1. Simple Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "import seaborn as sns\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Simple Linear Regression</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a simple linear regression model as in every econometrics textbooks\n",
    "$$\n",
    "Y_i=\\beta_1+\\beta_2X_i+u_i\n",
    "$$\n",
    "where $Y$ is **dependent variable**, $X$ is **independent variable** and $u$ is **disturbance term**. $\\beta_1$ and $\\beta_2$ are unknown parameters that we are aiming to estimate by feeding the data in the model. Without disturbance term, the model is simple a function of a straight line in $\\mathbb{R}^2$, such as\n",
    "$$\n",
    "Y = 2 + 3X\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the context of _machine learning_ (ML), the $X$ is usually called **feature variable** and $Y$ called **target variable**. And linear regression is the main tool in **supervised learning**, meaning that $Y$ is supervising $X$./\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(1, 10, 10)\n",
    "Y = 2 + 3 * X\n",
    "fig, ax = plt.subplots(figsize=(7, 7))\n",
    "ax.plot(X, Y)\n",
    "ax.scatter(X, Y, c=\"r\")\n",
    "ax.grid()\n",
    "ax.set_title(\"$Y=2+3x$\")\n",
    "ax.set_xlim(0, 10)\n",
    "ax.set_ylim(0, 40)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are five reasons justified that we need a disturbance term:\n",
    "\n",
    "<i>1. omission of independent variables</i><br>\n",
    "<i>2. aggregation of variables</i><br>\n",
    "<i>3. model misspecification</i><br>\n",
    "<i>4. function misspecification, eg. should be nonlinear rather than linear</i><br>\n",
    "<i>5. measurement error</i>\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second one means that if we intend to aggregate the variable to a macro level, for instance every family has a consumption function, but aggregation on a national level causes discrepancies which contribute to the disturbance term.\n",
    "\n",
    "The third and forth one will be discussed in details in later chapter.\n",
    "\n",
    "The fifth one includes all types of error, man-made or natural. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Odinary Least Squares</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Odinary Least Squares** is the most common estimation technique used in ML or econometrics, it is popular due to its _simplicity_ and _transparency_. You'll be able to derive the whole estimation process by hand-calculation, all steps will have _closed-form expression_.\n",
    "\n",
    "We'll demonstrate OLS with our first plot. Every time you run this script, the result will be different than mine, because no random seeds are set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta1, beta2 = 2, 3\n",
    "\n",
    "\n",
    "def gen_linreg_data(beta1, beta2, samp_size, disturb_scale):\n",
    "\n",
    "    X = np.linspace(1, 10, samp_size)\n",
    "    u = disturb_scale * np.random.randn(samp_size)\n",
    "    Y = beta1 + beta2 * X + u\n",
    "    Y_hat = beta1 + beta2 * X\n",
    "    return X, Y, Y_hat\n",
    "\n",
    "\n",
    "def plot_lin_reg(X, Y, Y_hat):\n",
    "    fig, ax = plt.subplots(figsize=(7, 7))\n",
    "\n",
    "    for i in range(len(Y)):\n",
    "        dot_fit_values = [X[i], X[i]]\n",
    "        dot_org_values = [Y[i], Y_hat[i]]\n",
    "        ax.plot(\n",
    "            dot_fit_values,\n",
    "            dot_org_values,\n",
    "            linestyle=\"--\",\n",
    "            color=\"red\",\n",
    "            label=\"residual\",\n",
    "        )\n",
    "\n",
    "    ax.plot(X, Y_hat)\n",
    "    ax.scatter(X, Y_hat, c=\"k\")\n",
    "    ax.scatter(X, Y, c=\"r\")\n",
    "    ax.grid()\n",
    "    ax.set_title(\"$\\hat Y ={}+{}X$\".format(beta1, beta2))\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    X, Y, Y_hat = gen_linreg_data(\n",
    "        beta1=beta1, beta2=beta2, samp_size=10, disturb_scale=5\n",
    "    )\n",
    "    plot_lin_reg(X, Y, Y_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have plotted a fitted line onto $10$ observations (red dots) which was generated by $Y_i = 2+3X_i+5u_i$, where $u_i \\sim N(0, 1)$. For easy demonstration, say we have a 'perfect' estimator that provides\n",
    "$$\n",
    "\\hat{\\beta}_1 = 2\\\\\n",
    "\\hat{\\beta}_2 = 3\n",
    "$$\n",
    "where $\\hat{\\beta}_1 $ and $\\hat{\\beta}_2$ are estimates, in contrast $\\beta_1$ and $\\beta_2$ are model parameters.\n",
    "\n",
    "Therefore we can plot a fitted line (blue line) $\\hat{Y} = 2+3X$. The red dashed line is the difference of $Y_i$ and $\\hat{Y}_i$, we officially call it **residual**, denoted as $\\varepsilon_i$.\n",
    "$$\n",
    "\\varepsilon_i = Y_i - \\hat{Y}_i = Y_i - \\hat{\\beta}_1-\\hat{\\beta}_2X_i\n",
    "$$\n",
    "The OLS algorithm is aiming find the estimates of $\\beta_1$ and $\\beta_2$ such that\n",
    "$$\n",
    "\\text{min}\\text{ RSS}=\\sum_{i=1}^n \\varepsilon^2_i \n",
    "$$\n",
    "where $RSS$ is the **residual sum of squares** $(\\text{RSS})$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In ML context, notation is slightly different, but the ideas are the same, a **cost function** is defined with $\\text{RSS}$\n",
    "$$\n",
    "J(\\hat{\\beta_1}, \\hat{\\beta}_2) = \\frac{1}{2m} \\sum_{i=1}^n \\varepsilon^2_i \n",
    "$$\n",
    "Then minimize the cost function\n",
    "$$\n",
    "\\text{min }J(\\hat{\\beta_1}, \\hat{\\beta}_2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To minimise the $RSS$, we simply take _partial derivatives_ w.r.t. $b_2$ and $b_1$ respectively. The results are the OLS estimators of simple linear regression, which are \n",
    "\\begin{align}\n",
    "\\hat{\\beta}_2 &=\\frac{\\sum_{i=1}^n(X_i-\\bar{X})(Y_i-\\bar{Y})}{\\sum^n_{i=1}(X_i-\\bar{X})^2}=\\frac{\\text{Cov}(X, Y)}{\\text{Var}(X)}\\\\\n",
    "\\hat{\\beta}_1 &= \\bar{Y}-\\hat{\\beta}_2\\bar{X}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these formulae in mind, let's perform a serious OLS estimation. Considering possible repetitive use of OLS in this tutorial, we will write a class for OLS. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class S_OLS:\n",
    "    \"\"\"Create instances with S_OLS(X, Y), where X and Y are data array.\"\"\"\n",
    "\n",
    "    def __init__(self, X, Y):\n",
    "        self.X = X\n",
    "        self.Y = Y\n",
    "\n",
    "    def ols(self):\n",
    "        \"\"\"Estimate the data with OLS method, and return b1 and b2.\"\"\"\n",
    "        cov_mat = np.cov(self.X, self.Y)\n",
    "        self.b2 = cov_mat[0, 1] / cov_mat[0, 0]\n",
    "        self.b1 = np.mean(self.Y) - self.b2 * np.mean(self.X)\n",
    "        self.Y_hat = self.b1 + self.b2 * self.X\n",
    "        print(\"b1 estimate: {:.4f}\".format(self.b1))\n",
    "        print(\"b2 estimate: {:.4f}\".format(self.b2))\n",
    "        return self.Y_hat, self.b2, self.b1\n",
    "\n",
    "    def simul_plot(self, beta1, beta2):\n",
    "        \"\"\"Plot scatter plot and fitted line with ols_plot(self, beta1, beta2),\n",
    "        beta1 and beta2 are parameters of data generation process.\"\"\"\n",
    "        fig, ax = plt.subplots(figsize=(7, 7))\n",
    "        for i in range(len(Y)):\n",
    "            dot_fit_values = [self.X[i], self.X[i]]\n",
    "            dot_org_values = [self.Y[i], self.Y_hat[i]]\n",
    "            ax.plot(dot_fit_values, dot_org_values, linestyle=\"--\", color=\"red\")\n",
    "        ax.scatter(self.X, self.Y_hat, c=\"k\")\n",
    "        ax.scatter(self.X, self.Y, c=\"r\")\n",
    "        ax.plot(self.X, self.Y_hat, label=\"$b_1$= {:.2f}, $b_2$={:.2f}\".format(b1, b2))\n",
    "        ax.grid()\n",
    "        ax.set_title(\"$\\hat Y ={:.2f}+{:.2f}X$\".format(b1, b2))\n",
    "        Y_hat_perfect = beta1 + beta2 * X\n",
    "        ax.plot(X, Y_hat_perfect, label=r\"$\\beta_1=2, \\beta_2=3$\")\n",
    "        ax.legend()\n",
    "        plt.show()\n",
    "\n",
    "    def ols_plot(self, xlabel, ylabel):\n",
    "        self.xlabel = xlabel\n",
    "        self.ylabel = ylabel\n",
    "        fig, ax = plt.subplots(figsize=(7, 7))\n",
    "        ax.scatter(self.X, self.Y_hat, c=\"k\")\n",
    "        ax.scatter(self.X, self.Y, c=\"r\")\n",
    "        ax.plot(\n",
    "            self.X,\n",
    "            self.Y_hat,\n",
    "            label=\"$b_1$= {:.2f}, $b_2$={:.2f}\".format(self.b1, self.b2),\n",
    "        )\n",
    "        ax.grid()\n",
    "        ax.set_title(\"$\\hat Y ={:.2f}+{:.2f}X$\".format(self.b1, self.b2))\n",
    "        ax.set_xlabel(self.xlabel)\n",
    "        ax.set_ylabel(self.ylabel)\n",
    "\n",
    "    def r_sq(self):\n",
    "        \"\"\"Calculate coefficient of determination and correlation of Y and Yhat\"\"\"\n",
    "        self.ESS = np.var(self.Y_hat)\n",
    "        self.RSS = np.var(self.Y - self.Y_hat)\n",
    "        self.R_sq = self.ESS / self.RSS\n",
    "        return self.ESS, self.RSS, self.R_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y, Y_hat = gen_linreg_data(beta1=4, beta2=2, samp_size=15, disturb_scale=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.88496253],\n",
       "       [0.88496253, 1.        ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b1 estimate: 4.8314\n",
      "b2 estimate: 1.9802\n"
     ]
    }
   ],
   "source": [
    "s_ols = S_OLS(X, Y)\n",
    "Y_hat, betahat2, betahat1 = s_ols.ols()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A convenient function ```np.polyfit``` of curve fitting could verify our results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.98022248, 4.83137211])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(X, Y, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot the fitted line $b_1+b_2X$, original line $\\beta_1+\\beta_2X$ and observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_ols.ols_plot(\"X\", \"Y\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the estimation result and graph above, we can notice $\\hat{\\beta}_1$ and $\\hat{\\beta}_2$ are close to true parameters $\\beta_1$ and $\\beta_2$ if scalar of disturbance term is small."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Interpretation of Estimated Coefficients</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will check on a real data set to understand basic principles of interpreting estimates. The data set collected  average apartment price ¥/$m^2$ and average annual disposable income from $25$ Chinese cities in 2020. \n",
    "\n",
    "Load the data with Pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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></th>\n",
       "      <th>cities</th>\n",
       "      <th>house_price</th>\n",
       "      <th>salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Shenzhen</td>\n",
       "      <td>87957</td>\n",
       "      <td>64878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Beijing</td>\n",
       "      <td>64721</td>\n",
       "      <td>69434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Shanghai</td>\n",
       "      <td>59072</td>\n",
       "      <td>72232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Xiamen</td>\n",
       "      <td>49803</td>\n",
       "      <td>58140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Guangzhou</td>\n",
       "      <td>39851</td>\n",
       "      <td>68304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      cities  house_price  salary\n",
       "0   Shenzhen        87957   64878\n",
       "1    Beijing        64721   69434\n",
       "2   Shanghai        59072   72232\n",
       "3     Xiamen        49803   58140\n",
       "4  Guangzhou        39851   68304"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel(\n",
    "    \"Basic_Econometrics_practice_data.xlsx\", sheet_name=\"CN_Cities_house_price\"\n",
    ")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimate parameters with OLS algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b1 estimate: -29181.1698\n",
      "b2 estimate: 1.1010\n"
     ]
    }
   ],
   "source": [
    "s_ols_house_income = S_OLS(df[\"salary\"], df[\"house_price\"])\n",
    "Y_hat, b2, b1 = s_ols_house_income.ols()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the observation and regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_ols_house_income.ols_plot(\"Disposable Income\", \"House Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{\\beta}_2$ can be interpreted literally as the graph shows, as disposable income increases $1$ yuan (Chinese currency unit), the house price increases $1.1$ yuan. \n",
    "\n",
    "As for $\\hat{\\beta}_1$, it is tricky to interpret the face value that if the disposable income is zero, i.e. the house price is $-29181$ yuan if disposable income is $0$, it doesn't make any sense. The basic principle of interpreting constant term is to check if it has a plausible meaning when all independent/feature variables equals zero. If no sensible meaning, you don't need to interpret it, this is a well known defect of linear regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Important Results of OLS</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some features of OLS could provide us insights of mechanism of the algorithm. \n",
    "\n",
    "The _first_ one is \n",
    "$$\n",
    "\\bar{\\varepsilon}=0\n",
    "$$\n",
    "It is true because\n",
    "$$\n",
    "\\bar{\\varepsilon}=\\bar{Y}-\\hat{\\beta}_1-\\hat{\\beta}_2\\bar{X}=\\bar{Y}-(\\bar{Y}-\\hat{\\beta}_2\\bar{X})-\\hat{\\beta}_2\\bar{X}=0\n",
    "$$\n",
    "holds. We can demonstrate numerically with the variables that we have defined in house price example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.473825588822365e-12"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "epsilon = df[\"house_price\"] - Y_hat\n",
    "np.mean(epsilon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is not theoretically zero due to some numerical round-off errors, but we treat it as zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The _second_ feature is \n",
    "$$\n",
    "\\bar{\\hat{Y}}=\\bar{Y}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of Y hat: 30218.879999999994\n",
      "Mean of Y: 30218.88\n"
     ]
    }
   ],
   "source": [
    "print(\"Mean of Y hat: {}\".format(np.mean(Y_hat)))\n",
    "print(\"Mean of Y: {}\".format(np.mean(df[\"house_price\"])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The _third_ and _forth_ features are\n",
    "$$\n",
    "\\sum_i^n X_i\\varepsilon_i=0\\\\\n",
    "\\sum_i^n \\hat{Y}_i\\varepsilon_i=0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can be shown by using a _dot product_ function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.814697265625e-06\n",
      "1.9073486328125e-06\n"
     ]
    }
   ],
   "source": [
    "print(np.dot(df[\"salary\"], epsilon))\n",
    "print(np.dot(Y_hat, epsilon))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Actually, lots of econometric theory can be conveniently derived by linear algebra. \n",
    "\n",
    "For instance, in linear algebra, covariance has a geometric interpretation\n",
    "$$\n",
    "\\text{Cov}(X, Y)=x\\cdot y= ||x||||y||\\cos{\\theta}\n",
    "$$\n",
    "where $x$ and $y$ are vectors in $\\mathbb{R}^n$. If dot product equals zero, geometrically these two vectors are perpendicular, denote as $x\\perp y$. Therefore the third and forth features are equivalent to\n",
    "$$\n",
    "\\text{Cov}(X, e)=0\\\\\n",
    "\\text{Cov}(\\hat{Y}, e)=0\n",
    "$$\n",
    "i.e. $x\\perp e$ and $\\hat{y} \\perp e$. Traditionally, the vectors are denoted as lower case letters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Variance of Decomposition</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variance of decomposition** is based on analysis of variance (ANOVA), if you don't know what ANOVA is, <a href='https://github.com/MacroAnalyst/Basic_Statistics_With_Python/blob/main/Chapter%205%20-%20Analysis%20of%20Variance%20and%20Chi-Squared%20Test.ipynb'>check here</a>. We know that any observation can be decomposed as a fitted value and a residual\n",
    "$$\n",
    "Y_i = \\hat{Y}_i+\\varepsilon_i\n",
    "$$\n",
    "Take variance on both sides\n",
    "$$\n",
    "\\text{Var}(Y)=\\text{Var}(\\hat{Y}+\\varepsilon)=\\operatorname{Var}(\\hat{Y})+\\operatorname{Var}(\\varepsilon)+ \\underbrace{2 \\operatorname{Cov}(\\hat{Y}, \\varepsilon)}_{=0}\n",
    "$$\n",
    "Or in the explicit form\n",
    "$$\n",
    "\\frac{1}{n} \\sum_{i=1}^{n}\\left(Y_{i}-\\bar{Y}\\right)^{2}=\\frac{1}{n} \\sum_{i=1}^{n}\\left(\\hat{Y}_{i}-\\overline{\\hat{Y}}\\right)^{2}+\\frac{1}{n} \\sum_{i=1}^{n}\\left(\\varepsilon_{i}-\\bar{\\varepsilon}\\right)^{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the OLS features, i.e. $\\bar{\\hat{Y}}=\\bar{Y}$ and $\\bar{\\varepsilon}=0$, the equation simplifies into\n",
    "$$\n",
    "\\underbrace{\\sum_{i=1}^{n}\\left(Y_{i}-\\bar{Y}\\right)^{2}}_{TSS}=\\underbrace{\\sum_{i=1}^{n}\\left(\\hat{Y}_{i}-\\bar{Y}\\right)^{2}}_{ESS}+\\underbrace{\\sum_{i=1}^{n} \\varepsilon_{i}^{2}}_{RSS}\n",
    "$$\n",
    "where $TSS$ means **total sum of squares**, $ESS$ means **explained sum of squares**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Coefficient of Determination</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though $ESS$ is called 'explained' part, it might be entirely wrong due to misspecification of model. That being said, we still need a quantitative indicator that tells us how much the model is able to 'explain' the behaviour of the dependent variables. \n",
    "\n",
    "The **coefficient of determination** is most intuitive indicator\n",
    "$$\n",
    "R^2 = \\frac{ESS}{TSS}=\\frac{\\sum_{i=1}^{n}\\left(\\hat{Y}_{i}-\\bar{Y}\\right)^{2}}{\\sum_{i=1}^{n}\\left(Y_{i}-\\bar{Y}\\right)^{2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have written a ```r_sq()``` method in the ```S_OLS``` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5744603125471681\n"
     ]
    }
   ],
   "source": [
    "ess, rss, r_sq = s_ols_house_income.r_sq()\n",
    "print(r_sq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It means the disposable income can explain $57\\%$ of house price variation. Furthermore, \n",
    "$$\n",
    "R^2 = \\frac{TSS - RSS}{TSS}=1-\\frac{RSS}{TSS}\n",
    "$$\n",
    "it is clear that minimise $RSS$ is equivalent to maximise $R^2$.\n",
    "\n",
    "Alternatively, the $R^2$ can be shown its relationship with correlation coefficient $r_{Y, \\hat{Y}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "r_{Y, \\hat{Y}} &=\\frac{\\operatorname{Cov}(Y, \\hat{Y})}{\\sqrt{\\operatorname{Var}(Y) \\operatorname{Var}(\\hat{Y})}}=\\frac{\\operatorname{Cov}([\\hat{Y}+e], \\hat{Y})}{\\sqrt{\\operatorname{Var}(Y) \\operatorname{Var}(\\hat{Y})}}=\\frac{\\operatorname{Cov}(\\hat{Y}, \\hat{Y})+\\operatorname{Cov}(e, \\hat{Y})}{\\sqrt{\\operatorname{Var}(Y) \\operatorname{Var}(\\hat{Y})}}=\\frac{\\operatorname{Var}(\\hat{Y})}{\\sqrt{\\operatorname{Var}(Y) \\operatorname{Var}(\\hat{Y})}} \\\\\n",
    "&=\\frac{\\sqrt{\\operatorname{Var}(\\hat{Y}) \\operatorname{Var}(\\hat{Y})}}{\\sqrt{\\operatorname{Var}(Y) \\operatorname{Var}(\\hat{Y})}}=\\sqrt{\\frac{\\operatorname{Var}(\\hat{Y})}{\\operatorname{Var}(Y)}}=\\sqrt{R^{2}}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Gauss-Markov Conditions</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to achieve the best estimation by OLS, the disturbance term ideally has to satisfy four conditions which are called **Gauss-Markov Conditions**. Provided that all G-M conditions satisfied, OLS is the preferred over all other estimators, because mathematically it is proved to be the **Best Linear Unbiased Estimator** (BLUE). This conclusion is called **Gauss-Markov Theorem**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. $E(u_i|X_i)=0$\n",
    "2. $E(u_i^2|X_i)= \\sigma^2$ for all $i$, **homoscedasticity**\n",
    "3. $\\text{Cov}(u_i, u_j)=0, \\quad i\\neq j$, no **autocorrelation**.\n",
    "4. $\\text{Cov}(X_i, u_i)=0$, assuming $X_i$ is non-stochastic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to G-M conditions, we also assume normality of disturbance term, i.e. $u_i\\sim N(0, \\sigma^2_u)$, which is guaranteed by _Central Limit Theorem_.\n",
    "\n",
    "In practice, almost impossible to have all conditions satisfied simultaneously or even one perfectly, but we must be aware of severity of violations, because any violation of G-M condition will compromise the quality of estimation results. And identifying which condition is violated could also lead us to corresponding remedies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Random Components of Regression Coefficients</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the OLS formula of $\\beta_2$\n",
    "$$\n",
    "\\hat{\\beta}_{2}=\\frac{\\operatorname{Cov}(X, Y)}{\\operatorname{Var}(X)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plug in $Y=\\beta_1+\\beta_2X+u$:\n",
    "$$\n",
    "\\hat{\\beta}_{2}=\\frac{\\operatorname{Cov}(X, Y)}{\\operatorname{Var}(X)}=\\frac{\\operatorname{Cov}(X, \\beta_1+\\beta_2X+u)}{\\operatorname{Var}(X)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariance operation rules come in handy\n",
    "$$\n",
    "\\operatorname{Cov}(X, \\beta_1+\\beta_2X+u)=\\operatorname{Cov}\\left(X, \\beta_{1}\\right)+\\operatorname{Cov}\\left(X, \\beta_{2} X\\right)+\\operatorname{Cov}(X, u)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\operatorname{Cov}\\left(X, \\beta_{1}\\right)=0$, and $\\operatorname{Cov}\\left(X, \\beta_{2} X\\right)=\\beta_2 \\operatorname{Var}(X)$, therefore\n",
    "$$\n",
    "\\hat{\\beta}_{2}=\\frac{\\operatorname{Cov}(X, Y)}{\\operatorname{Var}(X)}=\\beta_{2}+\\frac{\\operatorname{Cov}(X, u)}{\\operatorname{Var}(X)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If $u$ perfectly uncorrelated with $X$ as in G-M condition, the second term should be $0$. However that rarely happens, so the $\\hat{\\beta}_2$ and $\\beta_2$ will always have certain level of discrepancy. And note that we can't decompose $\\hat{\\beta}_2$ in practice, because we don't know the true value of $\\beta_2$.\n",
    "\n",
    "And also note that there are two ways to improve the accuracy of $\\hat{\\beta}_2$, either lower the correlation of $X$ and $u$ or increase the variance of $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Monte Carlo Sampling Distribution</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to perform a Monte Carlo simulation to show the sampling distribution of $\\hat{\\beta}_1$ and $\\hat{\\beta}_2$. First, we write a simple class for OLS Monte Carlo experiment. \n",
    "\n",
    "We can set $\\beta_1$, $\\beta_2$, $N$ and $a_u$ for initialisation. The model is\n",
    "$$\n",
    "Y_i=\\beta_1+\\beta_2X_i +a_uu_i, \\qquad i\\in(1, n),\\qquad u_i\\sim N(0,1)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "class OLS_Monte_Carlo:\n",
    "    def __init__(self, beta1, beta2, N, u_scaler):\n",
    "        \"\"\"Input beta1, beta2, sample size, scaler of disturbance\"\"\"\n",
    "        self.beta1 = beta1\n",
    "        self.beta2 = beta2\n",
    "        self.u_scaler = u_scaler\n",
    "        self.N = N\n",
    "        self.X = self.N * np.random.rand(\n",
    "            self.N\n",
    "        )  # generate N random X's in the range of (0, N)\n",
    "\n",
    "    def ols(self):\n",
    "        \"\"\"Estimate the data with OLS method, and return b1 and b2.\"\"\"\n",
    "        self.u = self.u_scaler * np.random.randn(self.N)\n",
    "        self.Y = self.beta1 + self.beta2 * self.X + self.u\n",
    "        cov_mat = np.cov(self.X, self.Y)\n",
    "        self.b2 = cov_mat[0, 1] / cov_mat[0, 0]\n",
    "        self.b1 = np.mean(self.Y) - self.b2 * np.mean(self.X)\n",
    "        return self.b2, self.b1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instantiate the OLS Monte Carlo object with $\\beta_1=2$, $\\beta_2=3$, $n=10$ and $a_u=1$, then run $10000$ times of simulations, each time generated a new $u$. All estimated $\\hat{\\beta}_1$ and $\\hat{\\beta}_2$ are collected in their arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "ols_mt = OLS_Monte_Carlo(beta1=2, beta2=3, N=10, u_scaler=1)\n",
    "b2_array, b1_array = [], []\n",
    "for i in range(10000):\n",
    "    b2, b1 = ols_mt.ols()\n",
    "    b2_array.append(b2)\n",
    "    b1_array.append(b1)\n",
    "b2_mean = np.mean(b2_array)\n",
    "b1_mean = np.mean(b1_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the histogram and the mean of estimates. Not difficult to notice that the mean of the $\\hat{\\beta}_1$ and $\\hat{\\beta}_2$ are very close to 'true values'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 648x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=2, ncols=1, figsize=(9, 9))\n",
    "ax[0].hist(b1_array, bins=100)\n",
    "ax[0].axvline(b1_mean, color=\"salmon\", label=r\"$\\bar{\\beta}_1$=%f\" % b1_mean)\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].hist(b2_array, bins=100)\n",
    "ax[1].axvline(b2_mean, color=\"salmon\", label=r\"$\\bar{\\beta}_2$=%f\" % b2_mean)\n",
    "ax[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we try again with a larger disturbance scaler $a_u = 2$ and keep rest parameters unchanged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ols_mt = OLS_Monte_Carlo(beta1=2, beta2=3, N=10, u_scaler=2)\n",
    "b2_array, b1_array = [], []\n",
    "for i in range(10000):\n",
    "    b2, b1 = ols_mt.ols()\n",
    "    b2_array.append(b2)\n",
    "    b1_array.append(b1)\n",
    "b2_mean = np.mean(b2_array)\n",
    "b1_mean = np.mean(b1_array)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=2, ncols=1, figsize=(9, 9))\n",
    "ax[0].hist(b1_array, bins=50)\n",
    "ax[0].axvline(b1_mean, color=\"salmon\", label=r\"$\\bar{b}_1$=%f\" % b1_mean)\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].hist(b2_array, bins=50)\n",
    "ax[1].axvline(b2_mean, color=\"salmon\", label=r\"$\\bar{b}_2$=%f\" % b2_mean)\n",
    "ax[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Though the histogram has been scaled as seemingly identical as above, but pay attention to the $x$-axis and vertical line. Apparently the variance of $u$ affects the accuracy of estimates, i.e. the variance of sampling distribution of $b_1$ and $b_2$.\n",
    "\n",
    "It's straightforward to see why this happens from the formula\n",
    "$$\n",
    "\\hat{\\beta}_{2}=\\beta_{2}+\\frac{\\operatorname{Cov}(X, a_uu)}{\\operatorname{Var}(X)}=\\beta_{2}+a_u\\frac{\\operatorname{Cov}(X, u)}{\\operatorname{Var}(X)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know from statistics course the increase sample is always doing good for quality of estimates, thus we dial it up to $N=100$, rest are unchanged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 648x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ols_mt = OLS_Monte_Carlo(beta1=2, beta2=3, N=100, u_scaler=2)\n",
    "b2_array, b1_array = [], []\n",
    "for i in range(10000):\n",
    "    b2, b1 = ols_mt.ols()\n",
    "    b2_array.append(b2)\n",
    "    b1_array.append(b1)\n",
    "b2_mean = np.mean(b2)\n",
    "b1_mean = np.mean(b1)\n",
    "\n",
    "fig, ax = plt.subplots(nrows=2, ncols=1, figsize=(9, 9))\n",
    "ax[0].hist(b1_array, bins=50)\n",
    "ax[0].axvline(b1_mean, color=\"salmon\", label=r\"$\\bar{b}_1$=%f\" % b1_mean)\n",
    "ax[0].legend()\n",
    "\n",
    "ax[1].hist(b2_array, bins=50)\n",
    "ax[1].axvline(b2_mean, color=\"salmon\", label=r\"$\\bar{b}_2$=%f\" % b2_mean)\n",
    "ax[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Notice how we have improved the accuracy of estimates, pay attention to $x$-axis that the sample distributions are tremendously concentrated than previous runs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Statistical Features of Estimates</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After a visial exam of sample distributions, now we can formally discuss the statistical features of estimator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Unbiased of Estimator</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If an estimator is biased, we rarely perform any estimation with it, unless you have no choices which is also rare. But how to prove unbiasness of an estimator? \n",
    "\n",
    "The _rule of thumb_ is to take expectation on both sides of estimator. Here is the OLS example.\n",
    "$$\n",
    "E\\left(b_{2}\\right)=E\\left[\\beta_{2}+\\frac{\\operatorname{Cov}(X, u)}{\\operatorname{Var}(X)}\\right]=\\beta_{2}+E\\left[\\frac{\\operatorname{Cov}(X, u)}{\\operatorname{Var}(X)}\\right]=\\beta_2+\\frac{E[\\operatorname{Cov}(X, u)]}{E[\\operatorname{Var}(X)]}\n",
    "$$\n",
    "To show $E[\\operatorname{Cov}(X, u)]=0$, rewrite covariance in explicit form\n",
    "$$\n",
    "E[\\operatorname{Cov}(X, u)]=\\frac{1}{n} \\sum_{i=1}^{n}\\left(X_{i}-\\bar{X}\\right) E\\left(u_{i}-\\bar{u}\\right)=0\n",
    "$$\n",
    "Therefore\n",
    "$$\n",
    "E\\left(\\hat{\\beta}_{2}\\right)=\\beta_{2}\n",
    "$$\n",
    "Again take expectation on $b_1$, immediately we get\n",
    "$$\n",
    "E(\\hat{\\beta}_1) = E(\\bar{Y})-E(\\hat{\\beta}_2)E(\\bar{X})= E(\\bar{Y})-\\beta_2\\bar{X}=\\beta_1\n",
    "$$\n",
    "where we used $E(\\bar{Y})=\\beta_{1}+\\beta_{2} \\bar{X}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Precision of Estimator</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we know the variance of disturbance term, the population variance of $b_1$ and $b_2$ can be derived\n",
    "$$\n",
    "\\sigma_{\\hat{\\beta}_1}^{2}=\\frac{\\sigma_{u}^{2}}{n}\\left[1+\\frac{\\bar{X}^{2}}{\\operatorname{Var}(X)}\\right]\\\\\\sigma_{\\hat{\\beta}_2}^{2}=\\frac{\\sigma_{u}^{2}}{n \\operatorname{Var}(X)}\n",
    "$$\n",
    "Though we will never really know $\\sigma_{u}$, the formulae provide the intuition how the variance of coefficients are determined. \n",
    "\n",
    "In the visual example of last section, we have seen that the larger $\\sigma_{u}$ causes larger $\\sigma_{\\hat{\\beta}_1}^{2}$ and $\\sigma_{\\hat{\\beta}_2}^{2}$, here the formulae also present the relation. \n",
    "\n",
    "And there are two ways to contract the variance of $b_1$ and $b_2$, one is increasing sample size $n$, the other is increasing $\\operatorname{Var}(X)$.\n",
    "\n",
    "In practice, we substitute $\\sigma_{u}^{2}$ by its unbiased estimator\n",
    "$$\n",
    "s_{u}^{2}=\\frac{n}{n-2} \\operatorname{Var}(e)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\operatorname{Var}(\\epsilon)$ is the sample variance of residuals. The term $\\frac{n}{n-2}$ is for upscaling variance, because generally residuals are smaller than disturbance term, this is determined by its mathematical nature. You will get a very clear linear algebraic view in advanced econometric theory. \n",
    "\n",
    "After plug-in we get the _standard error_ of $\\hat{\\beta}_1$ and $\\hat{\\beta}_2$\n",
    "$$\n",
    "\\text { s.e. }\\left(\\hat{\\beta}_1\\right)=\\sqrt{\\frac{s_{u}^{2}}{n}\\left[1+\\frac{\\bar{X}^{2}}{\\operatorname{Var}(X)}\\right]}\\\\\n",
    "\\text { s.e. }\\left(\\hat{\\beta}_2\\right)=\\sqrt{\\frac{s_{u}^{2}}{n \\operatorname{Var}(X)}}\n",
    "$$\n",
    "The standard error is used when we are referring to the _standard deviation of sampling distribution of estimates_, specifically in econometric term, regression coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Hypothesis Testing and $t$-Test</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Essentially, hypothesis testing in econometrics is the same as statistics. We propose a theory and test against data collected by experiment or sampling. \n",
    "\n",
    "That being said, in econometrics, we mainly investigate if the linear relation between independent and dependent variables is plausible, so we rarely test a specific null hypothesis such that $\\beta_2 = 2$, but rather $\\beta_2 =0$. Therefore\n",
    "$$\n",
    "H_0: \\beta_1 = 0, \\beta_2 =0\\\\\n",
    "H_1: \\beta_1 \\neq 0, \\beta_2 \\neq 0 \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's reproduce the house price example. We have the estimates, but we would like to investigate how reliable the results are. Reliability hinges on relativity, that means even if the absolute value of estimates are small, such as $.1$, as long as the standard error are smaller enough, such as $.01$, we can safely conclude a rejection of null hyphothesis without hesitation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$t$ statistic of $\\hat{\\beta}_1$ and $\\hat{\\beta}_2$ are \n",
    "$$\n",
    "\\frac{\\hat{\\beta}_1-\\beta_1^0}{s.e.(\\hat{\\beta}_1)}\\qquad\\frac{\\hat{\\beta}_2-\\beta_2^0}{s.e.(\\hat{\\beta}_2)}\n",
    "$$\n",
    "where $\\beta^0$ is null hypothesis. \n",
    "\n",
    "Generally, statistics are intuitive to interpret, it measures how many standard deviations (with known $\\sigma$) or standard errors (with unknown $\\sigma$) away from the null hypothesis. The further way, the stronger evidence supporting the rejection of null hypothesis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b1 estimate: -29181.1698\n",
      "b2 estimate: 1.1010\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_excel(\n",
    "    \"Basic_Econometrics_practice_data.xlsx\", sheet_name=\"CN_Cities_house_price\"\n",
    ")\n",
    "s_ols_house_income = S_OLS(df[\"salary\"], df[\"house_price\"])\n",
    "Y_hat, b2, b1 = s_ols_house_income.ols()\n",
    "s_ols_house_income.ols_plot(\"Disposable Income\", \"House Price\")\n",
    "resid = df[\"house_price\"] - Y_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute $t$-statistic as in formulae"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_b1:-1.7580\n",
      "t_b2:3.6349\n"
     ]
    }
   ],
   "source": [
    "n = len(df[\"house_price\"])\n",
    "s_u_sqr = n / (n - 2) * np.var(resid)\n",
    "\n",
    "std_err_b1 = np.sqrt(\n",
    "    s_u_sqr / n * (1 + np.mean(df[\"salary\"]) ** 2 / np.var(df[\"salary\"]))\n",
    ")\n",
    "std_err_b2 = np.sqrt(s_u_sqr / (n * np.var(df[\"salary\"])))\n",
    "\n",
    "t_b1 = b1 / std_err_b1\n",
    "t_b2 = b2 / std_err_b2\n",
    "print(\"t_b1:{:.4f}\".format(t_b1))\n",
    "print(\"t_b2:{:.4f}\".format(t_b2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems both $t$'s are far away from null hypothesis $\\beta^0=0$, but how far is real far? Unless we have a quantitative criterion, the interpretations won't sound objective. \n",
    "\n",
    "That's why we have **significant level** (denoted as $\\alpha$) as the decisive criterion. The common levels is $5\\%$ and $1\\%$. If $t$ falls on the right of **critical value** of $t$ at $5\\%$, we can conclude a rejection of null hypothesis.\n",
    "$$\n",
    "t > t_{.05}\n",
    "$$\n",
    "However in econometrics two-side test is more common, then rejection rules of $\\alpha=.05$ are\n",
    "$$\n",
    "t<t_{-.025} \\text{ and }t > t_{.025}\n",
    "$$\n",
    "Critical value of $t$-distribution is obtained by ```sp.stats.t.ppf```, and the shape of $t$-distribution approximate to normal distribution as degree of freedom raise.\n",
    "\n",
    "The two-side test $t$-statistic is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0638985616280205"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_crit = sp.stats.t.ppf(0.975, df=n - 1)\n",
    "t_crit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore we conclude a rejections of $\\beta_2=0$ ($t_{b_2}>t_{crit}$) but fail to reject $\\beta_1=0$ ($t_{\\hat{\\beta}_1}<t_{crit}$). \n",
    "\n",
    "The $\\hat{\\beta}_2=1.1010$ is interpreted that every $1$ yuan increment of disposable income is accompanied by raising $1.1010$ yuan on house price.\n",
    "\n",
    "In contrast, $\\hat{\\beta}_1= -29181.16$ can't be interpreted that if every family has $0$ disposable income, the house price will be $-29181.16$, because it doesn't have any logical or economic sense. So the rule of thumb for interpretation of constant term: _it's unnecessary to interpret constant coefficient if the it has no logical sense_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<b>Side note of $t$-distribution</b><br>\n",
    "\n",
    "<p>Here below is a figure for refreshing $t$-statistics, we set $\\alpha=.05$. The first axes demonstrates how $t$-statistic changes as degree of freedom raises, the second shows that $t$-distribution approximates normal distribution indefinitely with rising degree of freedom.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1008x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree_frd = np.arange(1, 50, 1)\n",
    "t_array = sp.stats.t.ppf(0.975, df=degree_frd)\n",
    "fig, ax = plt.subplots(nrows=2, ncols=1, figsize=(14, 12))\n",
    "ax[0].plot(degree_frd, t_array)\n",
    "ax[0].set_xlim([0, 20])\n",
    "ax[0].set_xlabel(\"degree of freedom\")\n",
    "ax[0].set_ylabel(\"critical value of $t$-statistic\")\n",
    "ax[0].set_title(\"The Change of $t$-statistic As d.o.f. Increases\")\n",
    "x = np.linspace(-3, 3, len(degree_frd))\n",
    "for i in range(len(degree_frd)):\n",
    "    t_pdf = sp.stats.t.pdf(\n",
    "        x, degree_frd[i], loc=0, scale=1\n",
    "    )  # pdf(x, df, loc=0, scale=1)\n",
    "    if i % 8 == 0:\n",
    "        ax[1].plot(x, t_pdf, label=\"t-Distribution with d.o.f. = {}\".format(i))\n",
    "    else:\n",
    "        ax[1].plot(x, t_pdf)\n",
    "ax[1].set_title(\n",
    "    \"The Shape of $t$-Distribution Approximate Normal Distribution As d.o.f. Increases\"\n",
    ")\n",
    "ax[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> $p$-Values</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Personally, I myself prefer to $p$-values. It is more informative than $t$-statistic, $p$-value gives the probability of obtaining corresponding $t$-statistic if null hypothesis is true, which is exactly the probability of **type I error**. \n",
    "\n",
    "With proper use of ```sp.stats.t.cdf```, we can access $p$-value conveniently. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0006284669089314798"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - sp.stats.t.cdf(\n",
    "    t_b2, df=n\n",
    ")  # because t_b2 is positive, so p-value should be deducted from 1, if negative then without"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p$-value tells that if null hypothesis is true, the probability of obtaining $t_{b_2}=3.6349$ or even higher is merely $0.0006$. That means, very unlikely the null hypothesis is true, we can safely reject null hypothesis with a tiny probability of Type I error.\n",
    "\n",
    "Medical researches conventionally uses $p$-value, econometrics tend to use estimates with standard error bracketed below. But they just different ways of expressing the same ideas, pick based on your preference unless you don't are writing an economic paper. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<i><b>Side note of Type I and II Error</b><br>\n",
    "The blue shaded area are genuinely generated by null distribution, however they are too distant (i.e. $2\\sigma$ away) from the mean ($0$ in this example), and they are mistakenly rejected, this is what we call <b>Type I Error</b>.\n",
    "<br>\n",
    "<br>\n",
    "The orange shaded area are actually generated by alternative distribution, however they are in the adjacent area of mean of null hypothesis, so we failed to reject they, but wrongly. And this is called <b>Type II Error</b>.\n",
    "<br>\n",
    "<br>\n",
    "As you can see from the chart, if null distribution and alternative are far away from each other, the probability of both type of errors diminish to trivial. </i>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot_material import type12_error\n",
    "\n",
    "type12_error()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Confidence Interval </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why bother with confidence interval if we have hypothesis testing?\n",
    "\n",
    "If you have a theory that house price has a certain linear relationship with disposable income, you test theory with model, this is called _hypothesis testing_. But what if you don't have a theory yet, and runs the regression, you are wondering how confident these estimates can represent the true parameters, the range that you feel confident is called **confidence interval**.\n",
    "\n",
    "These two procedures complementing each other, that's why we see them often reported together."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall the rejection rules are\n",
    "$$\n",
    "\\frac{\\hat{\\beta}-\\beta}{\\text { s.e. }\\left(\\hat{\\beta}\\right)}>t_{\\text {crit }} \\quad \\text { or } \\quad \\frac{\\hat{\\beta}-\\beta}{\\text { s.e. }\\left(\\hat{\\beta}\\right)}<-t_{\\text {crit }}\n",
    "$$\n",
    "If we slight rearrange and join them, we get the confidence interval\n",
    "$$\n",
    "\\hat{\\beta}-\\text { s.e. }\\left(b\\right) \\times t_{\\text {crit }} \\leq \\beta\\leq \\hat{\\beta}+\\text { s.e. }\\left(\\hat{\\beta}\\right) \\times t_{\\text {crit }}\n",
    "$$\n",
    "The higher significance level, the smaller $\\alpha$ is, the larger confidence interval (because of larger $t_{crit}$). For example, if the significance level is $\\alpha=.05$, then confidence level is $0.95$.\n",
    "\n",
    "Here's the confidence interval ($95\\%$) of our house price example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C.I. of b1: [-63439.54567466995, 5077.206045321891]\n",
      "C.I. of b2: [0.4758472405690616, 1.7261233292171854]\n"
     ]
    }
   ],
   "source": [
    "t_crit = sp.stats.t.ppf(0.975, df=n - 1)\n",
    "print(\"C.I. of b1: [{}, {}]\".format(b1 - t_crit * std_err_b1, b1 + t_crit * std_err_b1))\n",
    "print(\"C.I. of b2: [{}, {}]\".format(b2 - t_crit * std_err_b2, b2 + t_crit * std_err_b2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are $95\\%$ chances the true parameter $\\beta$ will 'fall' in this confidence interval."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> One-Tailed vs Two-Tailed Test </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far we have been discussing about two-tailed test, but there are scenarios that one-tailed test make more sense. In our house price example, some practitioners would prefer to test the theory or common sense: _disposable income would not have negative effects on house price_. The alternative would be that _disposable income would have either no effect or positive effects on house price_.\n",
    "\n",
    "Thus the one-tailed test hypotheses are\n",
    "$$\n",
    "H_0: \\beta_2<0\\\\\n",
    "H_1: \\beta_2\\geq 0\n",
    "$$\n",
    "In one-tailed test, we don't split $\\alpha$ anymore since there is only one side, that means the critical value will be smaller, easier to reject null hypothesis. \n",
    "\n",
    "Here is $t_{crit}$ of $\\alpha=5\\%$. However, these are conventional rules, if you still prefer $2.5\\%$ on one-side, feel free to do so. Especially you have a very significant $t$-statistic, such as $10$, one-tailed or two-tailed won't really matter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7108820799094275"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_crit_oneside = sp.stats.t.ppf(0.95, df=n - 1)\n",
    "t_crit_oneside"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So here the rule of thumb for one-tailed test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<i><b>Rules of Thumb for One-Tailed Test</b><br>\n",
    "1. If the theory or common sense supports one side test, e.g. household consumption increases as disposable incomes increase.<br>\n",
    "2. If two-tailed test failed to reject, but one-tailed reject, you can report one-tailed test results if the first rule satisfied too.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> $F$-test</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$F$-test is based on _Analysis of Variance_ (ANOVA), the goal is to test **multiple restrictions** on the regression model. In simple linear regression model, the **joint hypothesis** is usually\n",
    "\\begin{align}\n",
    "H_0&: \\beta_1 = 0,\\qquad\\beta_2=0\\\\\n",
    "H_1&: \\text{One or more restrictions does not hold}\n",
    "\\end{align}\n",
    "\n",
    "once you have ANOVA done, $F$-statistic is an natural byproduct.\n",
    "$$\n",
    "F=\\frac{E S S /(k-1)}{R S S /(n-k)}\n",
    "$$\n",
    "where $k$ is the number of number of parameters in the regression model, here in simple regression model $k=2$ and $n$ is the sample size.\n",
    "\n",
    "You might have doubt now: why aren't we using same old $t$-tests such that\n",
    "$$\n",
    "H_0: \\hat{\\beta}_1=0 \\qquad H_0: \\hat{\\beta}_2=0 \\qquad \\\\\n",
    "H_1: \\hat{\\beta}_1\\neq0 \\qquad H_1: \\hat{\\beta}_2\\neq0\\qquad\\\\\n",
    "$$\n",
    "\n",
    "Apparently, the number of $t$-tests will be as large as ${k \\choose 2} $ where $k$ is the number of parameters. If there are $5$ parameters, then we have to test ${5 \\choose 2}=10$ pairs. With $95\\%$ confidence level, $10$ $t$-tests would cut back confidence level dramatically to $95\\%^{10}=59.8\\%$, which also means the probability of _type I_ error would be around $40\\%$.\n",
    "\n",
    "We have user-defined functions written in the OLS class, so $F$-statistic is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F-statistic is 13.2126.\n"
     ]
    }
   ],
   "source": [
    "f_stat = (ess / (2 - 1)) / (rss / (len(df[\"salary\"]) - 2))\n",
    "print(\"F-statistic is {:.4f}.\".format(f_stat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value is 0.0014.\n"
     ]
    }
   ],
   "source": [
    "p_value = 1 - sp.stats.f.cdf(\n",
    "    f_stat, 1, len(df[\"salary\"]) - 2\n",
    ")  # sp.stats.f.cdf(df on nominator, df on denom)\n",
    "print(\"p-value is {:.4f}.\".format(p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To explore further, we can even prove that in simple linear regression $F$ are the just the square of $t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<i><b>$F$-statistic and $t$-statistic</b><br>\n",
    "Here's the proof that $F$ and $t$ are connected\n",
    "$$\n",
    "F=\\frac{R^{2}}{\\left(1-R^{2}\\right) /(n-2)}=\\frac{\\frac{\\operatorname{Var}(\\hat{Y})}{\\operatorname{Var}(Y)}}{\\left\\{1-\\frac{\\operatorname{Var}(\\hat{Y})}{\\operatorname{Var}(Y)}\\right\\} /(n-2)}\\\\\n",
    "=\\frac{\\frac{\\operatorname{Var}(\\hat{Y})}{\\operatorname{Var}(Y)}}{\\left\\{\\frac{\\operatorname{Var}(Y)-\\operatorname{Var}(\\hat{Y})}{\\operatorname{Var}(Y)}\\right\\} /(n-2)}=\\frac{\\operatorname{Var}(\\hat{Y})}{\\operatorname{Var}(\\varepsilon) /(n-2)}\\\\\n",
    "=\\frac{\\operatorname{Var}\\left(\\hat{\\beta}_{1}+\\hat{\\beta}_{2} X\\right)}{\\left\\{\\frac{1}{n} \\sum_{i=1}^{n} \\varepsilon_{i}^{2}\\right\\} /(n-2)}=\\frac{\\hat{\\beta}_{2}^{2} \\operatorname{Var}(X)}{\\frac{1}{n} s_{u}^{2}}=\\frac{\\hat{\\beta}_{2}^{2}}{\\frac{s_{u}^{2}}{n \\operatorname{Var}(X)}}=\\frac{\\hat{\\beta}_{2}^{2}}{\\left[\\operatorname{s.e.} \\left(\\hat{\\beta}_{2}\\right)\\right]^{2}}=t^{2}\n",
    "$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<i><b>$F$-statistic and $R^2$</b><br>\n",
    "$F$-statistic is a different angle of evaluating the goodness of fit, it can be shown that $F$ and $R^2$ are closely connected, divide both nominator and denominator by $TSS$:\n",
    "$$\n",
    "F=\\frac{(E S S / T S S) /(k-1)}{(R S S / T S S) /(n-k)}=\\frac{R^{2} /(k-1)}{\\left(1-R^{2}\\right) /(n-k)}\n",
    "$$\n",
    "We prefer to $F$ for hypothesis test, it's because critical value of $F$ is straightforward, and critical value of $R^2$ has to be calculated based on $F_{crit}$:\n",
    "$$\n",
    "R_{\\mathrm{crit}}^{2}=\\frac{(k-1) F_{\\mathrm{crit}}}{(k-1) F_{\\text {crit }}+(n-k)}\n",
    "$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\">Regression vs Correlation</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the message for all beginner that misinterpret regression relationship as causation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<i><b>Does Regression Imply Causation</b><br>\n",
    "\n",
    "It's tempting to interpret regression result as causality, but it's not. <b>Regression only implies a statistical relationship</b>, the independent variables may or may not be the cause of dependent variables, sometimes we know thanks to theories, sometimes we don't.\n",
    "    \n",
    "For instance, researches found that parents with higher education tend to have healthier children, but this is hardly a causality. Perhaps higher education parents are in general wealthier, they can afford decent medical packages. Or they spend time with their kids on sports and dining. We can form some hypothesis, but not a definite causality based on one regression.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But regressions do resemble the correlation to some extent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<i><b>Does Regression Imply Correlation</b><br>\n",
    "From formula of $\\hat{\\beta}_2$\n",
    "$$\n",
    "\\hat{\\beta}_2 =\\frac{\\text{Cov}(X, Y)}{\\text{Var}(X)}\n",
    "$$\n",
    "We can see the regression indeed has a component of correlation (covariance in the formula), but it's normalized by variance (i.e. $\\sigma_X\\sigma_X$) rather than $\\sigma_X\\sigma_Y$. To compare with correlation coefficient of $X$ and $Y$ \n",
    "$$\n",
    "\\rho_{XY}=\\frac{\\text{Cov}(X, Y)}{\\sigma_X\\sigma_Y}\n",
    "$$\n",
    "We can see one important difference is that regression coefficient does not treat both variables symmetrically, but correlation coefficient does. Joining two formulae, we have a different view of the coefficient.<br><br>\n",
    "$$\n",
    "\\hat{\\beta}_2=\\frac{\\rho_{XY}\\sigma_X\\sigma_Y}{\\text{Var}(X)}= \\frac{\\rho_{XY}\\sigma_X\\sigma_Y}{\\sigma_X\\sigma_X}=\\rho_{XY}\\frac{\\sigma_Y}{\\sigma_X}\n",
    "$$\n",
    "    \n",
    "Besides that, the purpose of these two techniques are different, regression are mainly predicting dependent variables behaviors, but correlation are mainly summarizing the direction and strength among two or more variables. \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maybe a chart can share insight of their relationship. All data are simulated by $u\\sim N(0, 1)$. It's easy to notice the smaller correlation implies a smaller slope coefficient in terms of absolute value. And larger disturbance term also implies lower correlation coefficient. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1728x864 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from plot_material import reg_corr_plot\n",
    "\n",
    "reg_corr_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Joint Confidence Region</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Joint confidence region** are the joint distribution of regression coefficients, it is theoretically an ellipse. It shows the distributed location of the coefficient pair. \n",
    "\n",
    "Here is a Monte Carlo simulation, we set $\\beta_1 = 3$, $\\beta_2 = 4$ and $u\\sim N(0, 10)$, run $1000$ times then plot the estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta1, beta2 = 3, 4\n",
    "beta1_array, beta2_array = [], []\n",
    "for i in range(1000):\n",
    "    u = 10 * np.random.randn(30)\n",
    "    X2 = np.linspace(10, 100, 30)\n",
    "    Y = beta1 + beta2 * X2 + u\n",
    "\n",
    "    df = pd.DataFrame([Y, X2]).transpose()\n",
    "    df.columns = [\"Y\", \"X2\"]\n",
    "\n",
    "    X_inde = df[\"X2\"]\n",
    "    Y = df[\"Y\"]\n",
    "\n",
    "    X_inde = sm.add_constant(X_inde)\n",
    "\n",
    "    model = sm.OLS(Y, X_inde).fit()\n",
    "    beta1_array.append(model.params[0])\n",
    "    beta2_array.append(model.params[1])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "ax.grid()\n",
    "for i in range(1000):\n",
    "    ax.scatter(\n",
    "        beta1_array[i], beta2_array[i]\n",
    "    )  # no need for a loop, i just want different colors\n",
    "ax.set_xlabel(r\"$\\beta_1$\")\n",
    "ax.set_ylabel(r\"$\\beta_2$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But why the joint distribution of coefficient has an elliptic shape? If you take a look at any linear regression plot, it wouldn't be difficult to notice that the high slope coefficient $\\beta_2$ would cause low the intercept coefficient $\\beta_1$, this is a geometric feature of linear regression model.\n",
    "\n",
    "And from the plot, we can see the range of $\\beta_1$ is much larger than $\\beta_2$ and even include $0$, especial the data points are far away from $0$, $\\beta_1$ can have erratic results, that's also the reason we don't expect to interpret $\\beta_1$ most of time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Stochastic Regressors</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of G-M condition is $\\text{Cov}(X_i, u_i)=0$, assuming $X_i$ is non-stochastic. But we commonly encounters that $X_i$ is stochastic, for instance you sample $10$ family's annual income, you have no clue on how much they are earning eventually, therefore assuming they are stochastic would be more appropriate. \n",
    "\n",
    "If $X_i$ is stochastic and distributed independently of $u_i$, it guarantees that $\\text{Cov}(X_i, u_i)=0$, but not vice versa."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Maximum Likelihood Estimation</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In more advanced level of econometric research, **maximum likelihood estimation**(MLE) is used more often than OLS. The reason is that MLE is more flexible on assumption of disturbance term, i.e. not assuming the normality of the disturbance term. But it requires you to have an assumption of certain distribution, it can be exponential or gamma distribution or whatever. \n",
    "\n",
    "We will provide two examples to illustrate the philosophy of MLE, one is to estimate simple linear regression with MLE and the other is to estimate a mean of an exponential distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> MLE for Simple Linear Regression </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once you have a dataset, you should know the data are just observations of random variables. For instance, you are about to collect $100$ family's annual income data for year 2021, each family's income is essentially a random variable, hence it follows some distribution, it can be normal distribution or skewed gamma distribution. \n",
    "\n",
    "Once the data is collected, the observances are done. Each data point, i.e. $Y_1, Y_2, ..., Y_n$ is just single realization of its distribution, the joint distribution of all random variables is\n",
    "$$\n",
    "f\\left(Y_{1}, Y_{2}, \\ldots, Y_{n}\\right)\n",
    "$$\n",
    "We assume a simple linear regression $Y_{i}=\\beta_{1}+\\beta_{2} X_{i}+u_{i}$ model to explain $Y$, then the joint distribution is conditional\n",
    "$$\n",
    "f\\left(Y_{1}, Y_{2}, \\ldots, Y_{n} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right)\n",
    "$$\n",
    "We also assume each family's income is independent of rest, then joint distribution equals the product of all distributions.\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&f\\left(Y_{1}, Y_{2}, \\ldots, Y_{n} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right)=f\\left(Y_{1} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right) f\\left(Y_{2} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right) \\cdots f\\left(Y_{n} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right) =\\prod_{i=0}^nf\\left(Y_{i} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right)\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to ask ourselves, what distribution does $Y$ follow? It's the same as asking what's the distribution of $u$? It's reasonable to assume $u$ follow normal distribution, so are $Y$'s.\n",
    "$$\n",
    "f(Y_i)= \\frac{1}{\\sigma \\sqrt{2\\pi}}e^{-\\frac{1}{2}\\frac{[Y_i-E(Y_i)]^2}{\\sigma^2}}=\\frac{1}{\\sigma \\sqrt{2\\pi}}e^{-\\frac{1}{2}\\frac{[Y_i-\\beta_1-\\beta_2X_i]^2}{\\sigma^2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then the joint distribution is the product of this PDF function\n",
    "$$\n",
    "\\prod_{i=0}^nf\\left(Y_{i} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right)=\\frac{1}{\\sigma^{n}(\\sqrt{2 \\pi})^{n}} e^{-\\frac{1}{2} \\sum \\frac{\\left(Y_{i}-\\beta_{1}-\\beta_{2} X_{i}\\right)^{2}}{\\sigma^{2}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have joint distribution function, in a frequentist view, the observed data is generated by this distribution with certain parameters, in this case $\\beta_1, \\beta_2$ and $\\sigma^2$. So the fundamental the questions are what those parameters are? How to find them?\n",
    "\n",
    "We give a name to the join distribution function above - **likelihood function**, which means how likely a set of parameters can generate a set of data. We denote likelihood function as $LF(\\beta_1, \\beta_2, \\sigma^2)$.\n",
    "\n",
    "The MLE, as its name indicates, is to estimate the parameters that in such manner that the probability of generating $Y$'s is the highest. \n",
    "\n",
    "To derive a analytical solution, usually we use log form likelihood function\n",
    "$$\n",
    "\\ln{LF}=\\ln{\\prod_{i=0}^nf\\left(Y_{i} \\mid \\beta_{1}+\\beta_{2} X_{i}, \\sigma^{2}\\right)} =-\\frac{n}{2} \\ln \\sigma^{2}-\\frac{n}{2} \\ln (2 \\pi)-\\frac{1}{2} \\sum \\frac{\\left(Y_{i}-\\beta_{1}-\\beta_{2} X_{i}\\right)^{2}}{\\sigma^{2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take derivative with respect to $\\beta_1$, $\\beta_2$ and $\\sigma^2$ and equal them to $0$ will yield the **maximum likelihood estimators** for simple linear regression with assumption of normally distributed disturbance term\n",
    "\\begin{align}\n",
    "\\hat{\\beta}_2 &= \\frac{\\sum_{i=1}^n (X_i - \\bar{X})(Y_i-\\bar{Y})}{\\sum_{i=1}^n(X_i-\\bar{X})^2}=\\frac{\\text{Cov}(X, Y)}{\\text{Var}(X)}\\\\\n",
    "\\hat{\\beta}_1 &= \\bar{Y}-\\beta_2\\bar{X}\\\\\n",
    "s^2 &= \\frac{1}{n} \\sum_{i=1}^{n}\\left(Y_{i}-\\left(\\hat{\\beta}_{1}+\\hat{\\beta}_{2} X_{i}\\right)\\right)^{2} = \\frac{1}{n}\\sum_{i=1}^n e_i^2\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MLE $\\hat{\\beta}_1$ and $\\hat{\\beta}_2$ are exactly the same as OLS estimators, only the $s^2$ differs from OLS estimator $s^2 = \\frac{\\sum e^2_i}{n-2}$. The MLE $s^2$ is biased in small sample, but _consistent_ as sample size increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll experiment with MLE with simulated data. Generate a data for OLS estimation and print the estimated coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```statsmodel``` library doesn't have a direct api for maximum likelihood estimation, but we can construct it with ```Scipy```'s ```minimize``` function, so we define a negative log likelihood. The reason of negative function is because ```Scipy``` has only ```minimize``` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "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></th>\n",
       "      <th>cities</th>\n",
       "      <th>house_price</th>\n",
       "      <th>salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Shenzhen</td>\n",
       "      <td>87957</td>\n",
       "      <td>64878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Beijing</td>\n",
       "      <td>64721</td>\n",
       "      <td>69434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Shanghai</td>\n",
       "      <td>59072</td>\n",
       "      <td>72232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Xiamen</td>\n",
       "      <td>49803</td>\n",
       "      <td>58140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Guangzhou</td>\n",
       "      <td>39851</td>\n",
       "      <td>68304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      cities  house_price  salary\n",
       "0   Shenzhen        87957   64878\n",
       "1    Beijing        64721   69434\n",
       "2   Shanghai        59072   72232\n",
       "3     Xiamen        49803   58140\n",
       "4  Guangzhou        39851   68304"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_excel(\"Basic_Econometrics_practice_data.xlsx\", \"CN_Cities_house_price\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df[\"house_price\"]\n",
    "X = df[\"salary\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def neg_LL(theta_array):\n",
    "    y_fitted = theta_array[0] + theta_array[1] * X\n",
    "    sigma = theta_array[2]\n",
    "    LL = (\n",
    "        -(len(y_fitted) / 2) * np.log(theta_array[2] ** 2)\n",
    "        - (len(y_fitted) / 2) * np.log(2 * np.pi)\n",
    "        - 1 / (2 * theta_array[2] ** 2) * np.sum((y - y_fitted) ** 2)\n",
    "    )\n",
    "    return -LL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 274.077325\n",
      "         Iterations: 294\n",
      "         Function evaluations: 532\n"
     ]
    }
   ],
   "source": [
    "theta_start = np.array([1, 1, 1])\n",
    "res = minimize(neg_LL, theta_start, method=\"Nelder-Mead\", options={\"disp\": True})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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></th>\n",
       "      <th>parameters</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>-29181.169196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Slope</th>\n",
       "      <td>1.100985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sigma</th>\n",
       "      <td>13962.835305</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             parameters\n",
       "Intercept -29181.169196\n",
       "Slope          1.100985\n",
       "Sigma      13962.835305"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = pd.DataFrame({\"parameters\": res[\"x\"]})\n",
    "results.index = [\"Intercept\", \"Slope\", \"Sigma\"]\n",
    "results.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see the intercept and slope coefficients are the same as OLS, but $\\hat{\\sigma}$ is underestimated as the theory tells."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> MLE for Exponential Distribution </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MLE is more general than OLS, it can estimate any parameters as long as you know or assume the distribution, this example we will give an explicit function form for an exponential function. \n",
    "\n",
    "Consider \n",
    "$$\n",
    "f(Y_i; \\theta) = \\theta e^{-\\theta Y_i}\n",
    "$$\n",
    "The joint distribution (likelihood function) is \n",
    "$$\n",
    "\\prod_{i=1}^n f(Y_i; \\theta) = \\theta^ n  e^{-\\theta \\sum Y_i}\n",
    "$$\n",
    "Log likelihood function is\n",
    "$$\n",
    "\\ln \\prod_{i=1}^n f(Y_i; \\theta) = n\\ln{\\theta} - \\theta \\sum_{i=1}^n Y_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take derivative with respect to $\\theta$\n",
    "$$\n",
    "\\frac{\\partial LF}{\\partial \\theta} = \\frac{n}{\\theta}-\\sum_{i=1}^n Y_i = 0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is \n",
    "$$\n",
    "\\hat{\\theta} = \\frac{n}{n \\bar{Y}} = \\frac{1}{\\bar{Y}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimated parameter $\\hat{\\theta}$ is the reciprocal of mean of $Y_i$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\">Statsmodels Library </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fortunately, we don't need to program our own toolbox for estimations, ```statsmodels``` library will be our main tool from now on, all the codes are self-explanatory unless it requires further clarification.\n",
    "\n",
    "The estimation results are reported in as in Stata or Eview, there is a test run below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            house_price   R-squared:                       0.365\n",
      "Model:                            OLS   Adj. R-squared:                  0.337\n",
      "Method:                 Least Squares   F-statistic:                     13.21\n",
      "Date:                Sat, 07 Jan 2023   Prob (F-statistic):            0.00139\n",
      "Time:                        11:16:08   Log-Likelihood:                -274.08\n",
      "No. Observations:                  25   AIC:                             552.2\n",
      "Df Residuals:                      23   BIC:                             554.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const      -2.918e+04   1.66e+04     -1.758      0.092   -6.35e+04    5156.201\n",
      "salary         1.1010      0.303      3.635      0.001       0.474       1.728\n",
      "==============================================================================\n",
      "Omnibus:                       14.403   Durbin-Watson:                   0.926\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               14.263\n",
      "Skew:                           1.457   Prob(JB):                     0.000800\n",
      "Kurtosis:                       5.280   Cond. No.                     3.12e+05\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 3.12e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "X = df[\"salary\"]\n",
    "Y = df[\"house_price\"]\n",
    "\n",
    "X = sm.add_constant(X)  # adding a constant\n",
    "\n",
    "model = sm.OLS(Y, X).fit()\n",
    "\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, you might see some people using $R$-style formula such as\n",
    "```Y ~ X + Z```, which produces the same results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            house_price   R-squared:                       0.365\n",
      "Model:                            OLS   Adj. R-squared:                  0.337\n",
      "Method:                 Least Squares   F-statistic:                     13.21\n",
      "Date:                Sat, 07 Jan 2023   Prob (F-statistic):            0.00139\n",
      "Time:                        11:16:08   Log-Likelihood:                -274.08\n",
      "No. Observations:                  25   AIC:                             552.2\n",
      "Df Residuals:                      23   BIC:                             554.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept  -2.918e+04   1.66e+04     -1.758      0.092   -6.35e+04    5156.201\n",
      "salary         1.1010      0.303      3.635      0.001       0.474       1.728\n",
      "==============================================================================\n",
      "Omnibus:                       14.403   Durbin-Watson:                   0.926\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               14.263\n",
      "Skew:                           1.457   Prob(JB):                     0.000800\n",
      "Kurtosis:                       5.280   Cond. No.                     3.12e+05\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 3.12e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_excel(\n",
    "    \"Basic_Econometrics_practice_data.xlsx\", sheet_name=\"CN_Cities_house_price\"\n",
    ")\n",
    "df.head()\n",
    "\n",
    "model = smf.ols(formula=\"house_price ~ salary\", data=df)\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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></th>\n",
       "      <th>OLS estimates</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>-29181.169815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>salary</th>\n",
       "      <td>1.100985</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           OLS estimates\n",
       "Intercept  -29181.169815\n",
       "salary          1.100985"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = pd.DataFrame(results.params, columns=[\"OLS estimates\"])\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept   -29181.169815\n",
       "salary           1.100985\n",
       "dtype: float64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     42248.553499\n",
       "1     47264.642457\n",
       "2     50345.199284\n",
       "3     34830.114649\n",
       "4     46020.529085\n",
       "5     15460.480532\n",
       "6     38946.698629\n",
       "7     37545.144362\n",
       "8     15383.411562\n",
       "9     19101.438869\n",
       "10    36825.099985\n",
       "11    35198.944719\n",
       "12    33060.831296\n",
       "13    30299.560202\n",
       "14    39720.691285\n",
       "15    22736.892280\n",
       "16    12374.418778\n",
       "17    26266.651103\n",
       "18    26506.665895\n",
       "19    34223.471757\n",
       "20    23977.702696\n",
       "21    24319.008134\n",
       "22    28158.143823\n",
       "23    16928.093917\n",
       "24    17729.611204\n",
       "dtype: float64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.fittedvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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