Lecture02_Linear_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Data creation\n",
    "$$f(x)=\\frac{1}{2}x^2+\\frac{1}{2}x+\\text{error}\\\\ \\text{where} -2.5\\lt x\\lt2.5$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_samples = 200\n",
    "x = 5 * np.random.rand(num_samples, 1) - 2.5\n",
    "y = 1/2 * x**2 + 1/2 * x + np.random.rand(num_samples, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = x.reshape(-1,)\n",
    "y = y.reshape(-1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.268909</td>\n",
       "      <td>2.157489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.378413</td>\n",
       "      <td>1.232108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.135544</td>\n",
       "      <td>0.558797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.759255</td>\n",
       "      <td>2.823208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.039713</td>\n",
       "      <td>2.000724</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y\n",
       "0 -2.268909  2.157489\n",
       "1 -1.378413  1.232108\n",
       "2 -0.135544  0.558797\n",
       "3  1.759255  2.823208\n",
       "4  1.039713  2.000724"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_set = pd.DataFrame({'x': x, 'y': y})\n",
    "train_set.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1133685c0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113339f28>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_set.plot(x='x', y='y', kind='scatter', title='Non linear data set with error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Fitting the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2&#52264; &#51060;&#49345;&#51032; &#45796;&#54637;&#49885;&#51012; fitting &#54616;&#44592; &#50948;&#54644;&#49436; PolynomialFeatures&#47484; &#49324;&#50857;&#54633;&#45768;&#45796;.\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "x_poly = poly_features.fit_transform(x.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(x_poly, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5362133410732012"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.51306057, 0.50311102])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fitting &#44208;&#44284;\n",
    "lin_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trainin set&#44284; Predicted curve&#47484; &#48708;&#44368;&#54644;&#48372;&#51088;."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_new = np.linspace(-2.5, 2.5, 100).reshape(-1, 1)\n",
    "x_poly_new = poly_features.fit_transform(x_new)\n",
    "y_pred = lin_reg.predict(x_poly_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a22084c88>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJztnXl4FFXWxt+b0FkJBAIJhJAODIssgiCyCDKA+okwioq4EDAii+wMioMQxRFkkAEURFxQWSSNKDBuCAIqyiZIEBQwgKAEZA0giyRk6/P9UelOV3dVdXWn1/T5PU89SVXdW3Wqu+rtU+eee68gIjAMwzDBQ5i/DWAYhmFcg4WbYRgmyGDhZhiGCTJYuBmGYYIMFm6GYZggg4WbYRgmyGDhZhiGCTJYuBmGYYIMFm6GYZggo4o3DlqrVi1KS0vzxqEZhmEqJbt37z5PRLX1lPWKcKelpSE7O9sbh2YYhqmUCCFy9ZblUAnDMEyQwcLNMAwTZLBwMwzDBBks3AzDMEEGCzfDMEyQ4ZWsEi3MZjP++OMPXLt2zdenZhgAgMFgQGJiIqpVq+ZvU5ggx2QCMjOB48eB1FRg+nQgPd375/W5cJ8/fx5CCDRt2hRhYezwM76FiFBQUICTJ08CAIs34zYmEzBsGJCfL63n5krrgPfFW5dyCiGOCSH2CSH2CiEqlKB96dIlJCUlsWgzfkEIgZiYGNSrVw/nzp3ztzlMEJOZWS7aFvLzpe3exhWPuzsRna/oCUtLS2EwGCp6GIapENHR0SguLva3GUwQc/y4a9s9iV/cXiGEP07LMFb4HmQqSmqqfL0pDiIcJQ7bvYFe4SYAG4QQu4UQw5QKCCGGCSGyhRDZeXl5nrOQYRgmAJk+HYiJkf6PRj6+QQ/8Ilpg2T0fAWazV8+tV7g7E1FbAHcDGCWE6GpfgIgWElE7ImpXu7aucVIYAI888ggefPBBl+p07NgREyZM8JJFgc/169chhMCaNWv8bQoTwqSnAwsXAkYjMAavIxmn0YQO47bV/wSuX/fquXXFuInoVNnfc0KIjwG0B7DZm4YFCs5eqTMyMrBkyRK3j//222+DiFyqs3btWm4nYJgAID0dSP/HZaDBy8CfZRunTCl3xb2EU+EWQsQCCCOiq2X//x+AqV61KoA4ffq09f81a9Zg6NChsm3R0dGK9YqLi3WJa/Xq1V22qWbNmi7XYRjGS8yeDfxZptoNGwKDB3v9lHpCJUkAtgohfgLwA4AviOhL75qljckEpKUBYWHSX5PJe+eqU6eOdYmPj3fYVr16dRw8eBBCCKxcuRJ///vfERUVhaVLl+Ls2bN4+OGHUa9ePcTExKBly5Yw2RlrHyrp2LEjxo8fj2eeeQY1a9ZEnTp1MHnyZJlXbh8qqVOnDmbOnIknnngCcXFxqF+/Pl577TXZeX755Rd07twZUVFRaN68OTZu3IgqVapgxYoVqte+Z88edOvWDXFxcYiLi0ObNm2wdetWAEBhYSEGDRqEtLQ0REdHo0mTJnj11Vdldlqubdq0aUhKSkJ8fDymTJmC0tJSTJ48GbVq1ULdunUxd+5cax1LGOTtt9/GXXfdhejoaDRo0AAffvih5veUm5uLfv36IT4+HgkJCbj33nvx+++/a9ZhmApz9izw6qvl61OnAj54G3Yq3ET0GxG1LltaENF0r1ulgSXpPTcXICpPevemeOvl2Wefxfjx45GTk4NevXqhoKAAHTt2xBdffIH9+/djxIgRyMjIsIqfGosWLUL16tWxc+dOzJkzBzNnzsQnn3yiWWf27Nlo37499uzZg3HjxmHcuHH48ccfAQAlJSXo06cP4uLi8MMPP2DhwoWYPHkyzE4aUB566CE0aNAA2dnZ2LNnD5577jlERkZaj5mWloZVq1bhl19+wYsvvogpU6Zg+fLlsmNs2LABeXl52Lx5M+bNm4dp06ahd+/eMBgM+P777/Hss8/iqaeewv79+2X1nnvuOTz00EP46aef8Nhjj6F///7Yt2+fop1Xr15Ft27dUKNGDWzZsgVbt25FfHw87rzzThQWFmpeI8NUiBkzAEsv8BtvBB591DfnJSKPLzfffDOp8csvv6ju04PRSCRJtnwxGit0WF2sXLmSpI9MTk5ODgGg119/3ekx+vTpQ6NGjbKuP/zww9S3b1/reocOHahbt26yOl26dJHV6dChAz399NPW9aSkJHr88cdldVJSUmjWrFlERPTJJ5+QwWCgs2fPWvd//fXXBIA++OADRTvNZjNFRkbSihUrnF6ThXHjxlHv3r1l19awYUMqLS21bmvRogXdcsstsnp16tSh+fPnExFRQUEBAaDRo0fLynTu3JkGDx4sK/P5558TEdGCBQuoRYsWsvJFRUVUtWpV+vTTT1Xtrei9yIQ4ublEERHlIvTZZxU6HIBs0qmxPu/yXlH8mfTujHbt2snWS0pKMH36dKxatQonT55EUVERCgsLcffdd2sep1WrVrL15ORkp738tOocPHgQaWlpSExMtO7v0KGD5vGEEBg/fjwGDBiAd999Fz169MCDDz6Ixo0bW8vMnz8fS5YswfHjx1FQUIDi4mI0bdpUdpyWLVvKeskmJSXBflq7xMREh+vr1KmTw/q2bdsUbd29ezcOHjyIqlWryrbn5+fj6NGjmtfJMG7zwgtAUZH0f6dOwD/+4bNTB12/c7Xkdl8kvTsjNjZWtj59+nQsWLAAkyZNwqZNm7B371706tULRZYvWwX7Rk0hhNOwhlYdInKrw8mMGTOwf/9+9OrVC5s3b0aLFi2sMfqlS5di4sSJGDp0KDZs2IC9e/diyJAhDtemZJc716eF2WxGhw4dsHfvXtly+PBhDBo0yO3jMowqBw4A779fvj5jBuDDTl1BJ9y2Se8WYmKk7YHG1q1bcf/996N///5o3bo1GjZsiMOHD/vcjmbNmuHYsWOw7Rj1ww8/6KrbtGlTjB8/HuvWrUN6ejree+89ANK13XbbbRg+fDjatGmDRo0a4ddff/WYzTt27HBYb9asmWLZtm3b4vDhw0hKSkKjRo1ki6VBmWE8yuTJ5Z1s7r4b+PvffXr6oBNu26R3IaS/Cxf6ZihFV2nSpAnWr1+P77//Hjk5OXjyySdx6tQpn9vRu3dvpKamIiMjAz///DO2bduGZ599FkIIVU/88uXLGDt2LL777jvk5uZi+/bt+P7779G8eXMA0rXt3LkTGzduxOHDh/H8889j586dHrN5xYoVWLx4MQ4fPowXX3wR27dvx7hx4xTLZmRkIC4uDvfddx+2bNmC33//Hd999x3GjRuH3Fzd868yjD62bQM++6x8/T//8bkJQSfcgCTSx45JP3jHjgWmaAPAiy++iFatWuHOO+9Et27dkJiY6HIvSU9QpUoVfPrpp7h06RJuueUWDBkyBFOmTAEAREVFKdYxGAw4d+4cBg4ciCZNmqBfv37o3r07Zs6cCQAYM2YM+vTpg379+qFDhw44d+4cxowZ4zGbp06dCpPJhFatWmHx4sXIyspyiONbqFatGrZu3Yrk5GQ88MADaNasGQYNGoT8/Hy38uQZRhUi4Nlny9f79wduuskfdgRXVgnjGXbs2EEAaP/+/f42RYZ9xog34XuRcZnPP7dmkRTCQF2Sj1JWlmcOjcqcVcK4x8qVK1GjRg00atQIR48exT//+U+0b98eLVq08LdpDBMclJTg0vCJsLSavI0nsfVUQ/zoo8kTbAnKUAnjOpcvX8bw4cNxww034LHHHkObNm14kCaGcYWlSxF/8hcAwFVUxTQ8D8B3kyfYwh53iDBkyBAMGTLE32Y4JSoqyuVBtxjG6+TnS4NHlTELzyAP5f0ifN2PhD1uhmEYZ8ybB5RlhJ1GHbyCp2S7fd2PhIWbYRhGi/PngZdftq5OC/s3rqG8l67B4Pt+JCzcDMMwNtiPPnowfRpw5QoA4HLdplgSLh+21R+z4LFwMwwTstiL9MiR8tFHDbm/4m8b3rCW/1fJDBQUy5sGi4q4cZJhGMbrmEzAuHHAhQvl23JzgbfekgTbwgxMggEl0kqXLnhn632Kx+PGSYZhGC9iGdPfVrQt2Ip2J2zHg1hdvmH2bKQaleMi3DjJoGXLlvj3v/9tXU9LS8Ps2bN9bkd2djaEEDh27JjPz80w3iIzU8ru04YwB09b1z6LeQTo0CFgBrlj4dbB448/bh2QyWAwoGHDhpgwYQKuWWa+8DK7du3CyJEjdZVdsmSJw7jUDMOU4yysIQTwIFahE6QRKgsRAfNL0kBSgTLIHce4dXLHHXdg2bJlKC4uxpYtWzBkyBBcu3YNb775pmJ5vZMF66F27doeOU6w4MnPjmHsSU2V4tlKREQAT2Zcx4TFE2EJbR/tNRb3jW9gLZOe7v+B7djj1klkZCTq1KmD+vXro3///khPT7fOA/ntt99CCIG1a9eiffv2iIiIwPr16wEAn3/+OW6++WZERUWhQYMGyMzMlE02cO7cOfTp0wfR0dEwGo1YtGiRw7ntQyVXrlzBiBEjULduXURFRaFZs2b48MMP8e2332LQoEG4du2a9Q3BEnIpKirCxIkTkZKSgtjYWNxyyy1WGy18+eWXuOGGGxAVFYXbbrtN19jhRUVFmDx5MoxGIyIjI9GwYUPrRMWWz+X8+fPW8seOHYMQAtnZ2aqf3ZtvvgkhhMMckwsXLkStWrVQXFwMQJoAuXfv3oiLi0NiYiIeffRRnDlzxqnNTGijFO6wQAQ8fnU+UkvKJppOSEDzrMm+M04n7HG7SXR0tFVALEycOBFz5sxBo0aNEBcXh/Xr1yM9PR3z5s1D165dcfz4cQwfPhyFhYVWIX788ceRm5uLr776CjExMRg/frxmTJmIcPfdd+PPP//E4sWL0aRJExw6dAjXr1/Hrbfeirlz52Ly5MnWKbssYZNBgwbh6NGjWL58OVJSUrB27Vrcc8892LVrF1q3bo0TJ07gvvvuw9ChQzFq1Cj8/PPPeOqpp1TtsJCRkYEtW7Zg3rx5aNOmDXJzc3HixAmXP0/7z27ZsmUwmUx42abjg8lkwsMPPwyDwYDTp0+ja9euGDx4MGbPno3i4mJkZmbi3nvvxY4dO2TTpTGMLRZvOSMDKC2V76tenIdGH75UvuHf/wZq1PCZbbrRO4ygK4tLw7oqzfzrq0UnGRkZsklwd+7cSQkJCfTQQw8REdGmTZsIAK1atUpW77bbbqOpU6fKtn388ccUGxtLZrOZDh06RABo69at1v3Hjh2jsLAweuGFF6zbjEajdeLfDRs2kBBCdUjSxYsXU2xsrGzbkSNHSAhBubm5su19+vShESNGEBHRpEmTqHHjxmQ2m637p02bRgDo999/VzzX4cOHCQCtW7dOcb/lc8nLy7Nu+/333wkA7dq1S1bG/rObO3cupaamWu05fvw4CSFo+/btRET0/PPPU48ePWR1Ll68SABo586divbYw8O6hjZCOErCAowoX2nalKioyGf2gId19TxffvklqlatipKSEhQXF6NPnz6YP3++rIz9ZMG7d+/GDz/8YJ18AJDmRywoKMCZM2eQk5ODsLAwtG/f3rrfaDQiOTlZ1Y49e/agbt26qtN4KfHjjz+CiKyz11goLCxEjx49AAA5OTno2LGjbEYc+wl7lWwJCwtD9+7ddduihv1n9+ijj2LChAnYsmULunbtiuXLl6Nhw4ZWm3bv3o3NmzcrNsQePXpU9pkyjBL2se7mOIAn8Xb5htmzpf7sAQgLt066du2KhQsXwmAwIDk5WbHxzH6yYLPZjBdeeAH9+vVzKFu7dm23RsFzp47ZbIYQArt27XKwOzo62u3jOqtjCVfYlrMPL1mw/+wSExNxxx13wGQyoWvXrjCZTEi3aREym83o3bu3YppkUlKS7mtgQpfp06V8bik1UEr/C0fZPJJ33AH07u1P8zTxv3AHyRCeMTExaNSokUt12rZti4MHD6rWa9asGcxmM3bt2oVbb70VAHD8+HHNeSnbtm2L06dPIycnR9HrjoiIQKld4K5NmzYgIpw5c0bVO27evDlWr14tmxHefsJeJVvMZjM2bdqEnj17Ouy3ZMOcPn3a+v/evXs1j2nLgAEDMGbMGAwbNgz79u3D6tXlnSHatm2Ljz76CEajkTNQGLew+AGZmUDL3LXoibLG+rAwYM4c/wxCohe9MRVXlso2dZl9jNsepVguEdGXX35JVapUoeeff5727dtHOTk5tHLlSnrmmWesZXr27EktW7ak7du30549e6h79+4UGxurGuMuLS2ljh07UrNmzejLL7+k3377jTZs2EAff/wxERFt27aNANCGDRsoLy+Prl27RkRE6enplJqaSitXrqSjR4/Srl27aNasWbR69WoiIsrNzaWIiAgaO3YsHTx4kFauXEkpKSmaMW4iooceeojq1atHq1atot9++402b95M77//PhERFRUVUf369en++++nQ4cO0fr166lVq1aKMW77z46I6Nq1a1S1alVq3bo1tW/fXrbv5MmTVLt2bbr//vtpx44ddPToUdq4cSMNHTqUrly5omqvLcF4LzJeoLCQqEmT8tj2sGF+MQMuxLhZuHXgrnATEa1fv566dOlC0dHRFBcXRzfffDPNnz/fuv/MmTN0zz33UFRUFKWkpNA777xDLVq0UBVuIqI///yThgwZQrVq1aLIyEhq1qwZffjhh9b9w4cPp4SEBAJgPU5RURG98MIL1KBBAzIYDJSUlET33HMPZWdnW+utWbOGmjRpQpGRkXTrrbdSVlaWU+G+fv06PfPMM5ScnEwRERHUsGFD2fVt27aNWrduTVFRUdSxY0das2aNbuEmIho4cCABoNdee81h3+HDh6lv374UHx9PUVFR1KRJExo9ejQVFhaq2mtLMN6LjOtkZREZjVJjpNFIjnNEvvJKuWhXr0507pwfrHRNuAV5IVTRrl07suTp2qP2is8wvobvxcqPZVwS2y7uMTE2vR3z8oDGjYHLl6Wdc+YAOtJgvYEQYjcRtXNekjvgMAxTiVEal0Q2R+SUKeWi3aQJMHq0T+1zF93CLYQIF0LsEULwDLMMwwQFauOSHD8OYO9eyfW2MGeO1Oc9CHDF4x4HIMdbhjAMw3gateFWwwRhc5uxgLks/e+uuwI6/c8eXcIthEgB0BvAu941h2EYxnNMn67ch+ZB84foii0AgGJUwWe3zwvs9D879HrccwH8C7BkpzMMwwQH9nocg2uYjQnW9XkYh7ELmvrYqorhVLiFEP8AcI6IdjspN0wIkS2EyM7Ly9M8pjcyWRjGFfgeDA0yM6U5IW2ZhBlIwUkAwBkkYSqm+HzqsYqix+PuDOBeIcQxACsA9BBCZNkXIqKFRNSOiNppjR8dHh6u2u2ZYXxFQUEB97gMAewF+W84gmcwy7r+LF7GVVTz+dRjFcWpcBPRJCJKIaI0AI8A+IaIBrh7wvj4eJw9exZmM0ddGN9DRMjPz8fJkyeRmJjob3MYLyMXZMI8jEMkJBd8BzrgfTzml6nHKorPxyqpVasW/vjjDxw6dMjXp2YYAIDBYEBSUhKqVavmb1MYL2M7kNQ9+By9sRYAYIbAaLyOsPAwWV63v2e20YtLwk1E3wL4tiInDAsLQ2qwvZcwDBOUWIR46qQCzD3xT+v2o92HImdnO5SWdc7JzZUE3rZOIMM9JxmGqdSkpwOHBv8XDVE2HVnNmuj363+0e1QGOCzcDMNUbo4eBWbMKF+fPh0/n0xQLBos2SUs3AzDVF6IgLFjgcJCab1tW2DoUNSsqVxcbXugwcLNMEzl5dNPgbVSgySEAN58EwgP969NHoCFm2GYysm1a5K3beHJJ4GyuUgvXlSuorY90GDhZhimcvLSS8CJE9L/tWrJkrW1QiImk5ft8gAs3AzDVD4OHIB5VvlE0hNoFkzrnAewiaS0wEAXbxZuhmEqF2Yzzj0wHGGlJQCALeiCVy48JhNkrZBIMKQFsnAzDBOUmExAWpo0KXtamo2XvHgxEg9vBSAN2Tocb4Eg7yHprA9goKcFsnAzDBN0WOaSzM2VwhuWno+r3swD/vUva7nZmIBf0MK6bhHk6dOluSfVCPTO3SzcDMMEHWpzSYpnJljjIL+hAabheVkZiyCnp0uzliUo9MMJhkGnWLgZhgk6lEIZ3fEN+l5737o+IfJ1FKDcrbYX5PR04Px5ICsLMBqlNG+j0WYG+ACGhZthmKDANqYdZqdcUSjA23iyfMODD6Lve710CXJ6OnDsmDT95LFjgS/agB+GdWUYhnEVS0zbEh4pLZXvfw4voTGOSCvVqwOvvYb0usEhwu7AHjfDMAGPUkwbkHqv34h9+Bf+W77xv/8F6tb1nXF+gIWbYZiAxRIeyc1VKVBaip87DoMBUs42unQBhgzxlXl+g0MlDMMEJCNHAm+9JaX7qfFcjQXAjh3SisEgBbLtA+CVkMp/hQzDBB0mk3PRblTlGJ7Ln1S+YfJkoFkz7xsXALBwMwwTcGRmaos2QHhbPIkqhWWB7xYtJOEOEVi4GYYJOJx1OR+IZehRvEFaEQJ4910gIsL7hgUILNwMwwQcWl3OE3EWr2J8+YaxY4GOHb1vVADBws0wTMChNZbIAoxCAsqG90tLk8bdDjFYuBmGCTgsY4kYjfLtD2IlHsTq8g0LFwJVq/rWuACAhZthmIDE0hU9K0vyvmshDwswyrr/SLchwJ13+s9AP8J53AzDBDSWbutxw8YiMT8PAHCtZgoafTJbo1blhj1uhmECAtWJEQCkx3yMe/NXWNdjsxZKY5KEKOxxMwzjd+wHkbJMjAAA6f+XJ83QbiEjA7j7bt8bGUCwx80wjN9RmxghczJJfd/zpBAJkpOBuXN9b2CAwR43wzB+R63DTcfjHwHHV5VveO89ID7eN0YFMOxxMwzjd5Q63CThDN4MG1m+YcgQoGdP3xkVwDgVbiFElBDiByHET0KIA0KIF31hGMMwlRf7hshevew73BAWhw1BDXNZR5vUVGDOHN8bGqDo8bgLAfQgotYAbgLQUwgRWv1LGYbxGEoztC9dKrU5WqYa+1fN93C3+YvySosWAdWq+c/oAMOpcJPEX2WrhrJFc9wuhmEYNdQaIj/6SPq/Af2G5/+0G4vk9tt9Z2AQoCvGLYQIF0LsBXAOwEYi2qlQZpgQIlsIkZ1naQFmGIaxQ60h8sIF4ERuKZYgA1XLfMXLdZsCM2b40LrgQJdwE1EpEd0EIAVAeyFES4UyC4moHRG1q127tqftZBimkqA18t8EzMZt2AoAKEE4BtIy9dGmQhiXskqI6BKAbwFw0y7DMG7Rq5fy9jb4EdPwvHV9OjKx5uwtPrIquNCTVVJbCBFf9n80gDsAHPS2YQzDVE7WrnXcFo18mJCOCBQDAHaiPV7Cc5reeSijx+OuC2CTEOJnALsgxbjXeNcshmEqK0ox7pmYiGZl/uBfiMUAZKEEBvz1l3zMEkbCac9JIvoZQBsf2MIwTAiQmiqlAFroiXUYg9et6//EXBxBYwBSg6V1zJJ0X1oZ2HDPSYZhfIrt7DaJOIsleNy672Pch/cwWFY+P19KIWTKYeFmGKbCaA3JqkR0NCBgxlJkIAnnAACnUBdD8Q4A4VDe2eTBoQYPMsUwTIXQHJI1Xb3seMxFT6wHAJghMBDLcAG1FM/BjZRy2ONmGKZCqA7JqhDesJRtgx/xMp61bp+FZ/ANlHtHxsRI4RWmHBZuhmEqhFoYw7LdNoySmwtUxVWswCPW1L9daIfnMc1aLyICSEiQxiwxGqX5gLlhUg6HShiGqRD2WSK22+3DKADhDYxEE/wKQEr964/lKA2LgCCpzvTpLNTOYI+bYZgKYZslYsES3rAPo2RgKQYiy7o+HG/hCBojPBxYtkya1Z1F2zks3AzDVIj0dCmcYRmS1Ta8YRtGaYqDWIBR1vVFGAQTBgAAios55c8Vgkq4XU05YhjGN6SnS96y2Sz3mi3ZINHIx0r0Qywk9/sXNMMYzJcdg1P+9BM0wq00+PqwYSzeDBPIWMIor2M0bsR+AEABovAwPkQ+YmVlOeVPP0Ej3K6kHDEMExikpwNfpS/GE1hs3ba62+v4LeZGWTlO+XONoBFupVZrgF+vGCZQUAxl7t+PTlnlcW089hgGfPMEMjKA8HBpU3i4NG0ZN0rqJyiE22SSGj2U4NcrhvEvJhNQqxYwYIA8lPn00Cu4cmdfoKBAKti8OfDGGzAtF1i6FCgtlTaXlkpzTnLYUz8BL9wmk/RrTCqzXPKwjwzjPyxtTxcu2O8hLCgYhGpnDkurMTHAypVAbCyHPT1AQAu35aaw/DIrYRn2kcWbYXyPkggDwFN4BX3xv/IN77wjedxw3tOScU5gCfdPPwFHjlhX1W4Ke/jXmmH8g5LY3obNmImJ5RtGjwb697euqoU3Oeypn8AR7hUrgE6dgPvuk+IfcO0XmH+tGcb32IttMk5iJfqhCqTX5LxGHYE5c2RlevVybLPirBLXCAzhPnkSGDRIasQ4cED6n8ilX2D+tWYY32Pb3T0ChViNvtbxtfNEbWwZs1IaNaoMk0lqiLRtsxKCs0pcJTCEu1494K23ytdXrQJmzlQcAyEiAjAY5Nv415phfIN9yh9Q3t19PsagI3YCAEoQjn70EQZOSsHIkeV1MjIcw59EyhMIMxoQkceXm2++mdxizBgi6XskEoJo3TrKyiIyGqVVo5EoK4sUtzEM412ysohiYsofUUBaz8oiooULZTvG4VXZo2xbR2kRwt9X538AZJNOjRWklmdXAdq1a0fZ2dmuVywuBu64A9i8WVqPjwd27QIaNfKsgQzDuExamnJHuL5JW7HqYg/p+QWQhXQMxDIoTUGmhtEojXESygghdhNROz1lAyNUYsFgAD76CEhJkdYvXQLuvRe4csW/djEMo5gAkIITWHC2r1W09+AmDMNCuCLaAPfHcJXAEm4ASEoC/vc/IDJSWs/JkVKJSksVu9TyiIEM4xvsEwCikY9PcJ+1MfJ6tdp4NOoTFKC8YUqtx3OYnfJwfwwX0RtTcWVxO8ZtS1aWLAi2/55nHeJrBgNRRIRKzI1hmApj256UkCA9c9KzZqbleMT64BWhCt2G7wggCguTNhuNRCNDj4SoAAAbD0lEQVRGOMbFhSCKjVWOdRuNfr5gPwIXYtyBK9xERBMnyr7VAXjfaSNHqH/5DOMplBojIyIkAX8eU2U7nsSbDk6VxYEaMUJfA2WoN1K6ItyB1ThpT2kp0KcP8MUXAIBCRKAHvsF2dHZa1QuXxTAhhVpj5MhaH2HB+Yet629gBEbhDYdylgZHteMoEcqNlMHbOGlPeDiwfLl1jINIFOFj3A8jjjmtxjBMxVBqjGyHXZh9PsO6/hVuxzjM06yvt1cz98fQT2ALNwBUqwasWYPrcbUAAInIwxr8A3FQzzTRGpSKYRh92DdGpuAEPkUfROO6tKFJEzyVshIlMDhWBlCzpvJxLCQkKM9TyTgn8IUbABo0QNS6T1AcJnWdbYkDWIV+qIJi1SqcZcIwFaNXr/L/43AFX6A3knFa2lCjBrBmDbrcU8PpcdRmgZ83T3meSsY5ToVbCFFfCLFJCJEjhDgghBjnDUOcpfWZjnXGiCrvWtf/DxvwBkYCUA5mE89LyTBuYzJJHjAAhKMEH+EhtMI+AEARDMDq1UDjxppd1S9elP5qzQLPuImz1ksAdQG0Lfs/DsBhAM216riaVaLUem0wSK3Xlm7tCQnS9hfwgqzgRMzgLBOG0cDVISLkz6OZ3sSTsgcqA0usZbWyRfi5cw14Mx0QwKcA7tQq46pwG436UoUsN9JSDJRtfATLOcWIYRTQHF9EBdvn8Vn8R1b535giE2S1Z1cI7k/hKl4TbgBpAI4DqKZVzlXh1pvjafXGUUjfoJt1QyEM1B3fUHi49q8/30hMqKEmrFresOV5HID3ZZWWIZ1ios2y50jph0EIKXebcQ2vCDeAqgB2A3hAZf8wANkAslNTU10y2DWPW1ricZEOiOblG6pVozUzfna4iVzxNBimsqHmFGm9hRqNRHdgAxWhirXCV+hBUWGFis8Pj9bpGTwu3AAMANYDeEpPeU/EuJWWsDD5DfK/ublEycnlBZKTafKAXKeeN8OECu543F9M202XEWct/BNupDrRl1iQvYwrwq0nq0QAeA9ADhG9UvHmUEfsW53VsKQNWf7ePy4VWLdOyvUGgFOnMNB0F+JLz6seg6c4Y0IJtVS8Xr1Usrh+/RW9XuuJargKADiBFAyrtxaz36nOWSCBhDNlB9AFAAH4GcDesqWXVp2KjlXispfw9de2o9/QDrSnWFxlj5thyDGUoTTwU0wM0ar5p4jS0mzikfFE+/b52/yQAZ70uIloKxEJImpFRDeVLV6daEjNS1DtDtujB2AywVw2BnAH/ID/4QEYUKT/GAxTSUlPl7+prl3rOH1YRP6faP5Uz/KBQqKjgTVrYPqpJQ+bHIjoVXhXFk+MDuhOg8fkmm/K3IgP0Y/CUOI0q4QbV5hQwr7BMgZ/0TZ0Kt8QHk60Zo1bqYSM+6DSDOvqIllZRC8a5MNNLg0fRFnvl2rW4ZuTCWZcdTxsQ5ERuE7rcaf8AViyxKEchxu9T8gKNxFR1jIzvRc3Tn6njR1LZDYrluebkwlm3HE8LHXCUUyr8IC88rx51nLupBIy7hPSwk1ERKWlRIMGye+2zEzFonxzMsGIxct2Ne3VUi8MJWQS/eWVpk6VlWWnxre4ItzBMTqgDmSDVDUMw/Lu7wD9+pUXmD4dc+KnOTSyqA05ab+d57ZkAgWTSRo8TWtyAqW0V0u947lmLMQw9Kfl5TvHjweee05W3uUkAcZ36FV4VxZfe9xqr4vLlxQS9eol2/EMZspeJ/W8anIcnAkk9PQ0VvKKpXpmWoARssLLqg4nMpsVY+XccO87EGqhEs1XuoIC+sYgb3z5J16R3dzObk5+ZWT8SVZW+eiYehY1p0LATPMwRlZ4ER6nMJSycxIAhJxwa8Wps7KIonFNNiiVRbz1xrE5Ds74i6wsWd8yXZ62otiazbQoTi7aJjxKYSgho5Gdk0Ag5IRb66az7IvFVdqCzrICU2vMqfDxGcab6B2ATdM7NpulzCqbCh+iH4Wj2FqPnRP/44pwB23jpG1j4XmFoUksjSiWRpprqIq7sQ5b0MVa5vk/nwZmzXJ6Lm6kYfyFs7F1nM4oYzYDo0cDr71m3bRS9EN/LAfCqyAjQ6qnt5GeCRD0Krwri7c9bmejCdqOB2zvscTiKn2H2+Qbp05VzfO2PSc30jC+Riu27fSNr6SEaMgQWaVV4ZKnbfusANJ5IiJc8OIZj4PKHipxpVVdSeRrR1+lMzf8Xb5x0iSn4s0wvkQrvh0R4URUi4uJBgyQVVouHpWJtv1iP10gi7ZvqfTCrWfGHEvDpEXkLWN0W2/Ia9eI7rTr6jtunNR5h2F8hNabnJqDEhbmRFSvXyd6QN4jUsoeKdHt8DC+p9ILtx6POyHBeXrT8kUFtCH6Hnmhxx+XvBWG8TLOUvDcajD86y8Hh+RNPEkCpU6fGW6M9C+VXridxbhjYtRjg/YhFAMK6UP0kxe67z6igoIK28gxcUYLZ13Wnd3DDly8SNSpk6zwHIwnwKxLtNnj9i+VXriJ5MKYkFB+k2tNW2brUdg+NGEooYWQN+JQ9+5Ely65ZZfSA8cNPYw9zkJ+ERGOMW7V++jECaIWLWSFZ1Wf5pJo8z3qX0JCuO3RO2+lxaNwfGjMNBPPyDe2bk106pTHbGBvhrFFb8jP6ZvbL78Q1a8vrzh/vu5nwnJvsmj7l5AUbj0PgVaaoGX5F152vKMPHvSIDRw/ZGzRI6xO75nt24lq1iyvUKWKTIFt30zV3kbZoQgMQlK49WSa2L4OavUWezphsfwur1mTaOvWCtvADwhjj7vDsxIR0apVRJGR5YVjY4nWr9c8F49HEriEpHDr7Rps+zCMGKEwjZPlRv7iC/ldHhlJtGKF2zaoPSDciMkQuSiqZjPRnDnym7d2baIfftB1Hr7fApOQFG5X4nm2r5+aN/LOnUSJifLKM2aodtTR6jBhCdHosTkhgR+oUESXqBYXE40cKbthjlZpTJ/MOeJjaxlPE5LCTeR447ucTqXEb7/RpeQbZAc4cluG1MlBAVfOqeWhR0RwL7ZgxWte7Z9/OuRob0FnqonzHPKoBISscNvjiZheVhZRcvRFh2FhzzbpTHT2rEN5VzpN6I3LcywyePBaHPnIEaIb5A7EB3iYIlGg2yHhMElgw8JtQ0VvVotXbEAhvYsn5E9kairRjz8qlq+ox13hNwXGL3jkLc+eDRuIatSQHfAFvED2OdpaGSjcMBn4sHB7ELlXbKbxmEOlsNkYHU1bR5pknYH0jrLmSlze2YPJ+J+sLA9/d2Yz0axZ0uAkZQe6jkh6GB9o/jgoOSs8pnzgw8LtQZRu+F5YQ5dFNdnG2XjKOvKaK6OsuTItle1DyK+7gYfbaX02WL7fWPxFn8Q8KjvISZFMt2CnZihNzbNmZyDwYeH2IGoPwqf/PUjUtKlsx7foSnVwyi1Pxlk+LyCl6ao9sIxv0Prh1Gqz0PMdWe61JjhI+yDvvp4d2cl6b6n9oBOp30Pc+SbwYeH2EEresCxV79Il+hTy0QVPoQ51xbduezJ6wyb88PkeZ3FiNdFMSNB3fKORqC9W0mXEyQ5gqjqUInFdl8es9ePBMe7AhoXbA6jlZNsPYJ+WWkqT8ZIs7l2McPpv/EvSDCQuntOVTBM1r4upOO7EiSvUAFhQQK9jlKxyPqLocSyy2qDnR1urHIfZAhsWbg+gN15peVhvx0Y6i9rygnfcQXT6tEfOqWdhD8ozVCRO7JY4Hj5MdNNNsoMeRQO6CT/KRFfPjwJnjwQvHhVuAIsAnAOwX+9BK4Nwawmk/eup5WFNwQn6IVI+kzwlJkrd53Xgrret5YExrpGVpR4P9nic2Gwmeu89h8aLVXiA4nHRQXT1/iiwZx2ceFq4uwJoG0rCrZXW5fRBLS4mysx0UOElcaMoBtc0HyStGKk73fkZ19CTnukxb/bCBaK+feUHi4ignRkLyJhqZtENQTweKgGQFkrC7Sxkoeth2riRqE4dWcVfcAPdjF0u5XXHxEjjnNg2ktpOHKH1o8Kel2s4+97tP3e3x5RZt44oOVl+8BtucOjMxYQWfhFuAMMAZAPITk1N9dW1egVnIQvdnDtHX0bfJ6tcjHCahkxqnKo81om92I4YoS7mWt4fxzpdR+t7Nxj0d6xS5coVoqFDHQ8+fLg0eTUT0rDHXUE80ZHCgoCZnsC7dBXyOOZPuJEoO9ttW5xlCXBPOddRe4ux9Iit0Oe5fr3jl1K7NtEnn3jxiphggoW7gmRlOXpXFq/L3bFOGuAofYuusgOWIIzeqjaBPnhP3dtya6bvCtQLBrwVAlITZ0svWLc+zwsXiDIyHCv27Ut07pxnDGcqBSzcHsC+84278UzbkIVAKY3BPLqGaNlDfAQN6bV/KM9c4q7nXFGPO1Dj494MAWmJs8ufp9lMtGyZ43juNWsSmUyqY7ozoYuns0o+AHAaQDGAPwAMdlanMgi3J7Gf968hjtBX6OGgAsfaPyjN1m1X15lQKYlsRQQuECZ4UPvh8EYISM/0YS59njk5RN27Ox7o4YcVhwJmGCIveNyuLizc6pR7dWYahPfoIuLlD3dsLNHLL8smatDyfrUExV2v2Z0p2GypqLeudU1aDYieOpfa9Tq9rsuXiZ5+Wpqw1+Ygp8Lr0b341CX7AvWNh/EeLNwBjL0oJuIMLcFjDopxJfFvNLT2xyRgdiv3uyIeaEUmPfZEKEPrmpyl7HnqXLY/BE5FtKSEaNEioqQk2QFKw8JpXpWnqCquyMIuzn5kOCMoNGHhDmDUvMau+JYOGZo77PgG3VRzvz0+/nMZzsRR69ie+CHRijXr6STjiXMB0n6l8wlhM4fo+vVErVs7Vu7cme6q+5NbPzKcERSasHAHOEqzy0dEECXVLKIxeM0xfAJpmqquyb9aj+FMwCoa83V2bDUv1BPZLM5SIJ2NX+6Jc1l+JNT234xsOnnj/znuqFePaPlyIrNZ1xAGSt9TZc4IYtRh4Q4CbIUvIUE+EmFNnKf5GEXFkA+OUYxwosGDiY4dq3AcWo99SgLprPOPJ7xFrR6kerr+u3ouNaG0fD+225pjP63CA8ofzJQpRH/9ZT22nkHDlMSYPe7QhIU7yFB7UBvjEK1EX8cdBgO9jWHUAEcV63kyFmorxpZBlrQGW/JUfHbECPn5RozQJ4TunEtLVC3nvBE/0YfoJ5+2DpCmFRsyhOjkScXPzp0fGY5xhyYs3AGGWrqekkentHTEdtoU5pg+WIxweh8DqDn2e9Ur0xNXtvUevZVV4uzc7mZfaHm4X07ZRp/gXsUCa2IeJDpwQPPYWmEdLTHmrJLQg4U7gFASoYgI5Uka7JfwcLsHd9Mmoi5dFAuvRU/6R+QGylpmrtBDr1RX7zjhnvrRUDuft6bfsv+OwlBCj0SspnONOyme8HP0pk5RP3osJ55FmiFi4Q4o9Iqebm/MbCb6+mui229XrPhnSksaa3hDloJWkY43eoeT9eSrfEWm33JXBLOyiG5KyaOJeJlOhKcq/zjGPEBt8KNiLr3WObX2KzVUc1gkNGHhDiBcnRzBJcH5/nvKbXe/Y9wVoMuIozcwnG7GLkJZLrgzXPV0Hd4IPIQ7A2tpNaZq2mY2S28y6elEkZGOB4iIIBo0iGj/fsXqFe2hqtUwyoQWLNwBhCset6sPq0U0GuIIzcMYhxEILctetKLxeIXo1CnN43l6oll3PVFXxdCt1MgjR4hefJGoUSPlSgkJRJMmyT4zV8JIer5Lrfg3p/6FHizcAYTeGLc7r8f2olENl2gU5tMBNFNUA7MQtDWqBw3BO9Qm5ZzD+dzxdF25blfGC3flfLo7DOXmEr36KlHHjuqF27UjWrKEqKDA6fVo/dA5E15nGSfscYceLNwBhrOsEncbENUffDN1xbe0BI85jERoWUoQRt+F/Z12DXhVmqyWXPN0be2PjZWy4gDnqXsWQfJkrrK6gJqpNfbQf+NfIrrlFvUPrHp1olGjNGegcbWtwtl1aB3P0vmHCS1YuCsxelLzEhLKRbVl/Uv0/eB3aFtkd8VYuHX529+IRo2i78atptYp5zV/ZPR2hNHyRD3ZO9BWBOvgFPVHFr2HQXQC9dQNqVKF6J57iFasIMrPt362aj+mrrRV6Hl70jqetTs9E1KwcFdi3B1kSQiiZPxB4zGHtqCztogLIY2/MWIEbRv+PrWKOkQCpbLd7oi2xz3u4mKiffvo+8Hv0NLwQZSDptonr1KF6K67iBYuJMrLkx3K2duGKymRerxlteMlJLhw/UylgoW7EuPusKb2QpGE0zQUb9OG6HulWIcTRbqMONqMLvQaRtNwvEHd8A3VwSkCzG55onrCMhYPOBwl1KleLn01cQPR3LlEw4YRdehAFBXl/KQ1ahA9+qh0sIsXVT9XZz8knh7cintHMva4ItxCKu9Z2rVrR9nZ2R4/LgOkpQG5uY7bjUbg2DH1eiYTMGwYkJ9fvi0mBli4EEh/sBDYsgX4+mtg0yYgOxsoLdVlTz6ikQsjcmHEKSTjDOrgLJJwETVxCfG4jOooQDSiq0diQmYk7r0vzKpVX/yvEO+8VoDLZwrQqPZlPHH/n+jU9CJw9ix+234audtPIcUsHT0Cxfo+oIgIoFMn4PbbpaV9e6BKFc0qJhMwYIDyPiEAs7m8XGam9PkLIV2GBetnma7PTNvjHT8OpKYC06e7Vp+pXAghdhNRO12F9Sq8Kwt73N6jonnDuhpEr1wh2riRaOpU2mC4m86itj6X2h9L/fpEffoQzZxJtHWrQzaIO5+nHi+aezsyngbscVdufOmp1aoFXLhASMYp3IS9aIWfcQMO4gYcRBMcRg1c8s6J7TiLRBzF35CD5hg8pznQogXQpg2QmGgt487novYGA7jnRTOMu7jicbNwhxiuiltYmDwkYE91XIIRuUjFcbSoeQa1S88g8vJZxOOSdYnCdVQ1FOIG4/XyikJIYY3oaGmpVg2oUQOoWROoVQvPzKuH/Rfq4g+k4Hc0wDVUBaAeElIKBQkBDB8OvPGG+rUPHKh+fVlZLNqM7+BQCaOIO2EWvdkUlkZTpXZOZ+dQy3N3xVZnEyKoHU+t9yJ3gGF8DTirhFHCnRQ8vUO6agm6Vl6ylkC7Ekd2lm2jlX7H2R1MIMDCzTig1cVaT/ds29l6EhLKxdTZNGLOfhg8lc/srCeis3ksuaGR8TeuCHeYN2M2TGBgif+qERYmLWlpUlmTSfrfsg2Q4spmM3D+vLSYzdK2ixedn//4cdf3Xbgg2aGX6dOlmLYSYWFS6FyJ1FQpjm25vmPHOK7NBD7cOBkCaGVO2BMRIfmixTZp01rZFXqOrZVjrlXfWW66PSNHAm+9pdzY6Op1MYyvcaVxkj3uEEDL47WnqEguboCUqZGZqVx++nTt48XEaJfR2ueK3YCUPTJ8uPK+oiIpccVolDxzo5FFmwleWLhDgNTUih8jN1cePrGEMdLTgYQE5Trh4c7FUau+O3avXau+7+JFDokwlQMW7hBg+nTJ87UlJkZdMJUQQhJvIunvsGHl4j1vnvLxly7VJ45q9W29cfu4u1r8W8tL98QPGMMEBHpbMV1ZOKsk8NCbK600yYNaRob92NuWKc7cndldLbPDlZxuZ/nces7HMP4AnA7I6EXPJA+u5G17IwfalfxztZlqbHPJeWQ+JhBxRbh1ZZUIIXoCmAcgHMC7RPSyVnnOKqlcuJKVArieDeIMtW73lpH77Luy9+olxbrVuvW7O8Iiw3gTj2aVCCHCASwAcDeA5gAeFUI0r5iJTDChFCPXwtVsEHvs49laOdiWHHXb+PvSpZLNao2QavZV1G6G8RV6GifbAzhCRL8RURGAFQD6eNcsJpBIT5eyQ8LD9ZWvSCOgkhBfvQoYDPJylsbLzEz5wFKAdvqiln3ceMkEC3qEux6AEzbrf5RtY0KI9HTJk3WGs7xtQDtDREmItXKw3fGe1bJsnNnNMIGCHuFW6kjsEHEUQgwTQmQLIbLz8vIqbhkTcGjlXAP68raVPGrb1EKtLvBKuOM9W94guDMOE6w4bZwUQnQC8G8iuqtsfRIAENEMtTrcOFl50TvNlxrOGgbV9qtNFQZoTMnGQswEEZ7u8r4LQGMhRAMhRASARwB8VhEDmeCloj0dnYU2lMIY9qINlMex2XtmQhGnwk1EJQBGA1gPIAfAR0R0wNuGMYGLnp6OajgLbSgJsdpLoUXseXQ/JtTQ1eWdiNYSURMi+hsRcRNOiFMRL1dPw6C9EBuNysfiLBAmVOGxShi3cNfLdUf0OQuEYeRU8bcBTOiRnu5aOMNS1lcz2zNMoMPCzQQFroo9w1RmOFTCMAwTZLBwMwzDBBks3AzDMEEGCzfDMEyQwcLNMAwTZOiaSMHlgwqRB8CFofcDgloAzvvbCB/D1xwa8DUHB0Yiqq2noFeEOxgRQmTrHeClssDXHBrwNVc+OFTCMAwTZLBwMwzDBBks3OUs9LcBfoCvOTTga65kcIybYRgmyGCPm2EYJshg4bZBCDFLCHFQCPGzEOJjIUS8v23yNkKIfkKIA0IIsxCi0rbCCyF6CiEOCSGOCCGe9bc9vkAIsUgIcU4Isd/ftvgCIUR9IcQmIURO2T09zt82eQsWbjkbAbQkolYADgOY5Gd7fMF+AA8A2OxvQ7yFECIcwAIAdwNoDuBRIURz/1rlE5YA6OlvI3xICYCniagZgI4ARlXW75mF2wYi2lA2VRsA7ACQ4k97fAER5RDRIX/b4WXaAzhCRL8RURGAFQD6+Nkmr0NEmwFc9LcdvoKIThPRj2X/X4U01WI9/1rlHVi41XkCwDp/G8F4hHoATtis/4FK+kAzEkKINABtAOz0ryXeIeQmUhBCfAWgjsKuTCL6tKxMJqTXLpMvbfMWeq65kiMUtnE6VSVFCFEVwGoA/ySiK/62xxuEnHAT0R1a+4UQGQD+AeB2qiS5ks6uOQT4A0B9m/UUAKf8ZAvjRYQQBkiibSKi//nbHm/BoRIbhBA9AUwEcC8R5fvbHsZj7ALQWAjRQAgRAeARAJ/52SbGwwghBID3AOQQ0Sv+tsebsHDLeR1AHICNQoi9Qoi3/G2QtxFC3C+E+ANAJwBfCCHW+9smT1PW4DwawHpIDVYfEdEB/1rlfYQQHwD4HkBTIcQfQojB/rbJy3QGMBBAj7Lnd68Qope/jfIG3HOSYRgmyGCPm2EYJshg4WYYhgkyWLgZhmGCDBZuhmGYIIOFm2EYJshg4WYYhgkyWLgZhmGCDBZuhmGYIOP/AVKxQskY2xvEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a22042b00>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'bo', label='Training sample')\n",
    "plt.plot(x_new, y_pred.reshape(-1, 1), 'r-', linewidth=3, label='Predicted curve')\n",
    "plt.legend(loc='upper left', fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Underfitting vs Overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Underfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Degree of polynoimial : 1\n",
    "x = x.reshape(-1, 1)\n",
    "y = y.reshape(-1, 1)\n",
    "simple_polynomial_regression = Pipeline(\n",
    "    [('poly_features', PolynomialFeatures(degree=1, include_bias=False)), \n",
    "     ('lin_reg', LinearRegression())]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a22179c50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a220e20b8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Underfitting\n",
    "x_train, x_val, y_train, y_val = train_test_split(x, y, test_size=0.3, random_state=10)\n",
    "train_errors, val_errors = [], []\n",
    "for i in range(1, len(x_train)):\n",
    "    simple_polynomial_regression.fit(x[:i], y[:i])\n",
    "    train_pred = simple_polynomial_regression.predict(x[:i])\n",
    "    val_pred = simple_polynomial_regression.predict(x_val)\n",
    "    train_errors.append(mean_squared_error(y[:i], train_pred))\n",
    "    val_errors.append(mean_squared_error(y_val, val_pred))\n",
    "plt.axis([0, 150, 0, 1.5])\n",
    "plt.plot(np.sqrt(train_errors), 'r-+', linewidth=2, label='Train errors')\n",
    "plt.plot(np.sqrt(val_errors), 'b--', linewidth=2, label='Test errors')\n",
    "plt.xlabel('Num of samples', fontsize=14)\n",
    "plt.ylabel('RMSE', fontsize=14)\n",
    "plt.legend(fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Overfitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Degree of polynoimial : 10\n",
    "x = x.reshape(-1, 1)\n",
    "y = y.reshape(-1, 1)\n",
    "high_polynomial_regression = Pipeline(\n",
    "    [('poly_features', PolynomialFeatures(degree=10, include_bias=False)), \n",
    "     ('lin_reg', LinearRegression())]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a2225ec50>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a22167668>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Underfitting\n",
    "x_train, x_val, y_train, y_val = train_test_split(x, y, test_size=0.3, random_state=10)\n",
    "train_errors, val_errors = [], []\n",
    "for i in range(1, len(x_train)):\n",
    "    high_polynomial_regression.fit(x[:i], y[:i])\n",
    "    train_pred = high_polynomial_regression.predict(x[:i])\n",
    "    val_pred = high_polynomial_regression.predict(x_val)\n",
    "    train_errors.append(mean_squared_error(y[:i], train_pred))\n",
    "    val_errors.append(mean_squared_error(y_val, val_pred))\n",
    "plt.axis([0, 150, 0, 1.5])\n",
    "plt.plot(np.sqrt(train_errors), 'r-+', linewidth=2, label='Train errors')\n",
    "plt.plot(np.sqrt(val_errors), 'b--', linewidth=2, label='Test errors')\n",
    "plt.xlabel('Num of samples', fontsize=14)\n",
    "plt.ylabel('RMSE', fontsize=14)\n",
    "plt.legend(fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}