{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_poly(X, deg):\n",
    "    n = len(X)\n",
    "    data = [np.ones(n)]\n",
    "    for d in range(deg):\n",
    "        data.append(X**(d+1))\n",
    "    return np.vstack(data).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit(X, Y):\n",
    "    return np.linalg.solve(X.T.dot(X), X.T.dot(Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_and_display(X, Y, sample, deg):\n",
    "    N = len(X)\n",
    "    train_idx = np.random.choice(N, sample)\n",
    "    Xtrain = X[train_idx]\n",
    "    Ytrain = Y[train_idx]\n",
    "    \n",
    "    plt.scatter(Xtrain, Ytrain, edgecolors='k')\n",
    "    plt.show()\n",
    "    \n",
    "    Xtrain_poly = make_poly(Xtrain, deg)\n",
    "    w = fit(Xtrain_poly, Ytrain)\n",
    "    \n",
    "    X_poly = make_poly(X, deg)\n",
    "    Yhat = X_poly.dot(w)\n",
    "    plt.plot(X, Y, color='green')\n",
    "    plt.plot(X, Yhat, color='red')\n",
    "    plt.scatter(Xtrain, Ytrain)\n",
    "    plt.title('deg = %d' % deg)\n",
    "    plt.axis([0, 20, -5, 5])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mse(Y, Yhat):\n",
    "    d = Y - Yhat\n",
    "    return d.dot(d) / len(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_train_vs_test_curves(X, Y, sample=20, max_deg=20):\n",
    "    N = len(X)\n",
    "    train_idx = np.random.choice(N, sample)\n",
    "    Xtrain = X[train_idx]\n",
    "    Ytrain = Y[train_idx]\n",
    "    \n",
    "    test_idx = [idx for idx in range(N) if idx not in train_idx]\n",
    "    Xtest = X[test_idx]\n",
    "    Ytest = Y[test_idx]\n",
    "    \n",
    "    mse_trains = []\n",
    "    mse_tests = []\n",
    "    \n",
    "    for deg in range(max_deg+1):\n",
    "        Xtrain_poly = make_poly(Xtrain, deg)\n",
    "        w = fit(Xtrain_poly, Ytrain)\n",
    "        Yhat_train = Xtrain_poly.dot(w)\n",
    "        mse_train = get_mse(Ytrain, Yhat_train)\n",
    "        \n",
    "        Xtest_poly = make_poly(Xtest, deg)\n",
    "        Yhat_test = Xtest_poly.dot(w)\n",
    "        mse_test = get_mse(Ytest, Yhat_test)\n",
    "        \n",
    "        mse_trains.append(mse_train)\n",
    "        mse_tests.append(mse_test)\n",
    "        \n",
    "    plt.plot(mse_trains, label='train mse')\n",
    "    plt.plot(mse_tests, label='test mse')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'range'>\n",
      "<class 'range'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'range'>\n",
      "<class 'range'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'range'>\n",
      "<class 'range'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'range'>\n",
      "<class 'range'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'range'>\n",
      "<class 'range'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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eM7Nk2oo957bgX38VadLE9fsaNkyOZB2SSz66RMxwI2NTx1r7JgJYu5E/Sd0hM+X+7ldInkFWVIuUix94W9qN/MnS9dQbMlOaPPy5LKmdIHkGubVvitQZMkPqDZlp6XqCGZAqFmSwT7f4s/Oy6T6xOwt2LmBs97EMaDGgdCvYuhXmzYOTJ8HhgPx8CA93jfUTHu7qRkhLgz17XH3LBw5AdDQnelxDryZr+dn8wVfXf6UHfc8kLw95+GHMf/7DzMbw66uDaFl3MP+avcW6Pt6cHBg0CMaPh27dOPHJOK77cQCzts5i9FWjeaLdE9a9nwBVf+j3XLnxLT74di7z65djUK/3yY6sgIHSdcGVUkH/f0zOcT6cch//SDvC7X2bsqPlv/jlqassW08wC/gWf3ZetnSe0FnMcCMTVk84h/+NpZSfLzJ/vsj994tER4szOlr+07OmxDwTIjM3aUulWJmZ4uzUSQTk1XbI0B+eFKfT6Zl1OZ0i778vEhYmkpwsOds2S7+v+wnDkdcWv+aZdQaQe27uKXkGWVg3XpIem3Tq05jVLf5pK/bIec/MkrpDZsr5j0yWX2tVltwQ5OlBbYv/pK7OCha1+H0y+HPyc6TrF12F4chHKz4654101nbtErn+ehGQ3ZUjpNUDkbJ412Lvrd9fHD0qznbtJD/EyO29kMd+eMxzoV/YggUiCQkitWtL/sYNp8L/45Ufe37dfuqHfz8uJ0ORZTVj5fxHvrSmC64E01bskXYjf5J6Q2bKlc/PkC0Nq0lWGPLG2zd6Zx8JcAEb/E6nU26deqswHPv6cX/6SfJrVJfjEUb63xYra/atsacOX5SRIdKmjeSHhkjffsiD/33Qu3/QK1aIVK4sUq2a5K5eKVd9dpWEvhAq32781ns1+IlF374rxyKQbbXjZOpPy08FcruRP3kk9Ivi3LtX0quVk32xyL8nP+mVdQaygA3+5+c/LwxHXl74cpk2UJmlpcnJ5heJwyDDu8fLzsM77K3HF2RkiLRqJY6wUOl1A3LD1zfY8xH+999FqlcXqVRJslJ/lVbjWknUy1Hy866fvV+Lj1qz4kfZXd7I3grhcnznFltrcfy+To7HhsvvlZEJC96xtRZ/F5DB/8nKT4ThyJ3T7/SNj4VZWZLRo7MIyAddqsqxnGN2V2SfkydFLr9cHGGh0vemMGn3YTvJzsu2r56tW0Vq1RJJTJRDq5dK0rtJUvm1yrL98Hb7avIRu9M2yqpa4XI8wsiBJXPsLkdERHLnzpbcUCNzGxhZsGWu3eX4rYAL/vk75kvYi2Fy5WdXSm5+riUbyRIOh+zud40IyLt9GkvbV+Z4/eOy7fLzTx37uLd/nDR6p5GkZ6XbXZXIhg2ubp+6dWX7mkVSYVQFafLvJpJ5MtPuymyTeSJD5lxcTvINsnPCe3aX8xdZH7zn+ju6JEq2Hd5mdzl+KaCCf8eRHVLp1Upy/nvnS0Z2hmUbyTL5+bK0Q1MRkMeubu7xA2Q+xekUGTRIBGR032qSMCpBNh/cbHdV/5OaKhIfL3LeebLg/6ZI6Auh0v3L7pLvyLe7Mq9zOB3y5fXni4BsfPpeu8sp0pEBt4iAPHlHTTl68qjd5fidgAn+rNwsuXjMxVJ+ZHnfCpTTdHjpB5mZVFUE5J5e3Tx2SpzPGT1aBGRG9yQJeSFEftjyg90V/d3ChSJRUSJt2siYRW+eutgv2Ewc6QrV37ukuP5h+6LcXDnyj6aSFY4MGtFBT/M8S1YFv63DHYoId824i9X7VjPx2ok0rtTYznJKtOd4Po/2eI9FdWN4e+b3XLh3HgB/FhqwKuB89x0MHsyGK5rSq8VmRnUaxdWNrra7qr+79FL48ktYtox73/qZgRffzatLXuWb9d/YXZnXzPvxA7oM/5yd9Stw/jcLTw1H4nPCw0n4bg7OCgk8Nnoxo797yu6KgpKtwf+vX//FxHUTGdFxBNc0vsbOUs6oRkI0uWExPNDrddLKhTB+6ltUydxFjYRou0vzjDVr4KabONqkESlt13LDRf19+yrZPn3gjTdg6lTeXRBD65qtuePbO9iQvsHuyjxuy66VVL/tfggLpdqPv2BiYuwuqWSJicTO+IFax0No+vhrzNw4w+6Kgo5twb9g5wKGzB3Ctedfy9AOQ+0qo9SevDqZ6PBQjkXX4c5rHyU218nY6U8y+JJadpdmvf37oUcP8uNjad8jnUa1L+LDnh8WO0a7z3jkEXjoIcLeeptZGd2JCY+hz+Q+ZOZk2l2Zx2TlHGfrtZeTlO4k54vPiGp8nt0llYpp3Rp56026boW1g/qx9fBWu0sKLlb0FwFdgE3AVmDomaa/qPlFkjg6UZLfTfarAzyFr0q889Ye4gBZe8WFvtufei5yckTatxdndLTc8tR5Un5kedlyyN7zwM9Kfr5Ir14iISGy+pNXJfSFUOk7ua9vnB5sMafTKZ8MaCkCsuWJO+0u5+w5nZLZv684DDLwgXqSlZtld0U+D185uAuEAtuABkAEsBq4oKR54urGScyIGFm3f53ntpCHOZ1OmXxLcxGQ9c8MtLsc69x7rwjI2MGdhOHI9A3T7a7o7B075hqltVw5+ejzJ4ThyOtLXre7KstNGf+45IYgm9qdJ+Lw04OkWVmSeV59ORSFPDamT0D+g7aSLwV/W+DHQt8/BTxV4jzVkS/XfOmpbeM1WSePybyLykluCLL3h2/sLqfsxowRAVlzh2ucpKFzhtpd0bnbtUskMVGc9evLP8d1l9AXQmXRzkV2V2WZ1FWzZHc55M+qMeI4dNDucspm61Y5ERclK6oh4xe/a3c1lknLTJNOn3ay9GxFq4Lfij7+msDuQt/vcf/sL4wx9xhjUo0xqfEh8dzY9EYLVm2vmMg46kybx+4EQ0j//uT8ufvMM/mqJUvgwQfJvKI9bRr8xBX1ruClji/ZXdW5q1MHvv0W8+efjP34EMlx9eg3pR/7ju+zu7IySz+6l+zre1M52xD77SxCKvr57SgbNiRy0tc02w+RDzxMatr/2V1RmeU58uj3dT+W7llKnjPP7nL+xorgL+qI398G+ReRsSKSIiIpjav57mmbZ6thg5bsGP868cfz2HlNW9fY//5mzx649locdWpzeec0EmIrMem6SYSFlO52fD6rdWv45BPCfvmVn39rwtHsDPpP6U++0w9/R24Op4O5t7Sjw5Yc9r/2POXaXGp3SZYI6dad7GFDuGW1kxkPXc3h7MN2l1Qmg+cMZsnuJXzY80MuqHKB3eX8XVk/MnAOXT1ncwcufzHp8S4iIKsH9LC7lLNz4oRISoo44+LkgdFXSNiLYbLkjyV2V2Wt554TAUl9+AZhOPLEj0/YXdE5+/yF60RANvS9zO5SrOdwyOErO0huCPLE0//w26uvJ6+bLAxHHp71sOXLxof6+MOA7UB9/ndw98KS5gnE4M9z5Ml3l1YXAdn66Vt2l1M6TqfIrbeKgEx5xTUU9ttL37a7Kus5HK5bbBojY565RhiOTF432e6qztq8Hz+QjEhke+PKrkHzAtGRI3K4XjU5GI288dn9dldz1tYfWC+xI2Kl3YftJCc/x/Ll+0zwu2qhK7AZ19k9w840fSAGv4jI/vSdsrZGuGREh8iR9SvsLufM3nhDBGTzQ7eIGW6k/5T+gXtWRVaW65NNbKzc/mxTiR0R61dnlW3eniobqobIkdhQyd62ye5yPMq5ebMci4+U9ZWR73/7wu5ySu1I9hFp/E5jqTq6quw56pkxvKwKfksu4BKR/4pIkog0FJERVizTH1WtXJf8ryYh4uRAt8txnMiyu6Ti/fADPPEEx7teRetq39E0sSnje4z3/Yu0zlVMDMyYgalYkQ/HHSDpRDR9v+rL0ZNH7a7sjDKzM9jd83IaHXSS8+UEohok2V2SR5nGjQmfNoNGRwxRN93G5v3r7S7pjJzi5Japt7AjYwdTrp9CzXJluM+0F9g6ZEMgurh9X5aNuJ+kHZms7N0axPs3sz+j33+HG27A0eRCrui0GxMayvQbphMbEWt3ZZ5VvTp8/z2hJ7JZ9E050vdu48ZvbsThdNhdWbGc4mTWza3puO44O559kMSe/n82XGlEdurM0bdepeNWB2t7tyUj+4jdJZXo+fnP8/2W73mnyztcUvcSu8s5Mys+NpztI1C7egqbeWOKCMjXd/Wx5ZZ3xTpwQKR+fXFWqyZ3v99FQl4IkbnbguzGGLNni4SFyR+tz5ewZ133DPZVk55zHcxd16NNYF0hXko7HrpdBOSzjrWk7YgffefvqJApv08RhiN3fXuXx7tK8aWuHvV3nT9dzPymFen94TQS136FAGkZ2Tw1dS3TV6bZU9TJk9C3L+zdy3tPX8W49B94/arX6dSgkz312OWqq2DMGGov28Avi5N585c3+GjlR3ZX9Tc/THienq9MYWtyFS74ar7vjrjpQfXe+pgFXdtx67w9XD3nEd/4Oypk2Z5l3DrtVtrWast7Xd/zm65SDX4PCQ+P5MU+77KlUigfTB9LtaNrAcjOczD6x03eL8jhgJtvhsWLmfPszTx0eAL3pdzHI20e8X4tvmDAAHj5Zf4xfxNTf63DwO/uZeHOhXZXdcpv8z4nZeCLHKoUTZ0FKzFRUXaXZA9jeKb9C0xuUovnF2zgxhWjABv/jgrZfmQ7PSb2oHp8dab3n05kWKSt9ZwNDX4P2plTnnv6PkeoU/j062cod+IPwIYx/EXgvvtg6lTWD7uHLvkf07VxV9655h2/aaF4xNNPw6OP0nvOH7yxLIGek3qyat8qu6ti8/rFVLn+dkJCQomf+zMR1Xz7QKGnpWXm8HSXt5mRnMDIOYu5e+loELH1XhiHsw/T9Yuu5Dvz+e9N/6VqbFXbajkXGvweVCMhmt0VWvLP6+6nboaDsVMfJSLvsPfH8H/2WRg3jrRBt9M69kuaJTZj8nWT/f/K3LIyBl5/HW6/nUH/PcgTvxq6fN6FbYe32VZS2u71ZHfpROIxJyenfU35Ji1tq8VX1EiIxhEaySM9xjCxSTmGLVzIE4tGU6O8PZ+CsnKz6D2pNzsydjC9/3SSKyfbUkdZaPB7UMEY/qtrduW+XjfQKi2HN75/gEcu92IL7pVXYMQI0m/qxYU1plE1tiozb5pJXESc92rwZSEhMH48XH89z844yqC5mVw14Sr2Htvr9VL27tlI+iUtuCAtl7Rxb1Djyj5er8EXFfwdOUPjGNL1P4xJiWPQ0kX8Z/HrkJvr1VpO5J2gx8QeLNm9hAl9JnBpXT8dMsOKI8Rn+wiGs3oKFB7D/4XunUVAfmqTKMePH/Hsip1OkaeeEgE51OcaqTwiQeq9VU92Zezy7Hr9VV6eyM03i4CMvCJckt9Jkt1Hd3tt9ft2b5RVdaMkJxTZMH6U19brLwr/HbUcMVFe7xgvAnK0dXPXmWpekJ2XLVd9dpWY4UYmrJ7glXWeDl+6cvdsH8EU/KdLfeh6EZBFF1eQw4f/9MxKHA6Rhx4SATlwcx+pMrKi1H6jtuw4ssMz6wsU+fkiAwaIgPy7XYQ0eL2OpUPqFidt+2pZ7Q7938eP9Pj6AsG2w9vk4VuryIkwJLtmosiqVR5d37GcY9Ll8y5ihhv5eOXHHl1XSTT4/djKZ+4SAfk1OU72791m7cKPHRO54QYRkC139JSYl6Olzpt1ZOuhrdauJ1A5HCKPPur6ZJYULo1frCKr96322OrWzZssOyqFSnYYsnbsCI+tJxClZabJ9YPry+5ySH5UhMgnn3hkPbuP7paLx1wsIS+EyPjl4z2yjtLS4Pdza197QvINsr56uCyf+7k1C92wQeT888UZEiILBl4j5nmk9bjWsvfYXmuWH0zGjRNneLhsrRImzR+N8ciNg34Z84wcjUT2x4fIlu/t6TrwdwezDsrVo5vJvHqIgDj/+U/XuEwWWf7ncqnxrxoS/0q8fL/5e8uWe640+APAli/elYNxIZIVjswacq04znUYWofD1dqJixNH5Uoy/LnLhOFIv6/7yYncE9YWHUwWLZL8ypXkRESIPNQFGTj9bsnOyz6nRRXuo770hanydY/mkm+QjbVjZP+GVIsLDy7Hco7JzV/1lxcvRRwGybvwfJGtZfuE63A65N1l70rMiBip82aJ9C4xAAAOyUlEQVQdWbNvjUXVlo0Gf4A4un2jrG5SRQTkl4sry+bZk85uAQsXivzjHyIg+y9OkgufTpCIlyJkxKIR4nD66X1Yfcnu3eK45hoRkCW1kJ7PNpLZW2ef1SKmrdgj5z0zS+oOmSl9brpbNlUMFQGZ1aGBnDiS7qHCg4vT6ZQPUj+QbreFy6EYIyfLxcqif39xTsOlbEjfIO0/bC8MRzpP6OxTn5g1+AOIMz9fljzURzKijAjIquY1ZO+0CcV/ZD14UOTjj0W6uG7+klWtkrx0V5KY55C249vK7wd+92r9Ac/pFJkwQXIS4iXfIBMvRO57oZWkppWupd52xBzpffM9Mj25ogjI1gqhcu2Nd0q7kT95uPDgs3LvSun5chNZWwXJN8iwTldLncEzpO6QmXLeM7NKDP+1+9fKwO8GSuRLkVJhVAX5dNWnPjdMuVXBb1zL8q6UlBRJTU31+np93ZF9u1g27DZaTF5E1SzID4H0RjWIaJ5CrIkgIuskJv0g/PYbxukko2o5xrY0DG9+lCpV6jC43WAGpgwkNCTU7rcSmA4cIP+1V3GM+TeRWSdZVAdSm1cluuPVNOt6J/UTk0mISiAqLIoDB3awc940spbMo9KUOTTbn8ehaBjf8gI+bDWM3PDyGGDHqG52v6uA4xQnKc8P5bmv3qH3phxe6RDNyMs7EuNoRe34ZBY83o3Y8FiO5hxlzf41rNq3iukbpzN/53wiQyO55aJbGNFxBIlxiXa/lb8xxiwXkZQyL0eD3/ek7dvC4o9fIGvxPGpv3MuFByA7HI5FQGYULKwL08+DldXhigYdebDVg/RI6qGB7y2ZmWT/+x2yP3iPijv3A3AyFDIjXf+sHSFQ4xiEuv+01iZGML5lB2adN4Dc8PKnFlMzIZolQzva8Q4CXv2h3yOSw4uzh3PbqrU81jmUN9v9b/jtsJCwv9x7uV5CPQa2HMiAFgOoHFPZjpJLRYM/SKRlprFo1yIOZx8m42QGx3OPUy+hHhdXu5gmVZsE/hj6vu7AAY7/9AN/zp1G3tHD5OVk48jJJr92TWLaXUatTn1YeCSep6auJTvvf8ETHR7KyL5N6d08uMfh8ZT2o+aRlpFNiNPBuzNeo9umJTzYrQ+z2tbn3surkXEyg3KR5WhWrRnNEptRLa6aX4xbpcGvlB+ZvjKN0T9u4s+MbGokRPPk1cka+h40fWXaqX+2Efl5fDjlBdr+sYbf3vmEdoNutbu8c6bBr5RSJSj8z7ZhNHzz+ROUzz4GGzZAfLzd5Z0Tq4I/yIdnVEoFqt7Na/71U1XnitCuHbz4IowebV9hPkBH51RKBYe2beHOO+Gtt1z3nQ5iGvxKqeAxapSrm+eBB1w3KApSGvxKqeBRpQqMHAkLF8KXX9pdjW00+JVSweWuu6BFC1dff5C2+jX4lVLBJTQUBg2CzZth6VK7q7GFBr9SKvhcdx3ExMAnn9hdiS00+JVSwSc+3hX+kybBiRN2V+N1GvxKqeB0xx2QmQnTp9tdiddp8CulgtNll0G9ekHZ3aPBr5QKTiEhcPvtMHcu7N5tdzVepcGvlApet93mOqVzwgS7K/EqDX6lVPBq0MDV5fPZZ3ZX4lUa/Eqp4Na7N2zaBGlpdlfiNRr8Sqng1qGD63nxYnvr8KIyBb8xZrQxZqMxZo0xZpoxJsGqwpRSyisuvhhiYzX4z8IcoImIXARsBp4qe0lKKeVFYWHQpo0Gf2mJyGwRKbhj8VKgVtlLUkopL+vQAdasgaNH7a7EK6zs478TmGXh8pRSyjs6dACnM2gGbTtj8Btj5hpj1hXx6FVommFAPvBFCcu5xxiTaoxJTU9Pt6Z6pZSyQuvWrlE7g6S754z33BWRK0t63RhzO9Ad6CQl3LldRMYCY8F1s/WzrFMppTwnPt51kDdIgr+sZ/V0AYYAPUUk+Ia4U0oFjg4dYNkyyM21uxKPK2sf/3tAPDDHGLPKGDPGgpqUUsr7OnSA7GxYudLuSjzujF09JRGRRlYVopRStmrf3vW8eLGrzz+A6ZW7SikFUL06NGwYFP38GvxKKVWgQwdX8Af4Tdg1+JVSqkC7dnDwIOzYYXclHqXBr5RSBS64wPW8aZO9dXiYBr9SShVISnI9a/ArpVSQqFIFEhJg82a7K/EoDX6llCpgjKvVry1+pZQKIsnJ2uJXSqmgkpQEe/ZAVpbdlXiMBr9SShWWnOx63rLF3jo8SINfKaUKKwj+AO7n1+BXSqnCGrmHIAvgfn4NfqWUKiwmBurU0Ra/UkoFlaQkbfErpVRQKTilM0AHa9PgV0qp0yUlwdGjcOCA3ZV4hAa/UkqdruDMngDt7tHgV0qp0wX4YG0a/Eopdbo6dSAyUlv8SikVNEJDXefza4tfKaWCSAAP1qbBr5RSRUlKgm3bID/f7kosp8GvlFJFSU6GvDzYudPuSiynwa+UUkUpOLMnALt7NPiVUqootWu7ntPS7K3DAzT4lVKqKImJrue9e+2twwM0+JVSqigREa6br//5p92VWE6DXymlilO9urb4lVIqqNSooS1+pZQKKtriV0qpIFO9OuzbBw6H3ZVYSoNfKaWKU6OGK/QPHrS7Ektp8CulVHGqV3c9B1h3jwa/UkoVp0YN13OAHeDV4FdKqeJoi794xpgnjDFijKlsxfKUUsonVKvmetYW/18ZY2oDVwF/lL0cpZTyIZGRUKmStviL8CYwGBALlqWUUr4lAC/iKlPwG2N6AmkisroU095jjEk1xqSmp6eXZbVKKeU9AXgRV9iZJjDGzAWqFfHSMOBpoHNpViQiY4GxACkpKfrpQCnlH6pXhw0b7K7CUmcMfhG5sqifG2OaAvWB1cYYgFrACmNMKxHZZ2mVSilllxo1XC1+pxNCAuNEyDMGf3FEZC1QteB7Y8xOIEVEAusSN6VUcKte3XXf3UOHXMM0B4DA+PellFKeEoAXcVkW/CJST1v7SqmAE4AXcWmLXymlSqItfqWUCjIFV+9qi18ppYJEVBRUrKjBr5RSQaV6de3qUUqpoFJwLn+A0OBXSqkz0Ra/UkoFmYLxeiQwRpvR4FdKqTOpUQPy8lxX7wYADX6llDqTALuIS4NfKaXOJMAu4tLgV0qpM9EWv1JKBRkNfqWUCjLR0RATowd3lVIqqFSoAEeO2F2FJTT4lVKqNCpUgMOH7a7CEhr8SilVGhUrBkyL34gNV6IZY44Bm7y+4rNXGfCHm8tondbxhxpB67Sav9SZLCLxZV3IOd9zt4w2iUiKTesuNWNMqtZpHX+o0x9qBK3Tav5UpxXL0a4epZQKMhr8SikVZOwK/rE2rfdsaZ3W8oc6/aFG0DqtFlR12nJwVymllH20q0cppYKMBr9SSgUZjwa/MaaLMWaTMWarMWZoEa9HGmMmu19fZoyp58l6iqmxtjFmvjFmgzHmd2PMw0VMc7kx5qgxZpX78Zy363TXsdMYs9Zdw99O6zIu77i35xpjTAsv15dcaButMsZkGmMeOW0aW7alMeYjY8wBY8y6Qj+raIyZY4zZ4n6uUMy8t7un2WKMud2GOkcbYza6f6fTjDEJxcxb4v7hhTqHG2PSCv1uuxYzb4m54IU6JxeqcacxZlUx83plexaXQR7dP0XEIw8gFNgGNAAigNXABadNcz8wxv11f2Cyp+opoc7qQAv31/HA5iLqvByY6e3aiqh1J1C5hNe7ArMAA7QBltlYayiwD6jrC9sSuBRoAawr9LPXgKHur4cCrxYxX0Vgu/u5gvvrCl6uszMQ5v761aLqLM3+4YU6hwNPlGK/KDEXPF3naa//C3jOzu1ZXAZ5cv/0ZIu/FbBVRLaLSC4wCeh12jS9gE/dX08BOhljjAdr+hsR2SsiK9xfHwM2ADW9WYOFegGfictSIMEYU92mWjoB20Rkl03r/wsRWQScPtBK4f3vU6B3EbNeDcwRkcMicgSYA3TxZp0iMltE8t3fLgVqeWr9pVXM9iyN0uSCZUqq0501/YCJnlp/aZSQQR7bPz0Z/DWB3YW+38PfA/XUNO4d+yhQyYM1lcjd1dQcWFbEy22NMauNMbOMMRd6tbD/EWC2MWa5MeaeIl4vzTb3lv4U/wflC9sSIFFE9oLrjw+oWsQ0vrRNAe7E9amuKGfaP7xhkLtL6qNiuiZ8aXteAuwXkS3FvO717XlaBnls//Rk8BfVcj/93NHSTOMVxpg44BvgERHJPO3lFbi6LJoB7wLTvV2fW3sRaQFcAzxgjLn0tNd9YnsaYyKAnsDXRbzsK9uytHximwIYY4YB+cAXxUxypv3D0/4DNAQuBvbi6kY5nc9sT+BGSm7te3V7niGDip2tiJ+dcXt6Mvj3ALULfV8LOP2GlaemMcaEAeU5t4+PZWKMCce1wb8Qkamnvy4imSJy3P31f4FwY0xlL5eJiPzpfj4ATMP1sbmw0mxzb7gGWCEi+09/wVe2pdv+gq4w9/OBIqbxiW3qPmjXHbhZ3J27pyvF/uFRIrJfRBwi4gTGFbN+X9meYUBfYHJx03hzexaTQR7bPz0Z/P8HNDbG1He3APsDM06bZgZQcBT6OmBecTu1p7j7+T4ENojIG8VMU63g2IMxphWu7ebVW/EYY2KNMfEFX+M64LfutMlmALcZlzbA0YKPil5WbEvKF7ZlIYX3v9uBb4uY5kegszGmgrvrorP7Z15jjOkCDAF6isiJYqYpzf7hUacdT+pTzPpLkwvecCWwUUT2FPWiN7dnCRnkuf3Tw0eru+I6Qr0NGOb+2Yu4dmCAKFzdAVuB34AGnqynmBo74PpotAZY5X50BQYCA93TDAJ+x3UGwlKgnQ11NnCvf7W7loLtWbhOA7zv3t5rgRQb6ozBFeTlC/3M9m2J6x/RXiAPVytpAK7jST8BW9zPFd3TpgDjC817p3sf3Qr804Y6t+Lqxy3YPwvOhKsB/Lek/cPLdU5w73drcIVW9dPrdH//t1zwZp3un39SsE8WmtaW7VlCBnls/9QhG5RSKsjolbtKKRVkNPiVUirIaPArpVSQ0eBXSqkgo8GvlFJBRoNfKaWCjAa/UkoFmf8HuTk8DbUHq+EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n",
      "<class 'range'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "X = np.linspace(0, 6*np.pi, N)\n",
    "Y = np.sin(X)\n",
    "\n",
    "plt.plot(X, Y)\n",
    "plt.show()\n",
    "\n",
    "for deg in (5, 6, 7, 8, 9):\n",
    "    fit_and_display(X, Y, 10, deg)\n",
    "plot_train_vs_test_curves(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "13\n",
      "14\n",
      "15\n",
      "16\n",
      "17\n",
      "18\n",
      "19\n",
      "20\n",
      "21\n",
      "22\n",
      "23\n",
      "24\n",
      "25\n",
      "26\n",
      "27\n",
      "28\n",
      "29\n"
     ]
    }
   ],
   "source": [
    "for i in range(30):\n",
    "    print(i)"
   ]
  },
  {
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}