LR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9dd8ab5e",
   "metadata": {},
   "source": [
    "# Linear Regression Project\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d008fd7",
   "metadata": {},
   "source": [
    "## Importing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d4069f65",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "points = np.genfromtxt(\"data.csv\", delimiter=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28696fff",
   "metadata": {},
   "source": [
    "## Plotting the data using matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e5eb53cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0K21mljRr/F6+HCZPHrz95MnZ8qEcz3pG26qqIuLddRZf1GT75UCTT6SZjahVq2DpUng8Ff7Xr89eAyxenD0Ali3LqqfmzMmCRmV52eNZz/Cd42b9atmy6kW+4vHHs+UVixfDnXfC009nf5sFgCLHs57gwGHWr0a68duN6X3DgcOsX41047cb0/uGA4dZvxpK43cnj2ejlgOHWb9avBguuADmzgUp+3vBBUNvyB7p49mo1c0hR8ys2/K9p0bj8WxUconDzMxKceAwM7NSHDjMzKwUBw4zMyvFgcPMzEpx4DAzs1IcOMzMrBQHDjMzK8WBw8zay3N09JyGd45LemmB/Z+KiBtHMD1m1ks8R0dPajbkyNXAzwA12eYAYP+RTJCZ9ZBmc3Q4cIxZzQLHzyLitc12lnTlCKfHzHqJ5+joSQ3bOFoFjaLbmFkf8xwdPall47ikV0raPT0/VtJnJM1tf9LMbMzzHB09qUivqn8DHpf0YuBDwHrgi612knSxpM2Sbsotmybpckm3pr975dadKek2SeskvX4I78XMRhvP0dGTigSO7RERwDHAuRFxLrBHgf1WAG+oWXYGcEVEHAhckV4j6WBgEXBI2uc8SeMKvQOzfjVWurkuXgx33glPP539ddAY84oEjkclnQkcC3w7XdB3bbVTRFwDPFiz+BhgZXq+EnhbbvklEbEtIu4AbgNeViBtZv2p0s11/XqIqHZzHa3Bw3pKkRkA3wX8GXBCRNwraQ7wT0M836yIuAcgIu6RNDMtnw38OLfdxrRsJ5KWAksBZsyYwdq1a4eYlN6ydetW50XSD3lxxGmnMalON9cnTzuNH8+ufnU6lRcz16zhORdeyMTNm9k2cya3n3gimxcubPt5y+iHz0XHRETTB/CpIssa7Ls/cFPu9Zaa9Q+lv58Hjs0tvwj4k1bHP+igg8IyV111VbeTMGr0RV5IEVlZY/BDqm4zMBBPzJqVLZs7N2JgoD1pGRiImDx5cDomT27f+YaoLz4XBQHXRoFreKNHkaqqo+ose+MQ49QmSXsDpL+b0/KNwH657fYF7h7iOcx6X6PurNOmZX9TVdakTZvaX5XV7CY/60kNA4ekkyTdCMyT9Mvc4w5gqMOMXAosSc+XAN/ILV8kaaKkA4ADgZ8O8Rxmve3kkxvfQPfII1lw6OTF3Df59Z1mJY7/AN5CdlF/S+5xWES07BYh6cvAj8gCz0ZJJwBnA0dJupWsJHM2QETcDKwGfgV8F3h/ROwY8rsy61Unnwz/9m9ZKaKep57KgkPZi/lwemj5Jr++07BxPCIeBh4G3p16Us1K20+RNCUimv6ciIh3N1h1ZIPtlwO+K8ismQsuaL3Nhg3ZRXv9+p3X1buYD3cgwuXLB+8PvsmvxxW5c/yvgE3A5cC30+NbbU6XmdWzo0BBfM6ccndsN6rWWrKkWAnEN/n1nSLdcU8F5kXEA21Oi5m1Mm5c8+BRCQ7pov3kaacxafPmajCpdzFvVH1VOU+REsjixQ4UfaRIr6q7yKqszKzbKhfwemp/6S9ezI8vuaT1HdtF2iLcS8pyipQ4bgfWSvo2sK2yMCI+07ZUmVl9552X/T3//GoD+ZQp2euh/uKv10ZRj3tJWVKkxLGBrH1jAtkYVZWHmXXDK18Ju+1Wfb116/Du0ahtoxjXYJg495KypGXgiIiP1nt0InFmXTcaBxJsxz0a+YEIV670UOjWVLM5x/8lIk6V9E1gp07jEfHWtqbMrNtG63zZ7b7hrvLeKveDNGtYt77UrI3jS+nvOZ1IiNmoM1rnyy5zj8ZQuZeUNdFs6tjr0t+rye4AfyA9fpiWmfW2Tg2lUbY6zLPqWZcVuQFwPnAr2Qi25wG/kfTq9ibLbBToxFAaQ5lXo8gNdykYvea1rx09bTPWM4r0qvo08LqIeE1EvBp4PfDP7U2WWYfV+9XfiV/2Q23objarXi4YqVkwGo0N/zYmFAkcu0bEusqLiPgNBWYANBszGv3qh/YMpZG/YNdrq4DhVYcVCUaeQdCGoUjguFbSRZLmp8e/A9e1O2FmHdOqEbzsfNnNfsnXXrAbyVeHlS0ZFGmb8RwaNgxF7hw/CXg/8AFAwDVkbR1mvWEkGsErc2CsX5+VTipBobYLb70Ldj1HH109btkuwUV6XXkODRuGIjcAbgM+B3wU+Dvg82mZWW8YbiN4vhQBO5ck8r/ki16YL7ss+zuUkkGRtpmhvGe3iVhSpFfVm4DfAueSBZDbJA116liz0We4jeBFShHr12cX2qLBqBJgGgWa9esbX7xzva6iUdtM2ffsNhHLKdqrakFEzI+I1wALcK8q6yWVC+306dVl+bGgWilaili6NKuCqr1g17PLLq0DTbOLd2qbufrKK+u3zZSdQ8NtIpZTJHBsjojbcq9vBza3KT1m3fPEE9XnDzxQ/Bd10VLE449nVVD5C/b06TBhws7b7thRLNAM5+JdpuHfbSKWUyRw3CzpMknvlbQE+CbwM0lvl/T2NqfPrDOG84u6XrVPIxs2DL5g338/XHxx/RFpawNNs2O2m+cVt5wigWMS2dSxrwHmA/cB04C3AG9uW8rMOmk4v6jz1T6t1LvQLl6cBZFG51+8OAtOUvFjjjQPc2I5RXpVHdfkcfxQTirpbyTdLOkmSV+WNEnSNEmXS7o1/d1rKMe2PtCO3j3D/UVdKUU0mssCsgvt0UfXT3uj80yblm137LGN7/voxMXb84pbTsPAIanJHJXFt6mzz2yye0IOj4gXAuOARcAZwBURcSBwRXptNljZ3j1Fg0yrX9RFj9NsPvAlS7K5Luqlffly2LVmQIZddoFHH218d3mnDeVmSOtNEVH3QdYI/vYmjz8Bbm60f5Pjziabx3wa2Q2I3wJeB6wD9k7b7A2sa3Wsgw46KCxz1VVXdTsJnTF3bkR22R38mDv3mU2eyYuBgYjJkwdvN3lytryegYHsOFL2t7JdmeM0S1+zdQMDERMm1F/f6pF777X65nNRgPOiCrg2Sl678w9Fg+KvpC8UiDsPR8SpZYOVpFOA5cATwPcjYrGkLRExNbfNQxGxU3VVKuUsBZgxY8Zhq1evLnv6nrR161amTJnS7WS03Wte+9ps4L4aIWVdT6nmxRGLFjFp06adtn1y1ix+fMklhc9Z5jgz16xh3jnnMG5b9R7ZHRMnsu7003nBJz7RMO3bZs6se44iKu995po1POfCC5m4eTPbZs7k9hNP5PYjjtjpc1Fvu80LFw7p3GNJv3xHiliwYMF1EXH4kA8wnKgzlAewF3AlMINssMT/Ao4FttRs91CrY7nEUdU3v6bKlDik+ttK5c5Z9jiNSi7N0t7oHEVLHA1KRTcvW7Zz2sqUwnpI33xHCmCYJY4ivapG2kLgjoi4LyKeAr4G/BGwSdLeAOmv7xWxnZXp3dOowTmiXKN62YbzRm0BzdI+1J5Rlf0bdCd+zoUXDl7mG/lsBHQjcGwAjpA0WZKAI4FbgEuBJWmbJcA3upA2G+3K9O5pdn9FmSEzRqorarO0F7kXZNw4OOmk+vs36DY8cXPN7y/fyGcjYTjFlaE+yAZM/DVwE9nc5hOB6WS9qW5Nf6e1Oo6rqqpcDK8alBeVaqMhNCwPUlv9dNJJ9aujyhyjdp98WmurrhpVJ7V4f9v23HPw9gWq+nqVvyNVDLOqqshFfhZwEfCd9Ppg4IThnHSkHg4cVf5SVNXNi5Fq74gYWjvBSPXwyq+fPr1xQEyPHePGDd7XbRwWnQkc3wH+FLghvR4P3Dick47Uw4Gjyl+Kqrp50aorbJnSQ5lf7SNV4qk9Zu3Fv0x33bLvt0f4O1I13MBRpI3j2RGxGng6VW1tB5rc5WQ2CjVqpzj66PLDhRdtJ6idp6PMsZopOhlUo3P4Rj4bpiKB4zFJ04EAkHQE8HBbU2U20ho1TF92WbFeRvk7x3dp8LWprKv02CpygR9Kb6qywcYDEdoIKxI4PkjW4+m5kn4AfBH467amyqwd6v3SLlJ6qB3mpNGwIjt2DC61FBkqZOvW8mNtlQgEOyZO9ECENuKaBg5J48hGxX0N2b0WfwkcEhG/7EDazNqvyD0arUoO9Uogjz/efMDDikbzfjQbG6tR193p03fqrrvu9NNdFWUjrmngiIgdwDERsT0ibo6ImyK7ac9seEbL/NVF7tFoVTXUaEj0HTt2Pna9odFrq8ZaDeRYr9ptYCCb2+O886qlquXLsxsAu53H1ntatZ6TjSn1OeCPgZdWHsNpkR+ph3tVVY2pHiNt7hJaOi9a9TJq1iuqzGPcuMbr8t2CR+Jeiz7udtvImPqOtBkd6FX1R8AhwMfI5h//NHBOO4KY9YnRNuxFq15Gre7qnj692AyAO3Y0nowpoloqGIm7u0dbHltPGd9qg4hY0ImEWB8Za8NeVALJKadkbRJ5kyfDuedmz5cta90gHpEFj6w0P1ilSmratJ3PA+V6R421PLYxpWWJQ9KzJH1G0rXp8WlJz+pE4qwHrVrVuDvraO42unhx1oYwMFB/rKhKqaVRiSIvovE0s5VSwnDHxvIc4dZGRaqqLgYeJbt7/E+BR4AvtDNR1qMqjb71urOOpvmrmzXct6rWKnJhnju3eZB58MHhT9PqOcKtnVo1ggDXF1nWjYcbx6vGRMNfo0bf2vGUhmlYeVGmUbleo/rAQMSuuzZuBM8fq90DDg4MxBOzZvXd0CKNjInvSIfQgcbxJyS9qvJC0ivJZu4zK6dR/frTT4/ovQYz16wZXGI4+eTWXX8rpYxjjy1+J3m9LrMAX/hC1mBeUamaqy05tLtUsHhxNkOhhxaxkdYqsgCHAjcAd6bHL4AXDydajdTDJY6qMfFrqhNDeg8MxPaJExv/4q9XgigyaGDtKLoj9V7aPODgmPhcdIjzoop2lzgi4vqIeDHwIuBFEfGSiLihTXHMelkn6t2XLRs033ddtSWIoYwpNVK9ljzgoI1BRXpVfULS1Ih4JCIekbSXpI93InHWY8rM3jdURS/c+e1a7VMvuA2111K9hvfRche9WUFF2jjeGBFbKi8i4iHg6LalyHpbu39hF+1umt+u2T6NgttQSk/12kWOOw6OP77csO5D5QBlI6RI4BgnaWLlhaTdyKZ6NWuvoVzoli/PRoRtpvYCf/TRO3eNnTw5u2ejUXAbSumpXpXYU0/B738/eFk77vBuNf6VWRmtGkGADwH/A5wAHJ+ef2g4DSsj9XDjeFXPNfw16xbbokH55mXLGk+rOn364O1POmnnaWWlbPlIazR9bZHG+CF65nPRx3ONV/Tcd2QY6EDj+D8CHwdeQDZm1T+kZWbt02ispfe8J+sy2+SX8+aFC2HKlPrHnTKlWipYtQrOP3/n4T8isgmeiipaMipz1/ZI3+HtIUhsBBVpHN8d+H5EnA5cAEyUtOtwTippqqSvSvq1pFskvULSNEmXS7o1/d1rOOewMa7RBa32Ig/1q3aKXCiXLat/vGb71ypTBVSvXWTXXWHChMHL2nGHt4cgsRFUpI3jGmCSpNnAGuA4YMUwz3su8N2IeD7wYuAW4Azgiog4ELgivbZ+VfaCtn79M7/4Z65ZU+xC2Sw4FD1/o5LRkiU7l0DqtYt84Qtw8cXt7WkGHoLERlaruizg5+nvX5PaNoBfDLVuDNgTuANQzfJ1wN7p+d7AulbHchtHVc/V3xa5Ka/BY/vEiRFHHll/faXtYmCg8fwYUvEb8Yq0W3RxHoxBn4s232w42vXcd2QYGGYbh6JRUT2R9AvgZOCfgRMi4mZJN0bEHwwlUEk6lKzK61dkpY3rgFOA30XE1Nx2D0XETtVVkpYCSwFmzJhx2OrVq4eSjJ6zdetWpjSq1x+jZq5Zw3MuvJCJmzcTErs0mmmvjqd32aXu9k/OmsXtJ57I888+m13qDLYYwO+OOYbbTj210HmOWLSISZs2tdzuyVmzsuE/OqwXPxdD5byoWrBgwXURcfiQD9AqsgCvBi4FPpxePwf47FAjFXA4sB14eXp9LvAPwJaa7R5qdSyXOKp6/tfUMEogO5UmGvW4KlLSqP3VftJJxdI1Qr2kyur5z0UJzosqOtCr6pqIeGtEfCq9vj0iPjDkSAUbgY0R8ZP0+qtk09FukrQ3QPq7eRjnsF5T2z4wfXrWsNzIuHH1l8+ZU3+SJMgu8c3aFuo1hK9cmbVnVNLV7LxmPaJI4/iIioh7gbskzUuLjiSrtroUWJKWLQG+0em0WReUuckvf9f5lCnZzXN17Jg4MbvAj3RjcKOG8Msuq6Zr5Uo3QlvP63jgSP4aWCXpl2Sj734COBs4StKtwFHptfWyol1Z6wWXJj2i1p1+Opx3XuM7u/NDnudVljcKZkW6+HZiPC6zbmtVlwW8ssiybjzcxlE1Jutvi9zN3OgO8iZ3hrecvGhgIGLChMH7TZhQvSu90R3rY/Du6zH5uWgT50UVHZjI6V8LLrOxqluD3xW9Sa9e9RDUv5nu0UezXk7NSjCLF+9878TFF2fLG51v2TLfC2GWNAwc6W7u04AZkj6Ye5wFNGgBtDGnm4PfTZvWeHklkK1fX3+bevNy77ln8QEDa0fpheycjc63YYOrocyS8U3WTQCmpG32yC1/BHhHOxNlHdTsF3Y7L4irVsEjj+y8fPz4bHmjnk8Vc+Zk6cuncZcGv4NaDR9SCZ7NJnOq9IqqPadZH2oYOCLiauBqSSsiYj2ApF2AKRFR5xtvY1K3Br9btqx+r6gdOxqPH1XRqHpozpz6JYZKCWbDhmyb5csHX/xbzQDo6iizQYq0cXxS0p5psMNfAesk/W2b02Wd0unB7yrtKY2qhJoFjVbVQ/XaICZMyEowzarimgVJV0eZ7aRI4Dg4lTDeBlwGzAHe085EWQe1s8G3ttH95JOr7SmNNLqBbu7c1rMGpjaIJ2fNqgaZPfbYuWRT2+7RKEjOnet5wM3qKBI4dk3DqL8N+EZEPEU2pI/1gnY1+NZrdD///NZVQsO9cW/x4mxMqEqQefDB+tvlSxnuLWVWSpHA8f+AO4HdgWskzSVrILde0Y55wOu1GzSrhqoErGY37g1Fkaq4esFzyZLsPXh+brOdNOtVBUBEfBb4bG7RekkL2pck6wllGtcrVUIVI9lzafnynXtM1StN5M9Z28uq0i5S2c6szxWZAXCWpIskfSe9PpjqmFJm9TX6pS8Nft3uKqGhVMU166JsZoWqqlYA3wP2Sa9/A5zapvRYr2jUbvC+93X+BrqyVXGen9usqYZVVZLGR8R24NkRsVrSmQARsV3SzjPgmOVVLs7LljW+f2K0anQ/iIdGNwOalzh+mv4+Jmk6qSeVpCOAh9udMOsBjYb1GO0Nzu5lZdZUs8BRqYz+INlcGc+V9APgi2TDopsV164xsSr3ikjZcCUSRyxaNLzjekwqs6aa9aqaIemD6fnXyW7+E7ANWAj8ss1ps17SjjGxans/pTnEJ23aNPxeUB6TyqyhZiWOcWSDHO5Bdg/H+LRsMoMHPTRrrR0Nzs3GmHIvKLO2aVbiuCciPtaxlFhva0eDc6ug415QZm1RpI3DbPja0eDcKui4F5RZWzQLHEd2LBXW+4o2OJeZjbBeMKpwLyiztmk2H0eD0eHMhqhVg3PZoT7y94qsX5+NrLtjB0/OmsWkT3/ajdtmbVLkzvG2kDRO0i8kfSu9nibpckm3pr97dStt1iVDGeqjcq9IBGzfDhHZ6LgOGmZt07XAAZwC3JJ7fQZwRUQcCFyRXls/8VAfZmNCVwKHpH2BNwEX5hYfA6xMz1eSzf9h/aTTsxGa2ZAoWs3v3I6TSl8FPkl2P8jpEfFmSVsiYmpum4ciYqfqKklLgaUAM2bMOGz16tUdSvXotnXrVqZMmdLtZAzLzDVrmHfOOYzbtu2ZZTsmTmTd6aezeeHCwsfphbwYKc6LKudF1YIFC66LiMOHfICI6OgDeDNwXno+H/hWer6lZruHWh3roIMOCstcddVV3U7CyBgYiJg7N0LK/g4MlD5Ez+TFCHBeVDkvqoBrYxjX8ZYTObXBK4G3SjoamATsKWkA2CRp74i4R9LewOYupM26zUN9mI16HW/jiIgzI2LfiNgfWARcGRHHkg2kWJkgagnwjU6nzczMWutmr6paZwNHSboVOCq9NjOzUaYbVVXPiIi1wNr0/AF8t7qZ2ag3mkocZmY2BjhwmJlZKQ4cZmZWigOHdUaZUW/NbFTrauO49Ymyo96a2ajmEoe131BGvTWzUcuBw9rPo96a9RQHDms/j3pr1lMcOKz92jHfuJl1jQOHtV/R+cbNbExwryrrDI96a9YzXOIwM7NSHDjMzKwUBw4zMyvFgcPMzEpx4DAzs1IcOMzMrBQHDjMzK8WBw8zMSnHgMDOzUjoeOCTtJ+kqSbdIulnSKWn5NEmXS7o1/d2r02kzM7PWulHi2A6cFhEvAI4A3i/pYOAM4IqIOBC4Ir02M7NRpuOBIyLuiYifp+ePArcAs4FjgJVps5XA2zqdNjMza00R0b2TS/sD1wAvBDZExNTcuociYqfqKklLgaUAM2bMOGz16tWdSewot3XrVqZMmdLtZIwKzosq50WV86JqwYIF10XE4UPdv2uBQ9IU4GpgeUR8TdKWIoEjb968ebFu3bo2p3RsWLt2LfPnz+92MkYF50WV86LKeVElaViBoyu9qiTtCvwnsCoivpYWb5K0d1q/N7C5G2kzM7PmutGrSsBFwC0R8ZncqkuBJen5EuAbnU6bmZm11o2JnF4JvAe4UdL1adlHgLOB1ZJOADYA7+xC2szMrIWOB46I+B9ADVYf2cm0mJlZeb5z3MzMSnHgMDOzUhw4zMysFAcOMzMrxYHDzMxKceAwM7NSHDjMzKwUBw4zMyvFgcPMzEpx4DAzs1IcOMzMrBQHDjMzK8WBw8zMSnHgMDOzUhw4zMysFAcOMzMrxYHDzMxKceAwM7NSHDjMzKwUBw4zMytl1AUOSW+QtE7SbZLO6HZ6zMxssFEVOCSNAz4PvBE4GHi3pIO7myozM8sbVYEDeBlwW0TcHhG/By4BjulymszMLGd8txNQYzZwV+71RuDl+Q0kLQWWppfbJN3UobSNds8G7u92IkYJ50WV86LKeVE1bzg7j7bAoTrLYtCLiAuACwAkXRsRh3ciYaOd86LKeVHlvKhyXlRJunY4+4+2qqqNwH651/sCd3cpLWZmVsdoCxw/Aw6UdICkCcAi4NIup8nMzHJGVVVVRGyX9FfA94BxwMURcXOTXS7oTMrGBOdFlfOiynlR5byoGlZeKCJab2VmZpaMtqoqMzMb5Rw4zMyslDEbOPp5aBJJ+0m6StItkm6WdEpaPk3S5ZJuTX/36nZaO0HSOEm/kPSt9Lov8wFA0lRJX5X06/T5eEU/5oekv0nfjZskfVnSpH7KB0kXS9qcv8+t2fuXdGa6lq6T9PpWxx+TgcNDk7AdOC0iXgAcAbw/vf8zgCsi4kDgivS6H5wC3JJ73a/5AHAu8N2IeD7wYrJ86av8kDQb+ABweES8kKyjzSL6Kx9WAG+oWVb3/adrxyLgkLTPeeka29CYDBz0+dAkEXFPRPw8PX+U7OIwmywPVqbNVgJv60oCO0jSvsCbgAtzi/suHwAk7Qm8GrgIICJ+HxFb6M/8GA/sJmk8MJnsfrC+yYeIuAZ4sGZxo/d/DHBJRGyLiDuA28iusQ2N1cBRb2iS2V1KS1dJ2h94CfATYFZE3ANZcAFmdjFpnfIvwIeAp3PL+jEfAJ4D3Ad8IVXdXShpd/osPyLid8A5wAbgHuDhiPg+fZYPdTR6/6Wvp2M1cLQcmqQfSJoC/CdwakQ80u30dJqkNwObI+K6bqdllBgPvBT4t4h4CfAYvV0dU1equz8GOADYB9hd0rHdTdWoVvp6OlYDR98PTSJpV7KgsSoivpYWb5K0d1q/N7C5W+nrkFcCb5V0J1l15WslDdB/+VCxEdgYET9Jr79KFkj6LT8WAndExH0R8RTwNeCP6L98qNXo/Ze+no7VwNHXQ5NIElk99i0R8ZncqkuBJen5EuAbnU5bJ0XEmRGxb0TsT/YZuDIijqXP8qEiIu4F7pJUGfn0SOBX9F9+bACOkDQ5fVeOJGsH7Ld8qNXo/V8KLJI0UdIBwIHAT5sdaMzeOS7paLL67crQJMu7m6LOkfQq4L+BG6nW7X+ErJ1jNTCH7MvzzoiobSDrSZLmA6dHxJslTad/8+FQso4CE4DbgePIfiD2VX5I+ijwLrIeiL8ATgSm0Cf5IOnLwHyyoeQ3AX8P/BcN3r+kZcDxZPl1akR8p+nxx2rgMDOz7hirVVVmZtYlDhxmZlaKA4eZmZXiwGFmZqU4cJiZWSkOHGZmVooDh41JkqZLuj497pX0u/R8q6TzOpSGQ9P9RGX3O0vS6en5xyQtLLHv/vmhsnPL50t6WNJludffanCMVZIelPSOsmk3g1E257hZURHxAHAoZBdiYGtEnNPhZBwKHA5cNtQDRMTfjVhq4L8j4s0FzrlY0ooRPK/1GZc4rKfkf2mnX/YrJX1f0p2S3i7pHyXdKOm7abwvJB0m6WpJ10n6XmU8n5rjvjNNCnSDpGvSUDcfA96VSjrvypck0j43pdGLkbQsTZKzBpiX22ZF5Zd/o3Sk5TdI+hHw/hLZMUXVSZ1WpeE3zIbNgcN63XPJ5us4BhgAroqIPwCeAN6Ugse/Au+IiMOAi4F6w9f8HfD6iHgx8NY0D8zfAV+JiEMj4iuNEiDpMLKxtF4CvB34wzrbNEvHF4APRMQrSr73lwCnkk129hyyQSHNhs1VVdbrvhMRT0m6kWxcs++m5TcC+5P9+n8hcHn6QT6ObA6HWj8AVkhaTTbaahl/DHw9Ih4HkFRvQM666ZD0LGBqRFydtvsS2cyXRfw0Ijamc15P9n7/p2TazXbiwGG9bhtARDwt6amoDs72NNnnX8DNrX7NR8T7JL2crPRyfRpMsNZ2BpfiJ+UP0SKdddMhaWqBfRvZlnu+A3/fbYS4qsr63TpghqRXQFZlJOmQ2o0kPTcifpIas+8nm7/gUWCP3GZ3ks1/gaSXkk0kBHAN8L8l7SZpD+AtRdORpn59OI2IDLB4WO/WbAQ4cFhfS20V7wA+JekG4HqySX9q/VNqVL+JLBDcAFwFHFxpHCebWGtaqhY6CfhNOsfPga+kY/8n2ZD4ZdJxHPD51Dj+xPDftdnweFh1sx6Qn4+k4PYrgG9FxFfbmCzrUS5xmPWG3wMvrNwA2IykVcBrgCfbnirrSS5xmJlZKS5xmJlZKQ4cZmZWigOHmZmV4sBhZmal/H8i8VPSudUNEQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots() #create a figure and a axes project\n",
    "ax.plot(points[:,0], points[:,1], 'ro')\n",
    "ax.axis([0,100,0,150])\n",
    "ax.set(xlabel=\"Time studied [h]\", ylabel=\"Test score [points]\", title=\"Relationship between test score and time studied\") #titles (tottenham fans would not get it)\n",
    "ax.grid() #show the grid\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "099ee268",
   "metadata": {},
   "source": [
    "## Train function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2b6954d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train() :\n",
    "    #define the Hyperparameters\n",
    "    learning_rate = 0.0001\n",
    "    initial_b = 0\n",
    "    initial_m = 0\n",
    "    num_iterations = 1000\n",
    "    \n",
    "    # Start the gradient descent algorithm\n",
    "    print(\"Starting gradient descent at b = {0}, m = {1}, error = {2}\".format(initial_b, initial_m, compute_error_for_line_given_points(initial_b, initial_m, points)))\n",
    "    print(\"Running...\")\n",
    "    [b,m] = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)\n",
    "    print(\"After {0} iterations b = {1}, m = {2}, error = {3}\".format(num_iterations, b, m, compute_error_for_line_given_points(b, m, points)))\n",
    "    \n",
    "    # return the final result to the global scope\n",
    "    return [b,m]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc25b7ff",
   "metadata": {},
   "source": [
    "## Gradient descent function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "82fc1e0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations) :\n",
    "    b = starting_b\n",
    "    m = starting_m\n",
    "    \n",
    "    for i in range(num_iterations) :\n",
    "        b, m = step_gradient(b, m, np.array(points), learning_rate)\n",
    "        if i%100 == 0 :\n",
    "            print(\"Iteration {0}: b = {1:.2f}, m = {2:.2f}, error = {3:.5f}\".format(i, b, m, compute_error_for_line_given_points(b, m, points)))\n",
    "            \n",
    "    return [b, m]\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "511a1d11",
   "metadata": {},
   "source": [
    "## Step gradient\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c12696d9",
   "metadata": {},
   "source": [
    "![title](1_3YJx2rdqMW5ccRJZFH9v6w.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e0fc1092",
   "metadata": {},
   "outputs": [],
   "source": [
    "def step_gradient(b_current, m_current, points, learningRate) :\n",
    "    b_gradient = 0\n",
    "    m_gradient = 0\n",
    "    N = float(len(points))\n",
    "    for i in range(0,len(points)) :\n",
    "        x = points[i, 0]\n",
    "        y = points[i, 1]\n",
    "        m_gradient += -(2/N)*x*( y - ((m_current * x ) + b_current)) #see formula above\n",
    "        b_gradient += -(2/N)*( y -(( m_current * x ) + b_current))\n",
    "    new_b = b_current - (learningRate * b_gradient)\n",
    "    new_m = m_current - (learningRate * m_gradient)\n",
    "    \n",
    "    return [new_b, new_m]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d68c261",
   "metadata": {},
   "source": [
    "## Compute error\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "45268e7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_error_for_line_given_points(b, m, points) :\n",
    "    totalError = 0\n",
    "    for i in range(0, len(points)) : \n",
    "        x = points[i, 0]\n",
    "        y = points[i, 1]\n",
    "        totalError += (y - (m*x + b)) ** 2\n",
    "        \n",
    "    return totalError / float(len(points))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0922c736",
   "metadata": {},
   "source": [
    "## Train our model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ab639942",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting gradient descent at b = 0, m = 0, error = 5565.107834483211\n",
      "Running...\n",
      "Iteration 0: b = 0.01, m = 0.74, error = 1484.58656\n",
      "Iteration 100: b = 0.04, m = 1.48, error = 112.64702\n",
      "Iteration 200: b = 0.04, m = 1.48, error = 112.64342\n",
      "Iteration 300: b = 0.05, m = 1.48, error = 112.63982\n",
      "Iteration 400: b = 0.05, m = 1.48, error = 112.63622\n",
      "Iteration 500: b = 0.06, m = 1.48, error = 112.63263\n",
      "Iteration 600: b = 0.07, m = 1.48, error = 112.62905\n",
      "Iteration 700: b = 0.07, m = 1.48, error = 112.62547\n",
      "Iteration 800: b = 0.08, m = 1.48, error = 112.62190\n",
      "Iteration 900: b = 0.08, m = 1.48, error = 112.61834\n",
      "After 1000 iterations b = 0.08893651993741346, m = 1.4777440851894448, error = 112.61481011613473\n"
     ]
    }
   ],
   "source": [
    "[b, m] = train()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db10d0b5",
   "metadata": {},
   "source": [
    "## Testing\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c84df731",
   "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": [
    "# sample studied hours\n",
    "h = np.arange(0, 100, 5)\n",
    "\n",
    "# visualize our model\n",
    "fig, ax = plt.subplots()  # creates a figure and an axes object\n",
    "ax.plot(points[:,0], points[:,1], 'ro')\n",
    "ax.plot(h, m*h + b, 'b')\n",
    "ax.axis([0, 100, 0, 150])\n",
    "ax.set(xlabel='Time Studied [h]', ylabel='Test Score [Points]',\n",
    "       title='Relationship between Test Scores and Time Studied')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d982142",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}