LinearRegression-ClosedForm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression using Closed Form Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dataset = pd.read_csv('Salary_Data.csv')\n",
    "X = dataset.iloc[:, :-1].values\n",
    "y = dataset.iloc[:, 1].values\n",
    "origianl_X = X\n",
    "X = np.c_[np.ones((len(X), 1)), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applying Closed Form Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src = \"closed_form.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.linalg.inv(X.transpose().dot(X)).dot(X.transpose()).dot(y)\n",
    "b = theta[0]\n",
    "m = theta[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = m * origianl_X + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def error(b, m, X, y):\n",
    "    totalerror = 0\n",
    "    for i in range(len(X)):\n",
    "        totalerror += (y[i] - (m * X[i] + b))**2\n",
    "    return (totalerror/(float(len(X))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept :  25792.2001987\n",
      "Slope :  9449.96232146\n",
      "MSE :  [ 31270951.72228097]\n"
     ]
    }
   ],
   "source": [
    "print(\"Intercept : \", b)\n",
    "print(\"Slope : \", m)\n",
    "print(\"MSE : \", error(b, m, origianl_X, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pNtzdF+U2TpFoSvVUBicP5r7J95HqqbzQ9gV6ntmT0qVKxzo0kagwd12qgOCa\nTXJycqzDkBJgycYldB3blWnLp9Hm+DYktk/kuGp5Gm8jEnNmNtfd47Krl9MBApjZZQT3tFRIK8ts\nJmgR+av9qft57qvnePjzhylfujzDrhjGzc1uJhjJL1K85XTxtFcI7oe5gGAU2lUE10dEJAe+W/cd\n8UnxJK9J5sqGVzLg0gEcU/mYWIclUmBidVOnSImwZ/8eHv7sYc5IPIPlW5Yz6qpRfHDNB0o0UuLk\n9abOTeTxpk6RkmL2qtl0SepCyoYUbjzlRp6/5HmqV6oe67BEYiK3N3X+j+Buf8jjTZ0ixd2OvTt4\n6LOHeH7W89Q6rBbjrh/HZSdeFuuwRGIqu/tszgRWpt3UaWaHAguA7wkmxRSRCFN/mcotY2/h580/\nc1vcbTzR5gkOK39YrMMSibnsrtkMBvYCmFkr4ImwbCvhNC8iAlt3b6Xb2G60fr01pawUn3f6nIGX\nDVSiEQll141W2t03ha+vBRLd/X2CaWu+jW5oIkXDuB/Hceu4W1m7fS3/PvvfPHLBI1QqWynWYYkU\nKtkmm4j5yloTzpCcw31FirUNOzZw54Q7eXvh2zQ9sikfXvshZ9Y6M9ZhiRRK2SWMt4EvzOw3ghFp\n0wHMrD5BV5pIiePuvLPwHe6YcAdbd2/lkfMfofd5vSlXulysQxMptLJMNu7e38ymADWBT/2PuW1K\nEazaKVKirP59NbeNv42xP47lrFpnMeyKYTQ+snGswxIp9LLtCnP3WRmU/RidcEQKJ3dn6DdD+fek\nf7PvwD6evfhZ7jjrDk2cKZJDuu4iko2fNv3ELWNv4bNln3FBvQsYcvkQTjj8hFiHJVKkKNmIZOJA\n6gFenP0iCVMTKFu6LIntE+l6eldNnCmSB0o2IhlYtH4R8UnxzF49m/YntmfQZYOofVjtWIclUmQp\n2YhE2HtgL0/OeJJHpz1KlQpVeOvvb3Fdk+vUmhE5SEo2IqHkNcl0GdOFBesXcH2T63mh7QvUOKRG\nrMMSKRaUbKTE27VvF30/78szXz3D0YceTdJ1SVx+UlYrootIbuV0PRuRYmna8mmc8sopPDXzKeJP\niyelR0rGiWbkSKhXD0qVCp5HjizoUEWKNLVspET6fc/v9J7cm0HJgzi+2vFMuWkKFx53YcaVR46E\nbt1g587g/fLlwXuAjh0LJmCRIk4tGylxPlnyCU0GNuGV5Fe4u8XdfHfrd5knGoCEhD8STZqdO4Ny\nEckRtWykxNi4cyN3T7ybN757g0Y1GjEzfiYtarfIfscVK3JXLiJ/oWQjxZ67817Ke9z+8e1s3r2Z\nh1o9RELLBMqXKZ+zA9SpE3ReZEsCAAAVcElEQVSdZVQuIjmibjQp1tZuW8vf3/07146+ljpV6jC3\n21z+e8F/c55oAPr3h0rp1qepVCkoBw0eEMkBtWykWHJ3Xv32VXpN7MWeA3v4X5v/cffZd1OmVB7+\nyacNAkhICLrO6tQJEk3Hjho8IJJD9seqASVbXFycJycnxzoMyQe/bP6FbuO6MfnnybSs05KhVwzl\nxOonRudk9epl3MVWty4sWxadc4oUImY2193jsqunbjTJPzHuTkqbOLPJoCbMWjWLgZcO5PPOn0cv\n0YAGD4jkkLrRJH/EuDtp8YbFxCfF89Wqr2hbvy2D2w+mTpUCuICvwQMiOaKWjeSPGN2Lsu/APh6b\n/hjNBjfjh40/8PqVr/PxDR8XTKKB7AcPiAigZCP5JdrdSRl00c1bO4/mQ5uTMDWBDid1IKVHCv88\n9Z8FO0Nzx46QmBhcozELnhMTNThAJB11o0n+iGZ3Urouut2rl/PfNzrzv6Wp1Dj0SD645gP+dvLf\nDv48edWxo5KLSDbUspH8Ec3upIguui+PhWa3wuNn7+emHyuS0iMltolGRHJEyUbyRzS7k1asYHs5\nuKMdtOwCu8vAp6/D8Ld3Uq1itYM/vohEnZKN5J+OHYN7S1JTg+d86lr6tEUNmvSAl5vD7XNg4UC4\n6Gfy3kWnO/5FCpyu2UihtXnXZnp92ovXLlnPSRuN6cOdc1eGG/PaRac7/kViQi0bKZQ+WPwBjQY2\n4o35b/DgeQ/y7ZnDOLdUPnTRabkAkZiISbIxs6pmNtrMvjezxWZ2tpkdbmaTzGxJ+FwtrGtm9qKZ\nLTWz78zs9IjjdArrLzGzThHlZ5jZgnCfF61Ax8KWAFHshlq3fR1Xv3c1/3j3Hxx96NF8fcvX9G/d\nnwr/vDl/uuh0x79ITMSqZfMCMMHdGwKnAouB3sAUd28ATAnfA7QDGoSPbsAgADM7HOgLnAU0B/qm\nJaiwTreI/doWwGcqGdK6oZYvB/c/uqEOMuG4O6/Pf52TB5xM0g9JPHbhY8zpOofTap6WT4GHMrvO\nozv+RaKqwJONmR0GtAKGAbj7XnffAnQARoTVRgBXhq87AK97YBZQ1cxqApcAk9x9k7tvBiYBbcNt\nh7n7Vx7MMvp6xLHkYEWhG2rF1hVc+taldPqoEyfXOJn5t87ngZYPULZ02YMMNgO6418kJmLRsjke\n2AC8ambzzGyomR0CHOXuawHC5yPD+rWAlRH7rwrLsipflUH5X5hZNzNLNrPkDRs2HPwnKwnysRsq\n1VMZ+PVAGg9szPTl03mx7YtMv3k6DY9oeJBBZkF3/IvERCxGo5UBTgf+5e6zzewF/ugyy0hG11s8\nD+V/LXRPBBIhWGIgq6AllE8zBfy48Ue6JnVl+orpXHT8RSRenki9qvXyJ8bs6I5/kQIXi5bNKmCV\nu88O348mSD7rwi4wwuf1EfWPjdi/NrAmm/LaGZRLfjjIbqj9qft5csaTnDLoFBasX8CrHV5l4o0T\nCy7RiEhMFHiycfdfgZVmdlJY1BpIAZKAtBFlnYAx4esk4KZwVFoLYGvYzTYRuNjMqoUDAy4GJobb\ntplZi3AU2k0Rx5KDdRDdUPN/nc9ZQ8+i95TeXNrgUlJ6pNC5Wec/Js7Myyg33aApUjS4e4E/gGZA\nMvAd8BFQDahOMAptSfh8eFjXgAHAT8ACIC7iOF2ApeHj5ojyOGBhuM/LhCuSZvU444wzXLLw5pvu\ndeu6mwXPb76Z411379vtfab08TL/LeNHPnWkv7fovYyPX6mSezDGLXhUqpTxedJigSCenOwjIlEB\nJHsOfve1LHRIy0JnIf1d9xB0neWgRfPVyq+IT4pn8W+LuenUm3j24mepXqn6XyvmdHnljGLJbh8R\niZqcLgutZBNSsslCThNBhB17d5AwNYEXZ79I7cNqM7j9YNo1aJf5OUqVCtom6ZkFN3JmF0tW+4hI\n1OQ02WhuNMleLoc7T/55MreMvYVlW5bRI64HT7R5gsrlK2d9jpyOcssu0WS0j4jEnOZGk+zl8K77\nLbu30DWpKxe9cRFlS5Xli85fMOCyAdknGsj5KLfSpbM+jm7QFCmUlGwkezlIBGO+H0Ojp4/j1bnD\nuO9LmP/8blrNWEmO5XSU24EDmR9DN2iKFFrqRpPspf14JyQEXWd16gSJpmNH1u9Yzx2f3MGoRaM4\nZb2R9BHErQFYmfup+3Nys2Xdurm+fiQisacBAiENEMgdd+etBW9x54Q72bZ3Gw99XZH7xm+lXPqG\nR34ngYMYGSci+S+nAwTUjSa5tur3VVzxzhXc+OGN1D+8PvO6z6PP2N//mmgg/6fu19xmIkWSutEk\nx1I9lSFzh3DvpHs54Ad49uJnueOsOyhdqnS+zZmWI5rbTKTIUctGcmTppqW0fr01t46/lTNrncmC\n2xZw99l3B4kGNHW/iGRJyUaytD91P0/PfJqmg5ryzdpvGHL5ECb/czLHVzv+zxXVvSUiWVA3mmRq\nwboFxCfF8/War7nipCsYeOlAah2W4dJAAXVviUgmlGzkL/Ye2Mtj0x/jsemPUbVCVd75xztc0/ia\nP2ZnFhHJJSUb+ZM5q+cQnxTPwvULuaHpDbzQ9gWOqHRErMMSkSJOyUYA2LlvJw9/9jDPzXqOmofW\nZOz1Y2l/YvtYhyUixYSSjfD5ss/pmtSVnzb/RPczuvNkmyepUqFKrMMSkWJEyaYE27p7K/dPvp/B\ncwdzQrUTmHrTVC447oJYhyUixZCSTQk1/sfxdB/XnbXb19KrRS8evfBRKpWtlP2OIiJ5oGRTwvy2\n8zfumnAXIxeMpHGNxrx/zfucVfusWIclIsWckk0J4e68u+hd/vXJv9i8ezN9/68vD7Z8kHKly8U6\nNBEpAZRsSoA129Zw2/jbSPohibhj4phyxRSaHtU01mGJSAmiZFOMuTvD5w3nnk/vYc+BPTx10VPc\n1eIuypTSf3YRKVj61Smmft78M93GdmPKL1NoVbcVQy8fSoPqDWIdloiUUJqIM1pGjoR69aBUqeB5\n5MgCOe2B1AM8P+t5mg5qypzVcxh02SA+6/SZEo2IxJRaNtGQfjXJ5ctzv0RyHizesJj4pHi+WvUV\n7eq3Y3D7wRxb5dionU9EJKfUsomGhIQ/L1sMwfuEhKicbt+BffSf1p9mg5vxw8YfeONvbzD+hvFK\nNCJSaKhlEw2ZLYWc30skA9+s/YYuY7owf918rml8DS+1e4kjDzky388jInIw1LKJhsyWQs7HJZJ3\n7dtF78m9aT6kOet3rOfDaz9k1FWjlGhEpFBSsomGKC+RPGPFDJoNbsaTXz5J52adSemZwpUNr8yX\nY4uIRIOSTTREaYnkbXu2cfvHt9Py1ZbsXfYTk16HoXdMpur74/MpcBGR6NA1m2jJ5yWSJy6dSLdx\n3Vi5dSV3JZeh38T9HLIPoGBGuomIHAy1bAq5Tbs20fmjzrQd2ZZDyh7Cl+OO4rlxaYkmFMWRbiIi\n+UHJphB7P+V9Gg1oxMgFI+nTsg/zus/j7LnrMq4chZFuIiL5Rd1ohdCv23+l58c9+WDxB5xe83Qm\n3DiBZkc3CzbWqRPcJJpePo50ExHJb2rZFCLuzmvfvkajAY0Y/+N4nmj9BLO7zv4j0UDUR7qJiESD\nWjaFxPIty+k+rjsTf5rIeXXOY+jlQznpiJP+WjFtEEBCQtB1VqdOkGg0OEBECrGYtWzMrLSZzTOz\nceH748xstpktMbNRZlYuLC8fvl8abq8XcYwHwvIfzOySiPK2YdlSM+td0J8tN1I9lZfnvEzjgY35\ncuWXvNzuZb7o/EXGiSZNx46wbBmkpgbPSjQiUsjFshvtTmBxxPsngefcvQGwGYgPy+OBze5eH3gu\nrIeZNQKuAxoDbYGBYQIrDQwA2gGNgOvDuoXOD7/9QKtXW/GvT/7FeXXOY+FtC+nZvCelLI//WWI0\n07SISHZikmzMrDZwGTA0fG/AhcDosMoIIO2W+A7he8LtrcP6HYB33H2Pu/8CLAWah4+l7v6zu+8F\n3gnr5r88/rjvT93PEzOe4NRXTiVlQwqvdXiNTzp+Qt2qdQ8ulm7dgsED7n/MNK2EIyKFQKxaNs8D\n9wGp4fvqwBZ33x++XwXUCl/XAlYChNu3hvX/f3m6fTIr/wsz62ZmyWaWvGHDhtx9gjz+uH/767c0\nH9KcB6Y8QPsT25PSM4VOzToR5M+DUMAzTYuI5EaBJxszaw+sd/e5kcUZVPVstuW2/K+F7onuHufu\ncTVq1Mgi6gzk8sd99/7d9JnahzOHnMmabWsYffVoRl8zmqMPPTp3581MAc40LSKSW7Fo2ZwLXGFm\nywi6uC4kaOlUNbO00XG1gTXh61XAsQDh9irApsjydPtkVp6/cvHjPnPlTE4bfBr9p/en4yFnk5JY\nln80uTp/r6sUwEzTIiJ5VeDJxt0fcPfa7l6P4AL/VHfvCHwGXBVW6wSMCV8nhe8Jt091dw/LrwtH\nqx0HNADmAF8DDcLRbeXCcyTl+wfJwY/79r3bufOTOzlv+Hns3LeTCTXv47WH5nL4klX5f11F99+I\nSCFWmG7qvB/oZWZLCa7JDAvLhwHVw/JeQG8Ad18EvAukABOAnu5+ILyuczswkWC027th3fyVzY/7\n5J8n03RQU16c8yI9zuzBwtsWcsljo6J3XSVKM02LiOQHCxoJEhcX58nJybnbaeTIv9xcueUfl3HP\nxHsY/u1wGhzegGFXDKNl3ZZB/VKlghZNembBPTMiIkWMmc1197js6hWmlk3Rk+7myo/OOIRGAxox\nYv4Iep/bm/m3zv8j0YCuq4hIiaVkkw/WbV/HNe9dw99G/Y0jDzmS2V1n83ibx6lYtuKfK+q6ioiU\nUJob7SBN/WUqV793Ndv3bqffBf2479z7KFu6bMaVNa+ZiJRQSjYHqcHhDYg7Jo7nLnmORjVyMCtO\nPq/gKSJSFCjZHKRjqxzLxBsnxjoMEZFCTddsREQk6pRsREQk6pRsREQk6pRsREQk6pRsREQk6pRs\nREQk6pRsREQk6pRsREQk6jTrc8jMNgDLYx1HLh0B/BbrIGKopH9+0HdQ0j8/xP47qOvu2S51rGRT\nhJlZck6m9i6uSvrnB30HJf3zQ9H5DtSNJiIiUadkIyIiUadkU7QlxjqAGCvpnx/0HZT0zw9F5DvQ\nNRsREYk6tWxERCTqlGxERCTqlGyKGDM71sw+M7PFZrbIzO6MdUyxYGalzWyemY2LdSyxYGZVzWy0\nmX0f/ls4O9YxFTQzuzv8f2Chmb1tZhViHVO0mdlwM1tvZgsjyg43s0lmtiR8rhbLGDOjZFP07Afu\ncfeTgRZATzPLwXrUxc6dwOJYBxFDLwAT3L0hcCol7Lsws1rAHUCcuzcBSgPXxTaqAvEa0DZdWW9g\nirs3AKaE7wsdJZsixt3Xuvs34ettBD8ytWIbVcEys9rAZcDQWMcSC2Z2GNAKGAbg7nvdfUtso4qJ\nMkBFMysDVALWxDieqHP3acCmdMUdgBHh6xHAlQUaVA4p2RRhZlYPOA2YHdtICtzzwH1AaqwDiZHj\ngQ3Aq2FX4lAzOyTWQRUkd18NPA2sANYCW93909hGFTNHuftaCP4YBY6McTwZUrIposzsUOB94C53\n/z3W8RQUM2sPrHf3ubGOJYbKAKcDg9z9NGAHhbTrJFrC6xIdgOOAY4BDzOzG2EYlWVGyKYLMrCxB\nohnp7h/EOp4Cdi5whZktA94BLjSzN2MbUoFbBaxy97QW7WiC5FOStAF+cfcN7r4P+AA4J8Yxxco6\nM6sJED6vj3E8GVKyKWLMzAj66he7+7OxjqegufsD7l7b3esRXBCe6u4l6i9ad/8VWGlmJ4VFrYGU\nGIYUCyuAFmZWKfx/ojUlbJBEhCSgU/i6EzAmhrFkqkysA5BcOxf4J7DAzL4Nyx50949jGJMUvH8B\nI82sHPAzcHOM4ylQ7j7bzEYD3xCM0JxHEZm25WCY2dvA+cARZrYK6As8AbxrZvEESfjq2EWYOU1X\nIyIiUaduNBERiTolGxERiTolGxERiTolGxERiTolGxERiTolGynWLDDDzNpFlF1jZhNiHNO7Zvad\nmd2Rbls/M1ttZt9GPCpHOZ6J0T6HiIY+S7FnZk2A9wjmkSsNfAu0dfefDuKYZdx9fx73rQ184e4n\nZLCtH/Cbuz+f19hyEYcR/AaU1DnmpACpZSPFnrsvBMYC9xPcBPe6u/9kZp3MbE7YehhoZqUAzCzR\nzJLDtVIeTjuOma0ys4fM7Evgb+F6KilmNj+jKXPMrKKZjTCzBWb2jZm1Cjd9ChwTnjdHU6yY2X1m\nlhi+bhYes2LYEhoRrnG0xMy6ROzTO/x836V9DjOrH67/8grBDZE1w89VNdz+l+/EzMqY2RYzeyL8\nrF+Z2ZFh/aPNbEx4jvlmdlZmx8nVfzQpftxdDz2K/QM4BPgBWACUB5oAHwFlwu2JwA3h68PD5zLA\ndKBR+H4V0CvimGuBcuHrqhmc835gSPi6MbAcKAfUB77NJM5+wGqC1te3wOSwvBTwJcHkk/OAFhH1\nvwEqEMz2uwo4CrgUGAhYuO8EgrnD6hPMln1mxDlXAVUz+07C78GBdmH5s0Dv8PX7wO0R39dhWX23\nepTch6arkRLB3XeY2Shgu7vvMbM2wJlActCbREVgZVj9+nDqjzIEMwo34o+5x0ZFHHYR8KaZjSH4\ncU3vPOCp8PyLzGwNwY/93mzCfcrTdaO5e6qZdSZIQC+7+6yIzR+5+25gt5lNCz9XG6AdQWICOBQ4\nkWCSxp/c/esMzpvVd7LL3T8JX88FWoavzydctMyDbsXfs/lupYRSspGSJJU/1sAxYLi7PxRZwcwa\nEKwC2tzdt4TdY5HLDe+IeH0J8H8ErY0+ZtbE3Q9EHi6f428AbCdIgJHSX3j18Nz93H1Y5AYzq8+f\nP8OfNpPxd1KGPyfIA/z5tyP9+TM8jpRs6keVkmoycI2ZHQFgZtXNrA5BN9A2gr/QaxIklL8ws9JA\nbXefCtwL1CBYLTLSNKBjWP9koCawNC/BhtdUniOYiLWWmUWuxnilmZUPP0tLIBmYCMRbuKiamdVO\n+6xZyOw7ycpnwK1h/dIWrCKal+NIMaeWjZRI7r7AzB4BJocXr/cR/GgmE3SZLSSYTfnLTA5RBngr\nHDJcCnjSg2W6I70EDDazBeHxb3L3vWHXUlbuDbvM0lwO9AdecPelZnZzGPeMcPvXwCfAsUBfd18H\nfGxmDYFZ4fm2EVx/yVQW30lWyy3fDgwxs+4Esy93d/c5mRxnRXYfXIovDX0WKcIKcqi0yMFQN5qI\niESdWjYiIhJ1atmIiEjUKdmIiEjUKdmIiEjUKdmIiEjUKdmIiEjU/T9sYd6nQfou0wAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3285290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(origianl_X, y, color = 'red')\n",
    "plt.plot(origianl_X, y_pred, color = 'green')\n",
    "plt.title('Salary vs Experience')\n",
    "plt.xlabel('Years of Experience')\n",
    "plt.ylabel('Salary')\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}