnQgNDUgL2h5cGhlbiAvcGVyaW9kIDQ4IC96ZXJvIC9vbmUgL3R3byAvdGhyZWUgL2ZvdXIKL2ZpdmUgL3NpeCA1NiAvZWlnaHQgNjEgL2VxdWFsIDY1IC9BIDY3IC9DIC9EIDcwIC9GIDg1IC9VIDk1IC91bmRlcnNjb3JlIDk3Ci9hIC9iIC9jIC9kIC9lIC9mIC9nIC9oIC9pIDEwOCAvbCAvbSAvbiAvbyAvcCAxMTQgL3IgL3MgL3QgL3UgL3YgL3cgMTIxIC95Cl0KPj4KL1dpZHRocyAxMyAwIFIgPj4KZW5kb2JqCjE0IDAgb2JqCjw8IC9UeXBlIC9Gb250RGVzY3JpcHRvciAvRm9udE5hbWUgL0JNUVFEVitEZWphVnVTYW5zIC9GbGFncyAzMgovRm9udEJCb3ggWyAtMTAyMSAtNDYzIDE3OTQgMTIzMyBdIC9Bc2NlbnQgOTI5IC9EZXNjZW50IC0yMzYgL0NhcEhlaWdodCAwCi9YSGVpZ2h0IDAgL0l0YWxpY0FuZ2xlIDAgL1N0ZW1WIDAgL01heFdpZHRoIDEzNDIgPj4KZW5kb2JqCjEzIDAgb2JqClsgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAKNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCAzMTggNDAxIDQ2MCA4MzggNjM2Cjk1MCA3ODAgMjc1IDM5MCAzOTAgNTAwIDgzOCAzMTggMzYxIDMxOCAzMzcgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNgo2MzYgNjM2IDMzNyAzMzcgODM4IDgzOCA4MzggNTMxIDEwMDAgNjg0IDY4NiA2OTggNzcwIDYzMiA1NzUgNzc1IDc1MiAyOTUKMjk1IDY1NiA1NTcgODYzIDc0OCA3ODcgNjAzIDc4NyA2OTUgNjM1IDYxMSA3MzIgNjg0IDk4OSA2ODUgNjExIDY4NSAzOTAgMzM3CjM5MCA4MzggNTAwIDUwMCA2MTMgNjM1IDU1MCA2MzUgNjE1IDM1MiA2MzUgNjM0IDI3OCAyNzggNTc5IDI3OCA5NzQgNjM0IDYxMgo2MzUgNjM1IDQxMSA1MjEgMzkyIDYzNCA1OTIgODE4IDU5MiA1OTIgNTI1IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMCAzMTgKMzUyIDUxOCAxMDAwIDUwMCA1MDAgNTAwIDEzNDIgNjM1IDQwMCAxMDcwIDYwMCA2ODUgNjAwIDYwMCAzMTggMzE4IDUxOCA1MTgKNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUyMSA0MDAgMTAyMyA2MDAgNTI1IDYxMSAzMTggNDAxIDYzNiA2MzYgNjM2IDYzNiAzMzcKNTAwIDUwMCAxMDAwIDQ3MSA2MTIgODM4IDM2MSAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDYzNiA2MzYgMzE4IDUwMAo0MDEgNDcxIDYxMiA5NjkgOTY5IDk2OSA1MzEgNjg0IDY4NCA2ODQgNjg0IDY4NCA2ODQgOTc0IDY5OCA2MzIgNjMyIDYzMiA2MzIKMjk1IDI5NSAyOTUgMjk1IDc3NSA3NDggNzg3IDc4NyA3ODcgNzg3IDc4NyA4MzggNzg3IDczMiA3MzIgNzMyIDczMiA2MTEgNjA1CjYzMCA2MTMgNjEzIDYxMyA2MTMgNjEzIDYxMyA5ODIgNTUwIDYxNSA2MTUgNjE1IDYxNSAyNzggMjc4IDI3OCAyNzggNjEyIDYzNAo2MTIgNjEyIDYxMiA2MTIgNjEyIDgzOCA2MTIgNjM0IDYzNCA2MzQgNjM0IDU5MiA2MzUgNTkyIF0KZW5kb2JqCjE2IDAgb2JqCjw8IC9BIDE3IDAgUiAvQyAxOCAwIFIgL0QgMTkgMCBSIC9GIDIwIDAgUiAvVSAyMSAwIFIgL2EgMjIgMCBSIC9iIDIzIDAgUgovYyAyNCAwIFIgL2QgMjUgMCBSIC9lIDI2IDAgUiAvZWlnaHQgMjcgMCBSIC9lcXVhbCAyOCAwIFIgL2YgMjkgMCBSCi9maXZlIDMwIDAgUiAvZm91ciAzMSAwIFIgL2cgMzIgMCBSIC9oIDMzIDAgUiAvaHlwaGVuIDM0IDAgUiAvaSAzNSAwIFIKL2wgMzYgMCBSIC9tIDM3IDAgUiAvbiAzOSAwIFIgL28gNDAgMCBSIC9vbmUgNDEgMCBSIC9wIDQyIDAgUgovcGVyY2VudCA0MyAwIFIgL3BlcmlvZCA0NCAwIFIgL3IgNDUgMCBSIC9zIDQ2IDAgUiAvc2l4IDQ3IDAgUgovc3BhY2UgNDggMCBSIC90IDQ5IDAgUiAvdGhyZWUgNTAgMCBSIC90d28gNTEgMCBSIC91IDUyIDAgUgovdW5kZXJzY29yZSA1MyAwIFIgL3YgNTQgMCBSIC93IDU1IDAgUiAveSA1NiAwIFIgL3plcm8gNTcgMCBSID4+CmVuZG9iagozIDAgb2JqCjw8IC9GMSAxNSAwIFIgPj4KZW5kb2JqCjQgMCBvYmoKPDwgL0ExIDw8IC9UeXBlIC9FeHRHU3RhdGUgL0NBIDAgL2NhIDEgPj4KL0EyIDw8IC9UeXBlIC9FeHRHU3RhdGUgL0NBIDEgL2NhIDEgPj4KL0EzIDw8IC9UeXBlIC9FeHRHU3RhdGUgL0NBIDAuNSAvY2EgMC41ID4+Ci9BNCA8PCAvVHlwZSAvRXh0R1N0YXRlIC9DQSAwLjggL2NhIDAuOCA+PiA+PgplbmRvYmoKNSAwIG9iago8PCA+PgplbmRvYmoKNiAwIG9iago8PCA+PgplbmRvYmoKNyAwIG9iago8PCAvRjEtRGVqYVZ1U2Fucy1taW51cyAzOCAwIFIgPj4KZW5kb2JqCjIgMCBvYmoKPDwgL1R5cGUgL1BhZ2VzIC9LaWRzIFsgMTEgMCBSIF0gL0NvdW50IDEgPj4KZW5kb2JqCjU4IDAgb2JqCjw8IC9DcmVhdG9yIChNYXRwbG90bGliIHYzLjEwLjUsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcpCi9Qcm9kdWNlciAoTWF0cGxvdGxpYiBwZGYgYmFja2VuZCB2My4xMC41KQovQ3JlYXRpb25EYXRlIChEOjIwMjUwODEzMTgwMTMzWikgPj4KZW5kb2JqCnhyZWYKMCA1OQowMDAwMDAwMDAwIDY1NTM1IGYgCjAwMDAwMDAwMTYgMDAwMDAgbiAKMDAwMDAxNzQ2NCAwMDAwMCBuIAowMDAwMDE3MTU2IDAwMDAwIG4gCjAwMDAwMTcxODggMDAwMDAgbiAKMDAwMDAxNzM3MyAwMDAwMCBuIAowMDAwMDE3Mzk0IDAwMDAwIG4gCjAwMDAwMTc0MTUgMDAwMDAgbiAKMDAwMDAwMDA2NSAwMDAwMCBuIAowMDAwMDAwMzQxIDAwMDAwIG4gCjAwMDAwMDQ0NTUgMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDA0NDM0IDAwMDAwIG4gCjAwMDAwMTU2MjUgMDAwMDAgbiAKMDAwMDAxNTQxOCAwMDAwMCBuIAowMDAwMDE0ODg3IDAwMDAwIG4gCjAwMDAwMTY2NzggMDAwMDAgbiAKMDAwMDAwNDQ3NSAwMDAwMCBuIAowMDAwMDA0NjM4IDAwMDAwIG4gCjAwMDAwMDQ5NDYgMDAwMDAgbiAKMDAwMDAwNTE4MyAwMDAwMCBuIAowMDAwMDA1MzMxIDAwMDAwIG4gCjAwMDAwMDU1NjAgMDAwMDAgbiAKMDAwMDAwNTk0MCAwMDAwMCBuIAowMDAwMDA2MjU3IDAwMDAwIG4gCjAwMDAwMDY1NjIgMDAwMDAgbiAKMDAwMDAwNjg2NiAwMDAwMCBuIAowMDAwMDA3MTg4IDAwMDAwIG4gCjAwMDAwMDc2NTYgMDAwMDAgbiAKMDAwMDAwNzgwMiAwMDAwMCBuIAowMDAwMDA4MDExIDAwMDAwIG4gCjAwMDAwMDgzMzMgMDAwMDAgbiAKMDAwMDAwODQ5OSAwMDAwMCBuIAowMDAwMDA4OTEzIDAwMDAwIG4gCjAwMDAwMDkxNTAgMDAwMDAgbiAKMDAwMDAwOTI3NiAwMDAwMCBuIAowMDAwMDA5NDIwIDAwMDAwIG4gCjAwMDAwMDk1MzkgMDAwMDAgbiAKMDAwMDAwOTg3MCAwMDAwMCBuIAowMDAwMDEwMDQyIDAwMDAwIG4gCjAwMDAwMTAyNzggMDAwMDAgbiAKMDAwMDAxMDU2OSAwMDAwMCBuIAowMDAwMDEwNzI0IDAwMDAwIG4gCjAwMDAwMTEwMzYgMDAwMDAgbiAKMDAwMDAxMTUxNSAwMDAwMCBuIAowMDAwMDExNjM4IDAwMDAwIG4gCjAwMDAwMTE4NzEgMDAwMDAgbiAKMDAwMDAxMjI3OCAwMDAwMCBuIAowMDAwMDEyNjcxIDAwMDAwIG4gCjAwMDAwMTI3NjEgMDAwMDAgbiAKMDAwMDAxMjk2NyAwMDAwMCBuIAowMDAwMDEzMzgwIDAwMDAwIG4gCjAwMDAwMTM3MDQgMDAwMDAgbiAKMDAwMDAxMzk1MSAwMDAwMCBuIAowMDAwMDE0MDc3IDAwMDAwIG4gCjAwMDAwMTQyMjQgMDAwMDAgbiAKMDAwMDAxNDM4NSAwMDAwMCBuIAowMDAwMDE0NTk5IDAwMDAwIG4gCjAwMDAwMTc1MjQgMDAwMDAgbiAKdHJhaWxlcgo8PCAvU2l6ZSA1OSAvUm9vdCAxIDAgUiAvSW5mbyA1OCAwIFIgPj4Kc3RhcnR4cmVmCjE3Njc3CiUlRU9GCg==",
      "text/plain": [
       "<Figure size 1650x1050 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "#| fig-align: center\n",
    "\n",
    "from scipy.stats import t\n",
    "\n",
    "# Parameters\n",
    "df = 8  # Degrees of freedom\n",
    "alpha = 0.05  # Upper tail probability\n",
    "t_critical = t.ppf(1 - alpha, df)  # Critical t-value at the 95th percentile\n",
    "\n",
    "# Generate x values for the t-distribution\n",
    "x = np.linspace(-4, 4, 500)\n",
    "y = t.pdf(x, df)\n",
    "\n",
    "# Plot the t-distribution\n",
    "plt.plot(x, y, label=f't_{df} Distribution', color='blue')\n",
    "plt.fill_between(x, y, where=(x >= t_critical), color='red', alpha=0.5, label=f'Upper {alpha*100}% Area')\n",
    "\n",
    "# Annotate the critical t-value on the x-axis\n",
    "plt.axvline(t_critical, ymin=0.02, ymax=0.30,color='red', linestyle='--', label=f'Critical t-value = {t_critical:.2f}')\n",
    "plt.text(t_critical, -0.02, f'{t_critical:.2f}', color='red', ha='center', va='top')\n",
    "\n",
    "# Add a horizontal line at y = 0\n",
    "plt.axhline(0, color='black', linestyle='-', linewidth=0.8)\n",
    "\n",
    "# Labels, title, and legend\n",
    "plt.title(f\"t-Distribution with {df} Degrees of Freedom\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.legend()\n",
    "\n",
    "# Adjust plot limits\n",
    "\n",
    "\n",
    "# Show plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba7c2e26",
   "metadata": {},
   "source": [
    "So, we reject the null hypothesis $H_0$ at the $5\\%$ level and conclude that there is a very strong evidence that $\\beta>0$, i.e., the portfolio value is increasing over stock price.  \n",
    "\n",
    "**Alternatively,** let's put our analysis in a different approach. We claim that \n",
    "\n",
    "**$H_0: \\beta=1$, there is a linear relationship**  \n",
    "vs  \n",
    "**$H_1: \\beta \\ne 1$**  \n",
    "\n",
    "In this case,  \n",
    "\n",
    "$$\n",
    "se(\\hat{\\beta}) = \\sqrt{\\frac{\\hat{\\sigma}^2}{S_{xx}}} = \\sqrt{\\frac{0.1594}{8.53}} =0.1367\n",
    "$$  \n",
    "\n",
    "Therefore, the $95\\%$ confidence interval for $\\beta$ is \n",
    "\n",
    "$$\n",
    "\\hat{\\beta} \\pm \\left\\{t_{0.025,8}\\times se(\\hat{\\beta})\\right\\}=0.836 \\pm 2.306\\times 0.1367 = (0.5207,1.1512) \n",
    "$$  \n",
    "\n",
    "The $95\\%$ two-sided confidence interval contains the value $1$, so the two-sided test conducted at $5\\%$ level results in $H_0$ being accepted.  \n",
    "\n",
    "### Mean Response and Individual Response  \n",
    "\n",
    "#### Mean Response  \n",
    "<p style=\"text-align: justify\">\n",
    "If $\\mu_0$ is the expected (mean) response for a value $x_0$ of the predictor variable, that is \n",
    "$\\mu_0 = \\mathbb{E}[Y|x_0]=\\alpha +\\beta x_0$, then $\\mu_0$ is an unbiased estimator given by </p>\n",
    "\n",
    "$$\n",
    "\\hat{\\mu}_0 = \\hat{\\alpha}+\\hat{\\beta} x_0\n",
    "$$  \n",
    "\n",
    "and the variance of the estimator is given by  \n",
    "\n",
    "$$\n",
    "var(\\hat{\\mu}_0) = \\left(\\frac{1}{n}+\\frac{(x_0-\\bar{x})^2}{S_{xx}}\\right)\\sigma^2\n",
    "$$  \n",
    "\n",
    "Therefore, \n",
    "\n",
    "$$\n",
    "\\frac{\\hat{\\mu}_0-\\mu_0}{se[\\hat{\\mu}_0] }= \\frac{\\hat{\\mu}_0-\\mu_0}{\\sqrt{\\left(\\frac{1}{n}+\\frac{(x_0-\\bar{x})^2}{S_{xx}}\\right)\\sigma^2}}\\sim t_{n-2}\n",
    "$$  \n",
    "\n",
    "#### Individual Response  \n",
    "\n",
    "The actual estimate of an individual response\n",
    "$$\n",
    "\\hat{y}_0 = \\hat{\\alpha} +\\hat{\\beta}x_0\n",
    "$$  \n",
    "\n",
    "<p style=\"text-align: justify\">\n",
    "However, the uncertainty associated with this estimator, as indicated by its variance, is higher compared to the mean estimator because it relies on the value of an individual response $y_0$ rather than the more stable mean. To account for the additional variability of an individual response relative to the mean, an extra term, $\\sigma^2$, must be included in the variance expression for the estimator of a mean response.</p>  \n",
    "\n",
    "$$\n",
    "var[\\hat{y}_0] = \\left(1+\\frac{1}{n}+\\frac{(x_0-\\bar{x})^2}{S_{xx}}\\right)\\sigma^2\n",
    "$$  \n",
    "\n",
    "Thus, \n",
    "\n",
    "$$\n",
    "\\frac{\\hat{y}-y_0}{se[\\hat{y}_0]}=\\frac{\\hat{y}-y_0}{\\sqrt{\\left(1+\\frac{1}{n}+\\frac{(x_0-\\bar{x})^2}{S_{xx}}\\right)\\sigma^2}}\\sim t_{n-2}\n",
    "$$ \n",
    "\n",
    "<p style=\"text-align:justify\">\n",
    "Let's put this two idea through our example. If we want to find a $95\\%$ confidence interval or the \n",
    "expected portfolio value on stock price of say, 360. In that case,</p>\n",
    "\n",
    "$$\n",
    "\\text{Estimate of the expected portfolio value} = 0.266+0.836\\times 3.6 = 3.276\n",
    "$$  \n",
    "\n",
    "and \n",
    "\n",
    "$$\n",
    "\\text{se}[\\text{Estimate}] = \\sqrt{\\left(\\frac{1}{10}+\\frac{(3.6-3.566)^2}{8.53}\\right) 0.1594}=0.1263\n",
    "$$  \n",
    "\n",
    "So, the $95\\%$ CI  \n",
    "\n",
    "$$\n",
    "3.276\\pm (t_{0.025,8}\\times \\text{se}[\\text{Estimate}]) = 3.276 \\pm 2.306\\times 0.1263 = (2.985,3.567)\n",
    "$$  \n",
    "\n",
    "That is for a stock price of $\\$360$, the expected portfolio value would be in the range of $(\\$298.50,\\$356.70)$\n",
    "\n",
    "Similarly, the $95\\%$ CI for the predicted actual portfolio value\n",
    "\n",
    "\\begin{align*}\n",
    "3.276\\pm (t_{0.025,8}\\times \\text{se}[\\text{Estimate}]) &= 3.276 \\pm 2.306\\sqrt{\\left(1+\\frac{1}{10}+\\frac{(3.6-3.566)^2}{8.53}\\right) 0.1594}\\\\\n",
    "& = (2.3103,4.2417)\n",
    "\\end{align*} \n",
    "\n",
    "or $(\\$231.03,\\$424.17)$  \n",
    "\n",
    "### Model Accuracy  \n",
    "\n",
    "The residual from the fit at $x_i$ is the estimated error which is defined by \n",
    "$$\n",
    "\\hat{\\epsilon}_i = y_i - \\hat{y}_i\n",
    "$$ \n",
    "\n",
    "<p style=\"text-align: justify\">\n",
    "Scatter plots of residuals versus the explanatory variable (or the fitted response values) are particularly insightful. A lack of random scatter in the residuals, such as the presence of a discernible pattern, indicates potential shortcomings in the model.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "de4c92fb",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1650x1050 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "df = pd.DataFrame({\n",
    "    'Stock': ['Apple', 'Citi', 'MS', 'WF', 'GS', 'Google', 'Amazon', 'Tesla', 'Toyota', 'SPY'],\n",
    "    'StockPrice': [2.11, 2.42, 2.52, 3.21, 3.62, 3.86, 4.13, 4.27, 4.51, 5.01], \n",
    "    'Portfolio': [2.12, 2.16, 2.51, 2.65, 3.62, 3.15, 4.32, 3.31, 4.18, 4.45]\n",
    "})\n",
    "x = df.StockPrice.values\n",
    "y = df.Portfolio.values \n",
    "\n",
    "y_hat = [0.266+0.836*i for i in x]\n",
    "plt.scatter(x, y-y_hat)\n",
    "plt.axhline(0)\n",
    "plt.ylabel('Residuals')\n",
    "plt.xlabel('Stock Price')\n",
    "plt.title('Scatter plot of the residuals from the fitted line')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e8b9d8c",
   "metadata": {},
   "source": [
    "<p style=\"text-align: justify\">\n",
    "In this plot, we can see that the residuals tend to increase as $x$ increases, indicates that the error variance is not bounded, but increasing with $x$. So, the model is not the best one. A transformation of the responses may stabilize the error variance. <br>\n",
    "<br>\n",
    "In certain case, for some growth models, the appropriate model is that the expected response is related to the exploratory variable through an exponential relationship, i.e.,\n",
    "</p>  \n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbb{E}[Y_i|X=x_i] &= \\alpha e^{\\beta x_i}\\\\\n",
    "\\implies z_i = \\log y_i & = \\eta + \\beta x_i + \\epsilon_i; \\hspace{4mm}\\text{where }\\eta=\\log \\alpha\n",
    "\\end{align*}  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "05f6edaf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum x: 35.66\n",
      "Sum y: 11.43\n",
      "Sₓₓ: 8.53\n",
      "Sᵧᵧ: 0.70\n",
      "Sₓᵧ: 2.29\n",
      " \n",
      "r : 0.94\n"
     ]
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "x = df.StockPrice.values\n",
    "y = np.log(df.Portfolio.values)\n",
    "\n",
    "n = len(x)\n",
    "\n",
    "x_sum, y_sum =0,0\n",
    "s_xx, s_yy, s_xy = 0,0,0\n",
    "for i in range(n):\n",
    "    x_sum += x[i]\n",
    "    s_xx += x[i]**2\n",
    "    y_sum += y[i]\n",
    "    s_yy += y[i]**2\n",
    "    s_xy += x[i]*y[i]    \n",
    "\n",
    "s_xx = s_xx - (x_sum)**2/n\n",
    "s_yy = s_yy - (y_sum)**2/n\n",
    "s_xy = s_xy - (x_sum * y_sum)/n\n",
    "\n",
    "r = s_xy/math.sqrt(s_xx * s_yy)\n",
    "\n",
    "# Print with formatted labels\n",
    "print(f\"Sum x: {x_sum:.2f}\")\n",
    "print(f\"Sum y: {y_sum:.2f}\")\n",
    "print(f\"Sₓₓ: {s_xx:.2f}\")\n",
    "print(f\"Sᵧᵧ: {s_yy:.2f}\")\n",
    "print(f\"Sₓᵧ: {s_xy:.2f}\")\n",
    "print(' ')\n",
    "print(f\"r : {r:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d33f1ac6",
   "metadata": {},
   "source": [
    "Now we have: \n",
    "\n",
    "\\begin{align*}\n",
    "n & = 10, \\hspace{4mm} \\sum x = 35.66, \\hspace{4mm} \\sum y = 11.43\\\\\n",
    "S_{xx} &= 8.53 \\hspace{4mm} S_{yy}=0.70, \\hspace{4mm} S_{xy}=2.29\\\\\n",
    "\\implies \\hat{\\beta} &=\\frac{S_{xy}}{S_{xx}}= \\frac{2.29}{8.53} = 0.268\\\\\n",
    "\\hat{\\alpha} &= \\frac{\\sum y}{n} - \\hat{\\beta} \\frac{\\sum x}{n} = \\bar{y}-\\hat{\\beta}\\bar{x}\\\\\n",
    "& = 1.143 - 0.268 \\times 3.566 = 0.1873\n",
    "\\end{align*} "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2397f8d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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",
      "text/plain": [
       "<Figure size 1650x1050 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| code-fold: true\n",
    "import numpy as np\n",
    "z_hat = [np.log(0.1873)+0.268*i for i in x]\n",
    "z = np.log(y)\n",
    "plt.scatter(x, z-z_hat)\n",
    "plt.axhline(np.mean(z-z_hat))\n",
    "plt.ylabel('Residuals')\n",
    "plt.xlabel('Stock Price')\n",
    "plt.title('Scatter plot of the residuals from the fitted line')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cb12e39",
   "metadata": {},
   "source": [
    "Now the residuals look good, that is no special pattern or increasing the error variance. \n",
    "\n",
    "Thanks for reading.  \n",
    "\n",
    "## References  \n",
    "\n",
    "1. **Montgomery, D. C., & Runger, G. C.** (2014). *Applied Statistics and Probability for Engineers*. Wiley.  \n",
    "2. **Casella, G., & Berger, R. L.** (2002). *Statistical Inference*. Duxbury.  \n",
    "3. **Cohen, J., Cohen, P., West, S. G., & Aiken, L. S.** (2003). *Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences*. Routledge.  \n",
    "4. **Seber, G. A. F., & Lee, A. J.** (2003). *Linear Regression Analysis*. Wiley. \n",
    "5. **Neter, J., Kutner, M. H., Nachtsheim, C. J., & Wasserman, W.** (1996). *Applied Linear Statistical Models*. Irwin.  \n",
    "6. **Hastie, T., Tibshirani, R., & Friedman, J.** (2009). *The Elements of Statistical Learning: Data Mining, Inference, and Prediction*. Springer.  \n",
    "7. **Weisberg, S.** (2005). *Applied Linear Regression*. Wiley.  \n",
    "8. **Bivariate Normal Distribution Explanation**:  \n",
    "   - Rice, J. A. (2006). *Mathematical Statistics and Data Analysis*. Thomson Brooks/Cole.  \n",
    "   - A detailed exploration of the bivariate normal distribution and its properties.\n",
    "9. **Fisher's Transformation of Correlation Coefficients**:  \n",
    "   - Fisher, R. A. (1921). *On the probable error of a coefficient of correlation*. Metron, 1, 3-32.  \n",
    "   - The foundational paper describing Fisher's transformation and its use in hypothesis testing.\n",
    "\n",
    "\n",
    "\n",
    "**Share on** \n",
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