{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c000",
   "metadata": {},
   "source": [
    "# L2 In-Class Activity: Gradient Descent Solutions\n",
    "\n",
    "### E190BO — Fall 2026\n",
    "\n",
    "This is the **Exercise** from the L2 slides, made executable. Same model, same loss,\n",
    "same three parts:\n",
    "\n",
    "> **Model**: $\\hat{y}_i = a x_i + b$\n",
    "> **Loss**: $\\text{MSE} = \\dfrac{1}{N} \\sum_{i=1}^{N} (y_i - \\hat{y}_i)^2$\n",
    ">\n",
    "> (a) Derive the gradient   (b) Implement in this notebook   (c) Plot MSE vs iteration for several $\\gamma$\n",
    "\n",
    "The data is `testScores.csv`: 25 students, three midterm scores and a final exam score.\n",
    "We will use **midterm 1 only** to predict the final.\n",
    "\n",
    "Work with a partner. Get through (a)-(c); the challenges at the end are there if you finish early."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c001",
   "metadata": {},
   "source": [
    "## Setup (provided — just run it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c002",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 25 students\n"
     ]
    },
    {
     "data": {
      "image/png": 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pXr16jtsJhPKgNUGeC6lja0RjjZXORaUzcOcW8dqVk8vn5LI5vXyUzb64d+65b0eOHDEVGZ7v8ZwQCOXB0xymQVC0BkLa7VXPzWlfNk4vn5PL5vTyUTb74t65777F5DFvnrP+OgEAAOQDgRAAAHAtAiEAAOBaBEIAAMC1CIQAAIBr2SoQWrp0qfTo0cMMjqRZ4HPnzs11/yVLlpj9si6pqakRO2cAABC9bBUIHTt2TJo2bSpTpkzJ1+u2bNkiKSkp3kVndAYAALDVOELdu3c3S35p4FO2bNmwnBMAALAvWwVCBdWsWTM5efKkNGrUSJ555hm55JJLctxX99PFd2RKz2BOukQbPSedTyUazy0UnFw+J5fN6eWjbPbFvXPPfcsMcl9HB0JVq1aVadOmSatWrUxwM336dOnQoYOsWLFCWrRoEfA1o0ePluHDh2dbr0N766iW0UZvdFpamvmAOG30XqeXz8llc3r5KJt9ce+iR2amJb/sS5e0E6cloUQxubBKaYmNjQnZfdMJV4MRY+lRbUiTnj/++GO5/vrr8/W6yy+/XGrWrClvv/120DVCOlfJoUOHonaKDafO5+T08jm5bE4vH2WzL+5ddFiwMVVGfvazpKb9r4IhMSFenr6moXS9KDFkc42VK1fOBFC5fX87ukYokNatW8t3332X4/a4uDizZKUXPlr/mGtQGM3nd66cXD4nl83p5aNs9sW9K1zzN6TIX2etkf/UwvyvBigl7aRZP/WOFtKtUdVzvm9B7ycus3btWtNkBgAAIutspiXD5/383yDIn2edbtf9IsVWNUJHjx6VrVu3ep/v2LHDBDbly5c3zV1DhgyRPXv2yFtvvWW2T5w4UZKSkuSiiy4y+T2aI7R48WL56quvCrEUAAC408odByXFpzksKw1/dLvu1za5QkTOyVaB0E8//SQdO3b0Ph8wYID52bt3b5k5c6YZI2j37t3e7adOnZKBAwea4KhkyZLSpEkT+frrr/2OAQAAImN/ekZI93NdIKQ9vnLL7dZgyNegQYPMAgAACl/l0vEh3S8UXJcjBAAACkfrpPJSNSHeJ0Xan67X7bpfpBAIAQCAiCgSGyPDejQ0j7MGQ57nul33ixQCIQAAEDHaNV67yOu4Qb70eU5d58PJVjlCAADA/ro1qiqdGyaa3mGaGK05QdocFsmaIA8CIQAAEHEa9ESqi3xuaBoDAACuRSAEAABci6YxAABg6NQWkcrbieR75YZACAAAiE6GqvN8+U6BoWP6aHf2UPfkiuR75YWmMQAAXG7+hhTp/87qbPOApaZlmPW63Y7vFQwCIQAAXOxsBGeEj8bZ5wmEAABwsZX5mBHeTu8VLAIhAABcbH8EZ4SPxtnnCYQAAHCxyhGcEZ7Z5wEAgGtnhG/N7PMAAMCtM8IXYfZ5AADg5hnhuzH7PAAAcPOM8N2YfR4AALh5RvgizD4PAABQuOg+DwAAXItACAAAuBaBEAAAcC0CIQAA4FoEQgAAwLUIhAAAgGsRCAEAANciEAIAAK5FIAQAAFyLQAgAALiWrQKhpUuXSo8ePaRatWoSExMjc+fOzfM1S5YskRYtWkhcXJzUrVtXZs6cGZFzBQAA0c9WgdCxY8ekadOmMmXKlKD237Fjh1x99dXSsWNHWbt2rTz88MNyzz33yIIFC8J+rgAAIPoVFRvp3r27WYI1bdo0SUpKknHjxpnnDRo0kO+++04mTJggXbt2DeOZAgBgP2czLVm546DsT8+QyqXjpXVSeTNLvJPZKhDKr2XLlkmnTp381mkApDVDAADgf+ZvSJHh836WlLQM77qqCfEyrEdD6daoqmMvlaMDodTUVKlSpYrfOn1+5MgROXHihJQoUSLba06ePGkWD91XZWZmmiXa6DlZlhWV5xYKTi6fk8vm9PJRNvvi3gW2YGOqPDBrtVhZcmb2p52Q+99ZJX+/vYV0vShR7HTfgt3X0YFQQYwePVqGDx+ebf2BAwckI+N/UXK00BudlpZmPiCxsbZK+RK3l8/JZXN6+SibfXHvAl0TS2YvWS/1y2kYlJ02jOn2phViJLaQmskKct/S09OD2s/RgVBiYqLs27fPb50+L1OmTMDaIDVkyBAZMGCAX41QjRo1pFKlSuZ10UY/HNqDTs/PaV82Ti+fk8vm9PJRNvvi3mW3fPtB+X7P6f+GPDk4dFp2Hi8mF9cpL3a5b/Hx8UHt5+hAqG3btvLFF1/4rVu4cKFZnxPtZq9LVnrho/WPuX44ovn8zpWTy+fksjm9fJTNvrh3/g4cPSmZuQVBPvsV5u9yfu9b0PuJjRw9etR0g9fF0z1eH+/evdtbm3PXXXd597/vvvtk+/btMmjQINm8ebO8/PLL8sEHH8gjjzxSaGUAACCaVCwVF9L97MZWNUI//fSTGRPIw9OE1bt3bzNQYkpKijcoUtp1/vPPPzeBz0svvSTVq1eX6dOn03UeAMLIjV2wbS0mxPvZjK0CoQ4dOphEqZwEGjVaX7NmzZownxkAwM1dsO3s96MnQ7qf3diqaQwAEN1BUP93VvsFQSo1LcOs1+2IPpVLx4d0P7shEAIAhKQ5TGuCAtXZe9bpdt0P0aV1UnlTa5dTy5eu1+26nxMRCAEAzpnmBGWtCfKl4Y9u1/0QXYrExpimS5U1GPI81+1OzfMiEAIAnDNNjA7lfoisbo2qytQ7Wkhign/zlz7X9U7O77JVsjQAIDq5Pc/ECbo1qiqdGya6rscfgRAAIGR5JpoYHSgLKOa/tQtOzTNxiiKxMdI2uYK4CU1jAIBz5vY8E9gXgRAAICTcnGcC+6JpDAAQMm7NM4F9EQgBAELKjXkmBcFUJNGBQAgAgAhjKpLoQY4QAAARxFQk0YVACACACGEqkuhDIAQAQIQwFUn0IRACACBCmIok+hAIAQAQIUxFEn0IhAAAiPBUJDmNqqTrdTtTkUQOgRAAABHCVCTRh0AIAIAIYiqS6MKAigCAQuHkkZXzKhtTkUQPAiEAQMQ5eWTlYMvGVCTRgaYxAEBEOXlkZSeXzakIhAAAEePkkZWdXDYnIxACAESMk0dWdnLZnIxACAAQMU4eWdnJZXMyAiEAQMQ4eWRlJ5fNyeg1BgAuEC1d1T0jK2vycKBMGT2jxEIaWTnYa5TTftFcNuSMQAgAHC6auqp7RlbWHlQaGPgGDJ6QQ7dHOkgL9hrltV80lg25o2kMABwsGrtzR9vIysFeo2D2i7ayIW/UCAGAQ+XVnVvrJXR754aJEa+liJaRlYO9RlfUrxL0tYyWsiE4BEIA4FD56c7dNrmCRFo0jKwc7DV6e9nOfF3LaCgbHNo0NmXKFKldu7bEx8dLmzZtZOXKlTnuO3PmTImJifFb9HUA4AZ05w7dNdp18HhIrzmih60Coffff18GDBggw4YNk9WrV0vTpk2la9eusn///hxfU6ZMGUlJSfEuu3btiug5A0BhoTt36K5RrfIlQ3rNET1sFQiNHz9e+vXrJ3fffbc0bNhQpk2bJiVLlpQ33ngjx9doLVBiYqJ3qVKlSkTPGQAKi6c7d06ZKbq+qsu7cwd7je5sW5tr6VC2yRE6deqUrFq1SoYMGeJdFxsbK506dZJly5bl+LqjR49KrVq1JDMzU1q0aCHPPfecXHTRRTnuf/LkSbN4HDlyxPzU1+sSbfScLMuKynMLBSeXz8llc3r57FI2/RIfek0DeWDWavM8UHdu3R4jWhbLVmUrqKzlC/YaFY3N/7WMNCffu8wClC3YfW0TCP3+++9y9uzZbDU6+nzz5s0BX1OvXj1TW9SkSRNJS0uTF198Udq1aycbN26U6tWrB3zN6NGjZfjw4dnWHzhwQDIyoq/tV2+0lk0/IBoYOo2Ty+fksjm9fHYqW/NKsTLphjry3spf5eDxU9715UsWl1tb1zDbfdML7FS2gghUvmCvUX6vZaQ5+d5lFqBs6enpQe0XY+lRbWDv3r1y/vnnyw8//CBt27b1rh80aJB8++23smLFijyPcfr0aWnQoIHcdtttMnLkyKBrhGrUqCGHDh0y+UbR+OHQIK1SpUqO++A7vXxOLpvTy2fHsmk38R93HpID6RlSqXS8/Kl2uYDdue1YtvzIrXzBXqNg94s0J9+7zAKUTb+/y5UrZwKo3L6/bVMjVLFiRSlSpIjs27fPb70+19yfYBQrVkyaN28uW7duzXGfuLg4s2SlFz5aP1iaBxXN53eunFw+J5fN6eWzW9n0NNvVrejIsuVXTuUL9hrl51pGmpPvXUw+yxb0fmITxYsXl5YtW8qiRYv8IkR97ltDlBttWlu/fr1UrcrIngAAwEY1Qkq7zvfu3VtatWolrVu3lokTJ8qxY8dMLzJ11113meYzzfNRI0aMkIsvvljq1q0rhw8flrFjx5ru8/fcc08hlwQAAEQDWwVCt9xyi2kjHDp0qKSmpkqzZs1k/vz53gTq3bt3+1WFaV6PdrfXfbWdUGuUNMdIu94DAADYKhBSDzzwgFkCWbJkid/zCRMmmAUAAMDWOUIAAAChRiAEAABci0AIAAC4FoEQAABwLQIhAADgWgRCAADAtQiEAACAaxEIAQAA1yIQAgAArkUgBAAAXItACAAAuBaBEAAAcC0CIQAA4FoEQgAAwLUIhAAAgGsRCAEAANcKWSB0+PBhmT17dqgOBwAAYJ9AaNeuXXLnnXeG6nAAAABhR9MYAABwLQIhAADgWgRCAADAtYoGu+OkSZNy3b5nz55QnA8AAED0BUITJkzIc5+aNWue6/kAAABEXyC0Y8eO8J4JAKBQnc20ZMX2g3Jg/x9S6WhRaVOnghSJjeGuwNGCDoSCGUfonXfekQceeCBUhwQARMj8DSkyfN7Psi/thDQoZ8mmQzukSkIJGdajoXRrVJX7AMc652TpRYsWSa9evaRq1aoybNiw0JwVACCiQVD/d1ZLSlqG3/rUtAyzXrcDTlWgQOjXX3+VESNGSFJSknTp0kViYmLk448/ltTU1NCfIQAgrM1hWhNkBdjmWafbdT/A1YHQ6dOn5cMPP5SuXbtKvXr1ZO3atTJ27FiJjY2VJ598Urp16ybFihUL79kCAEJq5Y6D2WqCfGn4o9t1P8DVOULnn3++1K9fX+644w557733pFy5cmb9bbfdFs7zAwCE0f70jJDuBzi2RujMmTOmCUyXIkWKhPesAAARUbl0fEj3AxwbCO3du1fuvfdeeffddyUxMVFuuukmkxekgREAwJ5aJ5WXqgnxktNfcl2v23U/wNWBUHx8vNx+++2yePFiWb9+vTRo0ED+9re/mZqiUaNGycKFC+Xs2bPhPVsRmTJlitSuXducT5s2bWTlypW57q95Tdqkp/s3btxYvvjii7CfIwDYhY4TpF3kVdZgyPNctzOeEJyqQL3GkpOT5dlnn5Vdu3bJ559/LidPnpRrrrlGqlSpIuH0/vvvy4ABA0w3/dWrV0vTpk1N8vb+/fsD7v/DDz+YHKa+ffvKmjVr5PrrrzfLhg0bwnqeAGAnOk7Q1DtaSGKCf/OXPtf1jCMEJ4uxLCskfSIPHDggb7/9tglUwkVrgP70pz/J3//+d/M8MzNTatSoIQ8++KAMHjw42/633HKLHDt2TD777DPvuosvvliaNWsm06ZNC+o9jxw5IgkJCZKWliZlypSRaKPXQAPBypUrmx58TuPk8jm5bE4vn1PL9p+Rpf+QA/v3SaXKVRw5srRT752ibAX7/g7ZyNKVKlUKaxB06tQpWbVqlQwZMsS7Tj/EnTp1kmXLlgV8ja7Pek5agzR37twc30drt3TxvZCeD5gu0UbPSWPZaDy3UHBy+ZxcNqeXz6ll05Cnde2ycqDUaalUqazEiJbRWeMHOfXeKcrmL9h7HHQgpIMn5pUYrdu3bdsm4fD777+bHKSszW/6fPPmzQFfowM8Bto/t4EfR48eLcOHDw9Y45WREX3dR/VGa7Srv9hO+9+N08vn5LI5vXyUzb64d/ZUkPuWnp4e2kDo4YcfznHbzp075ZVXXvGrSbErrXHyrUXSGiFtftMar2htGtMAVM/PaV82Ti+fk8vm9PJRNvvi3rnnvsXHx4c2EHrooYeyrTt48KCMHDlSpk6davJ3xowZI+FSsWJFM37Rvn37/Nbrc+3OH4iuz8/+Ki4uzixZ6YWP1j/m+uGI5vM7V04un5PL5vTyUTb74t65477FBrtfQU7mxIkTpsu89h775ptvZM6cOfLtt9+aRORwKV68uLRs2dJM8uobIerztm3bBnyNrvfdX2k3/5z2BwAA7pKvZGnN0XnttddMDo1WOU2aNMlMuRGpQRW1yap3797SqlUrad26tUycONH0Crv77rvN9rvuustMBaJ5Pp5arMsvv1zGjRsnV199tZka5KeffpJXX301IucLAAAcEgh98MEH8tRTT8nhw4fNJKv9+/c3tTSRpN3hNWl56NChJuFZu8HPnz/fmxC9e/duv6qwdu3ayezZs815P/HEE3LBBReYHmONGjWK6HkDAACbjyOkAUaJEiXMAIW5JQ2PHz9enIRxhAoX42LYF/cu+sYI0hnkdfJUnTdMp8wINEaQk++b08tH2cI8jlD79u3z7B7PvGMAEH3mb0iR4fN+lpS0/w0BovOH6dQZjBoNtws6EFqyZEl4zwQAEJYgqP87qyVr1X9qWoZZzxQacDtn1QsCAPyaw7QmKFD+g2edbtf9ALcKukYo2OkznJYjBAB2pTlBvs1hWWn4o9t1v7bJFSJ6boDtAiGdvT0v5AgBQPTQxOhQ7ge4OhDSgRMBAPahvcNCuR/g6hwhJ87UCwBOpl3ktXdYTkPe6nrdrvsBbhV0IFSsWDEz9oLHY489ZuYaAwBEJx0nSLvIq6zBkOe5bg80nhDgFkEHQlnHXdTZ5nWUaQBA9NJxgrSLfGKCf/OXPqfrPJDPucZ8BTkgNQAgCoKhzg0TgxpZGnCbAgdCAAD70KCHLvLAOQZCOtlpyZIlzeNTp07JqFGjzDwevhhHCAAA2EW+5hrbsmWL38zu27dv99uHcYQAAICdMNcYAABwLeYaAwAArkUgBAAAXItACAAAuBaBEAAAcC0CIQAA4FpB9Rpbt25d0Ads0qTJuZwPAABAdAVCzZo1M2ME6bQaeY0VdPbs2VCdGwAAQOE3je3YscMMnqg/P/roI0lKSpKXX35Z1qxZYxZ9nJycbLYBAAA4qkaoVq1a3sc9e/aUSZMmyVVXXeXXHFajRg15+umn5frrrw/PmQIAABR2svT69etNjVBWuu7nn38O1XkBAABEXyDUoEEDGT16tJl01UMf6zrdBgBOdjbTkuXbD8qK7X+Yn/rcKZxcNiAks8+radOmSY8ePaR69ereHmLaq0yTqOfNm5ffwwGAbczfkCLD5/0s+9JOSINylmw6tEOqJJSQYT0aSrdGVcXOnFw2IKQ1Qq1btzaJ088++6wJhHQZNWqUWafbAMCJNFDo/85qSUnL8FufmpZh1ut2u3Jy2YCQ1wipUqVKyb333luQlwKA7WgTkdaWBGoo0nU6qIhu79wwUYrE5j7ESLRxctmAsI0s/fbbb8ull14q1apVk127dpl1EyZMkE8++aQghwOAqLZyx8FstSVZAwbdrvvZjZPLBoQlEJo6daoMGDBAunfvLocOHfIOoFiuXDmZOHFifg8HAFFvf3pGSPeLJk4uGxCWQGjy5Mny2muvyZNPPilFi/6vZa1Vq1ama324HDx4UG6//XYpU6aMlC1bVvr27StHjx7N9TUdOnQwSdy+y3333Re2cwTgTJVLx4d0v2ji5LIBYQmEdHTp5s2bZ1sfFxcnx44dk3DRIGjjxo2ycOFC+eyzz2Tp0qVB5Sn169dPUlJSvMsLL7wQtnME4Eytk8pL1YR4ky8TiK7X7bqf3Ti5bEBYAiEdOHHt2rXZ1s+fPz9s4wht2rTJHH/69OnSpk0bk5+kNVPvvfee7N27N9fXlixZUhITE72L1igBQH5okrB2I1dZAwbPc91ux2RiJ5cNCEsgpPlB999/v7z//vtmEtaVK1ea7vNDhgyRQYMGSTgsW7bMNIdp85tHp06dJDY2VlasWJHra2fNmiUVK1aURo0amXM8fvx4WM4RgLPpWDpT72ghiQn+TUT6XNfbeawdJ5cNCHn3+XvuuUdKlCghTz31lAkqevXqZXqPvfTSS3LrrbdKOKSmpkrlypX91ml+Uvny5c22nOi56Txpen466OPjjz8uW7ZskTlz5uT4mpMnT5rF48iRI+ZnZmamWaKNnpMGpNF4bqHg5PI5uWyhKp927f5x5yE5kJ4hlUrHy59qlyvUmokuDavIlfUrmx5Uv+/fJxUrVzFNRnpO4biPkSx/pMtWWJz8e0fZ/AV7j4sWNF9HFw2ENGE5a5ASrMGDB8uYMWPybBYrKN8cosaNG0vVqlXlyiuvlG3btklycnLA1+hUIcOHD8+2/sCBA5KREX29JvRGp6WlmV9srSFzGieXz8llC0X5Vu06KO+t/FUOHv/fdD7lSxaXW1vXkJa1CjdfJalUppQvX0QSSp2WP34/EJb3KKzyR6JshcnJv3eUzV96erqEJRAaMWKEydG54oorTP6NLkoTpceNGydDhw4N+lgDBw6UPn365LpPnTp1TG7P/v37/dafOXPG9CTTbcHS/CK1devWHAMhbT7T5j/fGqEaNWpIpUqVojK/SD/42htOz89pv9ROL5+Ty3au5VuwMVX+9vH2/w7y978akJhDp+WHj7fL328vK10vCv533273rjDLz+fSvpx87zILULb4+PjwBELPPPOMFCtWzNSc+AYMWjOkNSn5CYS0QLrkpW3btnL48GFZtWqVtGzZ0qxbvHixuTCe4CYYniRvrRnKifZ+0yUrvfDR+sHSD0c0n9+5cnL5nFy2gpZPm4NGfLZJzubQj0nX6vYuF1Ut1GaycN27aCg/n0v7cvK9i8ln2YLeryAn89Zbb8lzzz0nd999t98s9OGivdG6detmusJrcvb3338vDzzwgMlJ0vwftWfPHqlfv77ZrrT5a+TIkSZ42rlzp3z66ady1113Sfv27b2TxQKw/0jHGjgs2/aHfLJ2j/lp9xnTGekZiKwC5Qh17NjR9NbSWeh10MK5c+dKuGnvLw1+NMdHo7ybbrpJJk2a5N1++vRpkwjt6RVWvHhx+frrr81o19psp81b+hpN8gbgjJGOPTOm+wZOOuaNnWdMZ6RnIMoDIa2aUppjs3z5crn55ptNc9W0adMknLSH2OzZs3PcXrt2bZP85qGBz7fffhvWcwIQesGOYLzz9+My8etfsk0W6pkx3a7dvhnpGYisfDeN+QYbmjz8xRdfyA033CDXX399qM8NgAsFM9JxYpk4eXfl7hxnTFdaU2THZrJwjfTstCZEoNBqhGbMmCEJCQne59pMpU1UOu2GTnsBAKEY6VhrdfRL3/fr2hMc3Na6pkz4+t9B5RG1Ta7guPLnd6RnJzYhAoVWI9S7d++Avao0cVqDJAAI90jHtSuWcvSM6aEc6VmDIA2qsiage5oQdTvgZkHVCGmNjw5OqH3yfROUA+UPPfjgg6E8PwAupV/2nRsmmlodDWg0d8Yz0rE27Th9xvTcyh8sbf7SmqCcmhD1SLpd34e5xOBWQQVCEyZMMCNJayCkj3NCIAQglPTLOVDTliePRms1rJzyiBwwY3pO5Q9HV3y7NSECEQ2EduzYEfAxADglj8aJ6IoP5M15Q08CcAVmTM8bXfGBENUI+U6lkZfx48cHvS8AFHYejZO5pQkRCHsgtGbNGr/nq1evNpOe1qtXzzz/5ZdfpEiRIt55wADALnk0TkYTIhCiQOibb77xq/EpXbq0vPnmm1KuXDmz7tChQ6b7/GWXXRbM4QAAEW5CzDqOkNYEMY4QUIABFceNGydfffWVNwhS+vjZZ5+VLl26yMCBA7muABBFaEIEQhgIHTlyRA4cOJBtva5LT0/P7+EAABFAEyIQol5jOq+YNoPNmTNHfvvtN7N89NFH0rdvX7nxxhvzezgAAAD71AjpLPOPPvqo9OrVS06fPv2fgxQtagKhsWPHhuMcAQAACj8QOnv2rPz0008yatQoE/Rs27bNrE9OTpZSpYKb+wcAAMCWgZB2kdeE6E2bNklSUpI0adIkfGcGAAAQbTlCjRo1ku3bt4fnbAAAAKI5ENJu8poj9Nlnn0lKSorpRea7AAAAODZZ+qqrrjI/r732WjPbvIdlWea55hEBgFOdzbRkxfaDcmD/H1LpaFFpU6cCU3oAbgqEfEeZBgA3mb8hxYzQvC/thDQoZ8mmQzukSkIJRmgG3BQIXX755eE5EwCI8iCo/zurzeSlvjkFOqGprtdpLHQEZwAOD4Q8jh8/Lrt375ZTp075racnGYBQNkPlNbN8MPuE4jy0JijQDO66Tt9Nt3dumEgzGeD0QEin0tCRpb/88suA28kRAhDKZijfiUKrZpkoNJh9QkEDLd/3CBQM6Xbdr21yhZC9L4Ao7DX28MMPy+HDh2XFihVSokQJmT9/vpmJ/oILLpBPP/00PGcJwJXNUFmDD08zlG4PZp9Q0dqmUO4HwMY1QosXL5ZPPvlEWrVqJbGxsVKrVi3p3LmzlClTRkaPHi1XX311eM4UgCsE0wz1zKcbzaNINVVpk1so9wNg4xqhY8eOSeXKlc3jcuXKeWeib9y4saxevTr0ZwjAVYJphko9clJSjwTXVBUKmnekTW45hVS6XrfrfgAcHgjVq1dPtmzZYh43bdpUXnnlFdmzZ4+ZjLVqVXpMADg3oWxeCtWxtFZJ845U1mDI81y3hzpJG0AUBkIPPfSQGVFaDRs2zCRN16xZUyZNmiTPPfdcOM4RgIuEsnkplMfS5GvtIp+Y4H9MfU7XecBFOUJ33HGH93HLli1l165dsnnzZhMMVaxYMdTnB8BlPM1QmvQcKAdI61yqlIkzj/YdyXmfxDA0VWkwpHlHK7b/IQf275NKlaswsjTgthqhrEqWLCktWrQgCAIQsWaoZ669SJ65tnCaqvSYF9cpbwIg/UlzGOCCGqEBAwYEfcDx48efy/kAgLcZKusYQYlZxggKZh8AOOdAaM2aNX7PtXfYmTNnTOK0+uWXX6RIkSKmqSxcRo0aJZ9//rmsXbtWihcvbsYyyotOBKt5TK+99prZ/5JLLpGpU6eaMY8ARDdPM1Ruo0YHsw8AnHMg5DvRqtb4lC5d2gyiqN3n1aFDh8xo05dddpmEi07l0bNnT2nbtq28/vrrQb3mhRdeMEnceq5JSUny9NNPS9euXeXnn3+W+HjG+wCinQY0eY3UHMw+ABCyZOlx48bJV1995Q2ClD5+9tlnpUuXLjJw4EAJh+HDh5ufM2fODGp/rQ2aOHGiPPXUU3LdddeZdW+99ZZUqVJF5s6dK7feemtYzhMAADg4EDpy5Ih3EEVfui49PV2ixY4dOyQ1NVU6derkXZeQkCBt2rSRZcuW5RgInTx50iy+5VWZmZlmiTZ6Thr0ReO5hYKTy+fksjm9fJTNvrh37rlvmUHum+9A6IYbbjDNYFoz1Lp1a7NO5x177LHH5MYbb5RooUGQ0hogX/rcsy0QnSbEU/uUNdDLyIi+eYT0RqelpZkPiE554jROLp+Ty+b08lE2++Leuee+pQdZOZPvQEhHkH700UelV69ecvr06f8cpGhR6du3r4wdOzZfxxo8eLCMGTMm1302bdok9evXl0gZMmSIXy85rRGqUaOGVKpUycynFo0fjpiYGHN+TvuycXr5nFw2p5ePstkX98499y0+yFzgogUZN+jll182Qc+2bdvMuuTkZClVqlR+D2Xyifr06ZPrPnXq1JGCSExMND/37dvnN/WHPm/WrFmOr4uLizNLVnrho/WPuX44ovn8zpWTy+fksjm9fJTNvrh39pTf+xbsfvkOhDw08GnSpImcC43sdAkH7SWmwdCiRYu8gY/W7mgzXv/+/cPyngAAwF6KFmT2+eeff94EGPv378+WjLR9+3YJh927d8vBgwfNz7Nnz5rxhFTdunXlvPPOM4+1CU1zfDSPSSPHhx9+2PRm03GDPN3nq1WrJtdff31YzhEAADg8ELrnnnvk22+/lTvvvNM0OWnAEQlDhw414wF5NG/e3DvGUYcOHczjLVu2mGQqj0GDBpnA7d577zUDKl566aUyf/58xhACAAAFC4R0tnkd4VlHaY4kHT8orzGENJvclwZpI0aMMAsAAEBW+c5g1METy5cP7YzOAAAAtgiERo4caZqpjh8/Hp4zAgAAiOYpNrTbvA5MWLt2bSlWrFi2CVkBAAAcGQjR4woAALg2EBo2bFh4zgQAACDCnDfcKwAAQLhqhHQwwwkTJsgHH3xgBjc8deqU33Yd9BAAAMCRNUI6M/v48ePllltuMYMX6gSlOuu8zunxzDPPhOcsAQAAoiEQmjVrlrz22mtmwlSddf62226T6dOnmy71y5cvD8c5AgAAREcglJqaKo0bNzaPdY4vz5QW11xzjRlxGgAAwLGBUPXq1SUlJcU8Tk5Olq+++so8/vHHHyUuLi70ZwgAABAtgZDO7K4zz6sHH3zQzOius7vfdddd8uc//zkc5wgAABAdvcaef/5572NNmK5Vq5b88MMPJhjq0aNHqM8PAAAgegKhpUuXSrt27UyitLr44ovNcubMGbOtffv24ThPAACAwm8a69ixY8CxgjRpWrcBAAA4NhCyLEtiYmKyrf/jjz+kVKlSoTovAACA6Gka00ETlQZBffr08eshpqNNr1u3zjSZAQAAOC4QSkhI8NYIlS5dWkqUKOHdVrx4cZMn1K9fv/CcJQAAQGEGQjNmzDA/a9euLY8++ijNYAAAwH05QoMGDfLLEdq1a5dMnDjRO7AiAACAYwOh6667Tt566y3z+PDhw9K6dWsZN26cWT916tRwnCMAAEB0BEKrV6+Wyy67zDz+xz/+IYmJiaZWSIOjSZMmheMcAQAAoiMQOn78uEmWVtocpr3JYmNjTbK0BkQAAACODYTq1q0rc+fOlV9//VUWLFggXbp0Mev3798vZcqUCcc5AgAAREcgNHToUNNrTHuPtWnTRtq2beutHWrevHk4zhEAACA65hr7v//7P7n00kslJSVFmjZt6l1/5ZVXmpnpAQAAHBsIKU2Q1sWX9h4DAABwdNMYAACAUxAIAQAA1yIQAgAArkUgBAAAXMs2gdCoUaOkXbt2UrJkSSlbtmxQr+nTp4+ZF8136datW9jPFQAAOLjXWGE4deqU9OzZ04xb9Prrrwf9Og18ZsyY4X0eFxcXpjMEAAB2Y5tAaPjw4ebnzJkz8/U6DXyydvUHAACwVSBUUEuWLJHKlStLuXLl5IorrpBnn31WKlSokOP+J0+eNIvHkSNHzM/MzEyzRBs9J8uyovLcQsHJ5XNy2ZxePspmX9w799y3zCD3dXQgpM1iOilsUlKSbNu2TZ544gnp3r27LFu2TIoUKRLwNaNHj/bWPvk6cOCAZGRkSLTRG52WlmY+IDr5rdM4uXxOLpvTy0fZ7It75577lp6eHv2B0ODBg2XMmDG57rNp0yapX79+gY5/6623eh83btxYmjRpIsnJyaaWSKcECWTIkCEyYMAAvxqhGjVqSKVKlaJyUln9cGgSuJ6f075snF4+J5fN6eWjbPbFvXPPfYuPj4/+QGjgwIGmZ1du6tSpE7L302NVrFhRtm7dmmMgpDlFgRKq9cJH6x9z/XBE8/mdKyeXz8llc3r5KJt9ce/ccd9ig9yvUAMhjex0iZTffvtN/vjjD6latWrE3hMAAEQv2/w3bffu3bJ27Vrz8+zZs+axLkePHvXuo01oH3/8sXms6x977DFZvny57Ny5UxYtWiTXXXed1K1bV7p27VqIJQEAANHCNsnSQ4cOlTfffNP7vHnz5ubnN998Ix06dDCPt2zZYpKplCZDr1u3zrzm8OHDUq1aNenSpYuMHDmSsYQAAIC9AiEdPyivMYQ0m9yjRIkSsmDBggicGQAAsCvbNI0BAACEGoEQAABwLQIhAADgWgRCAADAtQiEAACAaxEIAQAA1yIQAgAArkUgBAAAXItACAAAuBaBEAAAcC0CIQAA4FoEQgAAwLUIhAAAgGsRCAEAANciEAIAAK5FIAQAAFyLQAgAALgWgRAAAHAtAiEAAOBaBEIAAMC1CIQAAIBrEQgBAADXIhACAACuRSAEAABci0AIAAC4FoEQAABwLQIhAADgWgRCAADAtQiEAACAaxUt7BNwo7OZlqzccVD2p2dI5dLx0jqpvBSJjSns0wIAwHVsUSO0c+dO6du3ryQlJUmJEiUkOTlZhg0bJqdOncr1dRkZGXL//fdLhQoV5LzzzpObbrpJ9u3bJ4Vp/oYUuXTMYrntteXy0HtrzU99rusBAEBk2SIQ2rx5s2RmZsorr7wiGzdulAkTJsi0adPkiSeeyPV1jzzyiMybN08+/PBD+fbbb2Xv3r1y4403SmHRYKf/O6slJS3Db31qWoZZTzAEAEBk2aJprFu3bmbxqFOnjmzZskWmTp0qL774YsDXpKWlyeuvvy6zZ8+WK664wqybMWOGNGjQQJYvXy4XX3yxRLo5bPi8n8UKsE3XacOYbu/cMJFmMgAAIsQWNUI5BTrly5fPcfuqVavk9OnT0qlTJ++6+vXrS82aNWXZsmUSaZoTlLUmKGswpNt1PwAAEBm2qBHKauvWrTJ58uQca4NUamqqFC9eXMqWLeu3vkqVKmZbTk6ePGkWjyNHjpif2jSnS0HtP3JCYgPWB2XfLz/vo/talnVO5xbNnFw+J5fN6eWjbPbFvXPPfcsMct9CDYQGDx4sY8aMyXWfTZs2mZocjz179phmsp49e0q/fv1Cfk6jR4+W4cOHZ1t/4MABk3xdUAlyXBqUs4Lab//+/fm60Vo7ph+Q2FjbVvC5snxOLpvTy0fZ7It75577lp6eHv2B0MCBA6VPnz657qP5QB6a7NyxY0dp166dvPrqq7m+LjEx0fQqO3z4sF+tkPYa0205GTJkiAwYMMCvRqhGjRpSqVIlKVOmjBRUhYqV5In5u2VfWkbAeiHNEaqSEC+XNE7OV46QfjhiYmLM+Tnty8bp5XNy2ZxePspmX9w799y3+Pj46A+EtEC6BENrgjQIatmypUl6zutC6H7FihWTRYsWmW7zShOsd+/eLW3bts3xdXFxcWbJSt/vXP6Y60uH9rjI9A5TvsFQzH+f6/ZiRYvk+9j64TjX84tmTi6fk8vm9PJRNvvi3rnjvsUGu5/YgAZBHTp0MInOmhekzVSa5+Ob66P7aBPaypUrzfOEhAQz9pDW7nzzzTcmefruu+82QVCke4x5dGtUVabe0UISE/yjVH2u63U7AACIHFskSy9cuNAkSOtSvXp1v23aXqi0h5jW+Bw/fty7Tccb0ohQa4Q0Abpr167y8ssvS2HSYEe7yDOyNAAAhc8WgZDmEeWVS1S7dm1vUOTbPjhlyhSzRBPNAWqbXKGwTwMAANezRdMYAABAOBAIAQAA1yIQAgAArkUgBAAAXItACAAAuBaBEAAAcC0CIQAA4FoEQgAAwLUIhAAAgGsRCAEAANciEAIAAK5FIAQAAFyLQAgAALgWgRAAAHAtAiEAAOBaBEIAAMC1CIQAAIBrEQgBAADXIhACAACuRSAEAABci0AIAAC4FoEQAABwLQIhAADgWgRCAADAtQiEAACAaxEIAQAA1yIQAgAArkUgBAAAXItACAAAuBaBEAAAcC0CIQAA4Fq2CIR27twpffv2laSkJClRooQkJyfLsGHD5NSpU7m+rkOHDhITE+O33HfffRE7bwAAEN2Kig1s3rxZMjMz5ZVXXpG6devKhg0bpF+/fnLs2DF58cUXc32t7jdixAjv85IlS0bgjAEAgB3YIhDq1q2bWTzq1KkjW7ZskalTp+YZCGngk5iYGIGzBAAAdmOLQCiQtLQ0KV++fJ77zZo1S9555x0TDPXo0UOefvrpXGuFTp48aRaPI0eOmJ9aI6VLtNFzsiwrKs8tFJxcPieXzenlo2z2xb1zz33LDHJfWwZCW7dulcmTJ+dZG9SrVy+pVauWVKtWTdatWyePP/64qUmaM2dOjq8ZPXq0DB8+PNv6AwcOSEZGhkQbvdEaFOoHJDbWFilf+eLk8jm5bE4vH2WzL+6de+5benp6UPvFWHrUQjJ48GAZM2ZMrvts2rRJ6tev732+Z88eufzyy00i9PTp0/P1fosXL5Yrr7zSBFKacB1sjVCNGjXk0KFDUqZMGYnGD4cGaZUqVXLcl43Ty+fksjm9fJTNvrh37rlvR44ckXLlypkAKrfv70KtERo4cKD06dMn1300H8hj79690rFjR2nXrp28+uqr+X6/Nm3amJ+5BUJxcXFmyUovfLT+MdfecNF8fufKyeVzctmcXj7KZl/cO3fct9gg9yvUQEgjO12CoTVBGgS1bNlSZsyYUaA/rGvXrjU/q1atmu/XInhnMy1ZueOg7E/PkMql46V1UnkpEhvDJQQARB1b5AhpEKRNYZrvo3lBWj3m4ekRpvtos9dbb70lrVu3lm3btsns2bPlqquukgoVKpgcoUceeUTat28vTZo0KcTSONv8DSkyfN7PkpL2v3yqqgnxMqxHQ+nWiAAUABBdbBEILVy40DRn6VK9enW/bZ4Up9OnT5tE6OPHj5vnxYsXl6+//lomTpxoxhvSPJ+bbrpJnnrqqUIpg1uCoP7vrJasSWepaRlm/dQ7WhAMAQCiii0CIc0jyiuXqHbt2t6gSGng8+2330bg7OBpDtOaoECZ97pOG8Z0e+eGiTSTAQCihvMyGFEoNCfItzksUDCk23U/AACiBYEQQkITo0O5HwAAkUAghJDQ3mGh3A8AgEggEEJIaBd57R2WUyd5Xa/bdT8AAKIFgRBCQscJ0i7yKmsw5Hmu2xlPCAAQTQiEEDI6TpB2kU9M8G/+0ud0nQcARCNbdJ+HvYIh7SLPyNIAADsgEELIafNX2+QKXFkAQNSjaQwAALgWgRAAAHAtAiEAAOBaBEIAAMC1CIQAAIBrEQgBAADXIhACAACuRSAEAABci0AIAAC4FiNL58GyLPPzyJEjEo0yMzMlPT1d4uPjJTbWeXGtk8vn5LI5vXyUzb64d+65b0f++73t+R7PCYFQHvTCqxo1agR3twAAQFR9jyckJOS4PcbKK1RyOY1C9+7dK6VLl5aYmBiJNhrxapD266+/SpkyZcRpnFw+J5fN6eWjbPbFvXPPfbMsywRB1apVy7UWiRqhPOjFq169ukQ7/WA47cvGLeVzctmcXj7KZl/cO3fct4RcaoI8nNVwDwAAkA8EQgAAwLUIhGwuLi5Ohg0bZn46kZPL5+SyOb18lM2+uHf2FBfGvyckSwMAANeiRggAALgWgRAAAHAtAiEAAOBaBEIAAMC1CIRsZufOndK3b19JSkqSEiVKSHJyssmkP3XqVK6v69ChgxkZ23e57777xCnly8jIkPvvv18qVKgg5513ntx0002yb98+iTajRo2Sdu3aScmSJaVs2bJBvaZPnz7Z7l23bt3ECWXTkV+HDh0qVatWNfe7U6dO8u9//1ui0cGDB+X22283g7lp+fRzevToUVv+3k2ZMkVq165t5m1q06aNrFy5Mtf9P/zwQ6lfv77Zv3HjxvLFF19INMtP+WbOnJntHunrotHSpUulR48eZqRkPc+5c+fm+ZolS5ZIixYtTG+runXrmvI6oWxLlizJdt90SU1Nzfd7EwjZzObNm820H6+88ops3LhRJkyYINOmTZMnnngiz9f269dPUlJSvMsLL7wgTinfI488IvPmzTN/sL/99lszLcqNN94o0UYDup49e0r//v3z9ToNfHzv3bvvvitOKJt+BidNmmTu8YoVK6RUqVLStWtXE9hGGw2C9DO5cOFC+eyzz8wf7nvvvdd2v3fvv/++DBgwwPwHY/Xq1dK0aVNzzffv3x9w/x9++EFuu+02E/itWbNGrr/+erNs2LBBolF+y6c0uPW9R7t27ZJodOzYMVMeDfSCsWPHDrn66qulY8eOsnbtWnn44YflnnvukQULFojdy+axZcsWv3tXuXJlyTedawz29sILL1hJSUm57nP55ZdbDz30kOXE8h0+fNgqVqyY9eGHH3rXbdq0SefQs5YtW2ZFoxkzZlgJCQlB7du7d2/ruuuus+wi2LJlZmZaiYmJ1tixY/3uZVxcnPXuu+9a0eTnn382n6cff/zRu+7LL7+0YmJirD179tjq965169bW/fff731+9uxZq1q1atbo0aMD7n/zzTdbV199td+6Nm3aWH/5y1+saJTf8uXndzGa6Ofx448/znWfQYMGWRdddJHfultuucXq2rWrZfeyffPNN2a/Q4cOnfP7USPkAGlpaVK+fPk895s1a5ZUrFhRGjVqJEOGDJHjx4+LE8q3atUqOX36tGlW8dBq/Jo1a8qyZcvECbQaWP+nU69ePVPj8scff4jd6f9WtRrb977pvEDalBFt903PR5vDWrVq5V2n561zEWpNll1+77TWTn9ffK+5lkGf53TNdb3v/kprWKLtHhW0fEqbOGvVqmUm9bzuuutMzZ8T2OneFVSzZs1M03rnzp3l+++/L9AxmHTV5rZu3SqTJ0+WF198Mdf9evXqZX7Rtf113bp18vjjj5sqxTlz5ojdy6dfpsWLF8+Wl1KlSpUCtRdHG20W02Y+zZvatm2baSbs3r27+WNWpEgRsSvPvdH7FO33Tc8na5V70aJFTYCe27lG2+/d77//LmfPng14zbVZOhAtnx3uUUHLp/+5eOONN6RJkybmP136t0Zz3TQYssOE27nJ6d7pTO4nTpwweXl2pcGPNqnrf05Onjwp06dPNzl5+h8TzYnKDwKhKDF48GAZM2ZMrvts2rTJ1HR47Nmzx3xJal6G5iHkxjeXQZMd9UN05ZVXmi9WTUi2e/kKU0HKlh+33nqr373TP9h6z7SWSO+hnctW2IItX0EV9u8d8ta2bVuzeGgQ1KBBA5OnOHLkSC5hlNIAVhff+6a/V5pX+vbbb+frWARCUWLgwIGmd1Bu6tSp432sycCaAKc3/9VXX833+2nzg6fGJRJ/kMNZvsTERFMlfvjwYb9aIe01ptuirWznSo+lTS1678IdCIWzbJ57o/dJAwQPfa7V3ZEQbPn0XLMm2545c8b0JMvPZyzSv3dZ6edGaxGz9qjM7XdF1+dn/8JUkPJlVaxYMWnevLm5R3aX073T5HA71wblpHXr1vLdd99JfhEIRYlKlSqZJRhaU6JBQsuWLWXGjBmmDTy/tAeB8v0Csmv5dD/947Vo0SLTbV5p88Pu3bv9/qcXDWULhd9++83kCEXi3oWzbNrUp3+o9b55Ah+tsteq7fz2qgt3+fRzpIG25p/o500tXrzY9HD0BDfR+HuXlTYh6/nrNdeeX0rLoM8feOCBHMuu27XHkYf2nIvE71YkypeVNq2tX79errrqKrE7vUdZhzqI1nsXCvr7VaDfrXNOt0ZE/fbbb1bdunWtK6+80jxOSUnxLr771KtXz1qxYoV5vnXrVmvEiBHWTz/9ZO3YscP65JNPrDp16ljt27d3RPnUfffdZ9WsWdNavHixKWfbtm3NEm127dplrVmzxho+fLh13nnnmce6pKene/fRss2ZM8c81vWPPvqo6f2m9+7rr7+2WrRoYV1wwQVWRkaGZeeyqeeff94qW7as+UyuW7fO9I7THoInTpywok23bt2s5s2bm8/dd999Z+7BbbfdZrvfu/fee8/0zJs5c6bpDXfvvfeae5Cammq233nnndbgwYO9+3///fdW0aJFrRdffNH0xhw2bJjppbl+/XorGuW3fPp5XbBggbVt2zZr1apV1q233mrFx8dbGzdutKKN/i55fq/063v8+PHmsf7uKS2Xls9j+/btVsmSJa3HHnvM3LspU6ZYRYoUsebPn2/ZvWwTJkyw5s6da/373/82n0XtnRkbG2v+RuYXgZDNaFdP/ZAEWjz0j64+1+6Favfu3eaPb/ny5c0fCA009BcjLS3NckL5lH5x/vWvf7XKlStnfvFvuOEGv+ApWmhX+EBl8y2LPtfroI4fP2516dLFqlSpkvnyqVWrltWvXz/vH3U7l83Thf7pp5+2qlSpYj6bGgBv2bLFikZ//PGHCXw0yCtTpox19913+wV5dvq9mzx5svmPQ/HixU138+XLl/t1+dd76euDDz6wLrzwQrO/dsf+/PPPrWiWn/I9/PDD3n31c3jVVVdZq1evtqKRp8t41sVTHv2p5cv6mmbNmpnyaSDu+/tn57KNGTPGSk5ONkGr/o516NDB/Ee4IGL0n5DUSQEAANgM4wgBAADXIhACAACuRSAEAABci0AIAAC4FoEQAABwLQIhAADgWgRCAADAtQiEAESUzhDtO11DOI9du3ZtmThxooTLzp07JSYmxjt1BgD7IRACXE4nHfXMy+Q0P/74o98M8IVBgzMNlrIu9913n9n+r3/9y8yR9emnn/q97qOPPpL4+HjZsGFDtrnmdP9GjRoFfD/P8ZcvX+63/uTJk1KhQgWzbcmSJd71o0aNMpMblyxZ0m/SYsAtCIQA2IoOhq8zvwdDJ1TVL/jC1q9fP0lJSfFbXnjhBbOtadOmMnToUBOw6WS6Sme610Bp+PDh2QKemTNnys033+ydoDaQGjVqmAmLfX388cdy3nnnZdv31KlT0rNnz4hNdAtEGwIhwAX+8Y9/SOPGjaVEiRKmVqBTp05y7NgxeeaZZ+TNN9+UTz75xFuT4KktePzxx+XCCy80gUSdOnXk6aefltOnT3uPqa/VWePffvtt0wSVkJAgt956q6Snp3v30fe46667zBewzgo9bty4bOemr2/VqpWULl3azEbfq1cvEwh46PnoeX355ZdmZvG4uDj57rvvgjq2b9OYBhCBama0HB7Tp0+XBg0amJqY+vXry8svv+x3vJUrV0rz5s3Ndj3nNWvWBHX99Rpq2XyXMmXKeLcPGTJEatasKffff795/pe//EUuuOACefTRR7MFgRrg3HnnneY6vf766wHfr3fv3vLee+/JiRMnvOveeOMNsz4rDbYeeeQR8/kAXClUE6YBiE579+41s4frbM46MajO8q6zUOuEobrcfPPNZmZ1naRWl5MnT5rXjRw50sw8rq/59NNPzYSUOtGhh85CrhOQ3njjjWb256VLl1qJiYnWE0884d2nf//+ZkJLnRFa3/eaa66xSpcubWaK9nj99detL774wsz+vWzZMqtt27ZW9+7ds03G2KRJE+urr74ys7rrBKjBHFsnqdVZqj0T2HrKqMu7775rroseU73zzjtW1apVrY8++sjM2q0/dTJHncVc6bXSyW979eplbdiwwZo3b56ZxFLPTWfJzolOFOl7TjnRmdJ1Akmd2LVEiRIBJ59dtGiRucZnzpwx11zLe/ToUb999Hw+/vhjc73efvtts05n8NaJX3/55ZdsE+F66GScCQkJeZ4n4DQEQoDDrVq1ynz57dy5M+B2ndX5uuuuy/M4Y8eOtVq2bOkXCJUsWdI6cuSId53Ort6mTRtv4KAzXuvM5R4awOiXfG6BwY8//mjO1zOzuycQmjt3rnefYI/tGwj50mBKg5wXXnjBu05nsp49e7bffhoMamCmXnnlFatChQrWiRMnvNunTp0aVCBUrFgxq1SpUn6LBl5ZDR482BzPN+D0pUGYzpbu0bRp02yziXsCoYkTJ1odO3Y064YPH27dcMMN1qFDhwiEgCxoGgMcTnNQrrzyStP0obkgr732mhw6dCjP173//vtyySWXmGYcbX566qmnZPfu3dmanrRJy0ObqDzNWtu2bTP5J23atPFuL1++vNSrV8/vGKtWrZIePXqYpiE91uWXX27WZ30vbYryCPbYgaSlpck111wjV199tTz22GNmnTaz6TH79u1ryupZnn32WbNebdq0SZo0aWKaxTzatm0rwbj99ttNzzLf5dprr/Xb5+jRo+aaazPaP//5z2zHOHz4sMyZM0fuuOMO7zp9nFPzmG5btmyZbN++3TQL/vnPfw7qXAG3KVrYJwAgvIoUKSILFy6UH374Qb766iuZPHmyPPnkkybRNikpKeBr9AtUv7w1f6Rr164m/0dzTrLm4RQrVszvuebcZGZmBn1uGoDo8XWZNWuWSW7WAEifa6Djq1SpUnKuzp49K7fccovJz3n11Vf9ghClQaJvcOW5fudKr1/dunVz3UeDMg2y9D5dfPHF8tZbb5kcKI/Zs2dLRkaG3/lpBZBe719++cXkc/nSXDAN+DS409d1797dL38LwH9QIwS4gAYoWrujgY0m+Gr3a+1FpPSxBgi+9Mu4Vq1aJmDSmhhN3N21a1e+3jM5OdkESr49m7QmSr+0PTZv3mx6Sj3//PNy2WWXmQRl30Tpczl2IJoUvH79epk7d65fzU6VKlWkWrVqpvZEAxbfxRMsahL1unXrTFDhkbWLekFpoKqJ2pq4rjV4WhOl4yFp7zIPrfkZOHCgX62Sdr3X66aJ0IFoLZAmm2tAFYqADnAiaoQAh9NgYdGiRdKlSxepXLmyeX7gwAHzxe5p3lqwYIFs2bLF1CJo7YUGPlozo7VAf/rTn+Tzzz/3Bk7B0qYlrY3Qmg49rr63Blaxsf/7/5c2h2kgprVU2l1cx8wZOXJkSI6dlfa20l5gWg4NDFNTU73H0kWDxL/97W+m/N26dTPj7vz0008mwBowYIDppaXvoV3htZeXDqb44osvBnUtjh8/7n0/D+39Vq5cOdMN3lMWvdaegE3PU7vUz5s3zwQ9q1evNrVmGiz6uu2222TEiBEmeCpa1P9PupZD77VvD7Ws9D4fPHjQ/NSA2DM4pAaBgbrbA46TNWkIgLNob6SuXbuaHk/ac+jCCy+0Jk+e7N2+f/9+q3PnzqYHmG+PIk181uRgXX/LLbeYpGPfXkWaLK3Jur50H01Q9k1qvuOOO0xStfY60+TkrL2oNEG5du3a5tw0MVl7qPkmIHuSpTXR11cwx/ZNltakcD1O1kXL4TFr1iyrWbNmJhG7XLlyVvv27a05c+Z4t2uvNi2zbtf9tGdZMMnSgd5X74m6++67rUaNGnl763loDy8t25tvvmk98MADVsOGDQMeX3vAxcbGWp988olfsnQggZKlc7ougXqWAU4Uo/8UdjAGAABQGMgRAgAArkUgBAAAXItACAAAuBaBEAAAcC0CIQAA4FoEQgAAwLUIhAAAgGsRCAEAANciEAIAAK5FIAQAAFyLQAgAALgWgRAAABC3+n/45+3slLCedwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# --- PROVIDED --- load the data and standardize every column to zero mean, unit variance\n",
    "df = pd.read_csv(\"testScores.csv\").dropna(axis=1, how=\"all\")\n",
    "z  = (df - df.mean()) / df.std(ddof=0)\n",
    "\n",
    "x = z[\"EXAM1\"].values   # standardized midterm 1 score, shape (N,)\n",
    "y = z[\"FINAL\"].values   # standardized final exam score, shape (N,)\n",
    "N = len(x)\n",
    "\n",
    "print(f\"N = {N} students\")\n",
    "plt.scatter(x, y)\n",
    "plt.xlabel(\"standardized EXAM1\"); plt.ylabel(\"standardized FINAL\")\n",
    "plt.title(\"The data we are trying to fit\"); plt.grid(alpha=.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c003",
   "metadata": {},
   "source": [
    "## (a) Derive the gradient\n",
    "\n",
    "On paper, work out $\\dfrac{\\partial e}{\\partial a}$ and $\\dfrac{\\partial e}{\\partial b}$ for\n",
    "\n",
    "$$e = \\frac{1}{N} \\sum_{i=1}^{N} (y_i - a x_i - b)^2$$\n",
    "\n",
    "Do this **before** you write any code. You cannot implement a gradient you have not derived."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c004",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial e}{\\partial a} = \\frac{1}{N} \\sum_{i=1}^{N} 2(y_i - a x_i - b)(-x_i)$$\n",
    "\n",
    "$$\\frac{\\partial e}{\\partial b} = \\frac{1}{N} \\sum_{i=1}^{N} 2(y_i - a x_i - b)(-1)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c005",
   "metadata": {},
   "source": [
    "## Plotting helpers (provided — just run it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c006",
   "metadata": {},
   "outputs": [],
   "source": [
    "# --- PROVIDED --- plotting helpers. You do not need to modify these.\n",
    "\n",
    "def mse(a, b):\n",
    "    \"\"\"Mean squared error of the model yhat = a*x + b.\"\"\"\n",
    "    return np.mean((y - (a * x + b)) ** 2)\n",
    "\n",
    "def plot_loss(histories, labels):\n",
    "    \"\"\"histories: list of 1-D arrays of MSE vs iteration.\"\"\"\n",
    "    plt.figure(figsize=(7, 4))\n",
    "    for h, lab in zip(histories, labels):\n",
    "        plt.semilogy(np.clip(h, 1e-12, 1e12), label=lab)\n",
    "    plt.xlabel(\"iteration\"); plt.ylabel(\"MSE (log scale)\")\n",
    "    plt.legend(); plt.grid(alpha=.3); plt.title(\"MSE vs iteration\"); plt.show()\n",
    "\n",
    "def plot_trajectory(w_hist):\n",
    "    \"\"\"w_hist: array of shape (numIterations+1, 2) holding (a, b) at each step.\"\"\"\n",
    "    w_hist = np.asarray(w_hist)\n",
    "    lo, hi = -0.4, 1.4\n",
    "    A, B = np.meshgrid(np.linspace(lo, hi, 120), np.linspace(-1, 1, 120))\n",
    "    Z = np.array([[mse(aa, bb) for aa in A[0]] for bb in B[:, 0]])\n",
    "    plt.figure(figsize=(6, 5))\n",
    "    plt.contour(A, B, Z, levels=np.logspace(-1.2, 1.2, 20), alpha=.6)\n",
    "    plt.plot(w_hist[:, 0], w_hist[:, 1], \"o-\", ms=3, lw=1, color=\"crimson\")\n",
    "    plt.plot(w_hist[0, 0], w_hist[0, 1], \"ks\", ms=8, label=\"start\")\n",
    "    plt.plot(w_hist[-1, 0], w_hist[-1, 1], \"g*\", ms=14, label=\"end\")\n",
    "    plt.xlabel(\"a\"); plt.ylabel(\"b\"); plt.legend()\n",
    "    plt.title(\"trajectory of (a, b) over the loss surface\"); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c007",
   "metadata": {},
   "source": [
    "## (b) Implement gradient descent\n",
    "\n",
    "Fill in the three `TODO` lines below. They correspond exactly to the three blanks in the\n",
    "L2 slide skeleton. Start from $a = 0$, $b = 0$.\n",
    "\n",
    "*Hint: `x` and `y` are numpy arrays, so `y - a*x - b` computes all $N$ residuals at once —\n",
    "no `for` loop over data points needed.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c008",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(gamma, numIterations=200):\n",
    "    \"\"\"Fit yhat = a*x + b by batch gradient descent, starting from a = b = 0.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    w_hist    : (numIterations+1, 2) array of [a, b] at every iteration\n",
    "    mse_hist  : (numIterations+1,)   array of the MSE at every iteration\n",
    "    \"\"\"\n",
    "    w = np.array([0.0, 0.0])          # [a, b]\n",
    "    w_hist, mse_hist = [w.copy()], [mse(w[0], w[1])]\n",
    "\n",
    "    for i in range(numIterations):\n",
    "        a, b = w\n",
    "\n",
    "        agrad = np.mean(-2 * x * (y - a * x - b))\n",
    "        bgrad = np.mean(-2 * (y - a * x - b))\n",
    "\n",
    "        w = w - gamma * np.array([agrad, bgrad])\n",
    "\n",
    "        w_hist.append(w.copy())\n",
    "        mse_hist.append(mse(w[0], w[1]))\n",
    "\n",
    "    return np.array(w_hist), np.array(mse_hist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c009",
   "metadata": {},
   "source": [
    "Now run it with a reasonable learning rate and look at the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c010",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 0.9461,  b = 0.0000,  final MSE = 0.1049\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_hist, mse_hist = gradient_descent(gamma=0.1, numIterations=200)\n",
    "a_hat, b_hat = w_hist[-1]\n",
    "print(f\"a = {a_hat:.4f},  b = {b_hat:.4f},  final MSE = {mse_hist[-1]:.4f}\")\n",
    "\n",
    "plot_loss([mse_hist], [\"gamma = 0.1\"])\n",
    "plot_trajectory(w_hist)\n",
    "\n",
    "# the fitted line on top of the data\n",
    "plt.scatter(x, y, label=\"data\")\n",
    "xs = np.linspace(x.min(), x.max(), 50)\n",
    "plt.plot(xs, a_hat * xs + b_hat, \"r-\", lw=2, label=f\"fit: y = {a_hat:.3f}x + {b_hat:.3f}\")\n",
    "plt.xlabel(\"standardized EXAM1\"); plt.ylabel(\"standardized FINAL\")\n",
    "plt.legend(); plt.grid(alpha=.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c011",
   "metadata": {},
   "source": [
    "## (c) The learning rate $\\gamma$\n",
    "\n",
    "Run gradient descent for several learning rates and plot all the MSE curves together.\n",
    "\n",
    "Use $\\gamma = 0.01,\\ 0.1,\\ 1.0,\\ 1.1$ and **only 60 iterations** (large $\\gamma$ blows up fast)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c012",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma = 0.01   final MSE = 0.1842\n",
      "gamma = 0.1    final MSE = 0.1049\n",
      "gamma = 1.0    final MSE = 1\n",
      "gamma = 1.1    final MSE = 2.842e+09\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gammas = [0.01, 0.1, 1.0, 1.1]\n",
    "\n",
    "histories = []\n",
    "for g in gammas:\n",
    "    with np.errstate(over=\"ignore\", invalid=\"ignore\"):\n",
    "        _, h = gradient_descent(gamma=g, numIterations=60)\n",
    "    histories.append(h)\n",
    "    print(f\"gamma = {g:<5}  final MSE = {h[-1]:.4g}\")\n",
    "\n",
    "plot_loss(histories, [f\"gamma = {g}\" for g in gammas])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c013",
   "metadata": {},
   "source": [
    "### Discuss with your partner, then write your answers here\n",
    "\n",
    "1. Describe the shape of the loss curve for each $\\gamma$. Which one is \"too small\",\n",
    "   which is \"about right\", and which one fails?\n",
    "2. $\\gamma = 1.0$ does something unusual — it neither converges nor blows up. What is it\n",
    "   doing to the estimate at each step? *(Try plotting the trajectory for this case.)*\n",
    "3. **The important one:** suppose you are fitting a model where you do **not** know the right\n",
    "   answer in advance. Looking only at the MSE-vs-iteration plot, how would you diagnose\n",
    "   each of these three failure modes — too small, too large, and just right?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c014",
   "metadata": {},
   "source": [
    "**1.** $\\gamma=0.01$ decreases steadily but has not converged after 60 iterations — correct\n",
    "direction, too slow. $\\gamma=0.1$ drops quickly and flattens out at the minimum. $\\gamma=1.1$\n",
    "increases without bound; the MSE overflows within a few dozen iterations.\n",
    "\n",
    "**2.** At $\\gamma=1.0$ the step overshoots the minimum by *exactly* the amount it started away\n",
    "from it, so the estimate bounces between two points forever with the MSE pinned at a constant\n",
    "value. This is the stability boundary: for this standardized data the loss curvature is exactly\n",
    "2, and gradient descent is stable only for $\\gamma < 2/2 = 1$. It is the dividing line between\n",
    "the $\\gamma=0.1$ and $\\gamma=1.1$ behaviors.\n",
    "\n",
    "**3.** *Too large*: loss increases, often to `inf`/`nan` — or oscillates up and down between\n",
    "iterations. *Too small*: loss decreases smoothly but is still visibly decreasing when you run\n",
    "out of iterations, i.e. the curve has not flattened. *Just right*: loss falls fast and then\n",
    "goes flat, and running longer changes nothing. The tell for \"too large\" is that the loss goes\n",
    "**up** — gradient descent should never increase the loss if $\\gamma$ is chosen well."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c015",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "# Challenges (optional)\n",
    "\n",
    "Only if you have finished (a)-(c)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c016",
   "metadata": {},
   "source": [
    "## C1 — A different loss function\n",
    "\n",
    "Redo part (b) with **mean absolute error** instead of mean squared error:\n",
    "\n",
    "$$e = \\frac{1}{N}\\sum_{i=1}^{N} |y_i - a x_i - b|$$\n",
    "\n",
    "- Derive the gradient. Where is it undefined, and what should your code do there?\n",
    "- How does the convergence behavior differ from MSE? Does the same $\\gamma$ still work?\n",
    "- Change one $y$ value to a wild outlier (say, $+10$). Refit with both losses.\n",
    "  Which fit moves more, and why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c017",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE fit: [ 0.938 -0.048]  MSE fit: [0.9461 0.    ]\n",
      "with outlier -> MSE fit: [0.7367 0.417 ]  MAE fit: [ 0.9347 -0.048 ]\n",
      "MAE is far less disturbed: squaring makes one bad point dominate the total loss.\n"
     ]
    }
   ],
   "source": [
    "# C1: mean absolute error\n",
    "def gradient_descent_mae(gamma, numIterations=200):\n",
    "    w = np.array([0.0, 0.0])\n",
    "    hist = []\n",
    "    for i in range(numIterations):\n",
    "        a, b = w\n",
    "        r = y - a * x - b\n",
    "        s = np.sign(r)                     # undefined at r == 0; np.sign gives 0, which is a\n",
    "        agrad = np.mean(-s * x)            # valid subgradient choice\n",
    "        bgrad = np.mean(-s)\n",
    "        w = w - gamma * np.array([agrad, bgrad])\n",
    "        hist.append(np.mean(np.abs(y - w[0] * x - w[1])))\n",
    "    return w, np.array(hist)\n",
    "\n",
    "w_mae, h_mae = gradient_descent_mae(gamma=0.05, numIterations=400)\n",
    "print(\"MAE fit:\", np.round(w_mae, 4), \" MSE fit:\", np.round(w_hist[-1], 4))\n",
    "\n",
    "# outlier test\n",
    "y_orig = y\n",
    "y = y.copy()          # z[\"FINAL\"].values can be read-only, so work on our own copy\n",
    "y[0] = 10.0\n",
    "w_out_mse = gradient_descent(gamma=0.1, numIterations=400)[0][-1]\n",
    "w_out_mae = gradient_descent_mae(gamma=0.05, numIterations=2000)[0]\n",
    "y = y_orig\n",
    "print(\"with outlier -> MSE fit:\", np.round(w_out_mse, 4), \" MAE fit:\", np.round(w_out_mae, 4))\n",
    "print(\"MAE is far less disturbed: squaring makes one bad point dominate the total loss.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c018",
   "metadata": {},
   "source": [
    "## C2 — A different model\n",
    "\n",
    "Fit a **quadratic** $\\hat{y}_i = a x_i^2 + b x_i + c$ by gradient descent.\n",
    "\n",
    "- Derive all three partial derivatives.\n",
    "- Find a $\\gamma$ that works. Is the usable range of $\\gamma$ wider or narrower than it was\n",
    "  for the straight line?\n",
    "- Now try it on the **raw, unstandardized** EXAM1 scores (values around 70-100, so $x^2$ is\n",
    "  around 5000). What happens, and what does that tell you about why we standardized the data\n",
    "  in the first place?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c019",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standardized x, gamma=0.05 -> [ 0.021   0.9624 -0.021 ]  final MSE 0.1041\n",
      "raw x, same gamma -> final MSE nan\n",
      "\n",
      "It overflows to nan. The x^2 column now has values ~5000x larger than the x column, so the\n",
      "loss surface is an extremely narrow valley: the curvature along the x^2 direction is huge,\n",
      "and gamma=0.05 is wildly unstable there. To get stability you would need a gamma several\n",
      "orders of magnitude smaller -- at which point the other directions barely move at all, and\n",
      "the fit takes forever. Standardizing puts every input on the same scale, so a single shared\n",
      "learning rate can work for all of them at once.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/td/h6n02fhs61z3vvrx2h8b1j8w0000gp/T/ipykernel_88097/360088995.py:11: RuntimeWarning: overflow encountered in square\n",
      "  hist.append(np.mean(r**2))\n"
     ]
    }
   ],
   "source": [
    "# C2: quadratic model\n",
    "def gradient_descent_quad(xd, yd, gamma, numIterations=500):\n",
    "    w = np.zeros(3)                                    # [a, b, c]\n",
    "    hist = []\n",
    "    for i in range(numIterations):\n",
    "        a, b, c = w\n",
    "        r = yd - (a * xd**2 + b * xd + c)\n",
    "        with np.errstate(over=\"ignore\", invalid=\"ignore\"):\n",
    "            g = np.array([np.mean(-2 * xd**2 * r), np.mean(-2 * xd * r), np.mean(-2 * r)])\n",
    "            w = w - gamma * g\n",
    "        hist.append(np.mean(r**2))\n",
    "    return w, np.array(hist)\n",
    "\n",
    "w_q, h_q = gradient_descent_quad(x, y, gamma=0.05)\n",
    "print(\"standardized x, gamma=0.05 ->\", np.round(w_q, 4), \" final MSE\", h_q[-1].round(4))\n",
    "\n",
    "x_raw = df[\"EXAM1\"].values.astype(float)\n",
    "_, h_raw = gradient_descent_quad(x_raw, y, gamma=0.05, numIterations=50)\n",
    "print(\"raw x, same gamma -> final MSE\", h_raw[-1])\n",
    "print(\"\"\"\n",
    "It overflows to nan. The x^2 column now has values ~5000x larger than the x column, so the\n",
    "loss surface is an extremely narrow valley: the curvature along the x^2 direction is huge,\n",
    "and gamma=0.05 is wildly unstable there. To get stability you would need a gamma several\n",
    "orders of magnitude smaller -- at which point the other directions barely move at all, and\n",
    "the fit takes forever. Standardizing puts every input on the same scale, so a single shared\n",
    "learning rate can work for all of them at once.\"\"\")"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "27f2499f-3d8a-4d06-b4ee-ed8822c86070",
   "metadata": {},
   "outputs": [],
   "source": []
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