Chapter 1 - Geometry of Ordinary Least Squares.ipynb

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 "cells": [
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda\\lib\\site-packages\\statsmodels\\compat\\pandas.py:65: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.\n",
      "  from pandas import Int64Index as NumericIndex\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy as sp\n",
    "import scipy.stats\n",
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "import plotly.express as px\n",
    "\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to follow this notes with least pain, it is strongly advised to study in <a href='https://github.com/MacroAnalyst/Linear_Algebra_With_Python'>linear algebra</a>, <a href='https://github.com/MacroAnalyst/Basic_Statistics_With_Python'>statistics</a>, <a href='https://github.com/MacroAnalyst/Probability_Theory'>probability theory</a> and <a href='https://github.com/MacroAnalyst/Basic_Econometrics_With_Python'>basic econometrics</a>.\n",
    "\n",
    "Click the hyperlink, you will find all course notes in my GitHub pages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Advanced econometrics aims to provide thorough mathematical foundation to econometric theory, which will be extremely useful in handling complicated data science projects. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Geometry of Vector Space </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our starting point of **Ordinary Least Square** is to understand that linear regression model usually takes the matrix form\n",
    "\n",
    "$$\n",
    "\\boldsymbol{y} = \\boldsymbol{X\\beta}+\\boldsymbol{u}\\tag{1}\\label{1}\n",
    "$$\n",
    "\n",
    "where $\\boldsymbol{y}$ and $\\boldsymbol{u}$ are $n\\times 1$ matrices, $\\boldsymbol{X}$ is a $n \\times k$ matrix and $\\boldsymbol{\\beta}$ is a $k \\times 1$ matrix.\n",
    "$$\n",
    "\\boldsymbol{y}=\\left[\\begin{array}{c}\n",
    "y_{1} \\\\\n",
    "y_{2} \\\\\n",
    "\\vdots \\\\\n",
    "y_{n}\n",
    "\\end{array}\\right], \\quad \\boldsymbol{u}=\\left[\\begin{array}{c}\n",
    "u_{1} \\\\\n",
    "u_{2} \\\\\n",
    "\\vdots \\\\\n",
    "u_{n}\n",
    "\\end{array}\\right], \\quad \\boldsymbol{X}_{n\\times k}=\\left[\\begin{array}{cccc}\n",
    "1 & X_{11} & X_{12} & \\ldots & X_{1k}  \\\\\n",
    "1 & X_{21} & X_{22} & \\ldots & X_{1k}\\\\\n",
    "\\vdots & \\vdots & \\vdots& \\ddots& \\vdots\\\\\n",
    "1 & X_{n1} & X_{n2} & \\ldots& X_{nk}\n",
    "\\end{array}\\right], \\quad \\text { and } \\quad \\boldsymbol{\\beta}=\\left[\\begin{array}{c}\n",
    "\\beta_{1} \\\\\n",
    "\\beta_{2} \\\\\n",
    "\\vdots\\\\\n",
    "\\beta_k\n",
    "\\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Two Inequalities </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two inequalities useful for further illustration in vector space. Define $\\boldsymbol{x}$ and $\\boldsymbol{y}$ as vectors in $\\mathbb{R}^n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font face=\"gotham\" color=\"purple\">The Cauchy-Schwarz Inequality</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "|\\boldsymbol{x}^T\\boldsymbol{y}| \\leq \\|\\boldsymbol{x}\\|\\|\\boldsymbol{y}\\| \\tag{2}\\label{2}\n",
    "$$\n",
    "$\\|\\|$ notation means the **modulus** or length of vector."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Cauchy-Schwarz inequality holds because of another famous formula dervied from law of cosine, recall that $-1 \\leq \\cos{\\vartheta} \\leq 1$\n",
    "\n",
    "\\begin{equation}\n",
    "\\boldsymbol{x}^T\\boldsymbol{y} = \\|\\boldsymbol{x}\\|\\|\\boldsymbol{y}\\| \\cos{\\vartheta} \\label{3}\\tag{3}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most important implication is that when $\\vartheta = 90^{\\circ}$, i.e. $\\boldsymbol{x}\\perp\\boldsymbol{y}$, then $\\boldsymbol{x}^T\\boldsymbol{y} = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font face=\"gotham\" color=\"purple\">The Triangle Inequality </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the vector version of a primary school concept: the length of the third edge is at least as long as the sum of other two edges."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\|\\boldsymbol{x}+\\boldsymbol{y}\\| \\leq \\|\\boldsymbol{x}\\| +  \\|\\boldsymbol{y}\\|\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\">Basis of Subspace  </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A set of vectors $\\boldsymbol{X}_{n\\times k} = (\\boldsymbol{x}_1, ..., \\boldsymbol{x}_k)$ which spans a subspace $W$ is denoted as \n",
    "\n",
    "$$\n",
    "W = \\text{Span}\\left(\\boldsymbol{x}_{1}, \\ldots, \\boldsymbol{x}_{k}\\right) \\equiv\\left\\{\\boldsymbol{z} \\in \\mathbb{R}^{n} \\bigg| \\boldsymbol{z}=\\sum_{i=1}^{k} b_{i} \\boldsymbol{x}_{i}, \\quad b_{i} \\in \\mathbb{R}\\right\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The orthogonal complement of $W$, is denoted as\n",
    "\n",
    "$$\n",
    "W^{\\perp} = \\text{Span}^\\perp(\\boldsymbol{x}_{1}, \\ldots, \\boldsymbol{x}_{k}) = \\left\\{\\boldsymbol{w} \\in \\mathbb{R}^{n} | \\boldsymbol{w}^{\\top} \\boldsymbol{z}=0 \\text { for all } \\boldsymbol{z} \\in \\text{Span}(\\boldsymbol{X})\\right\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $\\text{dim}W = k$ and $\\text{dim}W^\\perp = n-k$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Geometry of OLS Estimation</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take a look at the graph below, which is the geometric concept of OLS. The vectors are arbitrarily chosen only serving purpose of visualization in the codes, though demonstration is 3D, you shall imagine them exist in higher dimension, i.e. in $\\mathbb{R}^n$ rather than $\\mathbb{R}^3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = np.linspace(0, 10, 10)\n",
    "t = np.linspace(0, 10, 10)\n",
    "S, T = np.meshgrid(s, t)\n",
    "X = S\n",
    "Y = T\n",
    "Z = np.zeros((10, 10))\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (10, 10))\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, alpha = .4)\n",
    "\n",
    "y = np.array([6, 6, 5])\n",
    "y_vec = np.array([[0, 0, 0, y[0], y[1], y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'black', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "\n",
    "yhat = np.array([y[0], y[1], 0])\n",
    "yhat_vec = np.array([[0, 0, 0, yhat[0], yhat[1], yhat[2]]])\n",
    "X, Y, Z, U, V, W = zip(*yhat_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "yhat_vec = np.array([[0, 0, 0, 0, 0, y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*yhat_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = .6,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "Xbeta = np.array([6, 3, 0])\n",
    "y_vec = np.array([[0, 0, 0, Xbeta[0], Xbeta[1], Xbeta[2]]])\n",
    "X, Y, Z, U, V, W = zip(*y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'purple', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "u = y - Xbeta\n",
    "u_vec = np.array([[Xbeta[0], Xbeta[1], Xbeta[2], u[0], u[1], u[2]]])\n",
    "X, Y, Z, U, V, W = zip(*u_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'Aqua', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "point1 = [y[0], y[1], y[2]]\n",
    "point2 = [yhat[0], yhat[1], yhat[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.5, ls = '--')\n",
    "\n",
    "\n",
    "ax.text(x = y[0], y = y[1], z = y[2], s = '$y$', size = 16)\n",
    "ax.text(9, 9, 0, '$Col\\ X$', size = 16)\n",
    "ax.text(x = y[0], y = y[1], z = 0, s = r'$\\hat{y}=X\\hat{\\beta}$', size = 16)\n",
    "ax.text(x = 0, y = 0, z = y[2], s = r'$\\hat{u} = y-X\\hat{\\beta}$', size = 16)\n",
    "ax.text(x = Xbeta[0], y = Xbeta[1], z = Xbeta[2], s = r'$X\\beta$', size = 16)\n",
    "ax.text(x = 5.6, y = 4.1, z = 2.4, s = r'$u$', size = 16)\n",
    "\n",
    "for i in ['x', 'y', 'z']:\n",
    "    exec('ax.set_'+i+'lim3d(0, 10)')\n",
    "    \n",
    "ax.set_title('Geometric Mechanism of OLS', fontsize = 17)\n",
    "ax.set_xlabel('X-axis'),ax.set_ylabel('Y-axis'),ax.set_zlabel('Z-axis')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In words, OLS algorithm is to find a special linear combination with basis of $\\text{Col}\\boldsymbol{X}$ or $\\text{Span}\\boldsymbol{X}$.\n",
    "\n",
    "And this linear combination is the orthogonal projection $\\boldsymbol{\\hat{y}}$ of $\\boldsymbol{y}$ onto $\\text{Span}\\boldsymbol{X}$, which means the distance $\\|\\boldsymbol{y}-\\boldsymbol{\\hat{y}}\\|$ is the shortest among all other possible $\\|\\boldsymbol{y}-\\text{proj}_{\\text{Col}X}\\boldsymbol{y}\\|$, where $\\text{proj}_{\\text{Col}X}\\boldsymbol{y}$ means a projection of $\\boldsymbol{y}$ onto column space of $\\boldsymbol{X}$ i.e. $\\text{Col}\\boldsymbol{X}$, which is depicted as a transparent plane. \n",
    "\n",
    "And also note that orthogonal complement $\\boldsymbol{\\hat{u}}$ most possibly will smaller than $\\boldsymbol{u}$ itself, which is decided by the nature of OLS algorithm. In the graph, we give $\\boldsymbol{\\hat{u}}$ red color and aqua color to $\\boldsymbol{u}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To formulate mathematically the verbal description above, \n",
    "\n",
    "$$\n",
    "\\boldsymbol{X}^T(\\boldsymbol{y-X\\hat{\\beta}})=\\boldsymbol{X}^T\\boldsymbol{\\hat{u}}= \\boldsymbol{0}\\label{4}\\tag{4}\n",
    "$$\n",
    "\n",
    "which is called **orthogonality condition of OLS**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With orthogonality condition, we achieve the most famous OLS algorithm of $\\hat{\\boldsymbol{\\beta}}$\n",
    "\n",
    "$$\n",
    "\\boldsymbol{\\hat{\\beta}} = (\\boldsymbol{X}^T\\boldsymbol{X})^{-1}\\boldsymbol{X}^T\\boldsymbol{y}\\label{5}\\tag{5}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Test Trials of OLS Algorithm </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construct $\\boldsymbol{X}$ matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "const = np.ones(100)\n",
    "const = const[np.newaxis, :]\n",
    "\n",
    "X_inde = np.random.randn(3, 100)\n",
    "\n",
    "X = np.concatenate((const.T, X_inde.T), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set true $\\boldsymbol{\\beta} = [2, 3, 4, 5]^T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_array = np.array([2, 3, 4, 5])\n",
    "beta_array = beta_array[np.newaxis, :].T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate disturbance term $\\boldsymbol{u}$ with a standard normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.random.randn(100)\n",
    "u = u[np.newaxis, :].T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate $\\boldsymbol{y}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = X@beta_array + u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimate parameters with OLS algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta0:[2.04505556]\n",
      "beta1:[2.94315138]\n",
      "beta2:[4.15756857]\n",
      "beta3:[4.8987082]\n"
     ]
    }
   ],
   "source": [
    "beta_hat = np.linalg.inv(X.T@X)@X.T@y\n",
    "for i in range(len(beta_array)):\n",
    "    print('beta' + str(i) + ':' + str(beta_hat[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verify the results with ```statsmodels```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ols_obj = sm.OLS(y, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta0:2.045055557724158\n",
      "beta1:2.9431513755492107\n",
      "beta2:4.157568574882897\n",
      "beta3:4.898708197151764\n"
     ]
    }
   ],
   "source": [
    "ols_obj_fit = ols_obj.fit()\n",
    "beta_array_sm = ols_obj.fit().params\n",
    "for i in range(len(beta_array_sm)):\n",
    "    print('beta' + str(i) + ':' + str(beta_array_sm[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Monte Carlo Simulation of OLS Algorithm </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_hat = []\n",
    "for i in range(3000):\n",
    "    u = np.random.randn(100)\n",
    "    u = u[np.newaxis, :].T\n",
    "    y = X@beta_array + u\n",
    "    beta_hat.append(np.linalg.inv(X.T@X)@X.T@y)\n",
    "beta_hat = np.array(beta_hat).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare with true parameters\n",
    "$$\n",
    "\\boldsymbol{\\beta} = [2, 3, 4, 5]^T\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20, 5), nrows=1, ncols=4)\n",
    "for i in range(len(beta_hat[0])):\n",
    "    ax[i].hist(beta_hat[0][i], bins=100)\n",
    "    ax[i].axvline(x=np.mean(beta_hat[0][i]), color='red', label ='mean {}'.format(np.round(np.mean(beta_hat[0][i]),3)))\n",
    "    ax[i].set_title(r'$\\beta_{}$'.format(i+1))\n",
    "    ax[i].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Goodness of Fit in Pythagorean Theorem</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One important implication from orthogonality condition is that $\\sum_{t=1}^n\\hat{u}_t=0$. \n",
    "\n",
    "To see why this holds, we denote the first column of $\\boldsymbol{X}$ as $\\iota$ (iota), which contains all $1$'s, this vector is surly in the $\\text{Col}\\boldsymbol X$, thus\n",
    "\n",
    "$$\n",
    "\\iota^T \\boldsymbol{\\hat{u}} = \\sum_{t=1}^n\\hat{u}_t=0\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the residual of last round generated data, numerical value essentially equals $0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2683187833317788e-12"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(ols_obj_fit.resid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fitted value $\\boldsymbol{y}=\\boldsymbol{X\\hat{\\beta}}$ is the linear combination that we are seeking for, and it is orthogonal to OLS residuals $ \\boldsymbol{\\hat{u}}$ \n",
    "\n",
    "$$(\\boldsymbol{X} \\boldsymbol{\\hat{\\beta}})^{T} \\boldsymbol{\\hat{u}}= \\boldsymbol{\\hat{\\beta}}^{T} \\boldsymbol{X}^{T} \\boldsymbol{\\hat{u}}=\\mathbf{0}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\boldsymbol{\\hat{u}}$ can be seen as a function of $ \\boldsymbol{\\beta}$, denoted $\\boldsymbol{\\hat{u}(\\beta)}$, and $\\boldsymbol{\\hat{\\beta}}$ minimizes $\\|\\boldsymbol{\\hat{u}(\\beta)}\\|$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we have known that $\\boldsymbol{\\hat{u}}\\perp \\text{Col}X$, then the length of three vectors can be represented by Pythagoras' Theorem.\n",
    "\n",
    "$$\n",
    "\\|\\boldsymbol{y}\\|^2= \\|\\boldsymbol{X\\hat{\\beta}}\\|^2+\\|\\boldsymbol{\\hat{u}}\\|^2\\tag{5}\n",
    "$$\n",
    "\n",
    "This is geometric version of the classical property of OLS\n",
    "\n",
    "$$\n",
    "TSS = ESS + RSS\n",
    "$$\n",
    "\n",
    "Numerical version is\n",
    "\\begin{equation}\n",
    "\\underbrace{\\sum_{i=1}^n(y_i-\\bar{y})^2}_{TSS}=\\underbrace{\\sum_{i=1}^n(\\hat{y}_i-\\bar{y})^2}_{ESS}+\\underbrace{\\sum_{i=1}^n\\hat{u}^2_i}_{RSS}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "const = np.ones(100)\n",
    "const = const[np.newaxis, :]\n",
    "X_inde = np.random.randn(3, 100)\n",
    "X = np.concatenate((const.T, X_inde.T), axis=1)\n",
    "\n",
    "beta_array = np.array([2, 3, 4, 5])\n",
    "beta_array = beta_array[np.newaxis, :].T\n",
    "\n",
    "beta_hat = np.linalg.inv(X.T@X)@X.T@y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TSS : 6032.8146\n",
      "ESS : 1140.2611\n",
      "RSS : 4892.5535\n",
      "ESS + RSS : 6032.8146\n"
     ]
    }
   ],
   "source": [
    "TSS = np.linalg.norm(y)\n",
    "ESS = np.linalg.norm(X@beta_hat)\n",
    "RSS = np.linalg.norm(y-X@beta_hat)\n",
    "print('TSS : {:.4f}'.format(TSS**2))\n",
    "print('ESS : {:.4f}'.format(ESS**2))\n",
    "print('RSS : {:.4f}'.format(RSS**2))\n",
    "print('ESS + RSS : {:.4f}'.format(ESS**2+RSS**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare with ```statsmodel``` results, we can notice the $\\text{ESS}$ is different, because it is computed by subtracting $\\text{RSS}$ from centered $\\text{TSS}$. The difference between centered or uncentered values actually have little practical significance, i.e. in practice we report one of them and stick to it with further explanation. But we will explain later in this chapter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uncentered TSS from Statsmodels : 6032.8146\n",
      "ESS from Statsmodels : 169.8498\n",
      "RSS from Statsmodels : 4892.5535\n",
      "ESS + RSS, from Statsmodels : 5062.4033\n"
     ]
    }
   ],
   "source": [
    "ols_obj_fit = sm.OLS(y, X).fit()\n",
    "\n",
    "print('Uncentered TSS from Statsmodels : {:.4f}'.format(ols_obj_fit.uncentered_tss))\n",
    "print('ESS from Statsmodels : {:.4f}'.format(ols_obj_fit.ess))\n",
    "print('RSS from Statsmodels : {:.4f}'.format(ols_obj_fit.ssr))\n",
    "print('ESS + RSS, from Statsmodels : {:.4f}'.format(ols_obj_fit.ess+ols_obj_fit.ssr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Projection Matrix </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have known that $\\boldsymbol{X\\hat{\\beta}}$ is the orthogonal projection of $\\boldsymbol{y}$ , here we substitute OLS solution back into it\n",
    "\n",
    "$$\n",
    "\\boldsymbol{X\\hat{\\beta}}=\\boldsymbol{X}(\\boldsymbol{X}^T\\boldsymbol{X})^{-1}\\boldsymbol{X}^T\\boldsymbol{y}= \\boldsymbol{P}_{\\boldsymbol{X}}\\boldsymbol{y}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $ \\boldsymbol{P}_{\\boldsymbol{X}}=\\boldsymbol{X}(\\boldsymbol{X}^T\\boldsymbol{X})^{-1}\\boldsymbol{X}^T$ is a projection matrix which projects $\\boldsymbol{y}$ onto $\\text{Col}\\boldsymbol{X}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are familiar with linear algebra, you would have seen formula of orthogonal projection, below is a vector presentation of $\\boldsymbol{X}(\\boldsymbol{X}^T\\boldsymbol{X})^{-1}\\boldsymbol{X}^T\\boldsymbol{y}$\n",
    "\n",
    "\n",
    "$$\\hat{\\mathbf{y}}=\\frac{\\mathbf{y} \\cdot \\mathbf{x}_{1}}{\\mathbf{x}_{1} \\cdot \\mathbf{x}_{1}} \\mathbf{x}_{1}+\\cdots+\\frac{\\mathbf{y} \\cdot \\mathbf{x}_{k}}{\\mathbf{x}_{k} \\cdot \\mathbf{x}_{x}} \\mathbf{x}_k\n",
    "=\\frac{\\mathbf{x}_1^T \\mathbf{y}}{\\mathbf{x}_{1}^T  \\mathbf{x}_{1}} \\mathbf{x}_{1}+\\cdots+\\frac{\\mathbf{x}_k^T \\mathbf{y}}{\\mathbf{x}_{k}^T  \\mathbf{x}_{k}} \\mathbf{x}_{k}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another projection matrix $\\boldsymbol{M}_{\\boldsymbol{X}}=\\left(\\mathbf{I}-\\boldsymbol{X}\\left(\\boldsymbol{X}^{T} \\boldsymbol{X}\\right)^{-1} \\boldsymbol{X}^{T}\\right)= \\mathbf{I} - \\boldsymbol{P}_{\\boldsymbol{X}}$ is constructed from\n",
    "\n",
    "$$\n",
    "\\boldsymbol{\\hat{u}}=\\boldsymbol{y}-\\boldsymbol{X} \\boldsymbol{\\hat{\\beta}} =\\boldsymbol{y}-\\boldsymbol{P}_{\\boldsymbol{X}} \\boldsymbol{y}=\\left(\\mathbf{I}-\\boldsymbol{X}\\left(\\boldsymbol{X}^{T} \\boldsymbol{X}\\right)^{-1} \\boldsymbol{X}^{T}\\right) \\boldsymbol{y}=\\boldsymbol{M}_{\\boldsymbol{X}} \\boldsymbol{y}\n",
    "$$\n",
    "\n",
    "$\\boldsymbol{M}_X$ can project any vector into the subspace of $\\perp \\boldsymbol{X}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def proj_mat_P(X):\n",
    "##computing projection matrix P. Input X represents regressors.##\n",
    "    proj_matP = X@np.linalg.inv(X.T@X)@X.T\n",
    "    return proj_matP\n",
    "\n",
    "def proj_mat_M(X):\n",
    "##computing projection matrix M. Input X represents regressors.##\n",
    "    proj_matM =  np.eye(X.shape[0]) - X@np.linalg.inv(X.T@X)@X.T\n",
    "    return proj_matM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's verify if our projection matrix $\\boldsymbol{P}_{\\boldsymbol{X}}\\boldsymbol{y}$ yields the same result as $\\boldsymbol{\\hat{y}}$ from ```statsmodels```, calculate the difference then print the first $10$ entries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.44089210e-16],\n",
       "       [-4.44089210e-16],\n",
       "       [-2.22044605e-15],\n",
       "       [ 4.44089210e-16],\n",
       "       [-1.33226763e-15],\n",
       "       [-2.22044605e-15],\n",
       "       [ 0.00000000e+00],\n",
       "       [ 0.00000000e+00],\n",
       "       [-8.88178420e-16],\n",
       "       [ 4.44089210e-15]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fitted_discrp = proj_mat_P(X)@y - ols_obj_fit.fittedvalues[np.newaxis,:].T\n",
    "fitted_discrp[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, verify if $\\boldsymbol{M}_{\\boldsymbol{X}}\\boldsymbol{y} = \\boldsymbol{\\hat{u}}$, also print the first $10$ entries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.11022302e-16],\n",
       "       [-3.55271368e-15],\n",
       "       [-3.55271368e-15],\n",
       "       [-8.88178420e-16],\n",
       "       [ 0.00000000e+00],\n",
       "       [ 0.00000000e+00],\n",
       "       [ 6.66133815e-16],\n",
       "       [-1.77635684e-15],\n",
       "       [ 1.33226763e-15],\n",
       "       [-7.10542736e-15]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resid_discrp = proj_mat_M(X)@y - ols_obj_fit.resid[np.newaxis,:].T\n",
    "resid_discrp[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font face=\"gotham\" color=\"purple\"> Properties of Projection Matrix </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Geometrically, it is easy to visualize properties of projection matrices in your mind\n",
    "$$\n",
    "\\boldsymbol{P}_{\\boldsymbol{X}}\\boldsymbol{P}_{\\boldsymbol{X}}=\\boldsymbol{P}_{\\boldsymbol{X}}\\quad \\text{and}\\quad \\boldsymbol{M}_{\\boldsymbol{X}}\\boldsymbol{M}_{\\boldsymbol{X}}=\\boldsymbol{M}_{\\boldsymbol{X}}\n",
    "$$\n",
    "which are called **idempotent**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can verify numerically, if multiplication equal zero matrix\n",
    "$$\n",
    "\\boldsymbol{P}_{\\boldsymbol{X}}\\boldsymbol{P}_{\\boldsymbol{X}}-\\boldsymbol{P}_{\\boldsymbol{X}} = \\boldsymbol{O}\\\\\n",
    "\\boldsymbol{M}_{\\boldsymbol{X}}\\boldsymbol{M}_{\\boldsymbol{X}}-\\boldsymbol{M}_{\\boldsymbol{X}} = \\boldsymbol{O}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.93889390e-18,  8.67361738e-19, -3.46944695e-18, ...,\n",
       "        -1.21430643e-17,  0.00000000e+00, -1.38777878e-17],\n",
       "       [-8.67361738e-19,  3.46944695e-18, -1.73472348e-18, ...,\n",
       "        -8.67361738e-19, -6.93889390e-18, -1.76182853e-18],\n",
       "       [-3.46944695e-18, -1.73472348e-18,  0.00000000e+00, ...,\n",
       "         3.46944695e-18, -1.73472348e-18,  9.48676901e-19],\n",
       "       ...,\n",
       "       [-1.04083409e-17,  8.67361738e-19,  1.04083409e-17, ...,\n",
       "         1.38777878e-17, -1.73472348e-18, -6.93889390e-18],\n",
       "       [-1.73472348e-18, -5.20417043e-18, -1.73472348e-18, ...,\n",
       "         0.00000000e+00,  0.00000000e+00, -6.93889390e-18],\n",
       "       [ 0.00000000e+00, -1.92445886e-18,  3.36102673e-18, ...,\n",
       "         6.93889390e-18, -1.04083409e-17,  0.00000000e+00]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Proj_P_X = proj_mat_P(X)\n",
    "Proj_P_X@Proj_P_X - Proj_P_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.66133815e-16, -6.07153217e-18,  0.00000000e+00, ...,\n",
       "        -1.38777878e-17, -1.04083409e-17, -1.38777878e-17],\n",
       "       [-8.67361738e-18,  3.33066907e-16, -1.38777878e-17, ...,\n",
       "        -3.46944695e-18, -1.73472348e-18, -1.70761842e-18],\n",
       "       [ 3.46944695e-18, -8.67361738e-18,  0.00000000e+00, ...,\n",
       "         6.93889390e-18,  0.00000000e+00,  9.55453165e-19],\n",
       "       ...,\n",
       "       [-1.04083409e-17, -2.60208521e-18,  1.04083409e-17, ...,\n",
       "         1.11022302e-16, -3.46944695e-18, -1.38777878e-17],\n",
       "       [-1.04083409e-17, -1.73472348e-18,  1.73472348e-18, ...,\n",
       "        -1.73472348e-18,  0.00000000e+00, -6.93889390e-18],\n",
       "       [-6.93889390e-18, -2.08708918e-18,  3.15096256e-18, ...,\n",
       "        -6.93889390e-18, -1.04083409e-17,  0.00000000e+00]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Proj_M_X = proj_mat_M(X)\n",
    "Proj_M_X@Proj_M_X - Proj_M_X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\boldsymbol{P}_{\\boldsymbol{X}}$ and $\\boldsymbol{M}_{\\boldsymbol{X}}$ are _symmetric matrices_, can be easily shown with rules of transpose.\n",
    "\n",
    "$$\n",
    "\\boldsymbol{P}_{\\boldsymbol{X}}^T = \\boldsymbol{X}\\left[(\\boldsymbol{X}^T\\boldsymbol{X})^{-1}\\right]^{T}\\boldsymbol{X}^T = \\boldsymbol{X}\\left[(\\boldsymbol{X}^T\\boldsymbol{X})^{T}\\right]^{-1}\\boldsymbol{X}^T =\\boldsymbol{X}(\\boldsymbol{X}^T\\boldsymbol{X})^{-1}\\boldsymbol{X}^T=\\boldsymbol{P}_{\\boldsymbol{X}}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\boldsymbol{M}_{\\boldsymbol{X}}^T = (\\mathbf{I} - \\boldsymbol{P}_{\\boldsymbol{X}})^T = \\mathbf{I} - \\boldsymbol{P}_{\\boldsymbol{X}}^T =  \\mathbf{I} - \\boldsymbol{P}_{\\boldsymbol{X}} = \\boldsymbol{M}_{\\boldsymbol{X}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\boldsymbol{P}_{\\boldsymbol{X}}$ and $\\boldsymbol{M}_{\\boldsymbol{X}}$ are called **complementary projections**, because\n",
    "\n",
    "$$\n",
    "\\boldsymbol{P}_{\\boldsymbol{X}}+\\boldsymbol{M}_{\\boldsymbol{X}} = \\mathbf{I}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\boldsymbol{P}_{\\boldsymbol{X}}$ and $\\boldsymbol{M}_{\\boldsymbol{X}}$ **annihilate each other**,\n",
    "\n",
    "$$\n",
    "\\boldsymbol{P}_{\\boldsymbol{X}}\\boldsymbol{M}_{\\boldsymbol{X}} = \\mathbf{O}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., ..., 0., 0., 0.],\n",
       "       [0., 1., 0., ..., 0., 0., 0.],\n",
       "       [0., 0., 1., ..., 0., 0., 0.],\n",
       "       ...,\n",
       "       [0., 0., 0., ..., 1., 0., 0.],\n",
       "       [0., 0., 0., ..., 0., 1., 0.],\n",
       "       [0., 0., 0., ..., 0., 0., 1.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Proj_P_X + Proj_M_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-9.54097912e-18,  6.53909435e-19,  1.45626139e-18, ...,\n",
       "         1.34441069e-17,  1.51788304e-18,  1.38777878e-17],\n",
       "       [-1.22057448e-18,  8.81294768e-19, -3.81230422e-18, ...,\n",
       "         8.95313825e-19,  7.51529982e-18,  1.76182853e-18],\n",
       "       [ 3.80063683e-18, -5.26241470e-18,  1.08850785e-17, ...,\n",
       "        -4.91999087e-18,  3.48575234e-18, -9.55453165e-19],\n",
       "       ...,\n",
       "       [ 1.01915004e-17,  2.75624521e-18, -1.26182498e-17, ...,\n",
       "        -1.73472348e-18,  3.68628739e-18,  6.93889390e-18],\n",
       "       [ 9.43255890e-18,  1.64324392e-18, -2.40980873e-18, ...,\n",
       "         2.81892565e-18, -7.04731412e-19,  6.93889390e-18],\n",
       "       [ 8.67361738e-18,  2.08031292e-18, -3.14757443e-18, ...,\n",
       "         1.73472348e-18,  1.08420217e-17,  0.00000000e+00]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Proj_P_X@Proj_M_X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An  _orthogonal decomposition_ of $\\boldsymbol{y}$ by Pythagoras' Theorem\n",
    "\n",
    "$$\n",
    "\\|\\boldsymbol{y}\\|^2 = \\|\\boldsymbol{P}_{\\boldsymbol{X}}\\boldsymbol{y}\\|^2+\\| \\boldsymbol{M}_{\\boldsymbol{X}}\\boldsymbol{y}\\|^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, the projection matrix is not an efficient algorithm. In computation-wise, you shall either use OLS formula or QR decomposition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The residuals and fitted values are invariant to linear transformation of regressors (explanatory variables), which is exact reason that OLS algorithm holds even we have performed data handling, such as changing unit, in terms of projection matrix, $\\boldsymbol{XA}$ is the linear combination of $\\boldsymbol{X}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{P}_{\\boldsymbol{XA}} = \\boldsymbol{XA}(\\boldsymbol{A}^T\\boldsymbol{X}\\boldsymbol{XA})^{-1}\\boldsymbol{A}^T\\boldsymbol{X}^T= \\boldsymbol{X}\\boldsymbol{A}\\boldsymbol{A}^{-1}(\\boldsymbol{X}^T\\boldsymbol{X})^{-1}(\\boldsymbol{A}^T)^{-1}\\boldsymbol{A}^T\\boldsymbol{X}^T = \\boldsymbol{P}_{\\boldsymbol{X}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because $\\boldsymbol{XA}$ is still in $\\text{Col}\\boldsymbol{X}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Frisch-Waugh-Lovell Theorem </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now consider a single linear model\n",
    "\n",
    "$$\n",
    "\\boldsymbol{y}= \\beta_1\\boldsymbol{\\iota}+\\beta_2\\boldsymbol{x}+\\boldsymbol{u}\\label{6}\\tag{6}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And mostly, that $\\boldsymbol{x}$ and $\\boldsymbol{\\iota}$ are not completely independent. Geometrically speaking, they might not be orthogonal to each other.\n",
    "\n",
    "However, we can use one-step Gram-Schmidt process to orthogonalize them. If we choose to find the orthogonal complement of $\\text{proj}_{\\iota}\\boldsymbol{x}$, we can formulate a vector subtraction (if you don't know what's happening here, check my notebook of linear algebra.)\n",
    "\n",
    "$$\n",
    "\\boldsymbol{z} = \\boldsymbol{x}- \\frac{\\boldsymbol{x}\\cdot\\boldsymbol{\\iota}}{\\boldsymbol{\\iota}\\cdot\\boldsymbol{\\iota}}\\boldsymbol{\\iota} = \\boldsymbol{x}-\\frac{n\\bar{x}}{n}\\boldsymbol{\\iota}=\\boldsymbol{x}- \\bar{x}\\boldsymbol{\\iota}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we get $\\boldsymbol{z}\\perp \\boldsymbol{\\iota}$, in econometric term it is called **centering** the variable by subtracting the mean of itself. Substituting $\\boldsymbol{x}= \\boldsymbol{z}+\\bar{x}\\boldsymbol{\\iota}$ back in "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{y}=\\beta_1\\boldsymbol{\\iota}+\\beta_2(\\boldsymbol{z}+\\bar{x}\\boldsymbol{\\iota})+u = (\\beta_1+\\bar{x}\\beta_2)\\boldsymbol{\\iota}+\\beta_2\\boldsymbol{z}+u = \\alpha_1\\boldsymbol{\\iota}+\\alpha_2\\boldsymbol{z}+\\boldsymbol{u}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the we are sure that $\\boldsymbol{\\iota}^T \\boldsymbol{z} =0$, because of orthogonality, however note that coeffcients are no longer $\\beta$'s any more.\n",
    "\n",
    "It might not be clear at this moment why we want this property, read on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Multivariate Regression Model Visualization </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For multivariate regression model, we can partition $\\boldsymbol{X}$ in to $[\\boldsymbol{X}_1, \\boldsymbol{X}_2]$, where $\\boldsymbol{X}_1$ is $n \\times k_1$ and $\\boldsymbol{X}_2$ is $n \\times k_2$, $k_1+k_2 =k$.\n",
    "\n",
    "It is impossible to visualize any multivariate regression model which is in higher dimension, but we can visualize by imagining the subspace spanned by $\\boldsymbol{X}_1$ or $\\boldsymbol{X}_2$ each represented by a line. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regression model becomes\n",
    "\n",
    "$$\n",
    "\\boldsymbol{y}=  \\boldsymbol{X}_1\\beta_1 + \\boldsymbol{X}_2\\beta_2 +\\boldsymbol{u}\\label{7}\\tag{7}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We denote $\\boldsymbol{M}_1 = \\boldsymbol{M}_{\\boldsymbol{X}_1}=\\mathbf{I}-\\boldsymbol{P}_1$ where $\\boldsymbol{P}_1 = \\boldsymbol{P}_{\\boldsymbol{X}_1} = \\boldsymbol{X}_1(\\boldsymbol{X}_1^T\\boldsymbol{X}_1)^{-1}\\boldsymbol{X}_1^T$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\boldsymbol{X}_1$ and $\\boldsymbol{X}_2$ are not orthogonal, we can project $\\boldsymbol{X}_2$ off $\\boldsymbol{X}_1$ to obtain $\\boldsymbol{Z} = \\boldsymbol{M}_1\\boldsymbol{X}_1$, where $\\boldsymbol{Z}\\perp \\boldsymbol{X}_1$.\n",
    "\n",
    "Once we orthogonalize $\\boldsymbol{X}_2$, the model becomes\n",
    "\n",
    "$$\n",
    "\\boldsymbol{y} = \\boldsymbol{X}_1\\alpha_1+\\boldsymbol{M}_1\\boldsymbol{X}_1\\alpha_2+\\boldsymbol{u}\\label{8}\\tag{8}\n",
    "$$\n",
    "\n",
    "From the graph below, we can see that actually $\\hat{\\alpha}_2=\\hat{\\beta}_2$, because $\\boldsymbol{Z}$ and $\\boldsymbol{X}_2$ form two similar triangles that \n",
    "\n",
    "$$\n",
    "\\frac{\\|\\boldsymbol{Z}\\hat{\\alpha}_2\\|}{\\|\\boldsymbol{Z}\\|}=\\frac{\\|\\boldsymbol{X}_2\\hat{\\beta}_2\\|}{\\|\\boldsymbol{X}_2\\|}\\Longrightarrow \\frac{\\|\\boldsymbol{Z}\\|\\|\\hat{\\alpha}_2\\|}{\\|\\boldsymbol{Z}\\|}=\\frac{\\|\\boldsymbol{X}_2\\|\\|\\hat{\\beta}_2\\|}{\\|\\boldsymbol{X}_2\\|}\\Longrightarrow \\hat{\\alpha}_2 =\\hat{\\beta}_2 \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And also because $\\boldsymbol{Z}=\\boldsymbol{M}_1\\boldsymbol{X}_2$ and $\\boldsymbol{X}_1$ are mutally orthogonal, consequently two models\n",
    "\n",
    "\\begin{align}\n",
    "\\boldsymbol{y} &= \\boldsymbol{X}_1\\alpha_1+\\boldsymbol{M}_1\\boldsymbol{X}_2\\beta_2 + \\boldsymbol{u}\\\\\n",
    "\\boldsymbol{y} &= \\boldsymbol{M}_1\\boldsymbol{X}_2\\beta_2 +\\boldsymbol{v} \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "must yield the same estimates of $\\hat{\\beta}_2$. However the error terms are different, that's why we use $\\boldsymbol{v}$ in the second regression model. This is shown in the graph below with two different residual vectors $\\boldsymbol{\\hat{u}}$ and $\\boldsymbol{\\hat{v}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, if we want to have the same residual, we can project $\\boldsymbol{y}$ off $\\boldsymbol{X}_1$, i.e. to orthogonalize $\\boldsymbol{y}$ to $\\boldsymbol{X}_1$.\n",
    "\n",
    "$$\n",
    "\\boldsymbol{M}_1\\boldsymbol{y}=\\boldsymbol{M}_1\\boldsymbol{X}_2\\beta_2+\\boldsymbol{u}\\label{9}\\tag{9}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model is called $\\text{FWL}$ regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the visualization of $\\text{FWL}$ theorem, please walk through the plot with description above together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = np.linspace(0, 10, 10)\n",
    "t = np.linspace(0, 10, 10)\n",
    "S, T = np.meshgrid(s, t)\n",
    "X = S\n",
    "Y = T\n",
    "Z = np.zeros((10, 10))\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (10, 10))\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, alpha = .3)\n",
    "\n",
    "y = np.array([6, 6, 5])\n",
    "y_vec = np.array([[0, 0, 0, y[0], y[1], y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'black', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 5)\n",
    "\n",
    "\n",
    "yhat = np.array([y[0], y[1], 0])\n",
    "yhat_vec = np.array([[0, 0, 0, yhat[0], yhat[1], yhat[2]]])\n",
    "X, Y, Z, U, V, W = zip(*yhat_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = .6,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "# yhat_vec = np.array([[0, 0, 0, 0, 0, y[2]]])\n",
    "# X, Y, Z, U, V, W = zip(*yhat_vec)\n",
    "# ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = .6,arrow_length_ratio = .04, pivot = 'tail',\n",
    "#           linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "\n",
    "\n",
    "################################ regressors ########################################\n",
    "\n",
    "X1 = np.array([10, 0, 0])\n",
    "X2 = np.array([3, 10, 0])\n",
    "X1_vec = np.array([[0, 0, 0, X1[0], X1[1], X1[2]]])\n",
    "X, Y, Z, U, V, W = zip(*X1_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'purple', alpha = .5,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "X2 = np.array([3, 10, 0])\n",
    "X2_vec = np.array([[0, 0, 0, X2[0], X2[1], X2[2]]])\n",
    "X, Y, Z, U, V, W = zip(*X2_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'purple', alpha = .5,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "################################ OLS estimation ########################################\n",
    "X1 = np.array([10, 0, 0])\n",
    "X2 = np.array([3, 10, 0])\n",
    "X = np.vstack((X1, X2)).T\n",
    "beta_hat = np.linalg.inv(X.T@X)@X.T@y\n",
    "\n",
    "################################ OLS linear combination ########################################\n",
    "\n",
    "X1Beta1hat = beta_hat[0]*X1\n",
    "X1Beta1hat_vec = np.array([[0, 0, 0, X1Beta1hat[0], X1Beta1hat[1], X1Beta1hat[2]]])\n",
    "X, Y, Z, U, V, W = zip(*X1Beta1hat_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'aqua', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "\n",
    "X2Beta1hat = beta_hat[1]*X2\n",
    "X2Beta1hat_vec = np.array([[0, 0, 0, X2Beta1hat[0], X2Beta1hat[1], X2Beta1hat[2]]])\n",
    "X, Y, Z, U, V, W = zip(*X2Beta1hat_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'aqua', alpha = .8,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "##################################Orthogonalizing X2 ##################################\n",
    "Z_orth = np.array([0, 10, 0])\n",
    "Z_orth_vec = np.array([[0, 0, 0, Z_orth[0], Z_orth[1], Z_orth[2]]])\n",
    "X, Y, Z, U, V, W = zip(*Z_orth_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'Darkorange', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "######################################Projecting y onto Z##########################################\n",
    "\n",
    "projZorth_y = (np.dot(y, Z_orth)/(np.dot(Z_orth, Z_orth)))*Z_orth\n",
    "projZorth_y_vec = np.array([[0, 0, 0, projZorth_y[0], projZorth_y[1], projZorth_y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*projZorth_y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'aqua', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "######################################Projecting y onto X1 ##########################################\n",
    "\n",
    "projX1_y = (np.dot(y, X1)/(np.dot(X1, X1)))*X1\n",
    "projX1_y_vec = np.array([[0, 0, 0, projX1_y[0], projX1_y[1], projX1_y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*projX1_y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'LightSalmon', alpha = .7,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 4)\n",
    "\n",
    "\n",
    "###################################### M1y ##########################################\n",
    "M1y=y-projX1_y\n",
    "M1y_vec = np.array([[0, 0, 0, M1y[0], M1y[1], M1y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*M1y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'black', alpha = .5,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 4)\n",
    "##################################### Dashed Lines #############################################\n",
    "\n",
    "point1 = [y[0], y[1], y[2]]\n",
    "point2 = [yhat[0], yhat[1], yhat[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.5, ls = '--')\n",
    "\n",
    "## Z_orth to X ##\n",
    "point1 = [Z_orth[0], Z_orth[1], Z_orth[2]]\n",
    "point2 = [X2[0], X2[1], X2[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'k', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## Z_alpha2 to yhat ##\n",
    "point1 = [yhat[0], yhat[1], yhat[2]]\n",
    "point2 = [projZorth_y[0], projZorth_y[1], projZorth_y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'k', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## X1beta1 to yhat ##\n",
    "point1 = [yhat[0], yhat[1], yhat[2]]\n",
    "point2 = [X1Beta1hat[0], X1Beta1hat[1], X1Beta1hat[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'k', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## X1alpha1 to yhat ##\n",
    "point1 = [yhat[0], yhat[1], yhat[2]]\n",
    "point2 = [projX1_y[0], projX1_y[1], projX1_y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'k', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## M1y to y ##\n",
    "point1 = [y[0], y[1], y[2]]\n",
    "point2 = [M1y[0], M1y[1], M1y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'k', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## M1y to Zalpha2 ##\n",
    "point1 = [projZorth_y[0], projZorth_y[1], projZorth_y[2]]\n",
    "point2 = [M1y[0], M1y[1], M1y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'k', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## y to Zalpha2 ##\n",
    "point1 = [projZorth_y[0], projZorth_y[1], projZorth_y[2]]\n",
    "point2 = [y[0], y[1], y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "###########################################################################\n",
    "\n",
    "ax.text(x = y[0], y = y[1], z = y[2], s = '$y$', size = 16)\n",
    "ax.text(9, 9, 0, '$Col\\ X$', size = 16)\n",
    "ax.text(x = y[0], y = y[1], z = 0, s = r'$\\hat{y}=X\\hat{\\beta}$', size = 16)\n",
    "ax.text(x = X1[0], y = X1[1], z = X1[2], s = r'$X_1$', size = 16)\n",
    "ax.text(x = X2[0], y = X2[1], z = X2[2], s = r'$X_2$', size = 16)\n",
    "ax.text(x = X1Beta1hat[0], y = X1Beta1hat[1], z = X1Beta1hat[2], s = r'$X_1\\hat{\\beta}_1$', size = 16)\n",
    "ax.text(x = X2Beta1hat[0], y = X2Beta1hat[1], z = X2Beta1hat[2], s = r'$X_2\\hat{\\beta}_2$', size = 16)\n",
    "ax.text(x = Z_orth[0], y = Z_orth[1], z = Z_orth[2], s = r'$Z=M_1X_2$', size = 16)\n",
    "ax.text(x = projZorth_y[0], y = projZorth_y[1], z = projZorth_y[2], s = r'$Z\\hat{\\alpha}_2$', size = 16)\n",
    "ax.text(x = projX1_y[0], y = projX1_y[1], z = projX1_y[2], s = r'$X_1\\hat{\\alpha}_1$', size = 16)\n",
    "ax.text(x = M1y[0], y = M1y[1], z = M1y[2], s = r'$M_1y$', size = 16)\n",
    "ax.text(x = (y[0]+yhat[0])/2, y = (y[1]+yhat[1])/2, z = (y[2]+yhat[2])/2, s = r'$\\hat{u}$', size = 16, color = 'r')\n",
    "ax.text(x = (y[0]+projZorth_y[0])/2, y = (y[1]+projZorth_y[1])/2, z = (y[2]+projZorth_y[2])/2, s = r'$\\hat{v}$', size = 16, color = 'r')\n",
    "\n",
    "\n",
    "for i in ['x', 'y', 'z']:\n",
    "    exec('ax.set_'+i+'lim3d(0, 10)')\n",
    "    \n",
    "ax.set_title('Geometry of the Frisch-Waugh-Lovell Theorem', fontsize = 17)\n",
    "ax.set_xlabel('X-axis'),ax.set_ylabel('Y-axis'),ax.set_zlabel('Z-axis')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verbally, $\\text{FWL}$ theorems are \n",
    "\n",
    "1. The OLS estimates of $\\beta_2$ from \n",
    "\\begin{align}\n",
    "\\boldsymbol{y} &= \\boldsymbol{X}_1\\alpha_1+\\boldsymbol{M}_1\\boldsymbol{X}_2\\beta_2 + \\boldsymbol{u}\\\\\n",
    "\\boldsymbol{y} &= \\boldsymbol{M}_1\\boldsymbol{X}_2\\beta_2 +\\boldsymbol{v} \n",
    "\\end{align}\n",
    "are numerically identical.\n",
    "2. The residuals from models\n",
    "\\begin{align}\n",
    "\\boldsymbol{M}_1\\boldsymbol{y}&=\\boldsymbol{M}_1\\boldsymbol{X}_2\\beta_2+\\boldsymbol{u}\\\\\n",
    "\\boldsymbol{y}&=  \\boldsymbol{X}_1\\beta_1 + \\boldsymbol{X}_2\\beta_2 +\\boldsymbol{u}\n",
    "\\end{align}\n",
    "are numerically identical."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will see in later chapters that why we enjoy using $\\text{FWL}$ theorem, first it can reduce dimensions of any regression model and preserve the numerical estimates and residuals, second it provide closed-form algorithm for any estimates that we want to isolate from the rest. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Goodness of Fit, $\\mathbf{R}^2$ </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficient of determination $R^2$ is defined as\n",
    "\n",
    "$$\n",
    "R^2 = \\frac{ESS}{TSS} = \\frac{\\|\\boldsymbol{P_X}\\boldsymbol{y}\\|^2}{\\|\\boldsymbol{y}\\|^2}=\\cos^2{\\vartheta}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where angle $\\vartheta$ is between the vector $\\|\\boldsymbol{y}\\|$ and $\\|\\boldsymbol{P_Xy}\\|$. Reproduce a OLS simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "const = np.ones(100)\n",
    "const = const[np.newaxis, :]\n",
    "X_inde = np.random.randn(3, 100)\n",
    "X = np.concatenate((const.T, X_inde.T), axis=1)\n",
    "\n",
    "beta_array = np.array([2, 3, 4, 5])\n",
    "beta_array = beta_array[np.newaxis, :].T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.random.randn(100)\n",
    "u = u[np.newaxis, :].T\n",
    "y = X@beta_array + u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TSS : 5030.0745\n",
      "ESS : 4923.5607\n",
      "RSS : 106.5138\n",
      "ESS + RSS : 5030.0745\n"
     ]
    }
   ],
   "source": [
    "beta_hat = np.linalg.inv(X.T@X)@X.T@y\n",
    "\n",
    "TSS = np.linalg.norm(y)\n",
    "ESS = np.linalg.norm(X@beta_hat)\n",
    "RSS = np.linalg.norm(y-X@beta_hat)\n",
    "print('TSS : {:.4f}'.format(TSS**2))\n",
    "print('ESS : {:.4f}'.format(ESS**2))\n",
    "print('RSS : {:.4f}'.format(RSS**2))\n",
    "print('ESS + RSS : {:.4f}'.format(ESS**2+RSS**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-sqr : 0.9894\n"
     ]
    }
   ],
   "source": [
    "print('R-sqr : {:.4f}'.format(ESS/TSS))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare with ```statsmodels``` result, the discrepancy is due to ```statsmodels``` using centered $\\text{TSS}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9777822710827409"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols_obj = sm.OLS(y, X)\n",
    "ols_obj_fit = ols_obj.fit()\n",
    "ols_obj_fit.rsquared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a $\\text{2D}$ graphic demonstration. The larger of angle, the less of $\\text{ESS}$, i.e. ${R}^2$ is smaller. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (7, 7))\n",
    "ax.arrow(0, 0, 20, 0, color = 'red', width = .08, \n",
    "         length_includes_head = True,\n",
    "         head_width = .3, # default: 3*width\n",
    "         head_length = .6,\n",
    "         overhang = .4)\n",
    "ax.arrow(0, 0, 20, 20, color = 'red', width = .08, \n",
    "         length_includes_head = True,\n",
    "         head_width = .3, # default: 3*width\n",
    "         head_length = .6,\n",
    "         overhang = .4)\n",
    "\n",
    "point1 = [20, 0]\n",
    "point2 = [20, 20]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], c = 'k', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "ax.text(1.3, .2, r'$\\theta$', size = 18)\n",
    "ax.text(6, 7, '$TSS=\\|\\|y\\|\\|^2$', size = 18, rotation = 45)\n",
    "ax.text(6, .2, r'$ESS=\\|\\|P_Xy\\|\\|^2$', size = 18)\n",
    "ax.text(20, 4, r'$RSS=\\|\\|M_Xy\\|\\|^2$', size = 18, rotation = 90)\n",
    "\n",
    "ax.text(3,15,r'$\\cos^2{\\vartheta}= \\frac{ESS}{TSS}=\\mathbf{R}^2$', size = 21)\n",
    "ax.axis([0, 21, -.2, 21])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equality holds as long as $\\text{ESS}$ and $\\text{RSS}$ forms a right angle, hence any other estimation methods i.e. a non-OLS $\\tilde{\\beta}$'s $R^2$ no longer has this pure geometric interpretation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $R^2 = \\frac{ESS}{TSS}$ is **uncentered $R^2$** since we are using uncertered $\\text{TSS}$, sometimes it is denoted as $R^2_u$, because $R^2_u$ is not _invariant_ to change of $\\vartheta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see this, suppose the data matrix $\\boldsymbol{X} = [\\boldsymbol{\\iota}\\quad \\boldsymbol{x}]$, where $\\boldsymbol{\\iota}$ is the constant term, if we add $\\alpha \\boldsymbol{\\iota}$ onto $\\boldsymbol{y}$ then decompose $\\boldsymbol{y}+\\alpha \\boldsymbol{\\iota}$ \n",
    "\n",
    "$$\n",
    "\\boldsymbol{y}+\\alpha \\boldsymbol{\\iota} = \\boldsymbol{P_X}(\\boldsymbol{y}+\\alpha \\boldsymbol{\\iota})+\\boldsymbol{M_X}(\\boldsymbol{y}+\\alpha \\boldsymbol{\\iota})= \\boldsymbol{P_X}\\boldsymbol{y}+\\alpha \\boldsymbol{\\iota}+\\boldsymbol{M_X}\\boldsymbol{y}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $R^2_u$ is \n",
    "\n",
    "$$\n",
    "R^2_u = \\frac{\\|\\boldsymbol{P_X}\\boldsymbol{y}+\\alpha \\boldsymbol{\\iota}\\|^2}{\\|\\boldsymbol{y}+\\alpha \\boldsymbol{\\iota}\\|^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that if $\\alpha\\rightarrow \\infty$ , $R^2_u$ converges to $1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, if we project $\\boldsymbol{y}$ off $\\iota$, this won't be the case anymore, because $\\alpha$ doesn't exist in this case.\n",
    "\n",
    "$$\n",
    "R^2_c = \\frac{\\|\\boldsymbol{P_X}\\boldsymbol{M_\\iota}\\boldsymbol{y}\\|^2}{\\|\\boldsymbol{M_\\iota}\\boldsymbol{y}\\|^2}\n",
    "$$\n",
    "where $R^2_c$ means **centered** $R^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Visualizing $\\mathbf{R}^2_u$ and $\\mathbf{R}^2_c$ </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose $\\iota = (1,1,1)^T$, $\\boldsymbol{x} = (1,2,5)^T$ and $\\boldsymbol{y} = (2,1,10)^T$. We want to show that by adding $\\alpha\\boldsymbol{\\iota}$ onto $\\boldsymbol{y}$, the angle for calculating $R_u^2$ will change, in this case it becomes smaller, i.e. $R^2_u$ increases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([1, 2, 5])\n",
    "y = np.array([2, 1, 10])\n",
    "iota = np.array([1, 1, 1])\n",
    "\n",
    "s = np.linspace(-5, 10, 10)\n",
    "t = np.linspace(-5, 10, 10)\n",
    "S, T = np.meshgrid(s, t)\n",
    "X = S + x[0]*T\n",
    "Y = S + x[1]*T\n",
    "Z = S + x[2]*T\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, alpha = .3)\n",
    "\n",
    "\n",
    "y_vec = np.array([[0, 0, 0, y[0], y[1], y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "x_vec = np.array([[0, 0, 0, x[0], x[1], x[2]]])\n",
    "X, Y, Z, U, V, W = zip(*x_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'blue', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "\n",
    "iota_vec = np.array([[0, 0, 0, iota[0], iota[1], iota[2]]])\n",
    "X, Y, Z, U, V, W = zip(*iota_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'blue', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "X = np.vstack((iota, x)).T\n",
    "Px_y = X@np.linalg.inv(X.T@X)@X.T@y\n",
    "Px_y_vec = np.array([[0, 0, 0, Px_y[0], Px_y[1], Px_y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*Px_y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'aqua', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "##################################################################\n",
    "\n",
    "alpha = 5\n",
    "alpha_iota = np.array([alpha, alpha, alpha])\n",
    "alpha_iota_vec = np.array([[0, 0, 0, alpha_iota[0], alpha_iota[1], alpha_iota[2]]])\n",
    "X, Y, Z, U, V, W = zip(*alpha_iota_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'blue', alpha = .5,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "yhat_plus_ai = Px_y + alpha_iota\n",
    "yhat_plus_ai_vec = np.array([[0, 0, 0, yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2]]])\n",
    "X, Y, Z, U, V, W = zip(*yhat_plus_ai_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'Darkorange', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "y_plus_ai = y + alpha_iota\n",
    "y_plus_ai_vec = np.array([[0, 0, 0, y_plus_ai[0], y_plus_ai[1], y_plus_ai[2]]])\n",
    "X, Y, Z, U, V, W = zip(*y_plus_ai_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'Green', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "##################################################################\n",
    "## y to yhat ##\n",
    "point1 = [Px_y[0], Px_y[1], Px_y[2]]\n",
    "point2 = [y[0], y[1], y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## yhat+(alpha*iota) to yhat ##\n",
    "point1 = [yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2]]\n",
    "point2 = [Px_y[0], Px_y[1], Px_y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## yhat+(alpha*iota) to alpha*iota ##\n",
    "point1 = [yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2]]\n",
    "point2 = [alpha_iota[0], alpha_iota[1], alpha_iota[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## y to y+(alpha*iota) ##\n",
    "point1 = [y[0], y[1], y[2]]\n",
    "point2 = [y_plus_ai[0], y_plus_ai[1], y_plus_ai[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## alpha*iota to y+(alpha*iota) ##\n",
    "point1 = [alpha_iota[0], alpha_iota[1], alpha_iota[2]]\n",
    "point2 = [y_plus_ai[0], y_plus_ai[1], y_plus_ai[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "#####################################################################\n",
    "ax.text(alpha_iota[0], alpha_iota[1],alpha_iota[2], r'$\\alpha \\iota$', size = 18)\n",
    "ax.text(iota[0], iota[1],iota[2], r'$\\iota$', size = 18)\n",
    "ax.text(x[0], x[1],x[2], r'$x$', size = 18)\n",
    "ax.text(y[0], y[1],y[2], r'$y$', size = 18)\n",
    "ax.text(Px_y[0], Px_y[1], Px_y[2], r'$\\hat{y}$', size = 18)\n",
    "ax.text(yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2], r'$\\hat{y}+\\alpha \\iota$', size = 18)\n",
    "ax.text(y_plus_ai[0], y_plus_ai[1], y_plus_ai[2], r'$y+\\alpha \\iota$', size = 18)\n",
    "\n",
    "for i in ['x', 'y', 'z']:\n",
    "    exec('ax.set_'+i+'lim3d(0, 15)')\n",
    "    \n",
    "ax.set_title(r'Geometric Mechanism of $\\mathbf{R}^2_u$ and $\\mathbf{R}^2_c$', fontsize = 17)\n",
    "ax.set_xlabel('X-axis'),ax.set_ylabel('Y-axis'),ax.set_zlabel('Z-axis')\n",
    "\n",
    "ax.view_init(0, -35)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the graph above, the initial angle for $R^2_u$ is formed by vector $\\boldsymbol{y}$ and $\\boldsymbol{\\hat{y}}$, after adding $\\alpha\\boldsymbol{\\iota}$, the new angle is formed by $\\boldsymbol{y}+\\alpha\\boldsymbol{\\iota}$ and $\\boldsymbol{\\hat{y}}+\\alpha\\boldsymbol{\\iota}$. Let's evaluate the $\\cos^2 {\\vartheta}$ with numerical values in the graph.\n",
    "\n",
    "Recall that we have a formula\n",
    "\n",
    "$$\n",
    "\\mathbf{u}\\cdot \\mathbf{v} =\\|\\mathbf{u}\\|\\|\\mathbf{v}\\|\\cos{\\vartheta}\n",
    "$$\n",
    "Rearrange then take power of $2$\n",
    "$$\n",
    "\\cos^2{\\vartheta} = \\bigg(\\frac{\\mathbf{u}\\cdot \\mathbf{v}}{\\|\\mathbf{u}\\|\\|\\mathbf{v}\\|}\\bigg)^2=R^2_u\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficient of determinant before addition is 0.947.\n"
     ]
    }
   ],
   "source": [
    "cos_theta = np.inner(y, Px_y)/(np.linalg.norm(y)*np.linalg.norm(Px_y))\n",
    "print('The coefficient of determinant before addition is {0:.3f}.'.format(cos_theta**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coefficient of determinant after addition is 0.982.\n"
     ]
    }
   ],
   "source": [
    "cos_theta = np.inner(y_plus_ai, yhat_plus_ai)/(np.linalg.norm(y_plus_ai)*np.linalg.norm(yhat_plus_ai))\n",
    "print('The coefficient of determinant after addition is {0:.3f}.'.format(cos_theta**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $R^2_u$ before and after the addition shows that adding constants onto $\\boldsymbol{y}$ can change the value of $\\cos^2{\\vartheta}$.\n",
    "\n",
    "However, in practice you don't need to go into details of their difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But now we need to show how to solve this problem by using $R_c^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([1, 2, 5])\n",
    "y = np.array([2, 1, 10])\n",
    "iota = np.array([1, 1, 1])\n",
    "\n",
    "s = np.linspace(-8, 10, 10)\n",
    "t = np.linspace(-8, 10, 10)\n",
    "S, T = np.meshgrid(s, t)\n",
    "X = S + x[0]*T\n",
    "Y = S + x[1]*T\n",
    "Z = S + x[2]*T\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, alpha = .3)\n",
    "\n",
    "\n",
    "y_vec = np.array([[0, 0, 0, y[0], y[1], y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'red', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "X = np.vstack((iota, x)).T\n",
    "Px_y = X@np.linalg.inv(X.T@X)@X.T@y\n",
    "Px_y_vec = np.array([[0, 0, 0, Px_y[0], Px_y[1], Px_y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*Px_y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'aqua', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "##################################################################\n",
    "\n",
    "alpha = 5\n",
    "alpha_iota = np.array([alpha, alpha, alpha])\n",
    "alpha_iota_vec = np.array([[0, 0, 0, alpha_iota[0], alpha_iota[1], alpha_iota[2]]])\n",
    "X, Y, Z, U, V, W = zip(*alpha_iota_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'blue', alpha = .5,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "yhat_plus_ai = Px_y + alpha_iota\n",
    "yhat_plus_ai_vec = np.array([[0, 0, 0, yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2]]])\n",
    "X, Y, Z, U, V, W = zip(*yhat_plus_ai_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'Darkorange', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "y_plus_ai = y + alpha_iota\n",
    "y_plus_ai_vec = np.array([[0, 0, 0, y_plus_ai[0], y_plus_ai[1], y_plus_ai[2]]])\n",
    "X, Y, Z, U, V, W = zip(*y_plus_ai_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'Green', alpha = 1,arrow_length_ratio = .04, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "iota = iota[:,np.newaxis]\n",
    "M_iota_y = (np.eye(3,3) - iota@np.linalg.inv(iota.T@iota)@iota.T)@y\n",
    "M_iota_y_vec = np.array([[0, 0, 0, M_iota_y[0], M_iota_y[1], M_iota_y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*M_iota_y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'SteelBlue', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "\n",
    "x = np.array([1, 2, 5])\n",
    "iota = np.array([1, 1, 1])\n",
    "X = np.vstack((iota, x)).T\n",
    "Px_M_iota_y = X@np.linalg.inv(X.T@X)@X.T@M_iota_y\n",
    "Px_M_iota_y_vec = np.array([[0, 0, 0, Px_M_iota_y[0], Px_M_iota_y[1], Px_M_iota_y[2]]])\n",
    "X, Y, Z, U, V, W = zip(*Px_M_iota_y_vec)\n",
    "ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = 'Teal', alpha = 1,arrow_length_ratio = .08, pivot = 'tail',\n",
    "          linestyles = 'solid',linewidths = 3)\n",
    "##################################################################\n",
    "## y to yhat ##\n",
    "point1 = [Px_y[0], Px_y[1], Px_y[2]]\n",
    "point2 = [y[0], y[1], y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## yhat+(alpha*iota) to yhat ##\n",
    "point1 = [yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2]]\n",
    "point2 = [Px_y[0], Px_y[1], Px_y[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## yhat+(alpha*iota) to alpha*iota ##\n",
    "point1 = [yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2]]\n",
    "point2 = [alpha_iota[0], alpha_iota[1], alpha_iota[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## y to y+(alpha*iota) ##\n",
    "point1 = [y[0], y[1], y[2]]\n",
    "point2 = [y_plus_ai[0], y_plus_ai[1], y_plus_ai[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "## alpha*iota to y+(alpha*iota) ##\n",
    "point1 = [alpha_iota[0], alpha_iota[1], alpha_iota[2]]\n",
    "point2 = [y_plus_ai[0], y_plus_ai[1], y_plus_ai[2]]\n",
    "line1 = np.array([point1, point2])\n",
    "ax.plot(line1[:,0], line1[:,1], line1[:, 2], c = 'b', lw = 1.5,alpha =0.8, ls = '--')\n",
    "\n",
    "#####################################################################\n",
    "ax.text(alpha_iota[0], alpha_iota[1],alpha_iota[2], r'$\\alpha \\iota$', size = 18)\n",
    "ax.text(y[0], y[1],y[2], r'$y$', size = 18)\n",
    "ax.text(Px_y[0], Px_y[1], Px_y[2], r'$\\hat{y}$', size = 18)\n",
    "ax.text(yhat_plus_ai[0], yhat_plus_ai[1], yhat_plus_ai[2], r'$\\hat{y}+\\alpha \\iota$', size = 18)\n",
    "ax.text(y_plus_ai[0], y_plus_ai[1], y_plus_ai[2], r'$y+\\alpha \\iota$', size = 18)\n",
    "ax.text(M_iota_y[0], M_iota_y[1], M_iota_y[2], r'$M_\\iota y$', size = 18)\n",
    "ax.text(Px_M_iota_y[0], Px_M_iota_y[1], Px_M_iota_y[2], r'$P_X M_\\iota y$', size = 18)\n",
    "\n",
    "for i in ['x', 'y', 'z']:\n",
    "    exec('ax.set_'+i+'lim3d(0, 15)')\n",
    "    \n",
    "ax.set_title(r'Geometric Mechanism of $\\mathbf{R}^2_u$ and $\\mathbf{R}^2_c$', fontsize = 17)\n",
    "ax.set_xlabel('X-axis'),ax.set_ylabel('Y-axis'),ax.set_zlabel('Z-axis')\n",
    "\n",
    "ax.view_init(-64, -48)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have project $\\boldsymbol{y}$ off $\\boldsymbol{\\iota}$, the angle $\\vartheta$ will be preserved, no matter what contants being added onto $\\boldsymbol{y}$, we can also show this algebreically\n",
    "\n",
    "$$\n",
    "R^2_c = \\frac{\\|\\boldsymbol{P_X}\\boldsymbol{M_\\iota}(\\boldsymbol{y}+\\alpha\\iota)\\|^2}{\\|\\boldsymbol{M_\\iota}(\\boldsymbol{y}+\\alpha\\iota)\\|^2}= \\frac{\\|\\boldsymbol{P_X}\\boldsymbol{M_\\iota}\\boldsymbol{y}\\|^2}{\\|\\boldsymbol{M_\\iota}\\boldsymbol{y}\\|^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nevertheless, the $R^2_c$ does not make sense when there is no constant term. \n",
    "\n",
    "Again, when the estimates are other than OLS, say $\\tilde{\\beta}$, Pythagoras' Theorem will not hold, sometimes $R^2_c$ might be even higher than $1$ or lower than $0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Adjusted $\\mathbf{R}^2$ </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, $R^2$ is a misleading indicator, it is easy to lose the insight of it. And one problem the beginners facing constantly is that adding explanatory variables can reward you by gaining higher $R_u^2$ or $R_c^2$.\n",
    "\n",
    "It is easy to imagine the geometry why this is the case. Adding one variable means the $\\text{Span}(X)$ is also adding one dimension, the new $\\text{Span}(X^+)$ will be orthogonally closer to $\\boldsymbol{y}$, i.e. larger $\\text{ESS}$ and smaller $\\text{RSS}$. To neutralize this phenomenon, we invented $\\bar{R}^2$, the adjusted $R^2$.\n",
    "\n",
    "In OLS, $\\bar{R}^2$ can be negative, which signals a very poor fit.\n",
    "\n",
    "The formula of $\\bar{R}^{2}$ is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\bar{R}^{2} \\equiv 1-\\frac{\\frac{1}{n-k} \\sum_{t=1}^{n} \\hat{u}_{t}^{2}}{\\frac{1}{n-1} \\sum_{t=1}^{n}\\left(y_{t}-\\bar{y}\\right)^{2}}=1-\\frac{(n-1) \\boldsymbol{y}^{\\top} \\boldsymbol{M}_{\\boldsymbol{X}} \\boldsymbol{y}}{(n-k) \\boldsymbol{y}^{\\top} \\boldsymbol{M}_{\\iota} \\boldsymbol{y}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The numerator and denominator of $R_c^2$ were replaced by its unbiased estimator, there is no need to derive it, accept it as a fact."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Influential Observations </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From OLS formula, we have one insight, that each element of vector $\\boldsymbol{\\hat{\\beta}}$ is actually a weighted average of $\\boldsymbol{y}$ \n",
    "$$\n",
    "\\boldsymbol{\\hat{\\beta}} = (\\boldsymbol{X}^T\\boldsymbol{X})^{-1}\\boldsymbol{X}^T\\boldsymbol{y}\n",
    "$$\n",
    "\n",
    "In that sense, some observations have higher influence of $\\boldsymbol{\\hat{\\beta}}$ than others. Here are two plots, the main difference is that the right-side plot has one outlier (blue dot). Hence the regression lines are different due to influence of blue dot outlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 30\n",
    "const = np.ones(n)\n",
    "const = const[np.newaxis, :]\n",
    "x = np.arange(1, n+1)\n",
    "x = x[np.newaxis, :]\n",
    "X = np.concatenate((const.T, x.T), axis=1)\n",
    "\n",
    "u = np.random.randn(n)*20\n",
    "u = u[np.newaxis, :].T\n",
    "\n",
    "beta = np.array([2, 3])\n",
    "beta = beta[np.newaxis, :].T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = X@beta + u\n",
    "ols_obj_1_fit = sm.OLS(y, X).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = pd.DataFrame(y)\n",
    "X = pd.DataFrame(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_influ = pd.concat([y, pd.DataFrame([1])], axis = 0)\n",
    "X_influ = pd.concat([X, pd.DataFrame([[1, 35]])], axis = 0)\n",
    "ols_obj_2_fit = sm.OLS(y_influ, X_influ).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(18, 8), nrows=1, ncols=2)\n",
    "ax[0].scatter(X[1], y)\n",
    "ax[0].plot(X[1], ols_obj_1_fit.fittedvalues, color = 'k', lw = 3)\n",
    "ax[0].set_xlim([0, 36])\n",
    "ax[0].set_title('Without Outlier')\n",
    "\n",
    "ax[1].scatter(X_influ[1], y_influ)\n",
    "ax[1].plot(X_influ[1], ols_obj_2_fit.fittedvalues, color = 'k', lw = 3)\n",
    "ax[1].scatter(X_influ[1].iloc[30], y_influ.iloc[30], color = 'blue', s= 100)\n",
    "ax[1].set_xlim([0, 36])\n",
    "ax[1].set_title('With Outlier')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One common way of handling outliers is to include its corresponding dummy variable, in this example we can create a dummy variable $e_t$ that has $1$ at the $t$-th observation which is an outlier and rest of elements are $0$s.\n",
    "$$\n",
    "\\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta}+\\alpha{e_t} + \\boldsymbol{u}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reason that it holds can be seen from applying $\\text{FWL}$ theorem, i.e.\n",
    "$$\n",
    "\\boldsymbol{M_t y} = \\boldsymbol{M_t X}\\boldsymbol{\\beta} + \\boldsymbol{v}\n",
    "$$\n",
    "where $\\boldsymbol{M_t} = \\boldsymbol{M}_{e_t}=\\boldsymbol{I}- e_t(e_t^Te_t)^{-1}e_t^T$. With this expression, we can further conclude that $\\boldsymbol{M}_{t} \\boldsymbol{y}$ is the $\\boldsymbol{y}$ with $t$-th element $y_t$ as $0$.\n",
    "\n",
    "$$\n",
    "\\boldsymbol{M}_{t} \\boldsymbol{y}=\\boldsymbol{y}-\\boldsymbol{e}_{t} \\boldsymbol{e}_{t}^{\\top} \\boldsymbol{y}=\\boldsymbol{y}-y_{t} \\boldsymbol{e}_{t}\n",
    "$$\n",
    "\n",
    "Similarly, $\\boldsymbol{M_t X}$ replaces the $t$-th row of $\\boldsymbol{X}$ by $0$'s.\n",
    "\n",
    "Therefore, the models we need to estimate are\n",
    "$$\n",
    "\\boldsymbol{M_t y} = \\boldsymbol{M_t X}\\boldsymbol{\\beta} + \\boldsymbol{v}\\\\\n",
    "\\boldsymbol{y} = \\boldsymbol{X}\\boldsymbol{\\beta} + \\boldsymbol{u}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "dummy = np.zeros(30)\n",
    "dummy[-1] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X[2]=dummy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
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       "      0     1    2\n",
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    "X.tail()"
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  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
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    {
     "name": "stdout",
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     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      0   R-squared:                       0.660\n",
      "Model:                            OLS   Adj. R-squared:                  0.635\n",
      "Method:                 Least Squares   F-statistic:                     26.22\n",
      "Date:                Tue, 08 Mar 2022   Prob (F-statistic):           4.71e-07\n",
      "Time:                        19:15:59   Log-Likelihood:                -129.38\n",
      "No. Observations:                  30   AIC:                             264.8\n",
      "Df Residuals:                      27   BIC:                             269.0\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "0              5.5301      7.257      0.762      0.453      -9.360      20.421\n",
      "1              2.8625      0.423      6.775      0.000       1.996       3.729\n",
      "2              6.6023     20.374      0.324      0.748     -35.201      48.405\n",
      "==============================================================================\n",
      "Omnibus:                        0.090   Durbin-Watson:                   1.429\n",
      "Prob(Omnibus):                  0.956   Jarque-Bera (JB):                0.162\n",
      "Skew:                          -0.110   Prob(JB):                        0.922\n",
      "Kurtosis:                       2.716   Cond. No.                         104.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "ols_obj_3_fit = sm.OLS(y, X).fit()\n",
    "print(ols_obj_3_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> The Diagonal of $\\boldsymbol{P_X}$ </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We denote the $t^{th}$ diagonal element of $\\boldsymbol{P_X}$ as $h_t$. \n",
    "\n",
    "$$\n",
    "h_t = \\boldsymbol{e}_t^T\\boldsymbol{P_X}\\boldsymbol{e}_t =(\\boldsymbol{P_X}\\boldsymbol{e}_1)^T(\\boldsymbol{P_X}\\boldsymbol{e}_1)= \\|\\boldsymbol{P_X}\\boldsymbol{e}_t\\|^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\boldsymbol{e}_t$ means the $t^{th}$ element is $1$ and rest are $0$s."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From last equation, we can tell that $0 \\leq h_t$, also because $\\|\\boldsymbol{P_X}\\boldsymbol{e}_t\\|<\\|\\boldsymbol{e}_t\\|$ and  $\\|\\boldsymbol{e}_t\\|=1$.So we pin down the range of $h_t$:\n",
    "\n",
    "$$0 \\leq h_t < 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The use of $h_t$ will be shown again in next chapter when we discuss the statistical properties of residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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