PolynomialRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f8c6013c",
   "metadata": {},
   "source": [
    "In this notebook, we will expiriment with polynomials of different degrees, and see how it corresponds to overfitting. We will make use of the diabetes dataset from SciKit learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "41e615cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1ce7d8c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = datasets.load_diabetes(return_X_y=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "75c191f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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R8XD6+GXAO4HrgPOAi9P7z6UvuQ74tKT3AvOBE4Gbe5VfMzPLfi2vj0h6dUTsBki7614VEUV1zz0G+KwkSPL46Yj4V0nfA66R9DqS+VheDRARmyVdQzKSfy9wQUR4nIzZgOuHaXFnkqwB5ehaMAGIiAfTto1CRMR/As9rkP4j4JebvOZdwLuKylNevAOY5aM2LW5tJsPatLhAqfvUTN7Hs/byelzSwtoTScfToNHbWuuXeaHN+kGraXHLMtP38awB5W3AtyR9QtInSC5fv7q4bA2mKu4AZjVrN0xwxsU3csKqL3LGxTdW/iBYxWlxZ/o+nvXy9f8q6VTgdJIuum+JiPsLzdkAquIOYAbVrT5qZf7cESYa7DtlTos70/fxliUUSc9O708FFpJ0xZ0AFqZp1oF+mRe6l8o6K+63s/GiTefMuqzvsorT4s70fbxdCeWtwO8D72mwLICX5J6jAbZy2eIDzgKh/B2gmV40LJZ1VtyPZ+NF6/bMuszvsorT4vbTPl6EduNQfj+9f3FvsjPYitgBijjw9+og0eqsuMiDQlmfW2XdVh+V/V12Mi1uL06SqhjkeqndpVfOabU8Iq7NNzuDL895oYs68PfqIFFWffNMr+dupNsz6375LntZkuqHud+L0q7K66z0/mkk1/S6MX3+YuDrgANKiYo68PfqIFFWo2o3nzvoYwu6PbOuYsN4I2WXpGaKdlVe/xNA0heAk2pX+k2vo/WPxWfPWinqwN+rg0RZ9c2dfu5MaXPp5sy6iN+wiODdLyWpfpd1HMqiWjBJ3Qv8TAH5sQ4U1aOkV71nli8d5d3nnMLo3BEEjM4d4d3nnNKTxtxOPnemjy1oJe/fsKiBgd3uK+4N2Jmsl175uqR1wJUkvbtWAF8rLFfW1toNEzzy2N6D0vM48PeyYbGs+uZOPtdnt601+y7rSxpz5wwTAf89uafl/6moqql2JalGpSJgRpRM85R1YOObJL0SeGGadFlEfLa4bFkrU6tgauaODHPRK07O5c/ezYF+UNsZ+qWdoEqm/kcffGTP/mWtDsxFBe9WJ0nNqjQPnT3L7S4dylpCAfg+8HBEfEXSHElPjYiHi8qYNdfoLA7gyYfOLu2PPsjtDL1o6xm0YNzsP1rT7MDcLHgfPjLMGRffOK3vp9lJUrNSUbP8u2TaXKY2FEm/D/wL8H/TpFFgbUF5sjaKOoubTn3xILczFN3WM4gXFMzyX2y0TqP2u+FZ4ieP7S3s++l0v3HJtLmsJZQLSGZM/C5ARPywyMvXW2tFVMF0UsJodDY96O0M7aoAp1PCKKLdoOwST7P/6NR1pmpUNfXIY3sPqDKDfKuemuX1iDnD/HTP45Ub9V72b9tK1l5ej0bEY7Unkmbjy9eXpoheWFlLGM3Opg8fGW74vjPhbG66JYy8g3EVSjyN/qP1Wv1fly8d5durXsKdF/8a3171EnZPCSY1eZ2sNNufLjzr5FJ6IbZShd+2lawllG9I+ktgRNKvAH8IfL64bFkrRfTCynpQaxZ4njQ8i5HhocqdzdUUeVbXaQljal4OHxlm9+TBB80sXVobbVMVBvFN/Y9m7eXVSNGdItrtT1U5+4fqD9DMGlD+Ang9sAl4A3A98JGiMmXt5d3dNutO2yzw7H5kD5e8ZklpRfFWAaPoDgPtgnF93g4fGeYnj+1lz77Yn5fhITE8S+x5/IlCf7tg3Gib3nz1Ri66bnPD4NQqn0XJ6z/ai04R/XK5lKpXLbcNKJJmAbdGxHOBDxefJStD1p22VeApa6dsFzDyPqvrpIQxNW+N1tuzLzhizjBzDpmdORg360W1e3IPonF9dL9WP870Cy7Wq3oX9rYBJSIel3SLpIURcU8vMmW912inffGz57Fm3RbecvXG/TtxFS/P3S5gNGsc7uasrlHwalXCaNd9tubBR/Yw55DZXPKaJZkOlK3yHnBQUCn7N5qufilBtJJHtWsV9796Wau8jgU2S7oZ+EktMSJeUUiurGPd/lmbve6v1m7iU9+5Z/9BqXbW/xvPHz1gwNcRc4a58KzOBlPm3Z7Rqhpg7YaJXM/YGwWIViWMt1y9MfN7d1IV164XVZA0Ipd1Rl/lnkhlyKvateqltawB5R2F5qLPdbLzVGn+kmavG7/7gQOCSc3knn0Hpe9+ZA/jdz/Qdhtq2z2xe/KAA3we7RmtqgHWrNvSMJgIujqra9WGtOHtL8uct2ayVsU1OlOtNzp3hG+vKmf+u0Ee5NpIln06z2rXKpfW2k0B/CRJbwZeDTwb+HZEfKN260UGq66TbnxFdfnrdlBhs9c1CiY1U9MD+NR37mm5DX+1dhNvuXrj/gNro0D1js9vbpnXVlp1o24WAILuDm6dXmSw2UC9I+Y07mYN2ariaoMtG71P2VUggzLINctA36z7dNUb0/PSbhzKFcAYSe+uX6XxVMAzRqM/WCc7T1E7WrMz4HZnxq0Otp0I4K3X3NJ0h2sVoGoefGTPAa/vZNR+q5HszQ70o102YnY6BqhR3ta8+nlsePvLmuYha1Xc8qWjbHj7y/j71yyp1FiJQTh4Zg0UWffpmTLXfLsqr5Mi4hQASR8Fbi4+S9XUrBjf7no/9cXhZgfVLPN2typSD0nsi4PffUhq+b6dVse0si+iYbVGsyqnRmrF/26qTJpVA+TdiNlNHXbReataFUjVeyJlkbWKKmvwrHpjel7aBZT9fRwjYq/aHKAGWbM/WLODeaMuo820mymw3cG10ee3Sq9pVw/fqU52uEZq6+Zd31x7z7zarfI6gFe9gbVbg3DwzBoosgbPQf2tp2oXUJ4n6aH0sUhGyj+UPo6IOKzQ3FVIsz/YvoimI8SzdBltt6NlObiONvlTt6vWyXrdpE5k3eEaqe2EeVeZVO0Mvl6V8pZXh5FBOHhmDRSdBM8q/dZFaTcFcPOL8cwwzf5go+nO0mjnadVlVOl7ttvRshxcp3NGOPVP3qhUNTI8xKGzZzUdgV0vyw4HSePd43XP6/Pb7LueJXHCqi9W6gA1KN1j8+6Z1e8Hz6z71CAEzzx1Mh9KpUk6E3gfMAR8JCIuzvP9W/3Bmu08rYJQ1i6dWc6U8vxTN3svoG31WCc7XKv8NgtCtSq8qnRDrVr32Kpd8bifdbJP9XvwzJOiTT17P5A0BPwA+BVgO/A94NyIuL3Za8bGxmJ8fLyjz+l0h212tt9JL5xG7zE8JJ58yOyuLrSXdZuaTYk6dST91/59V+ZA0W2+ZjVppypzrAXAGRff2NUJQ96DUGvLpvNfO2HVF5uO17nz4l9r+/q8DUrJbxBJWh8RY42WDUoJ5TRga0T8J4Ckq4CzgaYBpRudnoksXzrK+N0PcOV3t7EvgiGJ33h+5+8BB1619cc/3bu/+mk6Z8WtBjZ+Zv3EQenvPueUtgfKvM7Y67/rE1Z9seE60+mGmscBq5u2nrwHodZeN90SRpV6ZlWt5GfZZZ0PpepGgW11z7enaQeQdL6kcUnju3btKjxTazdM8Jn1E/vPrvdF8Jn1Ex0PZFy+9In5IeYcMvuAa0ZB92NZmh2ErvzutlwHSk53nE3effjzGmDaTb7yHoRae910OzIUMcdOtwZlYORMNCgBpVF/5oNK8BFxWUSMRcTYvHnzCs/UdHaM2sC+Rau+yDNXX8+idIBfnhc6bNVzrZvPKGpAW94Hu7wOWN3kq9vvqNny2v9hukG31eDQXhuEgZEz1aBUeW0Hjqt7vgDYUVJe9ut2x5ha5K9vjO70QoetqnaaVXO0GlvTSlHVJnn3pMnrgNVNvrr9jpq9TiS/8XR6+k39j2S94nFRqlT9Zp0ZlBLK94ATJZ0g6RBgBXBdyXnq+qyx1fiV2qXJ6zU7cLSr2ml2hn3uzx3XVYmgyGqT+mq/b696ybQOeHlWoXWar26/o5XLFjcthtfaSbopYVRxStkqVb9ZZwYioETEXuBNwDrgDuCaiOj+aoM56XbHaHemXLs0ebsDR7uqnWYHob9efkpXB6cqVZu0UuYBq9vvaPnS0baX7ukm6FaxvaJf/kd2sEGp8iIirieZmrgyuq2qaTe6fEjK1F02S9VOs55r3fat74c++WUPRuv2O2p2RYTpVAVVtb2iH/5HdrCBCShV1c2O0e4aW+2u0VXjuujm+vGAVcQ1svwfmVmKHt8zEFVeg6ZW5G92teCsl17vRdVOJ5eZL0oV8tALRVQFub1i5uhFe5lLKBVVO0hM54y06KqdKgxAq0IeeinvklXZ1X/WO724vI4DSoXlsbMXWbVThes/VSEP/a4fq/+y8OVbDtSL9jIHlIqr8s5ehQbdKuTBqmemlVyz6EV7mdtQrGtVmNa0Cnmw6qlid+iy9aK9zAHFulaFBt0q5MGqxyXXg/VifI+rvKxrVWjQrUIerHrcHbqxoqvQB2I+lG50Mx+KmfWHPOYissZmwnwoZmb7ueRaDgcUMxtIVe4hOajcKG9mZrlwQDEzs1w4oJiZWS4cUMzMLBcOKGZmlgsHFDMzy4UDipmZ5cIBxczMcuGAYmZmufBIebOSeSIoGxQOKGYl8kRQNkgcUAaEz3L7k6cwtkHigDIAfJbbvzwRlA0SN8oPAE932r88hbENEgeUAeCz3P7lKYxtkDigDACf5favXszzbdYrbkMZACuXLW443anPcvuDJ4KyQVG5EoqkiyRNSNqY3l5et2y1pK2StkhaVpf+fEmb0mXvl6Rycl8On+WaWRVUtYRySUT8XX2CpJOAFcDJwHzgK5J+JiL2AZcC5wPfAa4HzgRu6G2Wy+WzXDMrW+VKKC2cDVwVEY9GxJ3AVuA0SccCh0XETRERwMeB5SXm08xsRqpqQHmTpFslfUzSEWnaKLCtbp3tadpo+nhq+kEknS9pXNL4rl27isi3mdmMVUpAkfQVSbc1uJ1NUn31TGAJsBN4T+1lDd4qWqQfnBhxWUSMRcTYvHnzpr8hZma2XyltKBHx0izrSfow8IX06XbguLrFC4AdafqCBulmZtZDlavySttEal4J3JY+vg5YIelQSScAJwI3R8RO4GFJp6e9u14LfK6nmTYzs0r28vpbSUtIqq3uAt4AEBGbJV0D3A7sBS5Ie3gBvBG4HBgh6d01o3p4mZlVgZKOUTPP2NhYjI+Pl50NM7O+Iml9RIw1Wla5Ki8zM+tPDihmZpYLBxQzM8uFA4qZmeXCAcXMzHLhgGJmZrlwQDEzs1w4oJiZWS4cUMzMLBcOKGZmlgsHFDMzy4UDipmZ5cIBxczMcuGAYmZmuXBAMTOzXDigmJlZLhxQzMwsFw4oZmaWCwcUMzPLhQOKmZnlwgHFzMxy4YBiZma5cEAxM7NcOKCYmVkuZpedATOztRsmWLNuCzt2TzJ/7ggrly1m+dLRsrNlHXJAMbNSrd0wweprNzG5Zx8AE7snWX3tJgAHlT7jKi8zK9WadVv2B5OayT37WLNuS0k5sm45oJhZqXbsnuwo3aqrlIAi6dWSNkt6XNLYlGWrJW2VtEXSsrr050valC57vySl6YdKujpN/66kRT3eHDObhvlzRzpKt+oqq4RyG3AO8M36REknASuAk4EzgQ9KGkoXXwqcD5yY3s5M018HPBgRzwIuAf6m8NybWW5WLlvMyPDQAWkjw0OsXLa4pBxZt0oJKBFxR0Q0qiA9G7gqIh6NiDuBrcBpko4FDouImyIigI8Dy+tec0X6+F+AX66VXsys+pYvHeXd55zC6NwRBIzOHeHd55ziBvk+VLVeXqPAd+qeb0/T9qSPp6bXXrMNICL2Svpv4Cjg/qlvLul8klIOCxcuzDvvZtal5UtHHUAGQGEBRdJXgKc3WPS2iPhcs5c1SIsW6a1ec3BixGXAZQBjY2MN1zEzs+4UFlAi4qVdvGw7cFzd8wXAjjR9QYP0+tdslzQbOBx4oIvPNjOzaahat+HrgBVpz60TSBrfb46IncDDkk5P20deC3yu7jXnpY9fBdyYtrOYmVkPldKGIumVwAeAecAXJW2MiGURsVnSNcDtwF7ggoiojXh6I3A5MALckN4APgp8QtJWkpLJit5tiZmZ1WimnsyPjY3F+Ph42dkwM+srktZHxFjDZTM1oEjaBdxdwkcfTYMeaANkkLdvkLcNvH39rlfbd3xEzGu0YMYGlLJIGm8W3QfBIG/fIG8bePv6XRW2r2qN8mZm1qccUMzMLBcOKL13WdkZKNggb98gbxt4+/pd6dvnNhQzM8uFSyhmZpYLBxQzM8uFA0qBJN2VTgq2UdJ4mnakpC9L+mF6f0TZ+cxK0sck3Sfptrq0ptvTbLK0qmqyfRdJmkh/w42SXl63rG+2T9Jxkr4m6Y50crs/SdMH4vdrsX2D8vs9SdLNkm5Jt+8daXq1fr+I8K2gG3AXcPSUtL8FVqWPVwF/U3Y+O9ieFwKnAre12x7gJOAW4FDgBOA/gKGyt6GL7bsI+LMG6/bV9gHHAqemj58K/CDdhoH4/Vps36D8fgKekj4eBr4LnF61388llN6rnxDsCp6YKKzyIuKbHHwl52bb03CytF7ks1tNtq+Zvtq+iNgZEd9PHz8M3EEyl9BA/H4ttq+Zftu+iIgfp0+H01tQsd/PAaVYAXxJ0vp0ci+AYyK5ejLp/dNKy10+mm3P/onPUvWTovWbN0m6Na0Sq1Up9O32SVoELCU5yx2432/K9sGA/H6ShiRtBO4DvhwRlfv9HFCKdUZEnAr8KnCBpBeWnaEeyjzxWcVdCjwTWALsBN6Tpvfl9kl6CvAZ4M0R8VCrVRuk9eP2DczvFxH7ImIJyXxQp0l6bovVS9k+B5QCRcSO9P4+4LMkRc57JR0LkN7fV14Oc9Fse5pNltZXIuLedEd+HPgwT1Qb9N32SRomOdh+KiKuTZMH5vdrtH2D9PvVRMRu4OvAmVTs93NAKYikJ0t6au0x8DLgNg6cEOw8npgorF81256Gk6WVkL9pqe2sqVeS/IbQZ9uXTkz3UeCOiHhv3aKB+P2abd8A/X7zJM1NH48ALwX+nar9fmX3XhjUG/AMkl4WtwCbgbel6UcBXwV+mN4fWXZeO9imK0mqDfaQnAG9rtX2AG8j6V2yBfjVsvPf5fZ9AtgE3Eqykx7bj9sH/AJJlcetwMb09vJB+f1abN+g/H7/A9iQbsdtwNvT9Er9fr70ipmZ5cJVXmZmlgsHFDMzy4UDipmZ5cIBxczMcuGAYmZmuXBAMSuQpFdKCknPbrPemyXNmcbn/J6kf+j29WZ5cEAxK9a5wLeAFW3WezPQdUAxqwIHFLOCpNeVOoNkgOSKNG1I0t8pmSfnVkl/JOmPgfnA1yR9LV3vx3Xv8ypJl6ePz5L0XUkbJH1F0jG93i6zZmaXnQGzAbYc+NeI+IGkBySdCvwcyfwUSyNir6QjI+IBSX8KvDgi7m/znt8CTo+IkPR64M+Btxa5EWZZOaCYFedc4O/Tx1elz58BfCgi9gJERNb5V2oWAFen16g6BLgzn6yaTZ8DilkBJB0FvAR4rqQAhkiuNbWebJcRr1/nSXWPPwC8NyKuk/QikhkJzSrBbShmxXgV8PGIOD4iFkXEcSSlie8DfyBpNiRzgqfrP0wydW3NvZKeI2kWyVVyaw4HJtLH52FWIQ4oZsU4l2QOnHqfIWl8vwe4VdItwG+lyy4Dbqg1ypPMD/4F4EaSKyDXXAT8s6R/A9q1t5j1lK82bGZmuXAJxczMcuGAYmZmuXBAMTOzXDigmJlZLhxQzMwsFw4oZmaWCwcUMzPLxf8H6bjmd1shnGgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7bq4+V9ULXlk+qtDSnG2V218CngnMl/RnTQ89Bsija2hFROyW9HjgS5J+2Ck7LdJaXgwkIi4BLoHkehr9Z3M0uW89H91cfa6qF7wCf1/y0KmlWZbPcraB8EcAj0q3e3RT+v3Ai/t984jYnf69W9KnSbqb7pJ0UkTskXQScHe6+S5gUdPTFwK7+82Dtdbt4K211831SKp6eVN/Xw7rJ3hWoaXZMWhExNeBr0u6NCLuyPONJf0ccFREPJDe/w3gb4BrgPOBDenfz6RPuQb4uKS/BxYApwLX55knO6wKNZ4iFFVbzno9kqpe8GpUvy8z9Rs8q9DSzDrl9gOSXhIR+wAkHUcyKL2yj/c+Efh0eu7H0cDHI+KfJX0fuErSK0mu2fESgIjYLukqkrPSDwAXRITPFSlIFWo8eStLbbmKF7waxe9LK/0Gzyq0NLMGjRMaAQMgIu5LxyF6FhH/BjytRfqPgV9r85y3AW/r530tmyrUePLm2nLvRu370q5F2m/wrEJLM2vQeEjSyRFxJ4CkU2gzCG31UIUaT95cW+7dKH1fOrVI8wieZW9pZp1y+ybgW5I+IukjwDeA9cVly4Zt1fJx3n7u6YzPG0PA+Lwx3n7u6aX+Mverm6mxdqRR+r50apGuXbmUsblHTiytW/DMujT6P0s6AziLZOrrGyLinkJzZkNX9hpP3oquLZdlSuqwB/urrlOLtArdS/2a7TyNJ0XED9OAAYenuJ6cdlf9oNjsWdEGdSArywGzkyJ/8P0Msuf52ZVlsL/KZuuCqnvwVET7oQlJ74+IP5L01RYPR0Q8t7is5WNiYiImJyeHnY1SmnkAgaRmnXe3wqDep8xWbLiu5YFmfN4Y317X/meU92fXaz7ssFH5Pkva3LQm4CGznafxR+nf5xSVMRueQc0W8qyk3gfZ8/7sPNjfu+YW32PH5vLIuUex72f7S9tyLsps3VPndno8Iq7ONzs2SK1qnJ3Se+UDVe+zavL+7EZtamxeZrYu9k3vZ2zuHC7+vWUjEywaZps99YL09krgg8DL0tsHgJcXmzUr2hy1Ws6rfXqv6jQrqdcVSHudVZP3ZzcKs3uK4NWHD+sYNCLiDyPiD0nOyTgtIn4nIn6H5JoWVnEH24xntUvvVV0OVP2sQNrrlNS8P7tRmhqbJ7eWD8t6ct/ixnLlqbuA/1JAfmyAxtt0VYzn3AKoyzTEfscXeplVU8RnV/fZPUVwt95hWYPG1yRtAi4naXWsBlrNqLIKGeRZvHU4UA2rtlmHz67qRumM99lkPbnvtZJeBDwrTbokIj5dXLYMij+3oS4tgEEZ5dpm3t/FIr/b7V67n/f0b+WwjudpHLFhst7UqRHxZUnHAnMi4oFCc5eDYZ2n0e+PYlTmglfJqO6TvMvd6fWgvwNzu9f+naeP86nNUyO37/rR7jyNTGtPSfoj4JPA/02TxoGNueWuZvK4ZKNna5TPqA4i5/1dbPd6F16zvbDfzeXf2+nfU06yjmlcQHJVve8BRMSP+l0avc7yOCFrEP3njdbQ1L5p5kgcjGA8rd2Bm+KtjOL4Qt7fxXbP2ze9/2Fpef1u2s0IHMXZT/3KGjQejIj/TC+YhKSj8dLobeXxIyu6/3xmM77xo5raN83aT94AAfsfOpzm9YlGV97fxXav104ev5tGpajV9tadrEujf13SXwJjkn4d+ATw2eKyVW15nJBV9LkNrVpDDfsPxqGA0TC9/yCvv3JrVye0jbpeTwQsy+s35P1dbPd6xx07t+X2efxuznvGolqcK1QGWVsafwG8CtgGvBq4luSscGshj+l57WZrQLLoXL/dRr02y93qyKbo1WR7ef1eJ2fkPXOo03e7qN/NquXjTJxyfO6zqkbRrLOnJB0F3BgRTx1MlvJV9tlT3Xxh85zF0m6106y8KmpnRa8m2+3rV2XmV7cHcM9SLE5Pq9wCRMRDkm5ovtyrzS7LgGm3tcU8Vzxt1RpqmDtHR4xptJLHAGLdanjN5Wn3yeU18NrtuFlVVhruZqJBHq25dp/LWz67vVSfS5lk7Z46Cdgu6Xrgp43EiHhhIbkaEe2+sG+86gbg4V/8PGexNDfjO82eatca6XcAsd0PfvKOe/nqD/dWLpC0qrG2ktfAa7eD03VcO6nIWYr3/Ww/G7dMVeK7N2hZg8ZbCs3FiOo0PfANV25l8o57eeuq0w+l5z2LZbZaXaO/t4jlE9r94D/23TsP1dKrNH7SaWJBQ54Dr92Om9XxbPYiZykCpWuFlUXH2VOSHinp9cBLgCcB346Irzdug8hgnXX6wQbwse/eecSMmGGsFlvUCW3tftgzu3WaT8Aa1GyhXnQ6UBVxImC3+6XVdwfgpw8e6PtzHNZ+yWuWYjtVboUVabaWxmXAfuCbwG8CpwF/WnSmRkWncQVIDqDNtZ1hrX9TxAlt3czV371vuvTXtu50fsBDOS8139DNfmls95bPbue+nx0+iW7f9P6+Psdh7pe8ZileeM32licWVrkVVqTZrhG+LSJOT+8fDVwfEWcMKnN5KPs1wjdumeKNV93Q9oxVAbdt+K3BZioHG7dMHXGAmjc2lwtf+JRDB5JW3V6i9RmjjaXay3xt6yxjGmWYlZP3rK5hX3M8j8kUnkHVWq+zpw6F34g4oJyv6GaHa2NvuHJrywNmFWs7G7dMsfaTN7D/4OES7Zvez9pPHB7gb9Vqes6T5rdcVG7tyqW84cqtLd+r0YUw7FVYZ5bnqBZnIJdhttKglgQZVNdOHq1gr2DbndmCxtMk3Z/eF8kZ4fen9yMiHlNo7kbEquXjTN5x7xGDwFDdM1Yv2rTjiIDRsP+heFh328wfZrsTsNrN5Fowbyz3LpJeX6+5PEvWfb7lNsPuJx/UkiBVq+yM4ppiveoYNCLi4SNn9jB51HLfuur0tgfMqul0YJztoNnux9up/3q2VVi7/UzzmMpZ1oNp3hcT8sWJRk/WKbfWRp613LrUdjoNcvczPRhaB4B2XVeNfdHtvsmjy6WsB9NBLQlSh+/xsJX15FcHjRa62VllOdO2TF+wtSuXPmxMA2DuUerroNkuqHaaudTLvsmjlVDmg2nelZO6VHbKpMyzBSsXNCSdDbwTmAN8ICI25Pn63e6sdjXqbtd16uegX7YvWKvpnTNnT+WpXa2+3Uym2VoMebUSfDC1XpWlMtpKpYKGpDnAPwK/DuwCvi/pmoi4Oa/36HZntVunf04XM836PegP8guWNbgN8oDZrlbfafC8l9cb9o/VRsewZ6V1UqmgQXL1wFsj4t8AJF0BnAPkFjS63Vntzq9ol95KloN+p6vsFfUFmxkgZk6JnRnchtlF1i5I9dpimPl6jbOeHURsEMo6kQKqFzTGgZ1N/+8CnjFzI0lrgDUAJ598cldv0O3OGm+z/XgXO3e2g36nq+ytv3objx2b2/GM1l4O5q1aPzOnBMORs5SKvn5Et2XIq8VQtu4/q7+yTqSA7FfuK4tWfT4Pq9JHxCURMRERE/Pnz+/qDbpd3ymP9aBmW0On02J40/sPItE2D40D3lS6XHfjgDfb+kCt3rPTct+zTXvtR69lgOSg/u11z+W2Db/Ft9c9t6eDfJFlM2ulqDXf8lC1lsYuYFHT/wuB3Xm+Qbe10zxqs7PVKmbrZtr3s/1c/HvLWuZhxYbrehrv6Hal0CL7YIc9KFjm/mWrr7JOpKha0Pg+cKqkJcAUsBp4ad5v0mpndeoe6XfnzhZ4Zlvcb8G8sbZ56PWA1+49Z64P1XyCXVF9sMM+aJe5f9ls0CrVPRURB4DXApuAW4CrImJ70e/bT/dIVp26Udotaw2zd4X1unx0u263l511cssmc5HLtuexBHY/hrEkvVlZVa2lQURcC1w7yPccdvdIc0uk1eypTnnodUBtGN10eZchL56Ca1VS9CzGjkuj10EeS6MvWff5loPAVVm2vExni/eqDmUwK1qey7z3ujS6Uf0+7bIOqHWjDmUwK9ogekUqNaYxLO7TNrMqGMSkEQeNDMo8Z9rMrGEQk0bcPZWRu0fMrOwGMWnEQcPMrCYGMdPPQcOO8Fcbt3H593ZyMII5Euc9YxFvXXX6sLNlZhkV3SvioGGH/NXGbXz0u3ce+v9gxKH/HTjMDDwQbk0u/97OrtLNGkvGL1n3eVZsuC7XVRKsnNzSsEPyuDaIjQ4vGT+aHDRGXPOZ1u10cxVCGx3DXl7HhsNBY4S1WnKglfOesajj4zaahr36sA2HxzRGWKeLO0HSwnj5WSd7ENxaGvbqwzYcbmmMsHY1wqosxGjDNezVh204HDRGUGMco93wtmuKloWXjB9NDhojZrZxDNcUrRvdnkjmJe6rz0GjpIr6cXUax8hyUSezXnmKbj04aJRQkT+uTuMY31733L5e2/pX55q4p+jWg2dPlVCnH1e/POOlvAZxLfph8hTdenDQKKEif1x5XFDKS0cUo8jKQhm4wlIPDholVOSPq98LStW9NjxMda+J+wqY9eAxjYL00zdd9Pz3fpZOdr90cap+LfrZeIpuPThoFKDfgewy/7jqXhsepiyVhaoPlPsKmNXnoFGAPGrjZf1x1b02PEyzVRY8ZdXKwEGjAHWujXvpiGJ1qiy4a9DKwAPhBajzLJF+B9Ktd3WujFh1uKVRgLrXxsvadVZ37hq0MnBLowCujVsRPGXVysAtjYK4Nm55K/OsOhsdDhpmFeLKiA3bULqnJF0oaUrS1vT2/KbH1ku6VdIOSSub0p8uaVv62LskX7jazGzQhjmmcXFELEtv1wJIOg1YDTwFOBt4j6RGJ+57gTXAqent7CHk2cxspJVtIPwc4IqIeDAibgNuBc6UdBLwmIj4TkQE8GFg1RDzaWY2koYZNF4r6UZJH5J0XJo2Duxs2mZXmjae3p+Z3pKkNZImJU3u3bs373ybmY2swoKGpC9LuqnF7RySrqYnAsuAPcA7Gk9r8VLRIb2liLgkIiYiYmL+/Pn9FcTMzA4pbPZURDwvy3aS3g98Lv13F7Co6eGFwO40fWGLdDMzG6BhzZ46qenfFwE3pfevAVZLOkbSEpIB7+sjYg/wgKSz0llTrwA+M9BMm5nZ0M7T+DtJy0i6mG4HXg0QEdslXQXcDBwALoiIxlocrwEuBcaAL6Q3MzMbICWTkeprYmIiJicnh50NM7NKkbQ5IiZmppdtyq2ZmZWYg4aZmWXmoGFmZpk5aJiZWWYOGmZmlpmDhpmZZeagYWZmmTlomJlZZg4aZmaWmYOGmZll5qBhZmaZOWiYmVlmDhpmZpaZg4aZmWXmoGFmZpkN6yJM1qONW6a4aNMOdu+bZsG8MdauXMqq5ePDzpaZjQgHjQrZuGWK9VdvY3p/cjHDqX3TrL96G0BpAoeDmlm9uXuqQi7atONQwGiY3n+QizbtGFKOjtQIalP7pgkOB7WNW6aGnTUzy4mDRoXs3jfdVfqglT2omVn/HDQqZMG8sa7SB63sQc3M+uegUSFrVy5lbO6cI9LG5s5h7cqlHZ+3ccsUKzZcx5J1n2fFhusK6y4qe1Azs/45aFTIquXjvP3c0xmfN4aA8XljvP3c0zsONA9ynKHXoGZm1eHZUxWzavl4V7OROo0z5D2rqfF6nj1lVl8OGjU36HGGboOamVWLu6dqzuMMZpYnB42a8ziDmeXJ3VM153EGM8uTg8YI8DiDmeXF3VNmZpaZg4aZmWXmoGFmZpk5aJiZWWYOGmZmlpkiYth5KJSkvcAdA37bE4B7Bvyeg+TyVVudy1fnssFgy3dKRMyfmVj7oDEMkiYjYmLY+SiKy1dtdS5fncsG5Sifu6fMzCwzBw0zM8vMQaMYlww7AwVz+aqtzuWrc9mgBOXzmIaZmWXmloaZmWXmoGFmZpk5aORA0u2StknaKmkyTTte0pck/Sj9e9yw85mVpA9JulvSTU1pbcsjab2kWyXtkLRyOLnOpk3ZLpQ0le6/rZKe3/RYZcoGIGmRpK9KukXSdkl/mqbXZf+1K1/l96GkR0q6XtINadnekqaXa99FhG993oDbgRNmpP0dsC69vw74X8POZxfleRZwBnDTbOUBTgNuAI4BlgD/CswZdhm6LNuFwP9osW2lypbm+STgjPT+o4F/SctRl/3XrnyV34eAgEel9+cC3wPOKtu+c0ujOOcAl6X3LwNWDS8r3YmIbwD3zkhuV55zgCsi4sGIuA24FThzEPnsRZuytVOpsgFExJ6I+EF6/wHgFmCc+uy/duVrpzLli8RP0n/npregZPvOQSMfAXxR0mZJa9K0EyNiDyRfdODxQ8tdPtqVZxzY2bTdLjr/iMvqtZJuTLuvGs3/SpdN0mJgOUmNtXb7b0b5oAb7UNIcSVuBu4EvRUTp9p2DRj5WRMQZwG8CF0h61rAzNEBqkVa1edzvBZ4ILAP2AO9I0ytbNkmPAj4FvD4i7u+0aYu00pexRflqsQ8j4mBELAMWAmdKemqHzYdSNgeNHETE7vTv3cCnSZqId0k6CSD9e/fwcpiLduXZBSxq2m4hsHvAeetLRNyV/lgfAt7P4SZ+JcsmaS7JAfVjEXF1mlyb/deqfHXbhxGxD/gacDYl23cOGn2S9HOSHt24D/wGcBNwDXB+utn5wGeGk8PctCvPNcBqScdIWgKcClw/hPz1rPGDTL2IZP9BBcsmScAHgVsi4u+bHqrF/mtXvjrsQ0nzJc1L748BzwN+SNn23bBnDFT9BjyBZAbDDcB24E1p+uOArwA/Sv8eP+y8dlGmy0ma+PtJajOv7FQe4E0kMzd2AL857Pz3ULaPANuAG0l+iCdVsWxpfn+ZpIviRmBrent+jfZfu/JVfh8C/xXYkpbhJuCv0/RS7TsvI2JmZpm5e8rMzDJz0DAzs8wcNMzMLDMHDTMzy8xBw8zMMnPQMOuTpBdJCklPmmW710s6to/3+QNJ/9Dr883y4KBh1r/zgG8Bq2fZ7vVAz0HDrAwcNMz6kK6BtILkJMHVadocSf9byTVWbpT0J5JeBywAvirpq+l2P2l6nRdLujS9/wJJ35O0RdKXJZ046HKZtXP0sDNgVnGrgH+OiH+RdK+kM4BnkFzfYHlEHJB0fETcK+nPgOdExD2zvOa3gLMiIiS9Cvhz4I1FFsIsKwcNs/6cB/yf9P4V6f9PAN4XEQcAIiLr9TsaFgJXpuspPQK4LZ+smvXPQcOsR5IeBzwXeKqkAOaQrIu0mWxLVDdv88im++8G/j4irpH0bJKr0pmVgsc0zHr3YuDDEXFKRCyOiEUkrYIfAH8s6WhIrvGcbv8AySVKG+6S9GRJR5GszNrwWGAqvX8+ZiXioGHWu/NIrp/S7FMkA953AjdKugF4afrYJcAXGgPhJNd7/hxwHcnKuw0XAp+Q9E1gtvEPs4HyKrdmZpaZWxpmZpaZg4aZmWXmoGFmZpk5aJiZWWYOGmZmlpmDhpmZZeagYWZmmf1/925epsZTTG8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import matplotlib.pyplot as plt\n",
    "import plotly.express as px\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "rmse_list = []\n",
    "degreeList = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] \n",
    "\n",
    "for i in degreeList:\n",
    "\n",
    "    poly = PolynomialFeatures(degree=i, include_bias=False)\n",
    "    poly_features = poly.fit_transform(X)\n",
    "    X_train, X_test, y_train, y_test = train_test_split(poly_features, \n",
    "                                                        y, train_size=0.8,\n",
    "                                                        random_state=42)\n",
    "    \n",
    "    polyReg = LinearRegression()\n",
    "    polyReg.fit(X_train, y_train)\n",
    "\n",
    "    polyReg_predicted = polyReg.predict(X_test)\n",
    "    polyReg_rmse = np.sqrt(mean_squared_error(y_test, polyReg_predicted))\n",
    "    rmse_list.append(polyReg_rmse)\n",
    "    \n",
    "\n",
    "\n",
    "    plt.plot(y_test, polyReg_predicted, 'o')\n",
    "    plt.xlabel('Actual')\n",
    "    plt.ylabel('Predicted')\n",
    "    plt.title('Actual vs. Predicted')\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aa02eeac",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4c3c6b8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(degreeList, rmse_list, color ='lightblue',width = 0.5)\n",
    " \n",
    "plt.xlabel(\"degree\")\n",
    "plt.ylabel(\"rmse\")\n",
    "plt.title(\"RMSE by degree\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4887adff",
   "metadata": {},
   "source": [
    "Here we can see that the root mean squared error increases dramatically after the first few degree increases. This is likely due to overfitting of the model on the training data."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}