{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4fba706f-796a-408b-a294-d640c4821d99",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b327e19-d1c1-4d83-94b9-873dc2517188",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Linear VS Nonlinear Model </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cd25926-6806-48fb-a745-748df2152162",
   "metadata": {},
   "source": [
    "Take a look at these models\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&Y_{i}=\\beta_{1}+\\beta_{2}\\left(\\frac{1}{X_{i}}\\right)+u_{i}\\\\\n",
    "&Y_{i}=\\beta_{1}+\\beta_{2} \\ln X_{i}+u_{i}\\\\\n",
    "&\\text { In } Y_{i}=\\beta_{1}+\\beta_{2} X_{i}+u_{i}\\\\\n",
    "&\\ln Y_{i}=\\ln \\beta_{1}+\\beta_{2} \\ln X_{i}+u_{i}\\\\\n",
    "&\\ln Y_{i}=\\beta_{1}-\\beta_{2}\\left(\\frac{1}{X_{i}}\\right)+u_{i}\n",
    "\\end{aligned}\n",
    "$$\n",
    "The variables might have some nonlinear form, but parameters are all linear (the $4$th model can denote $\\alpha_1=\\ln{\\beta_1}$), as long as we can convert them into linear form with some mathematical manipulation, we call them **intrinsically linear models**. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4027fde-8158-4037-a41e-c4f2c560d592",
   "metadata": {},
   "source": [
    "How about these two models?\n",
    "\\begin{aligned}\n",
    "&Y_{i}=e^{\\beta_{1}+\\beta_{2} X_{i}+u_{i}} \\\\\n",
    "&Y_{i}=\\frac{1}{1+e^{\\beta_{1}+\\beta_{2} X_{i}+u_{i}}} \\\\\n",
    "\\end{aligned}\n",
    "The first one can be easily converted into linear one by taking natural log\n",
    "$$\n",
    "\\ln{Y_i}=\\beta_{1}+\\beta_{2} X_{i}+u_{i}\n",
    "$$\n",
    "The second one is bit tricky, we will deal with it in more details in chapter of binary choice model. But you can be assured that with a little manipulation the model becomes\n",
    "$$\n",
    "\\ln \\left(\\frac{1-Y_{i}}{Y_{i}}\\right)=\\beta_{1}+\\beta_{2} X_{i}+u_{i}\n",
    "$$\n",
    "which is also intrinsically linear."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5df6706e-a6da-48aa-8628-32ae4604bf2f",
   "metadata": {},
   "source": [
    "These two models are **intrinsically nonlinear model**, there is no way to turn them into linear form.\n",
    "\\begin{aligned}\n",
    "&Y_{i}=\\beta_{1}+\\left(0.75-\\beta_{1}\\right) e^{-\\beta_{2}\\left(X_{i}-2\\right)}+u_{i} \\\\\n",
    "&Y_{i}=\\beta_{1}+\\beta_{2}^{3} X_{i}+u_{i}\\\\\n",
    "\\end{aligned}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63fe3d16-e606-416c-b514-c3e0a987a8bc",
   "metadata": {},
   "source": [
    "Can we transform Cobb-Douglas model into linear form? The first one can, by taking natural log. But the second one has an additive disturbance term, which make it intrinsically nonlinear.\n",
    "\\begin{aligned}\n",
    "&Y_{i}=\\beta_{1} X_{2 i}^{\\beta_{2}} X_{3 i}^{\\beta_{3}} u_{i}\\\\\n",
    "&Y_{i}=\\beta_{1} X_{2 i}^{\\beta_{2}} X_{3 i}^{\\beta_{3}}+ u_{i}\\\\\n",
    "\\end{aligned}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e0ee933-0309-49d7-8816-f8209fc02701",
   "metadata": {},
   "source": [
    "Here is another famous economic model, _constant elasticity of substitution_ (CES) production function.\n",
    "$$\n",
    "Y_{i}=A\\left[\\delta K_{i}^{-\\beta}+(1-\\delta) L_{i}^{-\\beta}\\right]^{-1 / \\beta}u_i\n",
    "$$\n",
    "No matter what you do with it, it can't be transformed into linear form, thus it is intrinsically nonlinear"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10de1167-ae4b-4809-860b-6bdbaa85ea74",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> OLS On A Nonlinear Model </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a57e6a5-d680-45c8-9b0a-9ad0bb62d888",
   "metadata": {},
   "source": [
    "Consider an intrinsically nonlinear model\n",
    "$$\n",
    "Y_{i}=\\beta_{1} e^{\\beta_{2}X_{i}}+u_{i}\n",
    "$$\n",
    "Use the OLS algorithm that minimize $RSS$\n",
    "$$\n",
    "\\begin{gathered}\n",
    "\\sum_{i=0}^n u_{i}^{2}=\\sum_{i=0}^n\\left(Y_{i}-\\beta_{1} e^{\\beta_{2} X_{i}}\\right)^{2}\n",
    "\\end{gathered}\n",
    "$$\n",
    "Take partial derivative with respect to both $\\beta_1$ and $\\beta_2$, the first order conditions are\n",
    "$$\n",
    "\\begin{gathered}\n",
    "\\frac{\\partial \\sum_{i=0}^n u_{i}^{2}}{\\partial \\beta_{1}}=2 \\sum_{i=0}^n\\left(Y_{i}-\\beta_{1} e^{\\beta_{2} X_{i}}\\right)\\left(-1 e^{\\beta_{2} X_{i}}\\right) =0\\\\\n",
    "\\frac{\\partial \\sum_{i=0}^n u_{i}^{2}}{\\partial \\beta_{2}}=2 \\sum_{i=0}^n\\left(Y_{i}-\\beta_{1} e^{\\beta_{2} X_{i}}\\right)\\left(-\\beta_{1} e^{\\beta_{2} X_{i}} X_{i}\\right)=0\n",
    "\\end{gathered}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59ca3c1e-af9f-43a1-94da-6bb1a8fe7a2e",
   "metadata": {},
   "source": [
    "Collecting terms and denote the estimated coefficients as $b_1$ and $b_2$\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\sum_{i=0}^n Y_{i} e^{b_{2} X_{i}} &=b_{1} e^{2 {b}_{2} X_{i}} \\\\\n",
    "\\sum_{i=0}^n Y_{i} X_{i} e^{b_{2} X_{i}} &={b}_{1} \\sum_{i=0}^n X_{i} e^{2 {b}_{2} X_{i}}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43c087fa-061e-47f2-b50b-08eac64cf9d4",
   "metadata": {},
   "source": [
    "These are solutions, but not **closed-form solution**, i.e. solve by plugging in data. So even if you have these formula, we can't input in Python, because unknowns are expressed in terms of unknowns."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adb925ae-0c0e-46c1-9aeb-ec9e6db05ca5",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Gauss-Newton Iterative Method </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db723ebb-cedc-4ff4-9c49-4a8962547edf",
   "metadata": {},
   "source": [
    "We will not talk about details of this algorithm, it only confuses you more than clarification. But this **Gauss-Newton Iterative Method** is kind of trial and error method that gradually approaching the optimized coefficients. It feeds the $RSS$ formula with parameters, record the result, then try another set of parameters, if $RSS$ gets smaller, the algorithm keeps feed parameters until the $RSS$ have no significant improvement."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "141a694a-b3fb-4b92-bd01-27153d2ffabd",
   "metadata": {},
   "source": [
    "Define the function\n",
    "$$\n",
    "Y_{i}=\\beta_{1} e^{\\beta_{2}X_{i}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b229a5bc-9e36-4d23-b7c3-b66f9ff0cac5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def exp_func(x, beta1, beta2):\n",
    "    return beta1 * np.exp(beta2 * x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c58d2d63-aeb7-4eec-b96d-94b81b3df151",
   "metadata": {},
   "source": [
    "Simulate data $Y$ then estimate the parameters with ```curve_fit``` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a6f1f5b7-9716-4fe3-8727-a2110ee6cc0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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okPTqWUP9hPqSCbtrsu1BkiSp3Nx4BcyfmzweVgufPT/desqIZ34lSZLKyQtPwf23rx7OrjuRm/e+siRbDEqR4VeSJKlcLF8GV01ZPcyM2pM/XDybttb2ZFxiG0qUItseJEmSysUfr4S57ySPhw7jhptHrw6+nUppQ4lSZPiVJEkqBy8/C823ZMefmsjbryxf56GlsqFEKTL8SpIklboVy+HKn0KMyXivBvjIMSW/oUQpMvxKkiSVulv/AO+9lTwePBTO+hqEUPIbSpQiL3iTJEkqZa+/CH+5KTs+41zYfAug9DeUKEWGX0mSpFLVtgL+56cQVyXj3faFwz/W7ZBS3lCiFNn2IEmSVKpuvw7enpU8HjgIzv46hJBuTWXO8CtJklSKZr8Kd16fHZ96DozeKr16KoThV5IkqdS0tyerO6xcmYx32gOOPindmiqE4VeSJKnU/Pl/kzO/ADUD4fPfhH7Gtnzwv6IkSVIpeWsm3HZNdnzyWTBm29TKqTSGX0mSpFKxciVc+TNob0vG43aBY05Nt6YKY/iVJEkqFbdfm6zrC9B/AJzzTejfP92aKozhV5IkqRS89sIa7Q5nwjbjUiunUhl+JUmS0rZsKfz2P2FVx2YWO+8Jx5+Rbk0VyvArSZKUthumwpy3k8eDh8IX/hn62e5QCIZfSZKkND35MDxwZ3b82fNh9Jj06qlwhl9JkqS0ZBbAVVOy4/0PhYMbUyunGhh+JUmS0hAjXPUzWJRJxiM2h7O+BiGkW1eFM/xKkiSl4f474OnHsuNzvgXDNk2vniph+JUkSSq2d99ILnLr9NFTYM8PpVZONTH8SpIkFVN7e7Ks2YrlyXjrsXDqOenWVEUMv5IkScV02zUw8+Xkcf8B8KVvw8BB6dZURQy/kiRJxfLKc3D7ddnxJ86G7XZIr54qZPiVJEkqhmWt8Lv/B7FjF7dd94ZjT023pipk+JUkSSqG6y6Hue8kj4dsAl/4P+7ilgLDryRJUqHNeBAevCs7PvOrsPkW6dVTxQy/kiRJhbRwHlx9aXZ8wJFw4FGplVPtDL+SJEmFEiP8z09h8QfJeOQomPCVdGuqcoZfSZKkQrnnT/DsjORxCHDuP8Mmw1MtqdoZfiVJkgrhtRfhxt9lx8ecCrvtk149Agy/kiRJ+de6GKb+CFa2J+NxOydr+ip1hl9JkqR86uzzff+9ZDxkKJz3HagZmG5dAnIIvyGEwSGEx0IIT4UQng0hXNIxv1kI4e4Qwssd9yMLX64kSVKJa74FnngoO/78N2H0VunVo25yOfO7HDg6xrgPsC9wfAjhIOAioDnGuDPQ3DGWJEmqXq+/CP/72+z46JNg/0PTq0dr2Wj4jYnFHcOajlsETgau6pi/CjilEAVKkiSVhdbF8Jsufb5jd4YzvphuTVpLTj2/IYT+IYQngTnA3THGR4EtY4zvAHTcr3ObkhDCxBDC9BDC9Llz5+apbEmSpBISI1z5s+59vl+2z7cUDcjloBjjSmDfEMII4I8hhL1yfYMY41RgKkBDQ0PsTZGSJEn51jKtheZJzWRmZ6itq6VxciP1E+p798X+eiv84+/ZsX2+JSun8NspxrgwhHAfcDzwXghhqxjjOyGErUjOCkuSJJW8lmktNE1soq21DYDMrAxNE5sAeh6AZ74EN/x3dmyfb0nLZbWH0R1nfAkhDAE+CrwA3Ap0Llh3NnBLgWqUJEnKq+ZJzauDb6e21jaaJzX37Au1LobLu/T51u1kn2+Jy+XM71bAVSGE/iRh+YYY420hhIeBG0II5wKzgTMKWKckSVLeZGZnejS/TjHCVVPg/XeTsX2+ZWGj4TfG+DSw3zrm5wGNhShKkiSpkGrrasnMWjvo1tbV5v5F7m2CGQ9mx2d/A7bYOg/VqZDc4U2SJFWdxsmN1Ayt6TZXM7SGxsk5ntdbs8/3qPHQcFgeK1Sh9OiCN0mSpErQeVFbr1Z7aF0Cv/l3aO/oGa7bCT75pQJWq3wy/EqSpKpUP6G+5ys7xAhX/QzmvpOM7fMtO7Y9SJIk5WqtPt8L7fMtM4ZfSZKkXLz8LFw/NTs+ajw0HJ5ePeoVw68kSdLGLHgffv3D7uv52udblgy/kiRJG9K2Igm+HyxIxsNq4SsX2+dbpgy/kiRJ6xMjXHMZvPZCMu7XL7nAbfMt061LvWb4lSRJWp8H7oC//Tk7PuNLsNs+6dWjPjP8SpIkrcvLz8I1v86ODzoaPnpKauUoP1znV5IkaU0L58HlXS9w2xHO+hot1zzTu40xVDIMv5IkSV21rYDLfgCZrhe4fZeWG1+maWITba3Jzm6ZWRmaJjYBGIDLiG0PkiRJXV3763Ve4NY8qXl18O3U1tpG86TmFIpUbxl+JUmSOt1/OzxwZ3Z8+hdXX+CWmZ1Z50vWN6/SZPiVJEkCeOW57he4HXgUHPOJ1cPautp1vmx98ypNhl9JkqSF8+DXP8he4LbdjvC5r0MIqw9pnNxIzdCabi+rGVpD4+TGYlaqPvKCN0mSVN3WusBt02QHt0GDux3WeVGbqz2UN8OvJEmqbl0vcAv94LzvwKgx6zy0fkK9YbfM2fYgSZKq1/13dL/A7YxzYfd9UytHhWf4lSRJ1emlZ+Cay7LjA4+CY05Nrx4VheFXkiRVn/fehl9dssEL3FSZDL+SJKm6LF4El14MSxYl4+Ej4KvfXesCN1Umw68kSaoe7W1w2ffhvbeScc1AuODfYPMtUy1LxWP4lSRJ1SFG+P3P4aWW7Ny5/ww77JZeTSo6w68kSaoOd1wPD92THZ96DjQcll49SoXhV5IkVb7H7oc/XpkdH3osnPDJ1MpRegy/kiSpsr36HFzxX9nxbvvAmRe4skOVMvxKkqTKNfdd+OUlyYVuAGO2hX/6VxhQk25dSo3hV5IkVabWxXDpd2FRJhkPq4WvfR82GZ5uXUqV4VeSJFWe9na4/EfwzuxkPKAGvvJd2GLrdOtS6gy/kiSpssQI1/wKnvtHdu6cb8LOe6ZXk0qG4VeSJFWWu26GB+7Mjk86Ew48Kr16VFIGpF2AJElSPrRMa2HmlGs4ce8nsgs5HHQ0jJ+Qal0qLZ75lSRJZa9lWguPX3QNx+/51Org+8acTXlm0DEuaaZuDL+SJKnszfjhrXzq8BZqBqwCYP4Hg7j2rl245+L7U65Mpca2B0mSVN4WzuPkvR9jkyHtACxd3p9r7tqdpctrWDo7k3JxKjWe+ZUkSeWrdTFM+VdGDl8OQFt7P665a3fmZYYAUFtXm2Z1KkGe+ZUkSeVpxfJk97Y3Xwdg1Sr437/uwptzkk0saobW0Di5Mc0Ke6xlWgvNk5rJzM5QW1dL4+RG6ifUp11WRfHMryRJKj8rV8J//we81LJ66q09P8WcfuMgQO3YWsZPHV9WwbFlWgtNE5vIzMpAhMysDE0Tm2iZ1rLxFytnnvmVJEnlJUb4wy/giYeyc2d8ke2OO50Lv5VeWX3VPKmZtta2bnNtrW00T2ouqxBf6jzzK0mSysufroK//Tk7Pu40OO709OrJk8x6Ls5b37x6x/ArSZLKxz1/gtuvy44P/iicdm5q5eTT+i7O86K9/DL8SpKk8vDovXDd5dnx3gfA2RdCv8qIM42TG6kZWtNtrhwv2it19vxKkqTS9+wMuOIn2fGOe8B534EBlRNlOvt6Xe2hsCrnb4wkSapMr70Il/0AViabWLD1WLjgEhg0ON26CqB+Qr1ht8Aq4/cEkiSpMr37Blx6MSxflow3Gw0X/hCGDU+3LpUtw68kSSpNC96Hn06CxR8k42Gbwjd+lARgqZcMv5IkqfQsysDPJsH8Ocl44CD42vdhq+3SrUtlz/ArSZJKy5JF8NPvwNuzknH//nD+xbDDbunWpYpg+JUkSaWjdUlyxveNV4FkM7c7n9yTlqcGpVyYKoWrPUiSpNKwrBV+fjHMfGn11K1/25EnX96EJyY2AbgSgvrMM7+SJCl9y5fBpd+DV59bPXXbgzvw5MtbANDW2kbzpOa0qlMFMfxKkqR0ta2AX14CL7Wsnrrz4XHMeHHLbodlZmeKXZkqkG0PkiQpPW0rkg0snn9i9dQDL+3KY89tttahtXW1xaxMFcrwK0mS0tHeDr/5d2h5PDt3ytmMzOxFzYwm2lrbVk/XDK2hcXJjCkWq0hh+JUlS8a1cCb/9D3jy4ezciZ+FEz9D5yVtzZOayczOUFtXS+PkRi92U14YfiVJUnGtWglX/BdM/1t27rjT4eSzVg/rJ9QbdlUQXvAmSZKKZ9UquOrn8Oi92bmPngKnnwshpFaWqofhV5IkFUeMMO1X8Pe7snNHfBw+dZ7BV0Vj+JUkSYUXI1z/G7j/9uzcocfChK8YfFVUhl9JklRYMcL1U+GeP2XnDjoaPvd16GcUUXF5wZskSSqcVatg2i/h/juycw2HwTnfgn7906tLVcvwK0mSCmPVSrjyZ/DQPdm5/Q+FL34b+ht8lQ7DryRJyr/2dvjd/4PH78/OHXR0csbX4KsUGX4lSVJ+ta1Idm7ruoHFYcfDWRfY6qDUGX4lSVL+rFgOl/0AnpmenTv6JPj0l724TSXB8CtJkvJj2VL45b/BC09l54473Q0sVFIMv5Ikqe9al8DPL4ZXn8vOjZ8AJ51p8FVJMfxKkqS+WbwIpnwHZr6cnTv1HPjYp9KrSVoPw68kSeq9DxbCT/8F3nw9O/fpL8NHT0mrImmDDL+SJKl3Fs6D/7oI3n0jGYcAZ14AR3ws3bqkDTD8SpKknpv3XhJ8576TjEM/OOeb8JGPpluXtBGGX0mS1DNvz4Ypk2D+3GTcv3+ya9uHD0+3LikHhl9JkpS7V5+DS78HSxYl4wE1cN53YL+D061LypHhV5Ik5eapR+E3P0o2sgAYNBjOvxj23D/duqQeMPxKkqSNe/Au+P0UWLUqGQ+vha//AMbtkmpZUk9tdJ/BEMJ2IYR7QwjPhxCeDSF8vWN+sxDC3SGElzvuRxa+XEmSVFQxwu3XwZU/zQbfUWPgop8afFWWcjnz2w58K8b4jxDCcGBGCOFu4PNAc4zxxyGEi4CLgG8XrlRJkqpPy7QWmic1k5mdobaulsbJjdRPqC/Om69aBdddDn+9NTu33Y5w4Q+gdrPi1CDl2UbDb4zxHeCdjseLQgjPA9sAJwNHdhx2FXAfhl9JkvKmZVoLTRObaGttAyAzK0PTxCaAwgfgthXwu/+C6Q9k53bbF75yMQzZpLDvLRXQRtseugohjAP2Ax4FtuwIxp0BeYu8VydJUhVrntS8Ovh2amtto3lSc2HfeOkS+Pl3uwffhsPh6983+Krs5XzBWwhhGHATcGGM8YMQQq6vmwhMBKirq+tNjZIkVaXM7EyP5vPzpvNhysXwxqvZuaNPSrYs7tejc2ZSScrpb3EIoYYk+E6LMd7cMf1eCGGrjue3Auas67UxxqkxxoYYY8Po0aPzUbMkSVWhtq62R/N99t5b8O/f7B58T/08fOafDL6qGLms9hCA3wHPxxh/2uWpW4GzOx6fDdyS//IkSapejZMbqRla022uZmgNjZMb8/9mM1+CH38T3n83GffrB5//Jnzs05Djb3ulcpBL28MhwFlASwjhyY657wA/Bm4IIZwLzAbOKEiFkiRVqc6L2gq+2sPTj8JvfgzLlybjgYOSXdv2OTC/7yOVgBBjLNqbNTQ0xOnTpxft/SRJ0gbECM23wPVTIXas4bvJcPjaJbDjHnl9q1SXbFNVCiHMiDE2rDnvDm+SJFWj9na49tdw/+3Zuc23gK//ELbO7wXqqS7ZJq3B7nVJkqpN62K49Lvdg++Ou8OkS/MefCHFJdukdfDMryRJ1WTuO3Dp9+Cd2dm5A46Ec74JNQML8papLNkmrYfhV5KkavHyM/CrH8DiLqHzpDNh/ISCruhQW1dLZtbaQbdgS7ZJG2DbgyRJ1eDhZvjJv2SD74Aa+NK3k/Dbw+DbMq2FKeOmcEm/S5gybgot01o2eHxRl2yTNsIzv5IkVbJVq+DWq+G2a7Nzw2vhq9/r1YoOvbl4rWhLtkk5cKkzSZIq1YrlcMVPYPoD2bmtxyZLmY0a06svOWXclHW3MIyt5cKZF/ayUCn/XOpMkqRqkpkPv7wEXn8xO7dXA5z3LzBkk26H9mQNXi9eU7kz/EqSVGneeA1+8W8wf0527uiT4FPnQf/+3Q7taRuDF6+p3HnBmyRJleSx++Dfv5ENvqEffPb85LZG8IWer8HrxWsqd575lSSpEqxcCTf+Du6+OTs3eCh8+TtJu8N69LSNwYvXVO4Mv5KkitSTPtayt2gh/Obf4YWnsnNbbgNf+W5ygdsG9KaNoX5CfeX+t1TFs+1BklRxOvtYM7MyELN9rBtbj7Ysvf4i/OCC7sF334M6tirecPAF2xhUfQy/kqSK09M+1rL14F/gP/4PzJ+bjEOAk8+C878LQzfZ8Gs71E+oZ/zU8dSOrYWQLFk2fup4z+yqYtn2IEmqOBW/HFd7G1x7Odx/e3ZuyCbJjm17H9DjL2cbg6qJ4VeSVHEqejmuhfPg1z+EV5/Pzm0zLjnbu+XWqZUllQvbHiRJFadi+1hffgZ+8NXuwbfhcPiXnxl8pRx55leSVHEqbjmuGOHeJrj+N8mSZpCs33v6F+DY05JeX0k5MfxKkipSxfSxLl8G034JD92TnRu2abJN8e77pVeXVKYMv5Iklaq3ZsJvfgRvz87Ojd0Zzv9X2HzL1MqSypnhV5KkUhNjsozZtb+GFcuz8x/5KJx5AQwclF5tUpkz/EqSVEqWtcLVv4BH783ODRwEnz0fDjnW/l6pjwy/kiSVitmvJm0O772Vndu6Ds77TrKcmaQ+M/xKkpS2GOG+2+D6qckGFp0OPRY+cz4MGpxebVKFMfxKkpSm1sVw1RSY8WB2btDgpLf34DJfl1gqQYZfSZLS8tqLMPVH8P572bntdkjaHMZsm15dUgUz/EqSVGwxwt1/hJuugJXt2fmjToRPToSagenVJlU4w68kSb3UMq2l57vILf4ArvgJPP1odm7IUDj7G9BwWGELlmT4lSSpN1qmtdA0sYm21uQCtcysDE0TmwDWH4CfmQ7/8xPILMjOjdsl2a1t9FaFLlkShl9JknqleVLz6uDbqa21jeZJzWuH3+XL4Mbfwr23dZ8/5lQ47RwYUFPgaiV1MvxKktQLmdmZ3OZfexF+95/d1u5dsnwgt9y/A3PuaaWx/YWNt0pIyhvDrySpz3rV+1rmautqycxaOwDX1tUmD9rb4Y7r4LZrYNWq1c+/+Mbm3PrA9rQuqwFyaJWQlFf90i5AklTeOntfM7MyELO9ry3TWtIuraAaJzdSM7R7u0LN0BoaJzfCu2/Cf3wLbv1DNvgOHspdz+7FdXft3BF8E52tEpKKw/ArSeqTDfW+VrL6CfWMnzqe2rG1EKB2bC3jf3Mi9VvPgu9/BV5/MXvwznvC9y7j4UeHA2Gtr7W+FgpJ+WfbgySpT3Lufa1A9RPqs+0KC+fBlVPgvsezB/QfAKd8Do47Dfr133irhKSCM/xKkvqkkgJdr3uXZzwIV1+arOHbaeux8MX/C3U7rp5qnNzYbXk06NIqIakoDL+SpD6plEDXq3V7Fy+C6y+Hh9do8TjmVDj182vt1Nb5dart4kCplIQYY9HerKGhIU6fPr1o7ydJKo5KWO1hyrgp6z6DPbaWC2deuPYLZjwI034FH3TZsGKz0XDOt2D3fQtWp6TchBBmxBgb1pz3zK8kqc+69b6WqZx7lzPz4ZrLkvDb1YFHwYSvwNBhBapQUj4YfiVJIofe5RjhoXvg+t9A6+IuB2wGZ10A+x5cpEol9YXhV5IkNtK7PG9OckHbM2u07h16HHzyS57tlcqI4VeSJNZzMdoPj6J+65nw3e/C8qXZg0eNgbO/Drvvl06xknrN8CtJUoduvcvvvQVXTYH7uuxUFwI0ngyf+DwMGpxGiZL6yPArSVJXK1fC3TfDLVdD24rs/Jjt4PPfgJ32SK82SX1m+JUkqdPsV+D3P4eZL2fn+vWD4z8J4z+71rq9ksqP4VeSpNYl8Ker4N7bIK7Kzm+3I5zzDajbKb3aJOWV4VeStJZK2LQiJzHCY/fBDVMh02WzigE1MH4CHHc6DPBHpVRJ/D9aktRNr7b5LUfvvpHs0Pb8k93nd98v2axizLaplCWpsAy/kqRumic1d1vrFqCttY3mSc2VEX5XLIc7roM/3wjtXf6ctZvBp86DDx+erOogqSIZfiVJ3eS8zW85evpRuObX8P672bnQL1m+7OQzYcgm6dWWR1XTtiL1guFXKjH+0FLaNrrNbzmaNweuuxyeeKj7/A67wZkXQN2O6dRVAFXTtiL1Ur+0C5CU1flDKzMrAzH7Q6tlWsvGXyzlSePkRmqG1nSbW73Nb7lpb4c7/xcu/lL34Dt0GHzu63DRTysq+MKG21YkeeZXKikV32upsrDObX7L8TcQLY/D9VOTC9u6OvRYOO0LMHxEKmUVWkW3rUh5YPiVSog/tFQqum3zW27enp0sXfbM9O7z24xLWhx23jOVsoqlIttWpDwy/EolxB9aUh8sXgS3Xg333QarumxUMXhosmZv48lVsWZv4+TGbj2/UMZtK1IBVP53AamM+ENL6oX2dnjgDrjlaliyKDsfAhx2PJz8OagdmV59RVYxbStSgRh+pRLiDy2ph56ZnvT1vjO7+/yueydr9lbYxWy5Kuu2FanADL9SifGHlpSDd95I+npbHu8+P2oMnPFF+NAhblQhaZ0Mv5Kk8rFkETRNg3ubYOXK7PygIXDiZ+Cjp0DNwNTKk1T6DL+SpNLXtgL+2pRsS7xmX+8hx8Inzk62J5akjTD8SpJK16qV8HBzcjHb/Lndn9ulHj59HtTtlE5tksqS4VeSVHpihKcegZuvhLdndX9u1Bg4/VzY/1D7eiX1mOFXklRaXn4GbroCXnmu+/zwWjjxs3DEx2BAzbpfK0kbYfiVpJS1TGtxeTuAt2bCzf8DTz3afX7QEDjuNDj21GTDCknqA8OvJKWoZVpLt41NMrMyNE1sAqieADxvDtzy+6S3N8bsfP8ByVneEz8Lm45IrTxJlcXwK0kpap7U3G1HP4C21jaaJzVXfvhdlIE7rk+WLWvv8t8gBDjgSDjlczB6q9TKk1SZDL+SlKLM7EyP5ivCogzcdRP89VZYvqz7c3s1wKnnVO3ObJIKz/ArSSmqraslM2vtoFtbV5tCNQW2+IMk9DbfCsuXdn9u+13htC/AbvukU5ukqmH4laQUNU5u7NbzC1AztIbGyY0pVpVnixd1hN5b1g6924yDk850O2JJRWP4laQUdfb1VuRqD4sXwd0dZ3qXtXZ/buuxcNIE+NCh0K9fOvVJqkqGX0lKWf2E+soIu52WLIK7/wjNf4Kla4beOhh/ZrJBhaFXUgoMv5Kk/GhdnITee/64dujdqg7GT4CGQ6Ff/3TqkyQMv5KkvsrMT0Lvfbev3d4wZrukvaHhMEOvpJJg+JUk9c6ct+EvN8Lf7+6+Ti/AmG2TM70fPtzQK6mkGH4lST3zxmtw5w3w+AMQV3V/bsx2cOJn4IAjDL2SSpLhV5KUm5eegTuvh5bH135u3C7wsU/Bvgd7IZukkmb4laQK1zKtpfdLqcUITz+WhN5Xnlv7+T0+BCd8MtmcwnV6JZWBjYbfEMIVwInAnBjjXh1zmwHXA+OAmcAnY4wLClemSk2ffphKKpqWaS3dNtHIzMrQNLEJYMP/z7a3w/QHkvaGt2Z2fy6EZFOKEz6ZnPHtQ21+H5FUbLmc+b0S+CXw+y5zFwHNMcYfhxAu6hh/O//lqRT1+odpCfKHrypd86TmbrvHAbS1ttE8qXndf9eXLIIH7oS/3goL3u/+XP8BcHAjHH960tvbB5X0fURSedlo+I0xPhBCGLfG9MnAkR2PrwLuw/BbNXr8w7RE+cNX1SAzO5Pb/LtvJptS/P1uWLG8+3ODBsPhH4NjT4WRo/JSV2++j/iPVUn50Nue3y1jjO8AxBjfCSFssb4DQwgTgYkAdXV1vXw7lZKcf5iWuEoJ8dXMMLRxtXW1ZGat/f9mbV1t0s/7wlPJGr1PP7r2i4ePgKPHw1HjYdimea2rp99H/MeqpHwp+AVvMcapwFSAhoaGWOj3U+Ft8IdpGamUEF+tDEO5aZzc2O2/E8DgYf057aubwiXnw5uvr/2ibbeHYz4BBxwJNQMLUldPv4/4j1VJ+dLb9WjeCyFsBdBxPyd/JanUNU5upGZoTbe5mqE1NE5uTKmi3lnfD9lyC/HVakNhSFn1E+oZP3U8tWNrGTqkjWOPnMs3z3qS7V64Ye3gu/eB8K0fw/cug0OOLVjwhZ5/H/Efq5Lypbdnfm8FzgZ+3HF/S94qUsnrPMtS7r9uXtcZsXIM8dXKMJS7+o8MpP57q+DRp5Kd2FZ0eXLgIDjkGGg8JdmVrVg19fD7SKX8xklS+nJZ6uxakovbRoUQ3gS+RxJ6bwghnAvMBs4oZJEqPfUT6ssu7K6pUkJ8tTIMbcTyZckObPc1wcyX135+5Cg4+mQ47HgYNrz49dGz7yP+Y1VSvuSy2sNn1vOU33FU9iohxFcrw9B6vPsm3H97smpD6+K1n99+16Sf90OHwoDy2efIf6xKypfy+c4nSV0YhrpYuRKeegTuux2e+8fazw+ogQOOgCNPTMJvme7E5j9WJeWD4VcqMJfjKpyqD0ML58Hf/pxsSrHmhhQAo7eCIz+eXLyW56XKJKlcGX6lAnI5LuXdqlXw/BNJ6H3ioeSsb1ehH+xzQHKWd48PQb/eLuojSZXJ8CsVkGuTKm/mvQcP3pX08s5fx+qSw0ckF68dcQJsvmXRy5OkcmH4lQrI5bjUJ20r4ImH4cG/JGd74zr2Cdp5LzjqRPjQIUlvryRpgwy/UgG5HJd65Y3XksD7yF9hyaK1nx+2KRzUCIcdB9uMK3p5klTODL9SAbkcl3LWugQeuw8e/PO61+UNIenhPew42Oeggu6+JkmVzPArFZDLcWmDVq5M2hkebk4uXluxfO1jNt8CDj0OPnJM8liS1CeGX6nAqn45LnUXI7zxahJ4H7sPMgvWPmZADez3keQs7277umKDJOWR4VeSimH+XHj03iT0vj1r3cdsu31ylvego12XV5IKxPArSYWydAnM+Ds80gwvPr3u1RpqR8IBR8HBjbDdDmW7+5oklQvDryTlU3tbssXwI3+FJx9Zdx/vwEHJ0mQHHQ277wf9+xe/TkmqUoZfSeqrlSvhhSfh8fvhHw9B6+K1jwn9YPd94eCjYb9DYPCQYlcpScLwK0m9s2olvPRMEnhn/B0Wr2fjku12SM7wHngUjNi8uDVKktZi+JWkXK1aBa8+B48/ADP+tu6VGiBZkqzh8CT0brdDcWuUJG2Q4VeSNiRGeP3F5Azv9L/BgvfXfdzIUbD/YfDhw2GH3bxwTZJKlOFXkta0ciW8/Az84+/J5hPrC7ybjoT9D4UDjoAd93A9XkkqA4ZfSQJoWwHP/iMJu089Aos/WPdxw2ph/0Pgw0fALntBP1dqkKRyYviVVL2WLoGWx5MVGloeh+VL133cJsNhv4OTwLvrPjDAb52SVK78Di6punywEJ58ODnD+/yTybq86zJyVLLF8H4fgV3qXYtXkiqE4VdSZYsR3nwdnnoUnn40uXhtXTutAWy5TbIG74c+AuN2sYdXkiqQ4VdS5WlbAS88lQ288+eu/9i6HZOzux86BLYe6yoNklThDL+SKsPCefD0Y0nYfe6JdW8rDMlOazvtkW1pGD2muHVKklJV0eG3ZVoLzZOayczOUFtXS+PkRuon1KddlqR8WLUSZr6cXKj29GMw6+X1HztkE6hvgH0Ogj0bYNjw4tUpSSopFRt+W6a10DSxibbW5GKWzKwMTRObAAzAUrlaOA+emQHPzoDn/gFLFq3/2DHbwt4Hwt4HwE57ukKDJAmo4PDbPKl5dfDt1NbaRvOkZsOvVC7aVsArzyaB95np8NbM9R/bvz/sXJ+E3X0OTC5ekyRpDRUbfjOzMz2al1Qi3nsbnp2eBN4Xnlx/7y5A7cikjWGvBthrfxg6LO/l2D4lSZWlYsNvbV0tmVlrB93autoUqpG0XpkFSch9/snk/v331n9s/wGw816w5/5J2N12+4KuzmD7lCRVnooNv42TG7v90AKoGVpD4+TGFKuSxNIl8GJLNvBuqJUBYIutO8JuA+y6NwweUoQiE7ZPSVLlqdjw2/mDqdC/rvRXotJGtK2AV5+H559Iwu7Ml2DVqvUfP2gw7LZPEnb33D8JvymxfUqSKk/Fhl9IAnAhg6i/EpXWoW1Fsovai0/DSy3wynPJ3Pr0HwA77g677wu77Qvb71oyKzPYPiVJlac0fsKUKX8lKgHLl8FrzyetDC+1wGsvQHvb+o8PAbbbMQm7u++b9PAOGlysanvE9ilJqjyG3z7wV6KqSkuXJG0MnWd2Z74EK1du+DVbbgO775eE3V33hmGbFqXUvipW+5QkqXgMv33gr0RVFRbOS1oXXnkOXnkGZr0KcQM9u5CE3V33hl3qk9tmo4tTawEUun1KklRcht8+8FeiqjirVsJbszqC7rPJGd73393467Yemw26u+wFIzYvfK2SJPWC4bcP/JWoyt6ypcnFaa88mwTe156Hpa0bfk0Iyfq6XcPu8BFFKVeSpL4y/PaRvxJV2Vi1Ct59E15/AV57Mbl/8/UNLzsGUDMwWYFhx91hpz1hpz1gk+HFqVmSpDwz/EqVatHCbMh97cXkDO/SJRt/3aYjk4C70x5J2K3bEQbUFLxcSZKKwfArVYIVy+GN15KA+9oLyS2XXt0Qkn7drmF31JiCbhksSVKaDL8Vyp3nKljbiqRdYebLMOslmPVKskXwxtoXAIbXwva7wQ67Jvfb7wJDhxW8ZEmSSoXhtwK581wFaW+DN2dmQ+7Ml5Kgu7F1dSFpVajbEXbYLenZ3WE3z+pKkqqe4bcCufNcmVq+DN58DWa/Bm+8mj2ju6Hd0rrachsYt0tyYdr2u8J2O9irK0nSGgy/Fcid58pAZkEScN94DWa/mjx+7y2IMbfXb7kNjN0Jxu6S3NftBEM3KWzNyoktR5JU2gy/Fcid50rIypUw5+2kR7dr0M3Mz/1rjN4Kxu4M43ZO7sfuZJ9uibLlSJJKn+G3AlXKznNldQYtxiTQvjUz6dF96/Uk8L49O/e2hdAPttouaVeo27HjfmcY5pq6+VLov1O2HElS6TP8VqBS3XmuJ8GjpM+gLVuahNrOgNsZeBf3oK1k4KAk3G63YzbsbjMumVdBFOPvlC1HklT6DL8VqtR2nutp8CiJM2jLWuHtN+DtWfDOLHhrdnI/b07Pvs7IUUmw3Xb7JOTW7QhbbA39+hekbK1bMf5O2XIkSaXP8Kui6GnwKOoZtKVL4J2OkPv27Oz9/B6G3EFDYNtx2aC7zTjYZnvbFkpEMf5OVUrLkSRVMsOviqKnwSPvZ9BWrYIFc5OQ++6bHbc3knFPLj4D6N8fttimI+SO6wi628PmW0C/fr2rTwVXjLOyxWo5Kqt+eEkqMYZfFUVPg0evz6AtW5qsrvDuG10C7pvw3pvJFsA90b9/sqTYVnXJFsDbjE0eb7mN6+eWoWKdlS10y1FJ98NLUhkw/Kooeho8NngGrW1FEnDnvJ2sjdt5m/M2LJzX8+L6D4Att04C7tZjYeuOsLvF1obcClKqF4L2VEn0w0tSGTP8qih6HDzaVlB/VC31txzcEXTfgnevgW+/BfPn5r4ZRFfDamGrbWHMdjCm8347GLVlcpZXqSrGr/JL7ULQ3nBFCUnqG8Ovimat4LF4Ebz+Isx9B+a8k9x33ha837s36d8fRo1J1svdctvkvjPsDts0P38Q5Z2/ys+dK0pIUt8YflU4bStg3nvwfuft3eQ2990k4LYu7t3XDf2Si8u23Ca5bbF1Em632Bo2L+xZXC80Kgx/lZ87V5SQpL4x/Kr32tuTM7Tvv9sRcjuC7fvvJePe9N92Cv1g89HJ1r5bbJ2srrDl1snZ3FFbQs3A/P05cuTZycLxV/m5q5TeZUlKi+FX67dsaRJi589NNnZY/fi9ZLxwPsRVvf/6Awcl4bbztkXn462TM7sDSuuvp2cnC8df5fdMJfQuS1JaSitdqHja2yEzD+a/n6x/O7/Lbd6cZIOHJYv69h6hX7K72agtO25jktvoMUnIrd0MQsjPn6cIPDtZOP4qX5JULIbfStTeDh8sSFoSVgfbjscL3k/GmQV9O2vbqXZkNtRu3hFyR3c83mx0RS0V5tnJwvFX+ZKkYjH8lpMYk614F7yf9NMumAcL31/jfh4sWti7pcDWNKAmOXPbGWQ33yJ5vPlo2GxL2GxUKr23afHsZGH5q3xJUjEYfteQytX8McKSxUkbQmZ+clu4IBkvnN9lbl7PdylbnxBg0xEwcnQSbEeO6rjvDLlbwKYj3a63C89OSpJU/gy/XeT9av62FUn7QWYhfDA/aTX4oOOWWdAl1M6H9raNfrmcdQbbEaO6h9rNRmXvR2zerSWhZVoLzec1k5n9bJdQt3n+aqoQnp2UJKm8GX67yOlq/mVLk7aCDxZ2uc9kA23XcLt0Sf6LHDgoCbQjNk9unY+73m86skcrJVTSEl6uwytJkjbE8LtieRJeF2UYtXImdTu2s8ngNjYZ0sYmg9sYOqSdTYa0wUVPJEE3X20Haxo0BEZslqyA0HnfeRuxeXZ+yCZ5XyGhUpbwqqQQL0mSCqOyw+/iD+CJh1aHWxZ/0HG/MDtevmz14Wcet4Gv9X4vdiPr3x+Gj0jOxNaO7H6/6cjuIXfwkJ5//TyplCW8KiXES5Kkwqns8JuZD1dNye/XHFDTEV5rk2A7fETSXzt8RBJsu4bbTYaXxQVjlbKEV6WEeEmSVDiVHX6Hj9j4Mf0HwPDa5DasloXzIq9Pn8+CuZFVQzdl5zMaGHviPh3hdkTSnlBGGzPkolKW8KqUEC9JkgqnssPvsOHwkY92BNsRHfebZsPu8FoYPLRbmB0B7JdWvSmplCW8KiXES5KkwgkxH5sh5KihoSFOnz69aO+n6uNqD5IkCSCEMCPG2LDmfGWf+a0QBrrcuQ6vJEnaEMNviXP5LkmSpPwp/aUIqtyGlu+SJElSzxh+S5zLd0mSJOWP4bfErW+ZLpfvkiRJ6jnDb4lrnNxIzdCabnMu3yVJktQ7XvBW4iplDV5JkqRSYPgtAy7fJUmSlB99Cr8hhOOBnwP9gd/GGH+cl6oklRzXm5YkVYJeh98QQn/gV8AxwJvA4yGEW2OMz+WrOEmlwfWmJUmVoi8XvB0AvBJjfC3GuAK4Djg5P2VJKiWuNy1JqhR9aXvYBnijy/hN4MC+lSOpNwrdkuB605KkStGX8BvWMRfXOiiEicBEgLq6uj68naR1KUZLQm1dLZlZawfdDa03bY+wJKkU9aXt4U1guy7jbYG31zwoxjg1xtgQY2wYPXp0H95O0roUoyWhp+tNdwbyzKwMxGwgb5nWkreaJEnqjb6E38eBnUMI24cQBgKfBm7NT1mSclWMloT6CfWMnzqe2rG1EKB2bC3jp45f75lce4QlSaWq120PMcb2EMJXgb+QLHV2RYzx2bxVJiknvWlJ6I2erDdtj7AkqVT1aXvjGOMdMcZdYow7xhgn56soSbkrxS2w1xe88x3IJUnqqT6FX0np62lLAiQ9uVPGTeGSfpcwZdyUvPfilmIglyQJ3N5Yqgg9aUkoxuoQnV/H1R4kSaUmxLjW6mQF09DQEKdPn16095O0tinjpqy7R3hsLRfOvLD4BUmSVAAhhBkxxoY15217kKqMF6NJkqqZbQ8pcPF/palYq0NIklSKPPNbZC7+r7R5MZokqZoZfovMxf+Vtt6sDiFJUqWw7aHI7LdUKejJ6hCSJFUSz/wWmYv/S5IkpcfwW2T2W0qSJKXHtocic/F/SZKk9Bh+U2C/pSRJUjpse5AkSVLVMPxKkiSpahh+JUmSVDUMv5IkSaoahl9JkiRVDcOvJEmSqobhV5IkSVXD8CtJkqSqYfiVJElS1TD8SpIkqWoYfiVJklQ1DL+SJEmqGoZfSZIkVQ3DryRJkqqG4VeSJElVI8QYi/dmIcwFZhXtDbNGAe+n8L4qLj/n6uDnXB38nCufn3F1SPNzHhtjHL3mZFHDb1pCCNNjjA1p16HC8nOuDn7O1cHPufL5GVeHUvycbXuQJElS1TD8SpIkqWpUS/idmnYBKgo/5+rg51wd/Jwrn59xdSi5z7kqen4lSZIkqJ4zv5IkSVJlhd8QwvEhhBdDCK+EEC5ax/MhhHBpx/NPhxA+lEad6pscPucJHZ/v0yGEh0II+6RRp/pmY59zl+M+HEJYGUI4vZj1qe9y+YxDCEeGEJ4MITwbQri/2DWq73L4nl0bQmgKITzV8Tmfk0ad6r0QwhUhhDkhhGfW83xJ5a+KCb8hhP7Ar4ATgD2Az4QQ9ljjsBOAnTtuE4FfF7VI9VmOn/PrwBExxr2BH1CC/UbasBw/587j/gP4S3ErVF/l8hmHEEYAlwEnxRj3BM4odp3qmxz/X/4K8FyMcR/gSOAnIYSBRS1UfXUlcPwGni+p/FUx4Rc4AHglxvhajHEFcB1w8hrHnAz8PiYeAUaEELYqdqHqk41+zjHGh2KMCzqGjwDbFrlG9V0u/z8DXADcBMwpZnHKi1w+488CN8cYZwPEGP2cy08un3MEhocQAjAMmA+0F7dM9UWM8QGSz219Sip/VVL43QZ4o8v4zY65nh6j0tbTz/Bc4M6CVqRC2OjnHELYBvgEcHkR61L+5PL/8i7AyBDCfSGEGSGEzxWtOuVLLp/zL4HdgbeBFuDrMcZVxSlPRVJS+WtAWm9cAGEdc2suZZHLMSptOX+GIYSjSMLvoQWtSIWQy+c8Bfh2jHFlcsJIZSaXz3gAsD/QCAwBHg4hPBJjfKnQxSlvcvmcjwOeBI4GdgTuDiH8Lcb4QYFrU/GUVP6qpPD7JrBdl/G2JP+K7OkxKm05fYYhhL2B3wInxBjnFak25U8un3MDcF1H8B0FfCyE0B5j/FNRKlRf5fo9+/0Y4xJgSQjhAWAfwPBbPnL5nM8BfhyTtVdfCSG8DuwGPFacElUEJZW/Kqnt4XFg5xDC9h2N8p8Gbl3jmFuBz3VcdXgQkIkxvlPsQtUnG/2cQwh1wM3AWZ4hKlsb/ZxjjNvHGMfFGMcBNwLnG3zLSi7fs28BDgshDAghDAUOBJ4vcp3qm1w+59kkZ/cJIWwJ7Aq8VtQqVWgllb8q5sxvjLE9hPBVkqu++wNXxBifDSF8ueP5y4E7gI8BrwCtJP/aVBnJ8XP+LrA5cFnHWcH2GGNDWjWr53L8nFXGcvmMY4zPhxD+DDwNrAJ+G2Nc51JKKk05/r/8A+DKEEILya/Hvx1jfD+1otVjIYRrSVbqGBVCeBP4HlADpZm/3OFNkiRJVaOS2h4kSZKkDTL8SpIkqWoYfiVJklQ1DL+SJEmqGoZfSZIkVQ3DryRJkqqG4VeSJElVw/ArSZKkqvH/AVIoGyiRjVvHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdata = np.linspace(0, 1, 50)\n",
    "y = exp_func(xdata, 2, 3)\n",
    "\n",
    "y_noise = 5 * np.random.randn(len(y))\n",
    "ydata = y + y_noise\n",
    "fig, ax = plt.subplots(figsize=(12, 8))\n",
    "ax.scatter(xdata, ydata, label=\"data\", color=\"purple\")\n",
    "popt, pcov = curve_fit(exp_func, xdata, ydata)\n",
    "ax.plot(xdata, exp_func(xdata, popt[0], popt[1]), lw=3, color=\"tomato\")\n",
    "ax.set_title(r\"$Y_{i}=\\beta_{1} e^{\\beta_{2}X_{i}}$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eb8bb44-08ea-4a52-8baa-1c4b13602fc6",
   "metadata": {},
   "source": [
    "Given the fact that this is elementary course on econometrics, we will not go any deeper in this topic. In Advanced Econometrics, we will have a very extensive discussion of nonlinear regression."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e705046-4f1d-45c9-bb9d-46d52c2574ca",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Shanghai Covid  </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "f5eaf3dc-2bc3-40cc-9e40-e8693c0cf08a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_shcovid = pd.read_excel(\"Shanghai Covid.xlsx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "636c604b-9656-4dd0-a845-d668f90d7260",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_shcovid.columns = [\"Date\", \"Cases\"]\n",
    "df_shcovid = df_shcovid.dropna()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c3cace8-ec00-47bc-84ef-110fe5452989",
   "metadata": {},
   "source": [
    "Define the function\n",
    "$$\n",
    "Y_{i}= \\beta_1 e^{\\beta_{2}X_{i}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efeea1ba-6199-48c1-94dd-a3445a8bf6ad",
   "metadata": {},
   "source": [
    "Take log on both sides. \n",
    "$$\n",
    "\\ln{Y_i}=\\ln{\\beta_1}+\\beta_2 X_i \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "0c8e47ec-3d58-480c-a3bf-7975c6cbb302",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Cases   R-squared:                       0.959\n",
      "Model:                            OLS   Adj. R-squared:                  0.957\n",
      "Method:                 Least Squares   F-statistic:                     463.3\n",
      "Date:                Thu, 07 Apr 2022   Prob (F-statistic):           2.65e-15\n",
      "Time:                        15:01:54   Log-Likelihood:                -3.9519\n",
      "No. Observations:                  22   AIC:                             11.90\n",
      "Df Residuals:                      20   BIC:                             14.09\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.4038      0.125     43.157      0.000       5.143       5.665\n",
      "x1             0.2197      0.010     21.524      0.000       0.198       0.241\n",
      "==============================================================================\n",
      "Omnibus:                        3.277   Durbin-Watson:                   0.593\n",
      "Prob(Omnibus):                  0.194   Jarque-Bera (JB):                1.649\n",
      "Skew:                          -0.355   Prob(JB):                        0.438\n",
      "Kurtosis:                       1.862   Cond. No.                         23.8\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "logY = np.log(df_shcovid[\"Cases\"])\n",
    "X = np.arange(len(Y))\n",
    "\n",
    "X = sm.add_constant(X)\n",
    "model = sm.OLS(Y, X).fit()\n",
    "\n",
    "print_model = model.summary()\n",
    "print(print_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "5eb93636-1fe2-4e11-8838-4f72e4465d76",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_1 = np.exp(model.params[0])\n",
    "beta_2 = model.params[1]\n",
    "\n",
    "Y = beta_1 * np.exp(beta_2 * X[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "7d4e08db-63de-4ec6-ae73-e0c5429aab65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 5), nrows=1, ncols=2)\n",
    "fig.autofmt_xdate(rotation=45)\n",
    "ax[0].scatter(df_shcovid[\"Date\"], df_shcovid[\"Cases\"])\n",
    "ax[0].set_ylabel(\"No-Symptom Case\")\n",
    "ax[1].plot(df_shcovid[\"Date\"], model.fittedvalues)\n",
    "ax[0].plot(df_shcovid[\"Date\"], Y)\n",
    "ax[1].set_ylabel(\"Log No-Symptom Case\")\n",
    "ax[1].scatter(df_shcovid[\"Date\"], ln_case)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e2543b8-b4b8-4b86-8e38-9913e4385af6",
   "metadata": {},
   "source": [
    "$$\n",
    "Y_{i}= 5.4 e^{0.21X_{i}}\n",
    "$$"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}