{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rO+6447797W8PGzaso/ORIy3FaIq20nfpEkcdFUuWxJQpSUcBAAAA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\nP590DgAAAAD2nWI0YxoaFKP7q3PnG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      "text/plain": [
       "Plot with title “Histogram of Fvals”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 900
      },
      "text/plain": {
       "height": 600,
       "width": 900
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=15, repr.plot.height=10)   # this command just formats the size of the figures. Adapt to view them nicely\n",
    "                                                    # in your browser.\n",
    "\n",
    "\n",
    "# Automatic repetition: Lets do 1000 experiments and do an ANOVA for each of them\n",
    "Fvals=rep(0,1000)  # create an empty vector for all the F-values\n",
    "\n",
    "for (i in seq(1,1000,by=1))  # run 1000 experiments and record the F-value for it. We have 5 groups with 10 datapoints each\n",
    "{\n",
    "n=10\n",
    "T1 = rnorm(n,mean=22,sd=3)\n",
    "T2 = rnorm(n,mean=18,sd=2)\n",
    "T3 = rnorm(n,mean=18,sd=4)\n",
    "T4 = rnorm(n,mean=18,sd=2.5)\n",
    "T5 = rnorm(n,mean=18,sd=3)\n",
    "\n",
    "datastructure = data.frame(T1,T2,T3,T4,T5)    # creates a dataframe from the 5 vectors (2D data)\n",
    "mydata = stack(datastructure)                 # Takes the data, labels it with group index, and generates one long stacked vector (1D data)\n",
    "\n",
    "analysis=anova(lm(values~ind,data=mydata))\n",
    "Fvals[i]=analysis$`F value`[1]                #Compute and store F-values each cycle\n",
    "    \n",
    "    if (Fvals[i]>7)                           #Save data if F by chance is strangely large\n",
    "        {luckydata=mydata}\n",
    "    \n",
    "}\n",
    "\n",
    "histdata=hist(Fvals,ylim=c(0,100),breaks=seq(0,20,by=0.1))\n",
    "\n",
    "# Compare to distribution function\n",
    "x=seq(0,6,by=0.01)\n",
    "y=100*df(x,df1 = 4, df2 = 45) # F distribution if all had same means. The red line is the theoretical distribution function.\n",
    "lines(x,y,col=\"red\")  \n",
    "abline(v=qf(p = 0.95,df1 = 4, df2 = 45),col=\"blue\")   #Critial value 5%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "str(histdata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.57873918431156"
      ],
      "text/latex": [
       "2.57873918431156"
      ],
      "text/markdown": [
       "2.57873918431156"
      ],
      "text/plain": [
       "[1] 2.578739"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qf(p = 0.95,df1 = 4, df2 = 45)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.212"
      ],
      "text/latex": [
       "0.212"
      ],
      "text/markdown": [
       "0.212"
      ],
      "text/plain": [
       "[1] 0.212"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(histdata$counts[1:27])/sum(histdata$counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7O04q6EEIAyaUkIk+Rh7xoFYMHWkhC+997U+n9macVdCSEAZeI1QgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhPCqF687tJHpzXlCv++4aKHvm2ts79x40UPTm6tg5XKe38Ze98XRa6d8fhlVz8374Xv\n3jL2/i+fu/qyx2e8ddOF11570bhvvuuqX9w39i/vtWijQIuUN4S11+1z8H356VkjG1gnhKX2\n+jrJYstWDLy/6Ct8/JOk9wpVff/UKmf/ZIuk9+CqPte1ysFKZdLoiu5DarqeW9Tih5dtN2jJ\nZPVX5rzsq10regyprkyWGNSuS7ueXZN2/at7XfnfVz2na82Q7hWj3eIhNWUN4YyfJPW2+TI7\n362howhhiX2y+Mg3M5mJh9QU+19/8vf/54VM5uvfVP25Fc7+7dDV6h88fXNaVetktTTqRi7z\nUCYz7dJOZxax+OlO+4zPZP6zZd85HtnVbbzcw5n3+qxcc9601RbpMGToo2dXX3JW1VXzXvWM\nTpfWPzB/cJlN61px80BTlDWEFyb9Th+7RjLs84wQpuuQlafmxtFrFHmFsxbLP0d40hIzWn72\n3/WbmBt/3X96yw9WKn/p+GZuvKrj+MYXj9g+N0xfc8/Zl93Y+Z1MZs81p/+h8+8W+WRY9aeZ\nzNmLfHtG7ylzX3N8x3wa3+j4l1bZNtB0ZQ3h2lWvZTK1JyVrfCmE6RpwYX58LvmguCusd3x+\n/KzisZaffaOj8uPnlQ+3/GCl8vN82zK1fa5tdO3nFYU/RVf3nn3hzjvXf+lzVWZ6z9UOyKzV\nrr7933S4d1L7B+a+6jV9avOT7Ue3fM9As5Q1hF03zA3nJ+t+/d8hfKtPz1k6JV819xwUo6rw\n4uA3yePFXWHg5YVJr5tafvblLilMFv1jyw9WKj84oTBZ8/RG176cfJqfPJrMfjvRhidnMlOS\nRzOZ1RY7LzM4ean+okF/yAy4Yu6rnr5mYXLCJi3eMtA8ZQ1hzaj8eGay0eT/CmHtuPtmOcQj\nwtJa5Ib8+F7yanFXWPns/Dit/b0tP/uwQlqmd7yz5QcrlW32L0yWu7DRte8lr+Und9bMfqVv\n80Mymbqa+v+FA5cbk1k1ebf+u5431na/ee6rjl2+MNlv25bvGWiWsoZw2bULkzHJpjt6ajRF\nW+yQH3/Xr7a4Kxywbn68uabYzxM04NA187m4vXpCyw9WKuculX8174XkxcYXL31qftxj49mX\nnTFoaiaz8R6Zp5N9Vq7dsGaQLHkAABHJSURBVH39v+gHKj68t/Ljua/5YvJCbpyyVHFvTwVa\nX1lDuF37mfeihyWVQpiiR6rGZoeHuxV77/tGx19k4/XSYoe3wtnf6XxMtr+vLHFQKxysVL5c\ndJdsCd9faYsiFl/SKfepoCuq5vg8ysS+o6dm7q86Z8i2H3bbumOHw2a8vvQe/x6w97xX3WKl\n9+u/Ttml/5ettHGgqcoawmuTWc8y7ZUIYZour1n90ONGVhxU9Hv27+w2ZP8Tt2w/amprnP2v\nPVbc76St2289pfGl6XlqsQF7nfzTLut9XsziYyp+cOzha1VfMOdlj/cfuPeYYUm3A48dliyy\neceulcttWbPZf/0Wgc/X67LDyXsttfjTrbVvoKnKGsKvzp31KbTaM45pYKEQltwbJ261yWH/\naMIVPjxlu40PuLuVzv7RqaNG7N+GXyDM+eK8nYbvfX2RHxd54siRmx//2tyXTTxnx+H7nHf8\nFiOPuOe326+31noj9rvtO/7iMeP6vYfvdF4rPOMMNJNfsQZAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhC\nCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghA\naEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQggLuKmX77Hhrhd+M8+ltTfts9EO\nZ0+Y+8Ipl+2+4c8vnly2rTXmw1NGjTjgrsZWfX3BLhvuceXUcmyoPD45ffsR+91el/Y25lZ3\n5/4jRp36cZOvN+P6vYfvdN4XJdhR5r6DNt72V+8VtfTrsbtuuMcVzb6NpBbCIwY08EMhhGJ9\nMLTnLmNG91v2X3Nd+tXGnUaN2XtQv0fmvPDd7/fadczP+67wZlk3OH93dR+y/4lbtd+u4fuv\nVwf1333Mz3qs9lGZdlVy9y+ywr4nbVOz+bdpb2ROU7au2fqk/Vbs8dcmXu/z9br8dMxeSy3+\ndKvvaPrPqjf/xYErdbm5iLWvLbNo/W2k56ofNvNcqYVwt4aOIoRQpLq11/2sfpi02Qpz5WTH\nFd6p/zpt716fzb6sdtjwifXDlyO/P72sW5yftzodX1s/vLzYoQ2t+naZLb+uH8avvX4bewjV\nXO91PXxG/fCvAfukvZM5HbTEq/Vfa4/p/E7TrrfFSu/Xf52yS/8vW3tHJ/R9tv5r3W9qXml0\n6ZTltsjdRtZZt5m3ESGEBdoD1fnnjj7vce0cl77Z7tHcOH3538y+8K4O+QdVn3W9qVy7a9BB\na+fHv7T/vIFVVy6Sv4t9p+qh0m+pHI5eNX9vfU/lJynvZA4Tqm/PjXVrNPi3kv/yYvJCbpyy\n1LmtvKNvOhVu0Bvv3ujaq3vmbyP/qR7XvJOVNYQ/ncPAeY9SO+6+WQ4RQijOyesWJtvuN8el\nVy5emBy56ewLjxtRmGzWtDu7UlnlzPw4rUNDz8ft+dPCZM1TSr2h8lj7V/mxttst6W5kTnd2\nmpGfnLZ6k643dvnCZL9tW3dDmYcrCq9lX7B8wwvr7T2qMFn71807WVlDmMxlnh++1afnLF2S\ntvNyPrRph29emOy10xyXnv/9wuTUdWZfeMB2hcmuo0u/ryIs84fCpM8NDazafmbgf3R0ifdT\nJt/7fWGy1JWp7mMuf1y0MLmk8ezM6fQ1C5MTNmnV/WTTXJjM2tr87TDzWeafHNm8k5U1hJ2X\nv32WjRs6yj+ThegdYlBK56xYmAw/Zo5Lb+lW+CM0evvZF562SmGy9kll2FjjNjwuP06oeLSB\nVYfPvIdd9vxSb6g8Ni08Hp/U/m/pbmROD1cV3vd51IiGF87jmj61+cn2rf2Xq+eTD/KTXzf+\nGPXIjQuT5X/XvJOVNYRrd5v9SmaDrxEKIRTp9cr884pPVc75BtGvul6YG9/ret3sC1+uGJcb\nH61o/bf4Ncc5/fOvDZ68+IwGVv296rnceHvVW2XYUxlc2Ht8bvxtnykp72QO0xfNP6k4od//\nNul64ztelRvf6HhrK++obpmjcuOkgb9pZGUm84/KZ3PjnVXNfEN0WUN4QPLGrLkQQqs4ssf1\ntZm6O/vvMtelF9T8vv4P0SODN6id48KDet1Uv/TWvnuWd4fzM3ml1V/IZL45perGBpftsPjd\nmcyMa7sfV6ZtldrUYUPr/yLy7ZlVV6e9kzldX3X65EzmudWGNrHOZ3S6dFom8+Aym7b6e3rv\nqDppUibzyjrLF/GOkZ0Wu6suM+O6Hsc0vvQ7lTWEfx724Oz5CQ0sFEIoVu2Yjh2HdKk+ZJ4/\nMxd2b79iz4qd5vqg84zjazoN6dL+yGnl3F8DPt4s6T24qu/1Da+acmBV1yEdO/6qtuFlC47x\nW7frNbi6Vxt6hTDr2j7Vg3snW3za1Oud07VmSPeK0SV4f+Mt/auW75v88P0ilk45qDp7Gzm5\nubeRtvmbZYQQivfZPb+/478/bT7pgQv//J95Lxx/9+/vbENv2s+8fsNFDzX+zriPbr/gngmN\nrlqAvHnjRePm/VVAqZv84EU3vtH4sv/y5X1j/1Lcr39pqikPX/yn14pc+9EdF9zzWePL5kMI\nAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEI\nTQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0I\nAQhNCAEITQgBCK1thvDJBADK5MkmZ6r0Icw89xQld1dy1tWw08C0d0BbsOy+ad8jpem5pleq\nDCGkDN5LXk97C7QBZ6+W9g5oC9Y6Le0dLGCEcOEghGQJIVlC2ERCuHAQQrKEkCwhbCIhXDgI\nIVlCSJYQNpEQLhyEkCwhJEsIm0gIFw5CSJYQkiWETSSECwchJEsIyRLCJhLChYMQkiWEZAlh\nEwnhwkEIyRJCsoSwiYRw4SCEZAkhWULYREK4cPgk+U/aW6ANOH+ttHdAW7DB2WnvYAEjhAuJ\nN9PeAG3Btx+kvQPagg8np72DBYwQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhAC\nEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEC7Q/nzgOp2Tnxa+WSHJ6Zfqjii/Sdfv\nMLhjt3Uvrc1/+8ZO/WqWPeGbdPdE+c19O3B30BRCuEAblnRbfnYIK3bLOjjVHVF+5ybt1xq1\nQVWyRe4e8MUe7TY/ZLVkLf8f5dHMfTtwd9AUQrhAG/d63e2zQ1iT6l5Iy01jv6j/+nLf5Lrs\nd2skl2cytTsmv053U5Td3LcDdwdNIYQLOiEk77Rkn/qvTyerZL95v2KJupT3QzrytwN3B00i\nhAu6OUJYfcruB1w8IdXdkJ6xSfZpsDOT43LfrZK8lu52SEn+duDuoEmEcEF3+zxvlulyXarb\nIS11ayX31Q97Jlfkvt0+uS3d/ZCOwu3A3UGTCOGCbnYIT73vo8kvHVhR+fdU90NKxiTbZIdR\nyS25b/dOrkp1O6SkcDtwd9AkQrigmx3CvBOSH6W0E9J0frLal9lxZgj3Sq5OdT+kY+btoMDd\nQXGEcEE3bwjfSnqltBNSdFYybGJu4qnR0GbdDgrcHRRHCBd084ZwYtIlpZ2QnjHJ2l/kZzPf\nLLOqN8sENPt2UODuoDhCuKCbN4S3JENT2gmpOSwZPqkwfTpZNTt8ULG4j0+EM8ftoMDdQXGE\ncEE3K4RPPJ/9+uRiyVlpbofyq90rGTn798iskVxZf9HOPlAfzly3A3cHTSKEC7Q/77bbxsnA\n3XY7IpN9TmyZH2yzartki2lp74ryOiOp2DH367Ry93kvdq/Y8tBhyZp+xVo0c90O3B00iRAu\n0E7I/2LdZED9/Jm9VlqkqvcmV3tGLJpjCreCZGTu2zd27NN+0PFfp7wpym6u24G7gyYRQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNC\nAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBC\nE0IAQhNCAEITQgBCE0IAQhNCAEITQmhr3ku2THsLEIkQQlsjhFBWQghtjRBCWQkhtDVCCGUl\nhJCSR5Kt85PB7SdkMpdsObBD9w1uyH6fD+HtyZjcT7svk1+9Tb/q/ju/mp3e9YP+7Rdd94zy\n7xgWTkIIaVmh+rPs8Hiybf3XdmuOPnb3vslvM98dwksq+ow+Zvv2nR/LZK5MFt3nxH3XXz6l\nXcNCRwghLacm52eH/ZPb6r++m51+s3rHid8ZwleqR06uH57vsnIms07lB9nLJ6axZVgYCSGk\n5b2K1eu/Tl2k7/Tct3VffPzRKcmt3xnCA5OHxmdtmbyTWaf9J2ntGBZKQgip2SR5OZO5KTks\nO39mi65J1tjvDOGwZKZHM+cnvQ+48aP0dg0LGyGE1FybHJ3JbJ48Vz99umPPo6+94+4jknO/\nM4QDk9vuy/sik7lm7YokWfsfKW4cFipCCKmZ3G2xGZ9WDc1Od07uyw6/mR3CO5MTspdMq8qG\ncGjyxJxX/PKv+1Z3fbfc24WFlBBCevZM/npuck52tm4yKTuMmB3CR5Jds5c8nmRDuE9y+DxX\nPTa5oqxbhYWXEEJ6/pHstGpV7q0vuyQ3Z7LPlc4O4aQO3T/KZL5YNxfCF6uqH8gum3R9JnNv\n7r01eyY3pLZtWLgIIaRo2epk89zk8cqaXU/cvHLU7BBmDkv67blr/8265T5H+IeqdiOPPWrz\nzt/LZHr12/6oYzdKvjc5xX3DwkQIIUW/TpKb8rNx63frNuKBq+cI4YwxA6oH/GJq4TfLPLvL\nku17fm/fcZnMhVsN6tR95d98ntaeYWEjhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQA\nhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQm\nhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACE9v/gXTxCTKhfjwAAAABJ\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 900
      },
      "text/plain": {
       "height": 600,
       "width": 900
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(luckydata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}