{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "http://ww2.amstat.org/publications/jse/v21n1/witt.pdf\n",
        "\n",
        "http://nsidc.org/research/bios/fetterer.html\n",
        "\n",
        "ftp://sidads.colorado.edu/DATASETS/NOAA/G02135/north/monthly/data/N_08_extent_v3.0.csv"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": true
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "import pandas as pd\n",
        "\n",
        "#from scipy import stats"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Read Data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": true
      },
      "outputs": [],
      "source": [
        "data = pd.read_csv('N_09_extent_v3.0.csv', dtype={'year': np.int32, 'extent': np.double})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "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>year</th>\n",
              "      <th>mo</th>\n",
              "      <th>data-type</th>\n",
              "      <th>region</th>\n",
              "      <th>extent</th>\n",
              "      <th>area</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <td>0</td>\n",
              "      <td>1979</td>\n",
              "      <td>9</td>\n",
              "      <td>Goddard</td>\n",
              "      <td>N</td>\n",
              "      <td>7.05</td>\n",
              "      <td>4.58</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>1</td>\n",
              "      <td>1980</td>\n",
              "      <td>9</td>\n",
              "      <td>Goddard</td>\n",
              "      <td>N</td>\n",
              "      <td>7.67</td>\n",
              "      <td>4.87</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>2</td>\n",
              "      <td>1981</td>\n",
              "      <td>9</td>\n",
              "      <td>Goddard</td>\n",
              "      <td>N</td>\n",
              "      <td>7.14</td>\n",
              "      <td>4.44</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>3</td>\n",
              "      <td>1982</td>\n",
              "      <td>9</td>\n",
              "      <td>Goddard</td>\n",
              "      <td>N</td>\n",
              "      <td>7.30</td>\n",
              "      <td>4.43</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <td>4</td>\n",
              "      <td>1983</td>\n",
              "      <td>9</td>\n",
              "      <td>Goddard</td>\n",
              "      <td>N</td>\n",
              "      <td>7.39</td>\n",
              "      <td>4.70</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   year   mo      data-type   region   extent     area\n",
              "0  1979    9        Goddard        N     7.05     4.58\n",
              "1  1980    9        Goddard        N     7.67     4.87\n",
              "2  1981    9        Goddard        N     7.14     4.44\n",
              "3  1982    9        Goddard        N     7.30     4.43\n",
              "4  1983    9        Goddard        N     7.39     4.70"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(39, 6)\n"
          ]
        }
      ],
      "source": [
        "print(data.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "metadata": {
        "collapsed": true
      },
      "outputs": [],
      "source": [
        "year = data['year']\n",
        "extent = data[' extent']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x11fa1e940>]"
            ]
          },
          "execution_count": 69,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIDEENwAkhuAGgMQQ3ACQmP8DMsYLm5LDbXQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(6,4))\n",
        "plt.plot(year, extent, 'o')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Try a linear fit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "number of data points =  39\n"
          ]
        }
      ],
      "source": [
        "npoints = data.shape[0]\n",
        "print('number of data points = ', npoints)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "collapsed": true
      },
      "outputs": [],
      "source": [
        "def fitfunction(t,coeffs):\n",
        "    fit = 0\n",
        "    for i,c in enumerate(coeffs):\n",
        "        fit += c*t**i\n",
        "    return  fit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [],
      "source": [
        "ndata = 20 #use the first ndata points for the fit\n",
        "year1 = year[:ndata]\n",
        "extent1 = extent[:ndata]\n",
        "\n",
        "A = np.array([\n",
        "    1+0*year1,\n",
        "    year1\n",
        "    ]).T\n",
        "\n",
        "b = np.array(extent1)\n",
        "\n",
        "x = la.solve(A.T@A,A.T@b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x115cb4b70>]"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAFx1JREFUeJzt3XuMXGd5x/Hfs+v1be2ddbwbx/ba\n2E4I4Njr4GzTpCmhxSVcg4vaWiltQQXJ/QNBikorUEsUUoHaipIQFQmllAgokLrQqCFqgZA2pFwS\nsEk8dhLnZux41yZ2CB7bie9++sc5szd25+I5Z855Z74faTWzZ2Znnz0788w7z3szdxcAIBwdWQcA\nAKgPiRsAAkPiBoDAkLgBIDAkbgAIDIkbAAJD4gaAwJC4ASAwJG4ACMyMNB60r6/PV6xYkcZDA0BL\n2rZt2wvu3l/LfVNJ3CtWrNDWrVvTeGgAaElmtrfW+1IqAYDAkLgBIDAkbgAIDIkbAAJD4gaAwIST\nuItbpFvXSDf3RpfFLVlHBACZSGU4YOKKW6RvflA6fTz6vrQv+l6SBjdlFxcAZCCMFvf9t4wl7bLT\nx6PjANBmwkjcpeH6jgNACwsjcRcG6jsOAC0sjMS94Sapa87EY11zouNoD3ROA6PC6Jwsd0Def0tU\nHikMREmbjsn2QOc0MEEYiVuKXqC8SNtTpc5pnhNoQ2GUStDe6JwGJiBxI//onAYmIHGjNll2DtI5\nDUwQTo0b2cm6c5DOaWACEjeqy0PnIJ3TwChKJc0S8jhkOgeBXCFxl6WZWMulhtI+ST5WaggledM5\nCOQKiVtKP7EmsUgWnYMAYiRuKf3VBxstNWTdYh/cJF1/u1RYJsmiy+tvp+YMZITOSSn9Gm5hIE66\nUxyvBZ2DAMZpnxZ3pVJD2jXcRksNdA4CGCdXidvd03ngaqWGtGu4tZQasnxjARCUXJVKNvzj99Q3\nf5YGlxY0uKxXg0sLesXCuTKzxh64WqmhGRM8KpUaqk1w2XDTxNslOgeBNpabxH3qzDm97pV9Ko6U\n9OWH9urk938mSeqZPUNrBwoaHIgS+dqBgpb2zqkvmddSasiyhpuHNxYAwchN4p45o0Mf37hGknT6\n7Dk99fxR7RguaftwSTtGDuufH9ytM+eiUsrC7plRMl8aJ/SBgi7smT39gzfaOZi2vL+xAMiV3CTu\n8bo6O3TZkoIuW1LQDVdGx06cPqtdPz+qHcOHVRwuacdISQ8+dUhxLteinllau7RX6wYKoy30C7pn\nRjfmvdSQ9zcWALmSy8Q9ldldnbp8Wa8uX9Y7euzlU2f0+P4jo4l8+/BhffeJ50dvX9o7R+uWFbR2\n6RV6w5Wf0Ct3fFodR0byV2rI+xsLgFyxNEZyDA0N+datWxN/3FocPXFaO0eOaMfI4ajMMlzScy++\nPHr7yr5urV1a0GDcKr9sSY+6Z+Xg/au4hRo20MbMbJu7D9V035ZJ3BUS3+GXT2nHSEnF4ZKKcanl\nQOmEJMlMuqR/3mitfO1AQasX92h2V2dz4291vDEBFbVf4p48nE6KSg0VpmUfPHpCO0dK2r6vFCf1\nw3rh2ClJ0owO06WL5o+2ygcHCrp00XzNnJGrYe/hOI//D9Bu2i9x37pmms69ZdKHdtb0EO6uA6UT\ncb38cNw6L6l0/LQkaWZnh16zeL4GB3q1dqCgdQO9uri/WzM6SeZVJfD/AVpdPYk7B8XdBCQwJdzM\ntKR3jpb0ztGb11wkKUrm+148rmKcyLfvO6y7HxnRlx/aK0ma09Wpy5b0jCbytQMFrVzYrY6OBicM\ntRqm7AOJyk/ibqQGmtJwOjPT8oVztXzhXL19cIkk6dw51+4XXprQKv/aj5/TnT/YI0maP2uG1sSd\nn+WEPrCgzglDrYbhjkCi8pG4G93TsInD6To6TJdcOE+XXDhP73xtlHjOnD2nZw4dU3FfScWRw9ox\nXNKdP9ijU2fPSZJ653aNjmRZu7RX65YVdFHP7PZJ5gx3BBJVtcZtZq+S9G/jDq2SdJO73zbdz9Rd\n406iBpqzUQunzkSzP7cPR4m8OFzSk88f1dl4xlDfvFnjJgtFCb1//qzz/4U5+/t/Rd7jAzKWWuek\nmXVKGpH06+6+d7r71Z24b+6VNFUcJt18uPbHybkTp8/q8QNHRhP5jpHDevrgMZX/BUsKs8fWZRko\naO3Sgnrnzqz+wIzaAIKXZufkBknPVkra56VNaqCzuzq1fvkCrV++YPTYSyfP6LH9R0bHl+8YKenb\nj43N/nzFwrkTyixrBwqaN3nCUB42WgDQNPUm7hskfS3xKNq4Bto9a4auXHmBrlx5weix0vHT2jky\n1ip/5LnDurd4QFI0YWhVX/doq3xwoKD1pWFNWS1n1AbQkmpO3GY2U9I7JH10mts3S9osScuXL68v\nCpYtnaAwp0vXXNKnay7pGz32i2MnVRwpaWe8YuIPn31Bdz8yIkn6/qyFGrAXpnig1vrEAiBSc43b\nzDZKer+7X1ftvlmuVdJOnj8STRg69chd+p1nPqFZfnL0tpd9pj477wP65SXvHF3H/NJF89XFhCEg\nl9Kqcf+h0iiT4Lwt6pmtN66eLa2+USoulsefWI7PWaz7lvyZHj15lYrb9+urDz8nSZo1o0Orl/TE\niTxaAndV/zx1MmEICEpNLW4zmytpn6RV7l6qdn9a3Plx7pxr74svT+j83DlS0sunzkqS5s7s1Jol\nYxOGBgd6tSKJ7eIA1CXxFre7vyxpYUNRIRMdHaaVfd1a2detjZcvlSSdPefafejY2GqJ5e3izkQT\nhhLZLg5AalpjkSk0bPx2ccV4tcRdB46e/3ZxAOrSfotMNUOLz/ybsF1cfOzE6bN68udHR8ssxeGp\nt4sbHJ39WdDCeQ3M/gRQExJ3LRpdSyVQs7s6tW5Zr9bVuV3c+HXM1ywtqDCnK4vwgZZFqaQWrCdd\nUXm7uHK9PJjt4oAcoVSSNNaTrmj+7C5dffFCXX3xWP/1L1+Ktosr7y70kz0v6p7t+yWxXRzQKBJ3\nLdpkLZUkLeieqWsv7de1l/aPHpu8Xdz3njqob/w0evMbv11ceR3zoLaLa/E+EOQLpZJa1LL6Hi/c\nutW7XdzgQEGX9M+beru4LM8/qzMiAe2352QzVEoMvHATM3m7uOLwYe0cOaJjJ89ImrhdXLlmvnL/\nf6nj3gzPP30gSACJu9l44abq3DnXz37x0tjsz+GSdu4v6cTpaMLQD2d9UEumXGSrSee/TdaTR7ro\nnGw2Oi9T1dFhurh/ni7un2K7uOGSFt/7iyl/zkvD+tS3d6W/XRx9IGgyEncSeOE23YzODr36oh69\n+qIe6f+mPv8HO/r0ue/tnrBd3NvWXqSPb1yTbDBtvJ48skHiTgIv3GxNc/4XXf9JPfaaN03YLq4n\njclArCePJqPGnRRGlWSL84/A0TkJAIGpJ3EHMrsBaFBxSzT65+be6LK4JeuIgPNGjRutr00XCUPr\nosWN1nf/LRM7LqXo+/tvySYeoEEkbkRauZTAOHu0GBI3xkoJpX2SfKyU0CrJe7rx9IyzR6BI3Gj9\nUsKGm6Jx9eMxzh4BI3EjmVJCnkstg5uiBacKyyRZdMkCYAgYo0rQ+JT9EEZtDG7KTyxAg2hxo/FS\nQquXWoCcIXGj8VICozaApqJUgkgjpQRWRwSaihY3GseoDaCpSNxoHKM2gKaiVIJkMGoDaBpa3EAt\n8jxOHW2HFjdQTQjj1NFWaHED1TBOHTlD4gaqYZw6cobEDVTD6oLIGRJ3u6Bz7fwxTh05Q+JuB62+\n3nYSKr2xNWOcOm+sqAO7vLeDW9dMMyV9mfShnc2PJ28mjxqRohZ1syYRZf37kQvs8o6JQuhcy7LF\nmfWokax/P4JD4m4Hee9cy7qUk/UbW9a/H8EhcbeDvHeuZd3izPqNLevfj+DUlLjNrNfMvm5mu8zs\nCTO7Ou3AkKC8LwKVdYsz6ze2rH8/glPrlPfPSPqWu/++mc2UNDfFmJCGPC8ClfV63uXzcv8t0ZtF\nYSBKms06X1n/fgSn6qgSM+uRtF3SKq9xCAqjSlAXRlVUV9xCYm9xSY8qWSXpkKQ7zewRM/u8mXU3\nFCEwXt5LOVnLuvMWuVNLi3tI0kOSrnH3h83sM5KOuPvHJt1vs6TNkrR8+fIr9u7dm1LIQJthHH5b\nSLrFPSxp2N0fjr//uqT1k+/k7ne4+5C7D/X399ceLYDKsu68Re5UTdzu/nNJ+8zsVfGhDZIeTzUq\nAGMYLohJah3H/QFJXzGzoqTLJX0yvZAATMBwQUxS03BAd39UUk21FwAJS2K4IKNSWgpblwHN0Gji\nbGQcPluvtRymvANpy3o4X9ZLCiBxJG4gbVknTkaltBwSN5C2rBMno1JaDokbSFvWiZNRKS2HxA2k\nLevEyZICLYdRJUDa8rD6X55Xh0TdSNxAM5A4kSBKJQAQGBI3AASGxA0AgSFxA0BgSNwAEBgSNwAE\nhsQNAIEhcQNAYEjcQCsobok2Fb65N7pkB/iWxsxJIHRslNB2aHEDoct6vW80HYkbCF3W632j6Ujc\nQOiyXu8bTUfiBkKX9XrfaDoSNxA6NkpoO4wqAVoB6323FVrcABAYEjcABIbEDQCBIXEDaBxT7puK\nzkkAjWHKfdPR4gbQmBCm3LfYJwJa3AAak4cp98Ut0RtFaTiaMbrhprHWfgt+IqDFDaAxWU+5Lyfm\n0j5JPpaYy63qED4R1InEDaAxWU+5r5aY8/CJIGEkbgCNyXrKfbXEnPUnghRQ4wbQuCyn3BcG4jLJ\nFMelqOU/vsYtBb8IFy1uAGGrVqrJ+hNBCmhxAwhbOQFPN6qkfJ+AE/VkJG4A4WuxxFwNpRIACExN\nLW4z2yPpqKSzks64+1CaQQEApldPqeS33f2F1CIBANSEUgkABKbWxO2SvmNm28xsc5oBAQAqq7VU\nco277zezCyXdZ2a73P3B8XeIE/pmSVq+fHnCYQIAympqcbv7/vjyoKS7JV05xX3ucPchdx/q7+9P\nNkoAwKiqidvMus1sfvm6pOsk7Uw7MADA1GoplSySdLeZle//VXf/VqpRAWgtldbLRt2qJm533y1p\nXRNiAdCKWnAjg6wxHBBAulpwI4OskbgBpKsFNzLIGokbQLpacCODX9HkzYhJ3ADSlfXWZmmrtudl\nCkjcANLVghsZTJBBDZ/1uAGkr5XXy86ghk+LGwAakUENn8QNoLomd74FJYMaPqUSAJUxgaayWva8\nTBiJG0BllTrfSNyRJtfwKZUAqKwdJtAEVgoicQOorNUn0GQwDrtRJG4AlbX6BJoA11IhcQOorBkT\naLIsVQRYCqJzEkB1aXa+ZT1qpTAQl0mmOJ5TtLgBZCvrUkWApSASN4BsZV2qqKUUlLNRJ5RKAGQr\nD6WKSqWgrEs5U6DFDSBbeS9VZF3KmQKJG0C28r7sa9alnClQKgGQvTwv+5qHUs4ktLgBoJIclnJI\n3ABQSQ5LOZRKAKCanJVyaHEDQGBI3AAQGBI3AASGxA0gd1O6URmdk0C7y+GUblRGixtodzmc0o3K\nSNxAu8vhlG5URuIG2l2r7ynZgkjcQLvL4ZRuVEbiBtpdDqd0ozJGlQDI3ZRuVEaLGwACQ+IGgMCQ\nuAEgMCRuAAgMiRsAAlNz4jazTjN7xMzuTTMgAEBl9bS4b5T0RFqBAABqU1PiNrMBSW+T9Pl0wwEA\nVFNri/s2SX8l6dx0dzCzzWa21cy2Hjp0KJHgAAC/qmriNrO3Szro7tsq3c/d73D3IXcf6u/vTyxA\nAMBEtbS4r5H0DjPbI+kuSW8ws39NNSoAwLSqJm53/6i7D7j7Ckk3SPofd//j1CMDAEyJcdwAEJi6\nVgd09wckPZBKJACAmtDiBoDAkLgBIDAkbgAIDIkbAAJD4gaAwJC4ASAwJG4ACAyJGwACQ+IGgMCQ\nuAEgMCRuAAgMiRsAAkPiBpB/xS3SrWukm3ujy+KWrCPKVF2rAwJA0xW3SN/8oHT6ePR9aV/0vSQN\nbsourgzR4gaQb/ffMpa0y04fj463KRI3gHwrDdd3vA2QuAHkW2GgvuNtgMQNIN823CR1zZl4rGtO\ndLxNkbgB5NvgJun626XCMkkWXV5/e9t2TEqMKgEQgsFNbZ2oJ6PFDQCBIXEDQGBI3AAQGBI3AASG\nxA0AgTF3T/5BzQ5J2pv4A0f6JL2Q0mMngfgaQ3yNIb7GZBnfK9y9v5Y7ppK402RmW919KOs4pkN8\njSG+xhBfY/IeXxmlEgAIDIkbAAITYuK+I+sAqiC+xhBfY4ivMXmPT1KANW4AaHchtrgBoK1lnrjN\n7AtmdtDMdo47ts7MfmRmO8zsm2bWEx/vMrMvxsefMLOPjvuZN5vZk2b2jJl9JIfx7YmPP2pmWzOK\nb6aZ3Rkf325mvzXuZ66Ijz9jZrebmeUsvgfi/++j8deFCcW3zMz+N/5/PWZmN8bHLzCz+8zs6fhy\nQXzc4vPzjJkVzWz9uMd6T3z/p83sPTmM7+y483dPRvG9Ov7fnzSzD096rMRfwwnHl8pr+Ly4e6Zf\nkq6VtF7SznHHfiLp9fH190r62/j6uyTdFV+fK2mPpBWSOiU9K2mVpJmStktanZf44u/3SOrL+Py9\nX9Kd8fULJW2T1BF//2NJV0sySf8t6S05i+8BSUMpnL/FktbH1+dLekrSakn/IOkj8fGPSPr7+Ppb\n4/Njkq6S9HB8/AJJu+PLBfH1BXmJL77tWA7O34WSfk3SJyR9eNzjpPIaTiq++LY9SuE1fD5fmbe4\n3f1BSS9OOvwqSQ/G1++T9Hvlu0vqNrMZkuZIOiXpiKQrJT3j7rvd/ZSkuyRtzFF8qakzvtWS7o9/\n7qCkw5KGzGyxpB53/5FHz9AvSfrdvMSXRBwV4jvg7j+Nrx+V9ISkpYqeP1+M7/ZFjZ2PjZK+5JGH\nJPXG5+9Nku5z9xfd/Zfx3/XmHMWXinrjc/eD7v4TSacnPVQqr+EE48uVzBP3NHZKekd8/Q8kLYuv\nf13SS5IOSHpO0qfc/UVF/4h9435+OD6Wl/ikKKl/x8y2mdnmFGOrFN92SRvNbIaZrZR0RXzbUkXn\nrCyr8zddfGV3xh9TP5ZUKWc8M1sh6bWSHpa0yN0PSNGLX1FLTJr+uZb6c7DB+CRptpltNbOHzCyR\nN+bziG86eTl/lTTzNVxRXhP3eyW938y2Kfp4cyo+fqWks5KWSFop6S/MbJWij4WTpTlcpt74JOka\nd18v6S3xz16bQXxfUPSC2CrpNkk/lHRG+Tl/08UnSX/k7mslvS7++pMkAzKzeZK+IenP3b3Sp6Tp\nzlWq5zCB+CRpuUezAt8l6TYzuziD+KZ9iCmOZXH+Kmnma7iiXCZud9/l7te5+xWSvqao9iVFT7hv\nufvp+KP0DxR9lB7WxJbZgKT9OYpP7r4/vjwo6W5FSb6p8bn7GXf/kLtf7u4bJfVKelrR+Ru/82om\n569CfHL3kfjyqKSvKsHzZ2Zdil7UX3H3/4gPP18uMcSXB+Pj0z3XUnsOJhTf+OfgbkV9Bq/NIL7p\n5OX8TauZr+Fqcpm4LR4xYGYdkv5G0ufim56T9Ia457xbUefLLkWdXa80s5VmNlPSDZIS6TVPIj4z\n6zaz+fHPdEu6TlG5oKnxmdnc+PfLzN4o6Yy7Px5/VDxqZlfFJYh3S/rPvMQXl0764uNdkt6uhM5f\n/Pf+i6Qn3P3T4266R1J5ZMh7NHY+7pH07vh/fJWkUnz+vi3pOjNbEI9QuC4+lov44rhmxY/ZJ+ka\nSY9nEN90UnkNJxVfs1/DVaXd+1ntS1GL64CizoBhSe+TdKOi3t+nJP2dxiYKzZP075IeU/Sk+8tx\nj/PW+P7PSvrrPMWnqKd8e/z1WIbxrZD0pKIOmu8qWo2s/DhDip6Iz0r6p/LP5CE+Sd2KRpgU4/P3\nGUmdCcX3m4o+khclPRp/vVXSQkUdpU/HlxfE9zdJn43P0w6NG+miqAT0TPz1p3mKT9JvxN9vjy/f\nl1F8F8XPgyOKOp+HFXWMSym8hpOKTym+hs/ni5mTABCYXJZKAADTI3EDQGBI3AAQGBI3AASGxA0A\ngSFxA0BgSNwAEBgSNwAE5v8BMcE9Kz+yEysAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(year1, fitfunction(year1,x))\n",
        "plt.plot(year, extent, 'o')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### How did the linear fit \"fit\" as time time progresses?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x1163798d0>"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk0AAAHVCAYAAADsJ8/rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nH6hoEhEREekDFU0iIiIiffD/AU+naSwuP08KAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.figure(figsize=(10,8))\n",
        "plt.plot(year, extent, 'o')\n",
        "\n",
        "for ndata in range(22, npoints):\n",
        "    \n",
        "    year1 = year[:ndata]\n",
        "    extent1 = extent[:ndata]\n",
        "\n",
        "    A = np.array([\n",
        "        1+0*year1,\n",
        "        year1\n",
        "        ]).T\n",
        "\n",
        "    b = np.array(extent1)\n",
        "\n",
        "    x = la.solve(A.T@A,A.T@b)\n",
        "    \n",
        "    plt.plot(year1, fitfunction(year1,x),  label='%d' % (year[0]+ndata))\n",
        "    \n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Let's try a quadratic fit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[6.79221628e+00 7.00452986e-07 3.50158197e-10]\n"
          ]
        }
      ],
      "source": [
        "ndata = 26 #use the first ndata points for the fit\n",
        "year1 = year[:ndata]\n",
        "extent1 = extent[:ndata]\n",
        "\n",
        "A = np.array([\n",
        "    1+0*year1,\n",
        "    year1,\n",
        "    year1**2\n",
        "    ]).T\n",
        "\n",
        "b = np.array(extent1)\n",
        "\n",
        "x = la.solve(A.T@A,A.T@b)\n",
        "\n",
        "print(x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x11f22f710>]"
            ]
          },
          "execution_count": 53,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAEn1JREFUeJzt3X+MXNV5xvHnNdjUGLAhXghgXEMV\nkSDqJLClJDRJGytuQgJu1daiaRvURHIjoYZETQtRE2JRtWqqqvxQK1UoDSIKCdqQWoVKoVC3lKgN\nJOvE3vArsbHs2JjURjQ2pFYx5O0f94y9u+zO3PG9d845934/0mpmr2dnX9+deebMe869Y+4uAEA+\nFsQuAAAwHIIbADJDcANAZghuAMgMwQ0AmSG4ASAzBDcAZIbgBoDMENwAkJkTm7jT5cuX+6pVq5q4\nawBopS1btjzv7mNlbttIcK9atUqTk5NN3DUAtJKZ7S57W1olAJAZghsAMkNwA0BmCG4AyAzBDQCZ\nySe4pyakWy6WNi4rLqcmYlcEAFE0shywdlMT0v0fk44cLr4/uKf4XpJWr49XFwBEkMeIe/PNx0K7\n58jhYjsAdEwewX1w73DbAaDF8gjupSuG2w4ALZZHcK+5SVq4eOa2hYuL7egGJqeBo/KYnOxNQG6+\nuWiPLF1RhDYTk93A5DQwQx7BLRVPUJ6k3dRvcprHBDooj1YJuo3JaWAGghvpY3IamIHgRjkxJweZ\nnAZmyKfHjXhiTw4yOQ3MQHBjsBQmB5mcBo6iVTIqOa9DZnIQSArB3dNksPZaDQf3SPJjrYZcwpvJ\nQSApBLfUfLDWcZIsJgcBBAS31PzZB6u2GmKP2Fevl666XVp6niQrLq+6nZ4zEAmTk1LzPdylK0Lo\nzrG9DCYHAUzTnRF3v1ZD0z3cqq0GJgcBTNON4B7Uami6h1um1RDzhQVAVrrRKhnUahjFAR79Wg2D\nDnBZc9PMf5eYHAQ6rBvBXabVELOHm8ILC4BsdCO4q04ONi31FxYASelGjzv1dcj0sAEMoRvBnfo6\n5NRfWAAkpRutEintVgM9bABDaE9wT03kHXwpv7DUIfe/D5CQdgR37PNFoz/+PkCt2tHjbvpcI6iG\nvw9Qq3YEN4eEp42/D1CrdIK7ymlLWU6XNv4+QK3SCO6qpy1lOV3a+PsAtRoY3GZ2oZltnfZ1yMw+\nXmsVVXugqa/THoWUPxqNvw9QK3P38jc2O0HSs5J+0d13z3e78fFxn5ycLF/FxmWS5qrDpI0/Ln8/\nXTV71YZUjGgJRyAbZrbF3cfL3HbYVskaSc/0C+3jQg+0GlZtAJ0ybHBfI+krtVdBD7QaVm0AnVI6\nuM1skaSrJX11nn/fYGaTZjZ54MCB4aqgB1oN71iATind4zazdZKuc/e1g247dI8b1dDjBrLXVI/7\nt9VEmwTV8Y4F6JRS5yoxs5MlvUfSHzRbDo5b209SBeCoUsHt7v8r6XUN1wIAKCGNIycBAKUR3GWl\nfGQigE5px/m4m8b5pAEkJKngfvCJH+mnQxyCPyrveuCzWjzHkYmHH/is/mPBO+IUBXRQgvEww6IT\nF2jNm85q/PckFdzX37NVh4+8GruM19h50j7JXrv9pJ88p49+6TujLwhAkpafcpImP92x4N503duT\nfEV95e5zteilZ1+7/dRz9PWPMuKGdNr2TRr71ue08KV9OnLKOTpw2Q069IZfj11WK9kcg6hUnLhg\nNMUlFdxvfP1psUuY29qNcx6ZuGjtRr3p7FAzH4YbV8z9PzUhfeOGo4+PRS89q3O/cYPOXbaYxwAa\nwaqSMgYdmVj1gyBQTez9z9kZMWJJjbiT1u/IxH5PXEZczYu9/zk7I0aMEXcdeOLGFXv/c3ZGjBjB\nXQeeuHHF3v+cTx4jRnDXgSduXLH3P2dnxIjR465D7wnKqpI4Utj/nJ0RIzTUhwWXxQcpAMBwmvyw\nYCBPnCQMLUKrBO3HScLQMoy40X4cIIOWIbhRaHMrIfY6b6BmBDfiHzLetNjrvIGaEdxofysh9jpv\noGYEN+ppJaTcauEAGbQMq0pQtAwO7pl7exk5rNrgABm0CCNuVG8ltL3VAiSG4Eb1VgKrNoCRolWC\nQpVWQtVWC4ChMOJGdazaAEaK4EZ1rNoARopWCerBqg1gZBhxA2WkvE4dncOIGxgkh3Xq6BRG3MAg\nrFNHYghuYBDWqSMxBDcwCGcXRGII7q5gcu34sU4diSG4u6Dt59uuQ78XtlGsU+eFFUPgU9674JaL\n5zkk/TzpE4+Pvp7UzF41IhUj6lEdRBT79yMJfMo7Zsphci3miDP2qpHYvx/ZIbi7IPXJtditnNgv\nbLF/P7JDcHdB6pNrsUecsV/YYv9+ZKdUcJvZMjO718yeNrOnzOxtTReGGqV+EqjYI87YL2yxfz+y\nU/aQ99skPeDuv2lmiySd3GBNaELKJ4GKfT7v3n7ZfHPxYrF0RRGao9pfsX8/sjNwVYmZnSZpm6QL\nvOQSFFaVYCisqhhsaoJgb7m6V5VcIOmApDvN7Ltm9nkzW1KpQmC61Fs5scWevEVyyoy4xyU9KukK\nd3/MzG6TdMjdPzPrdhskbZCklStXXrp79+6GSgY6hnX4nVD3iHuvpL3u/lj4/l5Jl8y+kbvf4e7j\n7j4+NjZWvloA/cWevEVyBga3u/9I0h4zuzBsWiPpyUarAnAMywUxS9l13H8o6W4zm5L0Fkl/0VxJ\nAGZguSBmKbUc0N23SirVewFQszqWC7IqpVX46DJgFKoGZ5V1+Hz0WutwyDvQtNjL+WKfUgC1I7iB\npsUOTlaltA7BDTQtdnCyKqV1CG6gabGDk1UprUNwA02LHZycUqB1WFUCNC2Fs/+lfHZIDI3gBkaB\n4ESNaJUAQGYIbgDIDMENAJkhuAEgMwQ3AGSG4AaAzBDcAJAZghsAMkNwA20wNVF8qPDGZcUlnwDf\nahw5CeSOD0roHEbcQO5in+8bI0dwA7mLfb5vjBzBDeQu9vm+MXIEN5C72Of7xsgR3EDu+KCEzmFV\nCdAGnO+7UxhxA0BmCG4AyAzBDQCZIbgBVMch9yPF5CSAajjkfuQYcQOoJodD7lv2joARN4BqUjjk\nfmqieKE4uLc4YnTNTcdG+y18R8CIG0A1sQ+57wXzwT2S/Fgw90bVObwjGBLBDaCa2IfcDwrmFN4R\n1IzgBlBN7EPuBwVz7HcEDaDHDaC6mIfcL10R2iRzbJeKkf/0HreU/Um4GHEDyNugVk3sdwQNYMQN\nIG+9AJ5vVUnvNhkH9WwEN4D8tSyYB6FVAgCZKTXiNrNdkl6U9KqkV9x9vMmiAADzG6ZV8ivu/nxj\nlQAASqFVAgCZKRvcLulBM9tiZhuaLAgA0F/ZVskV7r7PzM6U9JCZPe3uj0y/QQj0DZK0cuXKmssE\nAPSUGnG7+75wuV/SJkmXzXGbO9x93N3Hx8bG6q0SAHDUwOA2syVmdmrvuqS1kh5vujAAwNzKtErO\nkrTJzHq3/7K7P9BoVQDapd/5sjG0gcHt7jslvXkEtQBooxZ+kEFsLAcE0KwWfpBBbAQ3gGa18IMM\nYiO4ATSrhR9k8Boj/jBightAs2J/tFnTBn3mZQMIbgDNauEHGcwQoYfP+bgBNK/N58uO0MNnxA0A\nVUTo4RPcAAYb8eRbViL08GmVAOiPA2j6K/OZlzUjuAH012/yjeAujLiHT6sEQH9dOIAms1YQwQ2g\nv7YfQBNhHXZVBDeA/tp+AE2G51IhuAH0N4oDaGK2KjJsBTE5CWCwJiffYq9aWboitEnm2J4oRtwA\n4ordqsiwFURwA4grdquiTCsosVUntEoAxJVCq6JfKyh2K2cOjLgBxJV6qyJ2K2cOBDeAuFI/7Wvs\nVs4caJUAiC/l076m0MqZhRE3APSTYCuH4AaAfhJs5dAqAYBBEmvlMOIGgMwQ3ACQGYIbADJDcANI\n7pBu9MfkJNB1CR7Sjf4YcQNdl+Ah3eiP4Aa6LsFDutEfwQ10Xds/U7KFCG6g6xI8pBv9EdxA1yV4\nSDf6Y1UJgOQO6UZ/jLgBIDMENwBkhuAGgMwQ3ACQGYIbADJTOrjN7AQz+66Z/XOTBQEA+htmxH29\npKeaKgQAUE6p4DazFZLeL+nzzZYDABik7Ij7Vkl/Iumn893AzDaY2aSZTR44cKCW4gAArzUwuM3s\nA5L2u/uWfrdz9zvcfdzdx8fGxmorEAAwU5kR9xWSrjazXZLukfRuM/tSo1UBAOY1MLjd/VPuvsLd\nV0m6RtK/ufvvNl4ZAGBOrOMGgMwMdXZAd39Y0sONVAIAKIURNwBkhuAGgMwQ3ACQGYIbADJDcANA\nZghuAMgMwQ0AmSG4ASAzBDcAZIbgBoDMENwAkBmCGwAyQ3ADSN/UhHTLxdLGZcXl1ETsiqIa6uyA\nADByUxPS/R+Tjhwuvj+4p/heklavj1dXRIy4AaRt883HQrvnyOFie0cR3ADSdnDvcNs7gOAGkLal\nK4bb3gEEN4C0rblJWrh45raFi4vtHUVwA0jb6vXSVbdLS8+TZMXlVbd3dmJSYlUJgBysXt/poJ6N\nETcAZIbgBoDMENwAkBmCGwAyQ3ADQGbM3eu/U7MDknbXfseF5ZKeb+i+60B91VBfNdRXTcz6ftbd\nx8rcsJHgbpKZTbr7eOw65kN91VBfNdRXTer19dAqAYDMENwAkJkcg/uO2AUMQH3VUF811FdN6vVJ\nyrDHDQBdl+OIGwA6LXpwm9kXzGy/mT0+bdubzeybZvY9M7vfzE4L2xea2V1h+1Nm9qlpP/NeM/u+\nme0wsxsTrG9X2L7VzCYj1bfIzO4M27eZ2S9P+5lLw/YdZna7mVli9T0c/r5bw9eZNdV3npn9e/h7\nPWFm14ftZ5jZQ2a2PVyeHrZb2D87zGzKzC6Zdl/XhttvN7NrE6zv1Wn7775I9b0x/O3/z8w+Oeu+\nan8O11xfI8/h4+LuUb8kvVPSJZIen7bt25LeFa5/WNKfhesflHRPuH6ypF2SVkk6QdIzki6QtEjS\nNkkXpVJf+H6XpOWR9991ku4M18+UtEXSgvD9tyS9TZJJ+rqk9yVW38OSxhvYf2dLuiRcP1XSDyRd\nJOmvJN0Ytt8o6XPh+pVh/5ikyyU9FrafIWlnuDw9XD89lfrCv72UwP47U9IvSPpzSZ+cdj+NPIfr\nqi/82y418Bw+nq/oI253f0TSC7M2XyjpkXD9IUm/0bu5pCVmdqKkxZJelnRI0mWSdrj7Tnd/WdI9\nktYlVF9jhqzvIkmbw8/tl/RjSeNmdrak09z9m148Qr8o6ddSqa+OOvrU95y7fydcf1HSU5LOVfH4\nuSvc7C4d2x/rJH3RC49KWhb2369KesjdX3D3/wn/r/cmVF8jhq3P3fe7+7clHZl1V408h2usLynR\ng3sej0u6Olz/LUnnhev3SvqJpOck/VDSX7v7Cyr+EHum/fzesC2V+qQi1B80sy1mtqHB2vrVt03S\nOjM70czOl3Rp+LdzVeyznlj7b776eu4Mb1M/U1crZzozWyXprZIek3SWuz8nFU9+FSMxaf7HWuOP\nwYr1SdLPmNmkmT1qZrW8MB9HffNJZf/1M8rncF+pBveHJV1nZltUvL15OWy/TNKrks6RdL6kPzKz\nC1S8LZytyeUyw9YnSVe4+yWS3hd+9p0R6vuCiifEpKRbJf2XpFeUzv6brz5J+h13/3lJ7whfv1dn\nQWZ2iqSvSfq4u/d7lzTfvmp0H9ZQnySt9OKowA9KutXMfi5CffPexRzbYuy/fkb5HO4ryeB296fd\nfa27XyrpKyp6X1LxgHvA3Y+Et9L/qeKt9F7NHJmtkLQvofrk7vvC5X5Jm1SE/Ejrc/dX3P0T7v4W\nd18naZmk7Sr23/RPXo2y//rUJ3d/Nly+KOnLqnH/mdlCFU/qu939H8Pm/+61GMLl/rB9vsdaY4/B\nmuqb/hjcqWLO4K0R6ptPKvtvXqN8Dg+SZHBbWDFgZgskfVrS34d/+qGkd4eZ8yUqJl+eVjHZ9QYz\nO9/MFkm6RlIts+Z11GdmS8zs1PAzSyStVdEuGGl9ZnZy+P0ys/dIesXdnwxvFV80s8tDC+JDkv4p\nlfpC62R52L5Q0gdU0/4L/99/kPSUu//NtH+6T1JvZci1OrY/7pP0ofA3vlzSwbD//kXSWjM7PaxQ\nWBu2JVFfqOukcJ/LJV0h6ckI9c2nkedwXfWN+jk8UNOzn4O+VIy4nlMxGbBX0kckXa9i9vcHkv5S\nxw4UOkXSVyU9oeJB98fT7ufKcPtnJP1pSvWpmCnfFr6eiFjfKknfVzFB868qzkbWu59xFQ/EZyT9\nbe9nUqhP0hIVK0ymwv67TdIJNdX3Syrekk9J2hq+rpT0OhUTpdvD5Rnh9ibp78J++p6mrXRR0QLa\nEb5+P6X6JL09fL8tXH4kUn2vD4+DQyomn/eqmBiXGngO11WfGnwOH88XR04CQGaSbJUAAOZHcANA\nZghuAMgMwQ0AmSG4ASAzBDcAZIbgBoDMENwAkJn/BwCScoHxzKwxAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(year, fitfunction(year,x))\n",
        "plt.plot(year, extent, 'o')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### What went wrong?\n",
        "\n",
        "Let's try to use the least square function from scipy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[-5.78703451e+03  5.86799957e+00 -1.48565324e-03]\n"
          ]
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "coeffs,residual,rank,sval=np.linalg.lstsq(A,b,rcond=None)\n",
        "\n",
        "plt.plot(year, fitfunction(year,coeffs))\n",
        "plt.plot(year, extent, 'o')\n",
        "\n",
        "print(coeffs)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Seems to work with `lstsq`... what could be the issue with the Normal Equations method above?\n",
        "\n",
        "Let's check the condition number of the matrix A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "313354558941.1675\n",
            "[6.79221628e+00 7.00452986e-07 3.50158197e-10]\n",
            "2.799169975001837\n"
          ]
        }
      ],
      "source": [
        "print(la.cond(A))\n",
        "print(x)\n",
        "print(la.norm(A@x-b))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The matrix A becomes closer to singular as the number of columns increases (i.e., as the number of coefficients for the fit increase). We can scale the years, to mitigate this situation:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1593.2774157903386\n",
            "[ 7.32702301e+00 -2.55283521e-02 -1.60576890e-03]\n"
          ]
        }
      ],
      "source": [
        "year2 = year - 1980\n",
        "extent2 = extent\n",
        "\n",
        "A = np.array([\n",
        "    1+0*year2,\n",
        "    year2,\n",
        "    year2**2\n",
        "    ]).T\n",
        "\n",
        "b = np.array(extent2)\n",
        "\n",
        "x = la.solve(A.T@A,A.T@b)\n",
        "\n",
        "\n",
        "print(la.cond(A))\n",
        "print(x)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x11fd7f9b0>]"
            ]
          },
          "execution_count": 78,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njYV2RvlOqvcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(year2, fitfunction(year2,x))\n",
        "plt.plot(year2, extent, 'o')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true
      },
      "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": "3.6.9"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}