Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "import statsmodels.api as sm\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  radio  newspaper  sales\n",
       "1  230.1   37.8       69.2   22.1\n",
       "2   44.5   39.3       45.1   10.4\n",
       "3   17.2   45.9       69.3    9.3\n",
       "4  151.5   41.3       58.5   18.5\n",
       "5  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/Advertising.csv', index_col=0)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple linear regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "plt.scatter(data['TV'], data['sales'], c='black')\n",
    "plt.xlabel('Money spent on TV ads ($)')\n",
    "plt.ylabel('Sales (k$)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The linear model is: \n",
      " Y = 7.032593549127693 + 0.047536640433019764*TV\n"
     ]
    }
   ],
   "source": [
    "X = data['TV'].values.reshape(-1, 1)\n",
    "y = data['sales'].values.reshape(-1, 1)\n",
    "\n",
    "reg = LinearRegression()\n",
    "reg.fit(X, y)\n",
    "\n",
    "print(f\"The linear model is: \\n Y = {reg.intercept_[0]} + {reg.coef_[0][0]}*TV\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uPNQjjui8gi/aF/gcVmvtAmvt42v+/01J8yVtK+mzkmavaTZbbhALAAAADNLX19fW9rSL+rqcYfTvd7+T9trLTfMdN07q7q4frH71q+52a6UXX5S6ughWoyKQl8EYk5f0fyQ9Kmkra+0CyQ1qJW0ZRB8AAAAQL1EPwKIm6utyBtG/SkU65pjacjP77Sc9+ujwdl/4gvTXv9aWm7n8cmnTTT3rBjzke8BqjNlI0l2SzrLWLm3jft3GmLnGmLmvvvqqfx0EAABAJEU9AIsaP9bl9LLolR/96++XrrqqFqDm89KcOcPbvf/90n33SdWqG6Deeae0004d7xYB8nUdVmPMOEn3Svqltfb6Ndv+Kml/a+2CNfNcf2Ot3bnZ4zCHFQAAIJ1KpZIKhYL6+vqUy+VULBY9L7gUxD7iKIpFr6yV7r7bnYf6/PON240b585DPfVUKvjGRRhFl4zcOapLrLVnrbP9a5IWr1N06V3W2hnNHouAFQAAAH6IYlAWFVEpejVvnnTBBdK99zZvd/LJ0kUXuUWTED+BF12StI+k6ZIOMMY8ueY2TdLVkg40xjwn6cA1/wYAAAnBupnwQlDnUaFQGBSsSlJ/f78KhYIv+4uTsIpeLVkinXtuLc33Ax+oH6zuv7/0yCO1eai33kqwmkRj/Xpga+0fJJkGf/64X/sFAADhGTpaValU1N3dLUmpH61C64I8j6hE3Fgul6s7wup10atVq6TZs9003yVLGrebNMlN8z3ySGnMGE+7gAijWDMAAPAMo1XwQpDnEZWIG/Oz6NUf/iDts09tuZkTT6wfrM6cKb32mjuCumCBNH06wWraELACAADPMFqFdtVL/Q3yPKIScWNeVvX95z+lE06opfl+9KPSww8Pb3foodL8+bU032JR2mwzD54MYsvXKsFeoegSAADxEJUiLYiHRgWPNthgAy1evHhYe7/OI6oEe2/5cunGG90032Z22cVN8502zQ1kkV5hFF0CAAApw2gV2tEo9VdSoOdRV1eXyuWyqtWqyuUywWoHrJXuuUfaeWc38Mxm6wermYx07bVuQGut9Oc/S5/+NMEqGiNgBQCgDirddsbLFMKk4xxrnOK7ZMkSzqMYeOYZ6bOfdYPNTEY65BDp2WeHtzvxRDcl2Fpp9WrpP/5DWn/94PuLeCIlGACAIViXEX7jHHORQh4vr70mXX21m8LbzEc+Il1zjbT33sH0C8nQKCWYgBUAgCH4Eg2/cY65CNyjbfVqac4cN7V30aLG7SZOdAPUo4+mgi86xxxWAABaRKXb4KUtPTascyxqx5kU8uh5+GG3gq8x0tix0vHH1w9WzzvPXYbGWmnhQum44whW4Q9GWAEAGILRr2ClcZQtjHMsjccZI3vxRemSS6TvfKd5u89+VrrySreqL+AHRlgBAGgRlW6D1ahSbKFQCKlH/gvjHEvjcQ5T2KPZjfb/9tvSdde5o6HGSO9+d/1gdeed3aq/1ao7inr33QSrCAcjrAAA1MG6jMHJZDKq933EGKNqtRpCj4IR9DmW1uMchrBHs4fvf5qM+ZqsbR5xXnONdOaZ0gYb+N5FYBiKLgEAgEgiBTsYHOfghH2st93243rppdMlHdq03XHHSZdeKk2e7HuXgBGREgwAACKJFOxgcJyDE3RRrddfl2bOdFN8jZFeeukB1Q9WH9Lvf++m+For3X47wSqij4AVAACEikqxweA4ByeXy7W1vV2rV0uzZ0tbbeUGqJtvLl11Vb2WiyWdIGmsJCPH6dJHPuJJF4DAkBIMAAAAeMiPOayPPOIuJfO73zVv95WvSDvscKfOOedYKkIjVkgJBgAg5sKuOgqgNV6MZr/0knTyybU03w9/uH6w+pnPSH/6Uy3N92tfk04++TBG05EYjLACABADYVcdBeCvd96Rbr5ZmjFDWrWqcbsdd5RmzXLXRTUmuP4BfmOEFQCAGGMNTUQJo/2jZ630859LH/iAG3iuv750zjn1g9WrrpKWLXPv8+yz0iGHEKwiPQhYAQCIgaCrjiLawgwYB0b7K5WKrLWqVCrq7u4maG3Bs89Khx3mBpuZjDRtmjRv3vB2xxwjlcu1NN/zz5eGFHgGUoOAFQCAGPC76ijiI+yAkdH+1i1dKl14YW0e6s47Sz/60fB2e+4p/eY3tQD1+9+XHCfo3gLRRMAKAEAMsIYmBoQdMDLa31i1KvX2Stts4waom24qXXHF8Habbirddpu0YoUboD7yiLTffsH3F4gDAlYAAGKANTQxIOyAkdH+wf7f/5MOOMANUMeMkaZPlxYsGN7u7LOlV191A9TXX5e6u6Vx44LvLxA3BKwAAMREV1eXyuWyqtWqyuUywWpKhR0wpn20/+WXpdNOq6X5fuhD0oMPDm/3qU9JTz5ZS/O9/nppiy2C7y8QdwSsAIDEoHKp/zjG4Qs7YPRrtD+q59Y770jf/KZbxdcYaeutpVtuGd5u++2lO+9004Ktle67T/rgB4PvL5A0rMMKAEgE1in1H8c4OkqlkgqFgvr6+pTL5VQsFmP9GkTp3LJW+tvfpPvvd28/+UnjtldcIZ11lrThhsH1D0iqRuuwErACABIhn8+rUqkM2+44jsrlcvAdSiCOMfwS9rn1/PNSoSD98IfN2x11lHTZZdJ22/neJSB1CFgBAImWyWRU7zPNGKNqtRpCj5KHYwy/BH1uvfmmdO21bvDZyGGHSQceKH3iEwSoQBAaBazMYQUAJELYhWjSgGMMv/h9blWr0h13SJMnu/NQN9mkfrC68cbu/NQVK9zR1pNOIlgFwkbACgBIhLAL0aQBxxh+8ePceuwxd4R0YLmZI4+UXnhheLuzzpIWLnTnri5dKp1yCsvNAFFCwAoASATWKfUfxxh+8eLcWrhQOvPM2nIzU6dK//M/w9sddJD0xBO15Wa+/nVp4kQPn0yMRbVSM9KNOawAAACInRUrpG9/W5oxQ1qnuPAw+bw0a5b0+c9LGYZqGopSpWakE0WXAAAAEGsPPOAGqI8/3rzdZZdJZ58tbbRRMP1KgrArNQMUXQIAAEDgRpNm+ve/S11dtTTfT3yifrB65JHu2qkDab4XXkiw2q6+vr62tvuFtGQMNTbsDgAAACCZhqaZVioVdXd3S1LdNNO33pKuv166+OLmj7v77tI117gBLLyRy+XqjrAGWQW83fMF6cAIKwAAEcVIQ/yl/TUsFAqD5kRKUn9/vwqFgiR3uZkf/MCdZ2qMu6xMvWA1m5VuvFF65x13BPWxxwhWvRaFKuAjnS9IJwJWAEBqRTmYGBhpqFQqstauHWmIUh/RHK9ho3TS3VSp3LZ2uZnDD5fqDOzpjDOkl192A9Rly6TTT5fGj/e9y6kVhSrgUUlLRrRQdAkAkEpRr4hJAZT44zUcOAbLJH1V0pebtv3EJ6Srr5amTAmka4ggrpl0o+gSAADriHrqGSMNrYvqSHlaX8OVK6VbbnHTeyuVsqRXVS9YnTBhme64Q1q92h1Fvf9+gtW0i0JaMqKHgBUAkEpRDyYaFToJsgBKHEQ57TZNr+GDD0p77OHOQx0/XjrtNLeA0nCXSNpYktHy5Vtq9eoSa6NirSikJSN6eIsAAKRS1IMJRhpaE+WR8iS/huWyNH16bbmZAw6Q6s/eukPrr/8BTZiwhSQj6VJJbiQbldcJ0dLV1aVyuaxqtapyuUywCgJWAEA6RT2YiOpIQ9TSb6M8Uh7V17ATy5ZJxWItQN1uO6m3d3i7ceP+LOlAucGpkXSk3n57nhYvXlz3caPwOgGINoouAQBSq1QqqVAoqK+vT7lcTsViMZbBRFCiWKiKIi3+sFa66y7pvPOkv/+9cbv115dmzZJOPtlNBc5kMmrnuyWvE4ABFF0CAGAIUs/aE8X026iPlMfJ009L06a5I6iZjHTYYfWD1dNOkxYscIPa5culM8+sLTfTKKV+woQJvE4AOkLACgApELU0TsRTFNNvk5R2G7RFi6Rzzqml+X7wg9LPfz683QEHSH/8oxugWivddJM0aVL9x2z0A8INN9zA6wSgI6QEA0DCRTGNE/FE+m28rVolffe70owZ0tKljdtts42b5nvEEeqogi+p9gA6QUowAKRUFNM4EU+k34ankyyJUqmkSZO+JGMelTHSuHHSKafUD1YvvFB64w13BPXFF6Wurs6CVYlUewDeGht2BwAA/opiGifiaSDwYPQsWEOzJAbWmpU07NhXKtJFF0lz5khS15rbcIcdJl1xhbTTTj52HAA8QEowACQcaZxAvDW7hp95pqwbbpBmzhzpUZ6WNEO53F9UqZR96CUAjA4pwQCQUqRxAvE2PBviEEnPqlIpa8MNGwWrKySdJWk9ueuhflDSL/XPf5JZASBeCFgBIOGoogrE26RJn5D0U0l2ze0nknYc1u6UU6SXXnLnoTrOTpJukBu41jRadgYAooqAFQBSgCIoQHwsWSKde25tuZkFC34l6TPD2r33vS/rkUdqy83ccou09dbu38isAJAUBKwAAAAhWrVK+s53pAkT3AB1wgTp2muHtxszZqGko5XLba/e3pKeeWaS9tyz/mOSWQEgKQhYAQAAAvaHP0h77621y82cdJI7sjrUzJnSa6+5I6irVm0pa+eoUvl7S4EnmRWAPzpZZgqdY1kbAAAAn/3zn9LFF0vf+17zdoceKhWL0nveE0y/ALSnnWWm4A1GWAEgRfhVGAjG8uXSrFm1eai5XP1gdZddpHvvlapVdxT1rrsIVoEoKxQKa4PVAf39/SoUCiH1KPkIWAEgJQZ+Fa5UKrLWrv1VOIpBK4E14sZa6Z57pJ13dgPUbFY677zh7TIZd37q8uXuff78Z+nTn3bvE3Vcl97ieMbT8GWmmm8fite9fcZaG3YfRjR16lQ7d+7csLsBALGWz+dVqVSGbXccR+VyOfgONTA03Upyq5tSMAZR88wz0gUXSD/9afN2J54oXXKJtO22gXTLF1yX3uJ4xtdoPkt53ZszxjxmrZ06bDsBKwCkQyaTUb33fGOMqtVqCD2qLy6BNdLntdekq692U32b+ehH3XZ77x1Mv4LAdektjmd8jSbo5HVvrlHASkowAKRELpdra3tYRptuBXhl9Wp33unEiW7K7rveVT9Y3XJLt92qVW6a7+9+l6xgVeK69BrHM75Gs2QUr3tnCFgBICWKxaKy2eygbdlsVsViMaQe1ReXwBrJ9PDD7gipMdLYsdLxx0uLFg1vd/757jI01kqvvCIde6w0Zkzg3Q0M16U3BuYvNspw5HjGQ6dLRnEddYaAFQBSYjS/CgcpLoE1kuHFF901UAeq+e6zj7tG6lCHHOIWSLLWvV11lXTffekpnsJ1OXrrFr6rh+OZfFxHHbLWNr1J+rCkmyQ9LelVSX2S7pN0uqRNR7q/F7cpU6ZYAEB69Pb2WsdxrDHGOo5je3t7w+4SEmL5cmuvvdbaTGYg9Kx/e897rP3pT62tVus/Tm9vr81ms1bS2ls2m030ucp1OTqO4ww6X9a9cTzTg+uoMUlzbZ1YsGnRJWPMzyW9JOkeSXMlLZS0vqSdJH1M0mckXW+tHaE+3uhQdAkAEEWlUkmFQkF9fX3K5XIqFouRG7FOO2uln/1MmjFDmj+/edtZs6QzzpA22MD9d7PXl+Ip8RbGtRuXwndAWDqqEmyM2cJaW2fmRnttRouAFQAQNSxPEF3z50szZ0p339283fHHu8vNTJ48/G8jvb4EH/EV1rXLjxxAcyxrAwCAh/jyGR2vvy5dc427lEwze+/ttvvIR0Z+zJFeX17/+ArrteNHLqC5jpe1McZ8yRiz/Zr/39UY87wx5iVjzOf96CgAxMFApcc0FFtBfSxPEJ7Vq6XZs6WttnILJW2+ef1g9V3vkr7zHWnlSjc1+KGHWgtWpZFfX4qnxFdY125cCt8BUdNKleBzJb245v8vl/RlSVMkXexXpwAgytat9GitVaVSUXd3N0FrG5IQ8LM8QbAeeUTab7/acjPHHistXDi83Ve+Ii1e7AaoixdLJ5zgtm/XSK/vaIOPJFwDcRXmtdvpcihAqtWrxDRwkxuULpB0kaRLJS2WdMma7ZU12/dt9hhe3KgSDCBKGlV6dBwn7K7FQlKqqybleUTViy9a293dvJKvZO1nPruzVdcAACAASURBVGPtn/7k/f79fH05d8LF8QeiSZ1UCZYkY8xvJc2WtJWkD1hrj1yz/X+ttR8edcTcAuawAogSiq2MTpLm/lEl2DvvvCPdfLNbzXfVqsbtdtrJreZ78MHuaKuf/Hp9k3QNxBXXLhA9HRddMsa8V+6o6juSzrPWLjDG7CLpUGvtFU3ud7ukf5O00Fr7/jXbLpF0ktz1XCVpprX2vpE6T8AKIEr4sjk6SQ/4+SLcGmulX/zCDVDnzWve9uqrpTPPlIZMGY2tpF8DAFx8HrSn46JL1tr5ko621h5trV2wZtszkm4e4a7fl3RQne1ft9butuY2YrAKAFFDsZXRSfLcT+Y3N/fss9Jhh7kjo5mMNG1a/WD12GOlSqWW+HveeckJVqVkXwMAXHweeKeVokuS9GNjzNqSBcaYrSXd3+wO1trfSVoyir4BQCRR6XF0khzwFwqFQUtWSFJ/f78KhUJIPQrX0qXShRe6Aaox0s47Sz/60fB2e+0l/fa3tQD1e9+TGsVuUSxW1G6fknwNAHDxeeChehNbh97kpvHeLWmMpLykpyV9soX75SXNW+ffl0gqr7n/7ZI2b3LfbklzJc3N5XKeTugFAISrt7fXOo5jjTHWcZzEFDsxxtQtyGWMCbtrgVi92to5c6ydNKl5oaTNNrO2p8falSvbe/woFsvptE9JvQYAuNL+edAJdVp0aYAx5nS5Kb55SSdbax9u4T55Sffa2hzWrSQtWvOCXS5pa2vt8SM9DnNYAQBxkMb5zX/8o5uy+5vfNG93zjnSBRdIW2zR+b6ieHyj2CfUx3xCeKHV84j3hvZ1NIfVGHPOwE3S+pImS3pS0l5rtrXFWvuKtXa1tbYq6duSPtTuYwCIpyim8QFeS0Oq58svS6eeWkvz3XPP+sHqtGnSU0/VxlWvu250waok9fX1tbXdb6VSqe4XUim8PqE+5hPCC+2cR2n4PAjKSHNYN17ntpGkn0h6fp1tbVkz93XA5ySNUBcQQBLwRQFpkcT5ze+8I91wg7Teem6AuvXW0q23Dm+3/fbu/NRq1Q1Qf/Yzadddve1LlIoVDbyvNUIBpWhhPiG80M55lMTPg7C0nBLc9gMbc4ek/SVtIekVSRev+fduclOCy3JTixeM9FikBAPx1mpaDOlaSKOonffWSr/6lbvczNNPN29bLEpf/rK04YbB9G0gSFz3C2M2mw3lS2Cj97Uw+4TGWEoIXuA88lenKcE9xpj3N/jbhsaY440xdd+NrbVHWGu3ttaOs9a+21r7XWvtdGvtB6y1u1prD24lWAUQf62k8TEKizSKynn//PPSl75UW27moIPqB6vTp0v/+EctzddxSnrf+4JL9Y/SiEWzlF+C1eiJ0ug84ovzKBxNR1iNMbtJminpA3LTd1+VO5d1R0mbyK30e6u19h0/O8kIKxBvrYywUpwAaRTWef/mm9K110qXXda83R57SNdcI33sY8P/FqXRzjDwnhUvaT9f4Q3OI391NMJqrX3SWvtFSXtIuknS7yX9VNKJ1toPWmtv8DtYBRB/rRQeiFoxFSAIQZ331ap0xx3S5MnuKOomm9QPVjfZRLrlFmnFCncE9Y9/rB+sSv7OCYxDkTYKqsRLlEbnEV+cR+HwbQ6rlxhhBeJvpHl6jFYgjfw87x97zF1u5oEHmrc76yxp5kxp4sT2Ht+vuVxxGsGI2vxjAIizRiOsBKwAIiFOX1IBr3h53r/yinT55dJNNzVvd9BB0lVXSbvt1kmPa/wKtvnxCgDSqaOUYAAICmk2yROHtM6wjea8X7FC+ta3pA02cNN8J02qH6zm89IPf1hbbubnPx99sCr5lxLL9AAAwLraHmE1xmQkbWStXepPl4ZjhBUA4oURc3/cf7+73MyTTzZvd9ll0tlnSxtt5G9//EiJZRksAEinUaUEG2P+S9IpklZLekzSppKut9Z+zeuO1kPACgDxQlqnN/72N+mrX5X++7+btzvySDcdePvtg+mXn1r5sYMfRAAgeUabErzLmhHVQyTdJyknabqH/QMADBHnlFrSOjvz1lvSpZe6Kb7GSDvsUD9Y3X13d7R1YD3UUikZwarUWpq0nxWKAQDRMrbFduOMMePkBqw3WmtXGmOiX60JAGJq6AhSpVJRd3e3JMViBCmXy9UdYWVx9cGqVenOO90032axfDYrzZolnXSSNH58cP0LS1dXV9PznB9EACA9Wh1hvU1SWdKGkn5njHEkBTaHFQDSJu4jSKxR2dgTT0j/+q/uCOqYMdLhh9cPVs84Q3r5ZXcEddky6fTT0xGstqLRDx/8IAIAydNSwGqt/aa1dltr7TTrqkhqsJQ4AGC04j6CRNXnmldflb785Vqa7+67S7/61fB2Bx7orp06kOb7rW9JW20VfH/jgB9EACA9WgpYjTFbGWO+a4z5+Zp/7yLpGF97BgAploQRpK6uLpXLZVWrVZXL5dQEqytXSrfcIm28sRugbrml9M1vDm+Xy7nzU1evdgPUX/3KDWYxMn4QAYD0aDUl+PuSfilpmzX/flbSWX50CADACFLc/PrX0tSpboA6frx02mluAaWhLrlEWrrUDVArFelLX5IyrIjekbT+IAIAadPqx+QW1tofSqpKkrV2ldwlbgAkXJwr1cYZI0jR9o9/SEcdVUvz/fjH3XTeoQ4/XHruuVqa78UXuyOvAACgNa1WCV5mjJkgyUqSMWYvSW/41isAkRD3SrVxN1KlVARn2TLp61+XLrywebvddnOr+R54YDD9AgAg6Yy1I69OY4zZXdK3JL1f0jxJEyV9wVr7tL/dc02dOtXOnTs3iF0BWEc+n6+7NInjOCqXy8F3CAiItdKPfuQuN9PsVF9/fTdAPflkKvgCADAaxpjHrLVTh25vtUrw45L2k7S3pJMlvS+oYBVAeOJeqRZox1NPSZ/6lJvim8lIX/xio2D1Zr373Xuot7ek5culM88kWAWiyKspLUyNAcLVNCXYGHNogz/tZIyRtfbHPvQJQETkcrm6I6xxqlQLNLJokVQsSt/4RvN2Bxwg7bffz3XNNV9Ymx7/wgsiPR6IMK+mtDA1BgjfSCOsn2ly+zd/uwYgbEmoVMsv4xiwcqV0223Sppu6o6gTJ9YPVrfZRurtrS0388AD0u23n7r2C+uA/v5+FQqFgHoPoB2FQsGTa9arxwHQuaYBq7X2uCa344PqJIBwxL1S7cAv45VKRdbatb+ME7QGIwo/Fvz2t9Kee9aWmznlFHdZmaEOOeRPmjz5/TImo3Hj8pJKg5abIT0eiBevrlk/r/0ovEcCcdBS0SVJMsZ8WtL7JK0/sM1ae5lP/RqEoksAOkHRqPAMTaOT3NF5v3/wqFSkiy6S5sxp3u6LX5SuuELaccfW+sq5BMSLV9esX9d+WO+RQJSNquiSMeZWSV+SdKYkI+kwSY6nPQQAjzEqFp6g0uj6+6Wrrqqth5rP1w9Wd91V+sUvpGrVTfP9wQ/cYLXVviYhPR5IE6+uWb+ufVKNgda1FLBK2ttae7Sk16y1l0r6sKTJ/nULAEavUXEoikb5z68fC6yVfvITN9g0RtpwQ2nmzOHtxo9356e+/bZ7n6eekv71X937dNLXuKfHA2nj1TXr17XPD6pA61pdh/VRa+2exphHJB0qabGkedbaHf3uoERKMIDOkHIVHi/T6P70J+mCC6Sf/ax5u1NOcdOBt966rYcn3RdA4HjfAYYbVUqwpHuNMZtJ+pqkxyWVJd3hXfcAwHsj/TJOwQv/jCaNbvFi6T/+o5bmu+uu9YPV/feXHnnEHUG1Vrrlllqw2s5rS7pvunDdN8fxCQbvO0AbrLVt3SStJ2nTdu83mtuUKVMsAHipt7fXZrNZK2ntLZvN2t7e3rC7lhi9vb3WcRxrjLGO4zQ8titXWtvTY+1mmw2EnvVvkyZZO2eOtatWjbzfdl/bVvuKeOO6b47jEyzed4DBJM21dWLBpinBxpg9JP3TWvvymn8fLenzkiqSLrHWLvElih6ClGAAXiMdK1y//700Y4Y7QtrMzJluu003bf2xeW3Tp1QqqVAoqK+vT7lcTsVisW7aP+dGcxwfIJpafY+Lu05Tgm+TtGLNA+wr6WpJcyS9IanH604CQFAoeBGsvj7puONqab777ls/WD30UGn+/Nq4arHYXrDq7ovXNk3aWW+Zc6M5jg/CRkr6cKwpP3LAOmadUdQvSeqx1t5lrb1Q0g7+dg0A/EMFYX8tXy5dc00tQHUc6fvfH97ufe9z56cOLDdz113Se94zun3z2qZLO8uDcG40x/FBmAjM6mMJpBYCVmPM2DX//3FJv17nb2PrtAeAhqL0yykFL7xlrXTPPdLOO7sBajYrnX/+8HZjxkjXXecGtNZK8+ZJ06bVX26mU7y24Qjr+m5nVJBzozmOD8JEYFYfmQ9qXnRJUkHSQ5LukfSEasvg7CDpoWb39fJG0SUgHF4WhIhiMQ8KXozOvHnWHnxw80JJkrUnnWTtCy8E2zde22CFeX07jjNovwM3x3Ea9pVzozGOj3c4lu0xxtS9lo0xYXctVO2+x8WZGhRdaqUq8F6SPidpw3W27SRp95Hu69WNgBUIntdfQNP0hptUS5ZYO2PGyAHqvvta+/DDYfcWQQrz+o7ij2EA52X7+J5QX5rOpY4D1ijcCFiB4Hn9wcEvp+Hq5Jf+lSut/e53rd1ii+YB6pZbWvv974+83AySK+zrm5EsRA3BV/vSFJi1Ky3vcY0C1qbL2kQFy9oAwctkMqr3/mCMUbVabfvxWC4hPAOFLNadG5TNZtXT0zOsLP5DD7nLyDz8cPPHPP98t93mm/vRY8QN1zcw2EifoWlZpqRdHJd063RZGwAp5XW1SIp5hKdZIYsXXpBOOKFWzfcjH6kfrB5yiPTnP9fGVa+6imAVNVzfwGDNPkOphttYV1eXyuWyqtWqyuUywSokEbACaMDrL6BdXV3q6emR4zgyxshxnLojfPDe4EqC60v6iiSrSqWsyZOl228ffp/3vEf66U9ry8385CfSLrsE1OGIilKV66jh+k6GsM/xsPfvpWafoVTDBdpUL084ajfmsALhSMuciSSrVq2dOPF4Kz0zYrGkWbOs7e8Pu8fRxNwqJF3Y53jY+/dDo8/QsOd8A1El5rACQDrMny/NnCndfXfzdvvt97z+8z930OTJwfQrzpijiaQL+xwPe/9BStNzBdrBHFYAkZKk1K+wvf66dMEFtXmou+xSP1hdb725kj4qx8mrt7ek3/yGYLVVLNyOpAv7HA97/0FK+5xvPv/RLgJWAIGj4MTorF4tzZ4tbbWVG6Buvrl09dXD202YIH3nO9LKlW7S79tvT5W1v6eQRQe8LkIGRE3Y53jY+w9Smud88/mPThCwAggcBSfa98gj0n77uQHq2LHSscdKCxcOb3fuudLixW6AumiRWwF47NjW9tHOr95p+4U87SMiSL6wz/Gw99+J0bwPprUaLp//6Ei9ia1Ru1F0CUhWASQKTozsxRetPemk5kWSJGsPPtjaefNGv792Cp4ksThKK5J0DQL1hH2Oh73/dqT1fXC0ovz5H6fzL6lE0SUgvgZSaNb9VTKbzcY2hWiLLbbQ4sWLh22fMGGCFi1aFEKPwvf229JNN0nnneem/Day007SrFnSwQe7o61eaacICAVDAKQd74OdiepxS9r3rLii6BIQY6TQJI+10s9+Jr3vfW7gucEG0le+Uj9Yvfpqadky9z5//av02c96G6xK7RU8SVNxFHinXvpk2lLLR4NjNVjYx4P3wc5ENfWb71kRV2/YNWo3UoIRdX6nkUQ5haYTSXs+rfrLX6w99NCR03yPPdbaSiXYvjmOU/c1cRxnVG2tJc0K9dMnx40bZ8ePH09KZQtIPx2s0fk0YcKEwN5n2n0fRE0UPxPS+r0katQgJTj0YLSVGwEroiyILxJJ+2BM2vNp5PXXrZ05c+QAda+9rP3tb8Ptq19zWPmiDWsbX/NpeB/wQlreM1vVyvnk9/sM723JwjUWDQSsgE+CeJNL2gdj0p7PgNWrrZ0zx9pJk5oHqJttZm1Pj7UrV3q7/9H+at3O/Vtty5cAWNt49IIRjdYw+jNYq+eT3+8zURwpRGeS+r0kbghYAZ8E9UUiaR+MSXk+jz5q7f77jzyKes451i5a5F8/ovphyxdtWMsI62g1++EnKe+l7ZgwYQI/fsBzabyWoqZRwEqVYGCUolrxDv5YsEC67DLp1ltHavkzSRdI+lMglQajeh5GtV8IVr0KnOPGjZMxRitWrFi7jaqc9TWqYHrMMcdo9uzZqats2qjS/FC8zwDxQpVgwCdRrXjnh9FWZQy7qmMn3nlHuuEGab313Mq822xTP1jdYQfprrukXC4vyUj6N0l/khRMpcGoVqxM0/WBxrq6utTT0yPHcWSMkeM4+t73vqfbb7990LakB1qdqnf8enp6dN9996WysumSJUtGbMP7DJAg9YZdo3YjJRhRl4Y0ktGmnEY1ZXWoatXaX/zC2l13HTnN98orrX3rrcH3DysFNspzRdNwfQBhSGvKfaP3uzFjxvA+A8SYSAkGMBqjTe2Mcmroc89JhYJ0553N2x19tHTppVI+37hNWM+TRc9bVyqVVCgU1NfXp1wup2KxyDFCLEX5fdVPvN8ByURKMIBRGW3KaZRSVpculS66yE3xNUbaaaf6weqHPiQ9+GBtTHX27ObBqhReCmyjlEG+vA028EW3UqnIWqtKpaLu7u5YpKcDQ6U15Z73OyBdGGEF0JI4j7BWq9Idd0gzZkgvvdS43SabSLNmSccfL40b1/n+GMGLrrSOSCG5eL8BkBSMsAIYldH+kh/0SMDcudLHP+6OoI4ZIx11VP1g9ayzpIUL3RHUN96QTj55dMGq5P76Xy6XVa1WVS6XE/PlMYpFs9rtU5RG+gEvJPX9BgAGELAikaL4xTru2k3BGvoaSPI1heuVV6TTT6+l+e6xh/TrXw9vd9BB0hNP1NJ8v/51aeJET7qQaFFMpe2kT7lcrq3tAAAgXKQEI3EoxhC+IF6DFSuk225z03zffrtxu3zeTfP9whfcQBadiWIqbSd94v0BAIBoapQSTMCKxBiYx1PvC6wkjRkzRtVqlTk+AfAruLn/fjdAffLJ5u0uu0w6+2xpo4063hWGyGQyqvd5YYxRtVoNoUed94k5fwAARA9zWJFo66YGNrJ69erIpDImnVfzBP/2N+mII2ppvp/8ZP1g9cgj3bYDab4XXhifYDUu6etRTKXttE/M+QMAID4IWJEIhUJhUIrfSPr7+1UoFHzsUbp1Gki8+aa7zulAgLrDDtJ///fwdlOmSP/zP7UAtVSStt/ei54HK4rzQhuJ4vIZUewTAADwFgErEqGTCp9UBfVPq4FEtSr94AeS47gB6iabSJdcMvzxNtxQuukm6Z133AB1oAJwJ5qNaAY92lnvh5ao/pgSxXUPo9gnIGhxydIAgI5ZayN/mzJligWacRzHSqp7GzNmTN3tjuOE3e1Y6+3ttY7jWGOMdRzH9vb2tvT3xx+39pOfHBgbbXz793+39pVXvO9zNpsddB5ks1nb29vb9G9+McbUPTeNMb7tE+k00vWKeArjfQsA/CJprq0TC1J0CYnQrPKnJKqCeqydSqsLF0pXXCF961vNH/OTn5SuukrafXc/euxqVgxKUuBVcKNYeRfJQ2Xk5OI9BECSUHQJidYsNXA0aYOkWtXXLJV1xQo3fXfDDd003622qh+s5nLu/NTVq90x1V/+0t9gVWpeDMqrQlHt6GQOJuck2hWn1HO0J4z3LQAIGiOsQAOMSjQ2fDmRAyTNkjSl6f0uuUQ65xxp44197FwTURthldpbYoVzEp2I4pJE8AYjrACShBFWoE2MSjS29dZ7S+pVbdrUA6oXrB5+uPTcc7WZqRdfHF6wKjUf0Qyr4mw7S6xwToZvYITbGKOxY8fKGBP5ke4oLkkEb1ApG0AaELACDZBqVfPWW9Lll9eWm3nppT9IGh5YOc4S/epXtQD1jjvcpWmiwq/U8aBwToZr6HrPq1evlqRIL0ckEdQkWRzetwBgtEgJBhpIc6qVtdKPfiTNmCE1e6rGvC1rZyiX+7muvPISviT5LM3nZBQ0Ov4Dovw6tJN6DgBAGEgJBlqwbkGbt956S5nM4Etk3LhxiR2VeOop6VOfckdQMxnpi1+sH6yedpq0YIEb1Far68vab6pSeY4vvwFgpCxcI41k+zHS7VWRrXZSzwEAiBLfAlZjzO3GmIXGmHnrbHuXMeZ+Y8xza/67uV/7B9q1brqftVaLFy8eVpDEGBNS77y3aJF09tm1NN/ddpN+8Yvh7Q44QPrjH2tpvjfdJE2aFHx/Qfpf2Eaa8+n1nNCh70lRTz0GAMAPvqUEG2P2lfSWpDnW2vev2TZL0hJr7dXGmPMlbW6tPW+kxyIlGEEYKd1vQJTT/ppZuVK6/XY3zXfp0sbttt1WuuYa6Ygj3JFWAK56VZoH+FGtmRRwAECaBJ4SbK39naQlQzZ/VtLsNf8/W9Ihfu0faFer6XxxKnDz4IPSHnu4I6jjx0unnFI/WL3oIumNN9wR1BdekLq6/AtWWUcUcbXuCLckjRkzRpJ8G+mmyBYAAD4XXTLG5CXdu84I6+vW2s3W+ftr1tq6acHGmG5J3ZKUy+WmtDLyBYxGEkZYy2Xpwgul3t7m7b74RemKK6QddwykW2uxjijQOkZYAQBpEruiS9baHmvtVGvt1IkTJ4bdHaRAvYI2Q0WtwM2yZVKxWJuHut129YPVXXd156dWq+4o6g9+EHywKrGOKNAOimwBABB8wPqKMWZrSVrz34UB7x9oqF5Bm1NPPTVSBW6sle66S/qXf3ED1I02kr761eHtxo+XvvEN6e23pd7ekt54I69PfSqj7bYbOQXXz5TdpKU4tnKsSIFGpyiyBQCANDbg/f1U0jGSrl7z33sC3j/Qln322Uc333xzqH14+mnpgguk++4bqeUtki5TNrt07ZfaoSm4A1VGJdX90ttu+3blcrm6KY5eV1cNQivH6rTTTtOtt96qgakXXh9PJF9XVxfnCgAg1fysEnyHpP0lbSHpFUkXS7pb0g8l5ST1STrMWju0MNMwVAlGEKIyv3LxYunKK6Xrr2/ebv/9pb/85RC9/PLw330G5ri1OwfO7zlzUTnGXhjpWJVKJU2fPl313mOZgwgAADBYGFWCj7DWbm2tHWetfbe19rvW2sXW2o9ba3dc898Rg1XEy2jTH8NMnwxrfuWqVdK3vy1tvrmb5rvFFvWD1UmTpDlz3PbWuhWAX3nlp3UfcyDFtt0UXL9TdpOU4tjomFQqFWUyGR1zzDF1g9Vm9wUAAMBgkS26hPgZ7SL3o73/aAU5v/L3v5c+/GE3QB03Turull5/fXi7mTPd7dZKCxZI06dLa1bSkNQ4lXZg+0h/H+32TnR1dalcLqtarapcLscyWJWaHxNrrVavXt3RfQEAAFBDwArPjHaEMuwKsn4Ga3190nHH1ar57ruv9Mgjw9t9/vPS/PlugGqtWwF4000bP+5IVUTbrTIaZFXSuBcjaqWqdD3GGKq8AgAAtMpaG/nblClTLLzT29trHcexxhjrOI7t7e315HGNMVbSsJsxJpD7j1Zvb6/NZrOD9p3NZjs6PsuWWXvllQNhZ+Pb+99v7X33WVutjq7fzV7Pdl/vRu29PG+8PNZhWveY1Dt3653Lp556atjdBgAAiBxJc22dWDD0YLSVGwGrd/wMFBzHqfsl3XGcQO7vhU6DsmrV2h//2NoddmgeoI4da+3111u7fLnPT8RjXp83UXitvdboOY0ZM8bzH4cAAACSplHASkpwyniZdjs0pXPatGmjSicNMh21kXbmV86bJ33mM26KbyYjHXqo9Pzzw9t1d0svvOCGrCtXSmefLa2/vo9Pwgdep2snbT1WqfH5O3v27NjP1wUAAAgLAWvKeBUo1CuQNHv2bB1zzDEdV4CNegXZJUukc8+tzUP9wAeke+8d3m7ffaWHH66Nq952m7TttsH310teB5hBFHcKWtTPXwAAgDjybR1WL7EOq3e8WmfT7/U6o2DVKmn2bGnGDDdYbWTLLaVZs6SjjhpcwTdJvH69k7QeKwAAAEYv8HVYEU1epd0mMaVTkh56SNpnn9pyMyeeWD9YPf986bXX3BHUV16RjjkmucGq5H26NqORAAAAaAUBa8p4FSgkJaXzhRekE06opfl+5CNuOu9QhxwiPfNMLc33qqukzTYLvr9h8SPATMp6rAAAAPAPKcHoSFxTOpcvl2680U3zbeY973HTfP/t39xAFgAAAIB/SAmGp1oZcRtaRbhUKgXeT2ul//t/pfe+1w08s9nGweqsWVJ/v3uf+fNrFYARviicSwAAAAgeAWvKePnFv1lKZ70qwt3d3YEEGvPnS5/7XG25mYMPlv7yl+HtTjhB+uc/a2m+554rbbCB791rC4FaOOcSxx0AACAaSAlOkSDTeIOsIvzaa9I117i3ZvbZx22zzz6e7t43cU279lrQFak57gAAAMFrlBJMwJoiQX7xz2QyqnduGWNUrVZH9dirV0tz5ripvYsWNW63xRZumu/06dLYsaPaZSjCCNQKhYL6+vqUy+VULBYjEaD5eS7Vk4YlmwAAAKKGOawIdCkar6sI/+//Sh/9qJvmO3asdPzx9YPVGTOkxYvdFN9XX5WOOy6ewaoU7OsVZgr3SIKuSJ3UJZsAAADiiIA1Rfz+4r/uvL+33npL48ePH/T3dtbtfPFF6aSTasvN7L239Ic/DG938MHSvHm1eajXXCO9611ePJvwBRmoFQqFQSmwktTf369CoeD5vtrl9RqwI0nKkk0AAABJQMCaIn5+8R86Qrd48WJZazVhwoSW1u18+23puuukMWPcAPXd75a+853h7XbaSbr7bqladQPUe+6R3ve+UXffF6Mt3BNkOHcXWQAAF0ZJREFUoBblUUU/1oBtJugAGQAAAE1YayN/mzJlioU3ent7reM41hhjHcexvb29njyu4zhW0rCb4zh121er1t57r7W77DIwNtr4dvXV1i5b5kk3A9Pb22uz2eygY5HNZts+3n69XkO1+/olXVDHHQAAAC5Jc22dWJCiS/BEK4Vx/vpXaeZM6cc/bv5Yxx4rXXqpFOcMzLgV7qEyLgAAAMLUqOhSTMvRIGpyuVydAG0TbbxxUcY0v+9ee7lzT/fd17fuBS7KKbb1DASlUawSDAAAgPRiDis8USwWtcEGG0k6StJLcjNK39DSpWcMa7vZZlJPj7RypZv0+7//m6xgVYpn4Z6uri6Vy2VVq1WVy2WCVQAAAISOgBWj8sc/Sh/7mHTUUV1avvxNSf8paeth7c45x12GxlrptdfcCsBxXW6mFa0W7hltYSYAAAAgyQhYU6yTYGnBAunUU2vLzey5p/Sb3wxvN22a9NRTtdJJ110nTZjg/XOIqlYq20Z57VMAAAAgCii6lFKtFtl55x3p5pulGTOkVasaP94OO0izZkmHHKIR56zCFbfCTAAAAIBfGhVdImBNqUbBUi7n6NZby5oxQ5o3r/ljXHml9O//Lm24oU+dTLhWKisDAAAAadAoYCUlOKUGV6vdUdIPJVn19ZU1bVr9YPXoo6V//KOW5nvBBQSroxHHwkwAAABAkAhYU2jpUmmTTb4ht5KvlfSspMOGtfvQh6QHH6wFqLNnS/l8sH1NslYLMwEAAABpRcCaAtWqVCpJ227rzi/ddFPpjTf+vU7LN3TccY9qxQo3QH30UWn//YPubXq0UpgJAAAASDPmsCbU3LnSeedJv/5183Ybb/xdvfnmBXIcd2SPYAkAAABA0JjDmnAvvyydfnptuZk99qgfrB50kPTEE7U036VLT5C1C9dWpU3KmqCsbwoAAADE39iwO4DOrFgh3Xabu9zM2283bpfPu8vNfOELzZebGbrMzcCaoJJiN+qapOcCAAAApBkpwTFy//1ugPrkk83bXXaZdPbZ0kYbtf7YSVoTNEnPBQAAAEiDRinBjLBG2PPPS4WC9MMfNm931FFukLrddp3va/AyNyNvj7IkPRcAAAAgzZjDGiFvvildfHFtHuqOO9YPVqdOlS644H/kOHkZk9Hvf5/Xww+Pbo5mUGuCBjG3lPVNAQAAgGQgYA1RtSrdcYc0ebIboG6yiTtSOtRGG0k336y1y82cdVZJN9zwWVUqFVlr187RHE3wF8SaoANzS73sdz2sbwoAAAAkAwFrwB57TDrwQDdAHTNGOvJI6YUXhrfbeOPvSdpKjpPXrbeWdOqp0rhx7t8KhcLagkID+vv7VSgUOu7XaNcEbWXk1I9+18P6pgAAAEAyUHTJZwsXSpdfLt14Y/N2n/ykdNVV0vz5gyvcSu7o4LoBVyaTUb3XzRijarXqaf9bMbQqrzS8z1L0+g0AAAAgGhoVXSJg9diKFdK3v+1W8x0ymDhILucuN3PYYVJmnXHuVircRq0Kbqv9iVq/AQAAAERDo4CVlGAP/Pa30pQpbprveutJZ5xRP1i95BJp6VJ3HmqlIn3pS4ODVam1Crdez9EcbSGkVqvyMrcUAAAAQDsIWEfpgQek/feXHn98+N8OP1x67jk3QLXWrQC88cbNH6+VCrdeztH0ohDSSH0eCIinT5+uDTbYQBMmTGBuKQAAAIARkRI8Sk89Je22m/v/u+3mpvkeeGDnj9fqfFCveJGm26zPkgJ9PgAAAADihzmsMVIqlVQoFNTX16dcLqdisehbcOdVIaRGfWbeKgAAAICRELCiLr8DSioDAwAAABgJRZdQV7FY1LiBBV7XGDdunGeFkFqZkwsAAAAA9RCwRshoq/V2yhgz6N8rV67Ul7/8ZU/2T2VgAAAAAJ0iYI0IL6r1dqJQKGjFihXDti9evNiT/XtZ0RgAAABAujCHNSLCKk7UaI5pUPsHAAAAAOawRlxfX19b270y0lxSv/cPAAAAAI0QsEZEWMWJ6s0xDXL/AAAAANAIAWtEhFWcaGCO6YQJE4b9jeJIAAAAAMJEwBoRYRYn6urq0qJFi9Tb20txJAAAAACRQdElAAAAAECoKLoEAAAAAIgVAlYAAAAAQCQRsAIAAAAAIomANYVKpZLy+bwymYzy+bxKpVLYXQIAAACAYcaG3QEEq1Qqqbu7W/39/ZKkSqWi7u5uSaIiMAAAAIBIYYQ1ZQqFwtpgdUB/f78KhUJIPQIAAACA+ghYI8jPlN2+vr62tgMAAABAWAhYI2YgZbdSqchauzZl16ugNZfLtbUdAAAAAMJCwBoxnabstjoqWywWlc1mB23LZrMqFouj6zgAAAAAeIyANSIGAs5KpVL3781SdtsZle3q6lJPT48cx5ExRo7jqKenh4JLAAAAACLHWGvD7sOIpk6daufOnRt2N3wztHJvPY7jqFwu1/1bo0C32X0AAAAAICqMMY9Za6cO3c4IawTUSwNe10gpuxRSwv9v796DLCnLO45/f8tiYIlKEKQU2RkvJN5ZyUisYAhookisoAkJkEm8hHJSBmPMpRJ0krhqJqUmEZNUQjmJKJqRlaioUUQtLuEPi8twcblpJMgiQmQtEC9juPnkj9MHDuPMzuwue7p35vup2jrTb7/n9HO6nnpnn3nf7pYkSZJWIgvWIVvoWtNtFZbLWbLrjZQkSZIkrUQWrEO02LWm++2334L9+0t6l7q+9Nhjj92udkmSJEnaHViwDtFidwAGdurOveeee+52tUuSJEnS7sCCdYgWW/p755137tSde72GVZIkSdJKtLaNgya5Gfge8ABw/0J3g1qJ1q9fv+DdfNevX8/4+PgOP1pmW58rSZIkSburNmdYj66qDaulWAWYmpraqaW/w/5cSZIkSWqTS4KHaHx8fKeW/g77cyVJkiSpTamq4R80+TpwF1DA+6pqelv9x8bGanZ2diixSZIkSZKGK8kVC62+bWuG9YiqOgx4GXBKkiPnd0gykWQ2yezWrVuHH2GLFnpWqyRJkiStNq0UrFV1W/N6B3AOcPgCfaaraqyqxg444IBhh9iaxZ7VatEqSZIkabUZesGaZJ8kj+7/DLwEuHbYcXTVYs9qnZycbCkiSZIkSWpHG4+1ORA4J0n/+B+pqvNaiKOTfKaqJEmSJPUMvWCtqpuAQ4d93N2Fz1SVJEmSpB4fa9MxPlNVkiRJknosWDvGZ6pKkiRJUk8rz2HdXj6HVZIkSZJWrq49h1WSJEmSpG2yYJUkSZIkdZIFqyRJkiSpkyxYJUmSJEmdZMEqSZIkSeokC1ZJkiRJUidZsEqSJEmSOsmCVZIkSZLUSRaskiRJkqROsmCVJEmSJHWSBaskSZIkqZMsWCVJkiRJnWTBKkmSJEnqJAtWSZIkSVInWbBKkiRJkjrJglWSJEmS1EkWrJIkSZKkTrJgHYKZmRlGR0dZs2YNo6OjzMzMtB2SJEmSJHXe2rYDWOlmZmaYmJhgbm4OgC1btjAxMQHA+Ph4m6FJkiRJUqc5w7qLTU5OPlis9s3NzTE5OdlSRJIkSZK0e7Bg3cVuueWW7WqXJEmSJPVYsO5i69ev3652SZIkSVKPBesuNjU1xbp16x7Wtm7dOqamplqKSJIkSZJ2Dxasu9j4+DjT09OMjIyQhJGREaanp73hkiRJkiQtIVXVdgxLGhsbq9nZ2bbDkCRJkiTtAkmuqKqx+e3OsEqSJEmSOsmCVZIkSZLUSRaskiRJkqROsmCVJEmSJHWSBaskSZIkqZMsWCVJkiRJnWTBKkmSJEnqJAtWSZIkSVInWbBKkiRJkjrJglWSJEmS1EkWrJIkSZKkTrJglSRJkiR1kgWrJEmSJKmTLFglSZIkSZ1kwSpJkiRJ6iQLVkmSJElSJ1mwSpIkSZI6yYJ1J83MzDA6OsqaNWsYHR1lZmam7ZAkSZIkaUVY23YAu7OZmRkmJiaYm5sDYMuWLUxMTAAwPj7eZmiSJEmStNtzhnUnTE5OPlis9s3NzTE5OdlSRJIkSZK0cliw7oRbbrllu9olSZIkSctnwboT1q9fv13tkiRJkqTls2DdCVNTU6xbt+5hbevWrWNqaqqliCRJkiRp5bBg3Qnj4+NMT08zMjJCEkZGRpienvaGS5IkSZL0CEhVtR3DksbGxmp2drbtMCRJkiRJu0CSK6pqbH67M6ySJEmSpE6yYJUkSZIkdZIFqyRJkiSpkyxYJUmSJEmdZMEqSZIkSeokC1ZJkiRJUidZsEqSJEmSOsmCVZIkSZLUSRaskiRJkqROsmCVJEmSJHWSBaskSZIkqZMsWCVJkiRJnWTBKkmSJEnqJAtWSZIkSVInWbBKkiRJkjopVdV2DEtKshXY0nYci9gf+HbbQajTzBEtxRzRUswRLYd5oqWYI1pKmzkyUlUHzG/cLQrWLksyW1Vjbceh7jJHtBRzREsxR7Qc5omWYo5oKV3MEZcES5IkSZI6yYJVkiRJktRJFqw7b7rtANR55oiWYo5oKeaIlsM80VLMES2lczniNaySJEmSpE5yhlWSJEmS1EkWrDsoyTFJvprkxiSnth2PuiHJzUmuSXJ1ktmmbb8kX0zyteb1p9qOU8OV5IwkdyS5dqBtwbxIzz82Y8vmJIe1F7mGZZEc2Zjkm814cnWSYwf2vbnJka8meWk7UWuYkhyc5MIkNyS5LskfNu2OJQK2mSOOJQIgyV5JLkvy5SZH3ta0PznJpc048tEkj2raf6LZvrHZP9pG3BasOyDJHsA/Ay8DngmclOSZ7UalDjm6qjYM3BL8VOD8qjoEOL/Z1uryQeCYeW2L5cXLgEOafxPA6UOKUe36ID+eIwCnNePJhqo6F6D5fXMi8KzmPf/S/F7SynY/8CdV9QzgBcApTS44lqhvsRwBxxL13AO8qKoOBTYAxyR5AfAuejlyCHAXcHLT/2Tgrqp6GnBa02/oLFh3zOHAjVV1U1XdC2wCjms5JnXXccCZzc9nAq9oMRa1oKouBu6c17xYXhwHfKh6LgH2TfKE4USqtiySI4s5DthUVfdU1deBG+n9XtIKVlW3V9WVzc/fA24ADsKxRI1t5MhiHEtWmWY8+H6zuWfzr4AXAR9r2uePI/3x5WPAi5NkSOE+yIJ1xxwEfGNg+1a2PSBo9SjgC0muSDLRtB1YVbdD75cJ8PjWolOXLJYXji8a9IZmOecZA5cTmCOrXLMs73nApTiWaAHzcgQcS9RIskeSq4E7gC8C/wN8p6rub7oM5sGDOdLsvxt43HAjtmDdUQv9ZcHbLQvgiKo6jN5SrFOSHNl2QNrtOL6o73TgqfSWbd0O/H3Tbo6sYkl+Evg48Kaq+u62ui7QZp6sAgvkiGOJHlRVD1TVBuBJ9GbUn7FQt+a1EzliwbpjbgUOHth+EnBbS7GoQ6rqtub1DuAcegPBt/rLsJrXO9qLUB2yWF44vgiAqvpW8x+LHwH/ykNL9cyRVSrJnvQKkZmq+kTT7FiiBy2UI44lWkhVfQe4iN71zvsmWdvsGsyDB3Ok2f9Yln/5yiPGgnXHXA4c0txR61H0Llj/dMsxqWVJ9kny6P7PwEuAa+nlxqubbq8GPtVOhOqYxfLi08Crmjt8vgC4u7/cT6vLvOsNX0lvPIFejpzY3L3xyfRuqnPZsOPTcDXXjb0fuKGq3jOwy7FEwOI54liiviQHJNm3+Xlv4JfoXet8IXB8023+ONIfX44HLqiqoc+wrl26i+arqvuTvAH4PLAHcEZVXddyWGrfgcA5zbXoa4GPVNV5SS4Hzk5yMnAL8BstxqgWJDkLOArYP8mtwFuBd7JwXpwLHEvv5hdzwGuHHrCGbpEcOSrJBnrLr24Gfg+gqq5LcjZwPb27gp5SVQ+0EbeG6gjgd4BrmuvPAN6CY4kesliOnORYosYTgDObu0GvAc6uqs8kuR7YlOSvgavo/eGD5vXDSW6kN7N6YhtBp4UiWZIkSZKkJbkkWJIkSZLUSRaskiRJkqROsmCVJEmSJHWSBaskSZIkqZMsWCVJkiRJnWTBKknqjCSV5MMD22uTbE3ymTbj2lWSvGUXfOZrk1zd/Ls3yTXNz5uS3Jpkzbz+Vyc5fAePdVGSse3o/6Ykr5rXtnHe9gFJztuReCRJK48FqySpS34APLt5oDnALwPfbDGeXe0RL1ir6gNVtaGqNgC3AUc32ycC3wB+od83ydOBR1fVZY90HPMlWQv8LvCRZvuZSS4GXp/kyiQnNfFvBW5PcsSujkmS1H0WrJKkrvkc8CvNzycBZ/V3JNkvySeTbE5ySZLnNu0bk5zRzPjdlOSNA+/57SSXNTOJ70uyR5KTk5w20Od1Sd4zGETT74NJrm1mKf+oab8oyXuTfKnZd3jTvk8Tw+VJrkpyXNP+miSfSHJekq8leXfT/k5g7yaumfknIclJzXGvTfKugfbvJ5lK8uXmHBy4Hef2LB7+4PcTB8/vwDEOb77fVc3rzzTtezcztZuTfBTYe1vnap4XAVdW1f3N9kbgQ8DpwBHA5QN9PwmMb8f3kiStUBaskqSu2QScmGQv4LnApQP73gZcVVXPpTc7+aGBfU8HXgocDrw1yZ5JngGcABzRzDg+QK8Q2gT8apI9m/e+FvjAvDg2AAdV1bOr6jnz9u9TVT8P/D5wRtM2CVxQVc8Hjgb+Nsk+A591AvAc4IQkB1fVqcAPm9nPhxVnSZ4IvItekbcBeH6SV/SPDVxSVYcCFwOvW/xU/pizgVc0s500MW1aoN9XgCOr6nnAXwF/07S/Hphrzv8U8LMD32+xc9V3BHDFwPa9wOOBNVX1w6q6cWDfLAMzwZKk1cuCVZLUKVW1GRilN7t67rzdLwQ+3PS7AHhcksc2+z5bVfdU1beBO4ADgRfTK6ouT3J1s/2UqvoBcAHw8mZZ7J5Vdc28Y90EPCXJPyU5BvjuwL6zmhguBh6TZF/gJcCpzXEuAvYC1jf9z6+qu6vq/4DrgZElTsPzgYuqamszIzkDHNnsuxfoX9N7RXOulqWq/he4Dnhxkg3AfVV17QJdHwv8R5JrgdOAZzXtRwL/3nzWZmBz076tc9X3BGDrwPaf0yvg35DkP5McOrDvDuCJy/1ekqSVa+3SXSRJGrpPA38HHAU8bqA9C/St5vWegbYH6P2OC3BmVb15gff9G71Z2q+wwIxgVd3VFFEvBU4BfpPeNZiDxxyMIcCvV9VXB3ck+blFYtuWhb5n331V1T/+cj5rvv6y4G+xwHLgxjuAC6vqlUlG6RXgffO/+1Lnqu+H9Ir4/nu+CZyU5O30lgN/Anhqs3uvpr8kaZVzhlWS1EVnAG9fYNbzYpprG5McBXy7qhaazes7Hzg+yeOb9+yXZASgqi4FDgZ+i4Wv49yf3nLVjwN/CRw2sPuEps8Lgbur6m7g88AfJEmz73nL+J73DSxLHnQp8ItJ9k+yB73Z5v9axuctx8eBY1l8OTD0Zlj7N7t6zUD74Pl/Nr0l20udq74bgKf1N5L0Z21/RG+meJ+Bvj8NLDTzK0laZZxhlSR1TlXdCvzDArs2Ah9IshmYA169xOdcn+QvgC80j3O5j94M4Jamy9nAhqq6a4G3H9Qcq//H3cFZ2ruSfAl4DA/NJL4DeC+wuSlabwZevq34gOmm/5WD17FW1e1J3gxcSG+29dyq+tQSn7UsVfWdJJcAB1bV1xfp9m7gzCR/TG/pdN/pPHT+rwb6dxfe1rnq+xzNcu7GryV5P72lv8cDbxzYdzTw2e34WpKkFSoPrSqSJGl1Se/5rqdV1fnb8Z6LgD+tqtldFtgKleQc4M+q6msDbRurauO8fhcDxy3yhwRJ0irikmBJ0qqTZN8k/03vLr3LLla1006ld/OlQRcNbiQ5AHiPxaokCZxhlSRJkiR1lDOskiRJkqROsmCVJEmSJHWSBaskSZIkqZMsWCVJkiRJnWTBKkmSJEnqJAtWSZIkSVIn/T+lvKr/sFxZXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = reg.predict(X)\n",
    "\n",
    "plt.figure(figsize=(16,8))\n",
    "plt.scatter(X, y, c='black')\n",
    "plt.plot(X, predictions, c='blue', linewidth=2)\n",
    "plt.xlabel('Money spent on TV ads ($)')\n",
    "plt.ylabel('Sales (k$)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.612\n",
      "Model:                            OLS   Adj. R-squared:                  0.610\n",
      "Method:                 Least Squares   F-statistic:                     312.1\n",
      "Date:                Sat, 09 May 2020   Prob (F-statistic):           1.47e-42\n",
      "Time:                        15:19:51   Log-Likelihood:                -519.05\n",
      "No. Observations:                 200   AIC:                             1042.\n",
      "Df Residuals:                     198   BIC:                             1049.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          7.0326      0.458     15.360      0.000       6.130       7.935\n",
      "TV             0.0475      0.003     17.668      0.000       0.042       0.053\n",
      "==============================================================================\n",
      "Omnibus:                        0.531   Durbin-Watson:                   1.935\n",
      "Prob(Omnibus):                  0.767   Jarque-Bera (JB):                0.669\n",
      "Skew:                          -0.089   Prob(JB):                        0.716\n",
      "Kurtosis:                       2.779   Cond. No.                         338.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "X = data['TV']\n",
    "y = data['sales']\n",
    "\n",
    "exog = sm.add_constant(X)\n",
    "est = sm.OLS(y, exog).fit()\n",
    "\n",
    "print(est.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple linear regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The linear model is: \n",
      " Y = 2.9388893694594085 + 0.045764645455397615*TV + 0.18853001691820456*radio + -0.0010374930424763272*newspaper\n"
     ]
    }
   ],
   "source": [
    "Xs = data.drop(['sales'], axis=1)\n",
    "y = data['sales'].values.reshape(-1, 1)\n",
    "\n",
    "reg = LinearRegression()\n",
    "reg.fit(Xs, y)\n",
    "\n",
    "print(f\"The linear model is: \\n Y = {reg.intercept_[0]} + {reg.coef_[0][0]}*TV + {reg.coef_[0][1]}*radio + {reg.coef_[0][2]}*newspaper\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.897\n",
      "Model:                            OLS   Adj. R-squared:                  0.896\n",
      "Method:                 Least Squares   F-statistic:                     570.3\n",
      "Date:                Sat, 09 May 2020   Prob (F-statistic):           1.58e-96\n",
      "Time:                        15:24:10   Log-Likelihood:                -386.18\n",
      "No. Observations:                 200   AIC:                             780.4\n",
      "Df Residuals:                     196   BIC:                             793.6\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          2.9389      0.312      9.422      0.000       2.324       3.554\n",
      "x1             0.0458      0.001     32.809      0.000       0.043       0.049\n",
      "x2             0.1885      0.009     21.893      0.000       0.172       0.206\n",
      "x3            -0.0010      0.006     -0.177      0.860      -0.013       0.011\n",
      "==============================================================================\n",
      "Omnibus:                       60.414   Durbin-Watson:                   2.084\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              151.241\n",
      "Skew:                          -1.327   Prob(JB):                     1.44e-33\n",
      "Kurtosis:                       6.332   Cond. No.                         454.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "X = np.column_stack((data['TV'], data['radio'], data['newspaper']))\n",
    "y = data['sales'].values.reshape(-1,1)\n",
    "\n",
    "exog = sm.add_constant(X)\n",
    "est = sm.OLS(y, exog).fit()\n",
    "\n",
    "print(est.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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