acptp1ex1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Registered S3 methods overwritten by 'ggplot2':\n",
      "  method         from \n",
      "  [.quosures     rlang\n",
      "  c.quosures     rlang\n",
      "  print.quosures rlang\n"
     ]
    }
   ],
   "source": [
    "# Paramétrage\n",
    "n = 30\n",
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 90 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>X1</th><th scope=col>X2</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>-0.56047565</td><td> 0.99350386</td></tr>\n",
       "\t<tr><td>-0.23017749</td><td> 0.54839696</td></tr>\n",
       "\t<tr><td> 1.55870831</td><td> 0.23873174</td></tr>\n",
       "\t<tr><td> 0.07050839</td><td>-0.62790608</td></tr>\n",
       "\t<tr><td> 0.12928774</td><td> 1.36065245</td></tr>\n",
       "\t<tr><td> 1.71506499</td><td>-0.60025959</td></tr>\n",
       "\t<tr><td> 0.46091621</td><td> 2.18733299</td></tr>\n",
       "\t<tr><td>-1.26506123</td><td> 1.53261063</td></tr>\n",
       "\t<tr><td>-0.68685285</td><td>-0.23570036</td></tr>\n",
       "\t<tr><td>-0.44566197</td><td>-1.02642090</td></tr>\n",
       "\t<tr><td> 1.22408180</td><td>-0.71040656</td></tr>\n",
       "\t<tr><td> 0.35981383</td><td> 0.25688371</td></tr>\n",
       "\t<tr><td> 0.40077145</td><td>-0.24669188</td></tr>\n",
       "\t<tr><td> 0.11068272</td><td>-0.34754260</td></tr>\n",
       "\t<tr><td>-0.55584113</td><td>-0.95161857</td></tr>\n",
       "\t<tr><td> 1.78691314</td><td>-0.04502772</td></tr>\n",
       "\t<tr><td> 0.49785048</td><td>-0.78490447</td></tr>\n",
       "\t<tr><td>-1.96661716</td><td>-1.66794194</td></tr>\n",
       "\t<tr><td> 0.70135590</td><td>-0.38022652</td></tr>\n",
       "\t<tr><td>-0.47279141</td><td> 0.91899661</td></tr>\n",
       "\t<tr><td>-1.06782371</td><td>-0.57534696</td></tr>\n",
       "\t<tr><td>-0.21797491</td><td> 0.60796432</td></tr>\n",
       "\t<tr><td>-1.02600445</td><td>-1.61788271</td></tr>\n",
       "\t<tr><td>-0.72889123</td><td>-0.05556197</td></tr>\n",
       "\t<tr><td>-0.62503927</td><td> 0.51940720</td></tr>\n",
       "\t<tr><td>-1.68669331</td><td> 0.30115336</td></tr>\n",
       "\t<tr><td> 0.83778704</td><td> 0.10567619</td></tr>\n",
       "\t<tr><td> 0.15337312</td><td>-0.64070601</td></tr>\n",
       "\t<tr><td>-1.13813694</td><td>-0.84970435</td></tr>\n",
       "\t<tr><td> 1.25381492</td><td>-1.02412879</td></tr>\n",
       "\t<tr><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><td> 0.379639483</td><td>10.787739</td></tr>\n",
       "\t<tr><td>-0.502323453</td><td>10.769042</td></tr>\n",
       "\t<tr><td>-0.333207384</td><td>10.332203</td></tr>\n",
       "\t<tr><td>-1.018575383</td><td> 8.991623</td></tr>\n",
       "\t<tr><td>-1.071791226</td><td> 9.880547</td></tr>\n",
       "\t<tr><td> 0.303528641</td><td> 9.719605</td></tr>\n",
       "\t<tr><td> 0.448209779</td><td>10.562990</td></tr>\n",
       "\t<tr><td> 0.053004227</td><td> 9.627561</td></tr>\n",
       "\t<tr><td> 0.922267468</td><td>10.976973</td></tr>\n",
       "\t<tr><td> 2.050084686</td><td> 9.625419</td></tr>\n",
       "\t<tr><td>-0.491031166</td><td>11.052711</td></tr>\n",
       "\t<tr><td>-2.309168876</td><td> 8.950823</td></tr>\n",
       "\t<tr><td> 1.005738524</td><td> 8.739845</td></tr>\n",
       "\t<tr><td>-0.709200763</td><td>13.241040</td></tr>\n",
       "\t<tr><td>-0.688008616</td><td> 9.583142</td></tr>\n",
       "\t<tr><td> 1.025571370</td><td>10.298228</td></tr>\n",
       "\t<tr><td>-0.284773007</td><td>10.636570</td></tr>\n",
       "\t<tr><td>-1.220717712</td><td> 9.516219</td></tr>\n",
       "\t<tr><td> 0.181303480</td><td>10.516862</td></tr>\n",
       "\t<tr><td>-0.138891362</td><td>10.368965</td></tr>\n",
       "\t<tr><td> 0.005764186</td><td> 9.784619</td></tr>\n",
       "\t<tr><td> 0.385280401</td><td>10.065293</td></tr>\n",
       "\t<tr><td>-0.370660032</td><td> 9.965933</td></tr>\n",
       "\t<tr><td> 0.644376549</td><td>12.128452</td></tr>\n",
       "\t<tr><td>-0.220486562</td><td> 9.258664</td></tr>\n",
       "\t<tr><td> 0.331781964</td><td> 8.904004</td></tr>\n",
       "\t<tr><td> 1.096839013</td><td>10.037788</td></tr>\n",
       "\t<tr><td> 0.435181491</td><td>10.310481</td></tr>\n",
       "\t<tr><td>-0.325931586</td><td>10.436523</td></tr>\n",
       "\t<tr><td> 1.148807618</td><td> 9.541635</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 90 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       " X1 & X2\\\\\n",
       "\\hline\n",
       "\t -0.56047565 &  0.99350386\\\\\n",
       "\t -0.23017749 &  0.54839696\\\\\n",
       "\t  1.55870831 &  0.23873174\\\\\n",
       "\t  0.07050839 & -0.62790608\\\\\n",
       "\t  0.12928774 &  1.36065245\\\\\n",
       "\t  1.71506499 & -0.60025959\\\\\n",
       "\t  0.46091621 &  2.18733299\\\\\n",
       "\t -1.26506123 &  1.53261063\\\\\n",
       "\t -0.68685285 & -0.23570036\\\\\n",
       "\t -0.44566197 & -1.02642090\\\\\n",
       "\t  1.22408180 & -0.71040656\\\\\n",
       "\t  0.35981383 &  0.25688371\\\\\n",
       "\t  0.40077145 & -0.24669188\\\\\n",
       "\t  0.11068272 & -0.34754260\\\\\n",
       "\t -0.55584113 & -0.95161857\\\\\n",
       "\t  1.78691314 & -0.04502772\\\\\n",
       "\t  0.49785048 & -0.78490447\\\\\n",
       "\t -1.96661716 & -1.66794194\\\\\n",
       "\t  0.70135590 & -0.38022652\\\\\n",
       "\t -0.47279141 &  0.91899661\\\\\n",
       "\t -1.06782371 & -0.57534696\\\\\n",
       "\t -0.21797491 &  0.60796432\\\\\n",
       "\t -1.02600445 & -1.61788271\\\\\n",
       "\t -0.72889123 & -0.05556197\\\\\n",
       "\t -0.62503927 &  0.51940720\\\\\n",
       "\t -1.68669331 &  0.30115336\\\\\n",
       "\t  0.83778704 &  0.10567619\\\\\n",
       "\t  0.15337312 & -0.64070601\\\\\n",
       "\t -1.13813694 & -0.84970435\\\\\n",
       "\t  1.25381492 & -1.02412879\\\\\n",
       "\t ⋮ & ⋮\\\\\n",
       "\t  0.379639483 & 10.787739\\\\\n",
       "\t -0.502323453 & 10.769042\\\\\n",
       "\t -0.333207384 & 10.332203\\\\\n",
       "\t -1.018575383 &  8.991623\\\\\n",
       "\t -1.071791226 &  9.880547\\\\\n",
       "\t  0.303528641 &  9.719605\\\\\n",
       "\t  0.448209779 & 10.562990\\\\\n",
       "\t  0.053004227 &  9.627561\\\\\n",
       "\t  0.922267468 & 10.976973\\\\\n",
       "\t  2.050084686 &  9.625419\\\\\n",
       "\t -0.491031166 & 11.052711\\\\\n",
       "\t -2.309168876 &  8.950823\\\\\n",
       "\t  1.005738524 &  8.739845\\\\\n",
       "\t -0.709200763 & 13.241040\\\\\n",
       "\t -0.688008616 &  9.583142\\\\\n",
       "\t  1.025571370 & 10.298228\\\\\n",
       "\t -0.284773007 & 10.636570\\\\\n",
       "\t -1.220717712 &  9.516219\\\\\n",
       "\t  0.181303480 & 10.516862\\\\\n",
       "\t -0.138891362 & 10.368965\\\\\n",
       "\t  0.005764186 &  9.784619\\\\\n",
       "\t  0.385280401 & 10.065293\\\\\n",
       "\t -0.370660032 &  9.965933\\\\\n",
       "\t  0.644376549 & 12.128452\\\\\n",
       "\t -0.220486562 &  9.258664\\\\\n",
       "\t  0.331781964 &  8.904004\\\\\n",
       "\t  1.096839013 & 10.037788\\\\\n",
       "\t  0.435181491 & 10.310481\\\\\n",
       "\t -0.325931586 & 10.436523\\\\\n",
       "\t  1.148807618 &  9.541635\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 90 × 2 of type dbl\n",
       "\n",
       "| X1 | X2 |\n",
       "|---|---|\n",
       "| -0.56047565 |  0.99350386 |\n",
       "| -0.23017749 |  0.54839696 |\n",
       "|  1.55870831 |  0.23873174 |\n",
       "|  0.07050839 | -0.62790608 |\n",
       "|  0.12928774 |  1.36065245 |\n",
       "|  1.71506499 | -0.60025959 |\n",
       "|  0.46091621 |  2.18733299 |\n",
       "| -1.26506123 |  1.53261063 |\n",
       "| -0.68685285 | -0.23570036 |\n",
       "| -0.44566197 | -1.02642090 |\n",
       "|  1.22408180 | -0.71040656 |\n",
       "|  0.35981383 |  0.25688371 |\n",
       "|  0.40077145 | -0.24669188 |\n",
       "|  0.11068272 | -0.34754260 |\n",
       "| -0.55584113 | -0.95161857 |\n",
       "|  1.78691314 | -0.04502772 |\n",
       "|  0.49785048 | -0.78490447 |\n",
       "| -1.96661716 | -1.66794194 |\n",
       "|  0.70135590 | -0.38022652 |\n",
       "| -0.47279141 |  0.91899661 |\n",
       "| -1.06782371 | -0.57534696 |\n",
       "| -0.21797491 |  0.60796432 |\n",
       "| -1.02600445 | -1.61788271 |\n",
       "| -0.72889123 | -0.05556197 |\n",
       "| -0.62503927 |  0.51940720 |\n",
       "| -1.68669331 |  0.30115336 |\n",
       "|  0.83778704 |  0.10567619 |\n",
       "|  0.15337312 | -0.64070601 |\n",
       "| -1.13813694 | -0.84970435 |\n",
       "|  1.25381492 | -1.02412879 |\n",
       "| ⋮ | ⋮ |\n",
       "|  0.379639483 | 10.787739 |\n",
       "| -0.502323453 | 10.769042 |\n",
       "| -0.333207384 | 10.332203 |\n",
       "| -1.018575383 |  8.991623 |\n",
       "| -1.071791226 |  9.880547 |\n",
       "|  0.303528641 |  9.719605 |\n",
       "|  0.448209779 | 10.562990 |\n",
       "|  0.053004227 |  9.627561 |\n",
       "|  0.922267468 | 10.976973 |\n",
       "|  2.050084686 |  9.625419 |\n",
       "| -0.491031166 | 11.052711 |\n",
       "| -2.309168876 |  8.950823 |\n",
       "|  1.005738524 |  8.739845 |\n",
       "| -0.709200763 | 13.241040 |\n",
       "| -0.688008616 |  9.583142 |\n",
       "|  1.025571370 | 10.298228 |\n",
       "| -0.284773007 | 10.636570 |\n",
       "| -1.220717712 |  9.516219 |\n",
       "|  0.181303480 | 10.516862 |\n",
       "| -0.138891362 | 10.368965 |\n",
       "|  0.005764186 |  9.784619 |\n",
       "|  0.385280401 | 10.065293 |\n",
       "| -0.370660032 |  9.965933 |\n",
       "|  0.644376549 | 12.128452 |\n",
       "| -0.220486562 |  9.258664 |\n",
       "|  0.331781964 |  8.904004 |\n",
       "|  1.096839013 | 10.037788 |\n",
       "|  0.435181491 | 10.310481 |\n",
       "| -0.325931586 | 10.436523 |\n",
       "|  1.148807618 |  9.541635 |\n",
       "\n"
      ],
      "text/plain": [
       "      X1           X2         \n",
       " [1,] -0.56047565   0.99350386\n",
       " [2,] -0.23017749   0.54839696\n",
       " [3,]  1.55870831   0.23873174\n",
       " [4,]  0.07050839  -0.62790608\n",
       " [5,]  0.12928774   1.36065245\n",
       " [6,]  1.71506499  -0.60025959\n",
       " [7,]  0.46091621   2.18733299\n",
       " [8,] -1.26506123   1.53261063\n",
       " [9,] -0.68685285  -0.23570036\n",
       "[10,] -0.44566197  -1.02642090\n",
       "[11,]  1.22408180  -0.71040656\n",
       "[12,]  0.35981383   0.25688371\n",
       "[13,]  0.40077145  -0.24669188\n",
       "[14,]  0.11068272  -0.34754260\n",
       "[15,] -0.55584113  -0.95161857\n",
       "[16,]  1.78691314  -0.04502772\n",
       "[17,]  0.49785048  -0.78490447\n",
       "[18,] -1.96661716  -1.66794194\n",
       "[19,]  0.70135590  -0.38022652\n",
       "[20,] -0.47279141   0.91899661\n",
       "[21,] -1.06782371  -0.57534696\n",
       "[22,] -0.21797491   0.60796432\n",
       "[23,] -1.02600445  -1.61788271\n",
       "[24,] -0.72889123  -0.05556197\n",
       "[25,] -0.62503927   0.51940720\n",
       "[26,] -1.68669331   0.30115336\n",
       "[27,]  0.83778704   0.10567619\n",
       "[28,]  0.15337312  -0.64070601\n",
       "[29,] -1.13813694  -0.84970435\n",
       "[30,]  1.25381492  -1.02412879\n",
       "[31,] ⋮            ⋮          \n",
       "[32,]  0.379639483 10.787739  \n",
       "[33,] -0.502323453 10.769042  \n",
       "[34,] -0.333207384 10.332203  \n",
       "[35,] -1.018575383  8.991623  \n",
       "[36,] -1.071791226  9.880547  \n",
       "[37,]  0.303528641  9.719605  \n",
       "[38,]  0.448209779 10.562990  \n",
       "[39,]  0.053004227  9.627561  \n",
       "[40,]  0.922267468 10.976973  \n",
       "[41,]  2.050084686  9.625419  \n",
       "[42,] -0.491031166 11.052711  \n",
       "[43,] -2.309168876  8.950823  \n",
       "[44,]  1.005738524  8.739845  \n",
       "[45,] -0.709200763 13.241040  \n",
       "[46,] -0.688008616  9.583142  \n",
       "[47,]  1.025571370 10.298228  \n",
       "[48,] -0.284773007 10.636570  \n",
       "[49,] -1.220717712  9.516219  \n",
       "[50,]  0.181303480 10.516862  \n",
       "[51,] -0.138891362 10.368965  \n",
       "[52,]  0.005764186  9.784619  \n",
       "[53,]  0.385280401 10.065293  \n",
       "[54,] -0.370660032  9.965933  \n",
       "[55,]  0.644376549 12.128452  \n",
       "[56,] -0.220486562  9.258664  \n",
       "[57,]  0.331781964  8.904004  \n",
       "[58,]  1.096839013 10.037788  \n",
       "[59,]  0.435181491 10.310481  \n",
       "[60,] -0.325931586 10.436523  \n",
       "[61,]  1.148807618  9.541635  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Génération de loi normales ordonnées en 2 colonnes\n",
    "set.seed(123)\n",
    "x = matrix(rnorm(n * 3 * 2), n * 3, 2)\n",
    "for (i in 31:60) x[i,] <- x[i,] + c(10, 0)\n",
    "for (i in 61:90) x[i,] <- x[i,] + c(0, 10)\n",
    "colnames(x) <- c(\"X1\", \"X2\")\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tIH1549cm5I6weSH6SpHqR3AhkASLJ1Amn8Jqkfabenw1k/kHw3Ngx0HZ0ZzABA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\nAAISUQABiSiA/j9ujZG9ubCSQwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = as.data.frame(x)\n",
    "ggplot(x,aes(x=X1,y=X2)) + geom_point()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6jzA0kSkNKElMlUv/BBzPUMNJA6N53o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\nBHA9AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = scale(x)\n",
    "x=as.data.frame(x)\n",
    "ggplot(x,aes(x=X1,y=X2)) + geom_point()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>2</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "\t<li>3</li>\n",
       "</ol>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'1'</li>\n",
       "\t\t<li>'2'</li>\n",
       "\t\t<li>'3'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 2\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item '1'\n",
       "\\item '2'\n",
       "\\item '3'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 1\n",
       "3. 1\n",
       "4. 1\n",
       "5. 1\n",
       "6. 1\n",
       "7. 1\n",
       "8. 1\n",
       "9. 1\n",
       "10. 1\n",
       "11. 1\n",
       "12. 1\n",
       "13. 1\n",
       "14. 1\n",
       "15. 1\n",
       "16. 1\n",
       "17. 1\n",
       "18. 1\n",
       "19. 1\n",
       "20. 1\n",
       "21. 1\n",
       "22. 1\n",
       "23. 1\n",
       "24. 1\n",
       "25. 1\n",
       "26. 1\n",
       "27. 1\n",
       "28. 1\n",
       "29. 1\n",
       "30. 1\n",
       "31. 2\n",
       "32. 2\n",
       "33. 2\n",
       "34. 2\n",
       "35. 2\n",
       "36. 2\n",
       "37. 2\n",
       "38. 2\n",
       "39. 2\n",
       "40. 2\n",
       "41. 2\n",
       "42. 2\n",
       "43. 2\n",
       "44. 2\n",
       "45. 2\n",
       "46. 2\n",
       "47. 2\n",
       "48. 2\n",
       "49. 2\n",
       "50. 2\n",
       "51. 2\n",
       "52. 2\n",
       "53. 2\n",
       "54. 2\n",
       "55. 2\n",
       "56. 2\n",
       "57. 2\n",
       "58. 2\n",
       "59. 2\n",
       "60. 2\n",
       "61. 3\n",
       "62. 3\n",
       "63. 3\n",
       "64. 3\n",
       "65. 3\n",
       "66. 3\n",
       "67. 3\n",
       "68. 3\n",
       "69. 3\n",
       "70. 3\n",
       "71. 3\n",
       "72. 3\n",
       "73. 3\n",
       "74. 3\n",
       "75. 3\n",
       "76. 3\n",
       "77. 3\n",
       "78. 3\n",
       "79. 3\n",
       "80. 3\n",
       "81. 3\n",
       "82. 3\n",
       "83. 3\n",
       "84. 3\n",
       "85. 3\n",
       "86. 3\n",
       "87. 3\n",
       "88. 3\n",
       "89. 3\n",
       "90. 3\n",
       "\n",
       "\n",
       "\n",
       "**Levels**: 1. '1'\n",
       "2. '2'\n",
       "3. '3'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2\n",
       "[39] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n",
       "[77] 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n",
       "Levels: 1 2 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cl = as.factor(c(rep(1,n), rep(2,n), rep(3,n)))\n",
    "cl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAADDF67IpRJK6EY6ldcBOrY4ZupV3E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\nV4kmL4wAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(x,aes(x=X1,y=X2,colour=cl)) + geom_point()"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}