CerealsHandsOn.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "library('moments')\n",
    "library('plyr')\n",
    "library('dplyr')\n",
    "library('ggplot2')\n",
    "library('GGally')\n",
    "library('car')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# install.packages('moments')\n",
    "# install.packages('plyr')\n",
    "# install.packages('dplyr')\n",
    "# install.packages('ggplot2')\n",
    "# install.packages('GGally')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# desc http://davis.wpi.edu/xmdv/datasets/cereal.html\n",
    "\n",
    "url = \"http://lib.stat.cmu.edu/datasets/1993.expo/cereal\"\n",
    "\n",
    "cereals <-\n",
    "  read.table(url,\n",
    "             header = FALSE,\n",
    "             as.is = TRUE,\n",
    "             na.strings = \"-1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "names(cereals) <-\n",
    "  c(\n",
    "    'name',\n",
    "    'mfr',\n",
    "    'type',\n",
    "    'calories',\n",
    "    'protein',\n",
    "    'fat',\n",
    "    'sodium',\n",
    "    'fiber',\n",
    "    'carbo',\n",
    "    'sugars',\n",
    "    'shelf',\n",
    "    'potass',\n",
    "    'vitamins',\n",
    "    'weight',\n",
    "    'cups'\n",
    "  )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "15"
      ],
      "text/latex": [
       "15"
      ],
      "text/markdown": [
       "15"
      ],
      "text/plain": [
       "[1] 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#checking for missing data and its number\n",
    "sum(is.na(cereals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t65 obs. of  15 variables:\n",
      " $ name    : chr  \"100%_Bran\" \"All-Bran\" \"All-Bran_with_Extra_Fiber\" \"Apple_Cinnamon_Cheerios\" ...\n",
      " $ mfr     : chr  \"N\" \"K\" \"K\" \"G\" ...\n",
      " $ type    : chr  \"C\" \"C\" \"C\" \"C\" ...\n",
      " $ calories: int  70 70 50 110 110 130 90 90 120 110 ...\n",
      " $ protein : int  4 4 4 2 2 3 2 3 1 6 ...\n",
      " $ fat     : int  1 1 0 2 0 2 1 0 2 2 ...\n",
      " $ sodium  : int  130 260 140 180 125 210 200 210 220 290 ...\n",
      " $ fiber   : num  10 9 14 1.5 1 2 4 5 0 2 ...\n",
      " $ carbo   : num  5 7 8 10.5 11 18 15 13 12 17 ...\n",
      " $ sugars  : int  6 5 0 10 14 8 6 5 12 1 ...\n",
      " $ shelf   : int  3 3 3 1 2 3 1 3 2 1 ...\n",
      " $ potass  : int  280 320 330 70 30 100 125 190 35 105 ...\n",
      " $ vitamins: int  25 25 25 25 25 25 25 25 25 25 ...\n",
      " $ weight  : num  1 1 1 1 1 1.33 1 1 1 1 ...\n",
      " $ cups    : num  0.33 0.33 0.5 0.75 1 0.75 0.67 0.67 0.75 1.25 ...\n",
      " - attr(*, \"na.action\")= 'omit' Named int  2 5 21 39 44 45 46 51 56 58 ...\n",
      "  ..- attr(*, \"names\")= chr  \"2\" \"5\" \"21\" \"39\" ...\n"
     ]
    }
   ],
   "source": [
    "#deleting missing values, creating new data frame cereal. There exist imputation methods, but we're not studying them.\n",
    "cereals = na.omit(cereals)\n",
    "str(cereals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
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       "</style>\n",
       "<ol class=list-inline><li>3</li><li>3</li><li>3</li><li>1</li><li>2</li><li>3</li><li>1</li><li>3</li><li>2</li><li>1</li><li>2</li><li>3</li><li>2</li><li>1</li><li>1</li><li>2</li><li>2</li><li>3</li><li>3</li><li>3</li><li>3</li><li>2</li><li>1</li><li>2</li><li>3</li><li>3</li><li>2</li><li>1</li><li>2</li><li>3</li><li>3</li><li>3</li><li>2</li><li>1</li><li>1</li><li>3</li><li>2</li><li>2</li><li>2</li><li>3</li><li>1</li><li>2</li><li>3</li><li>3</li><li>3</li><li>3</li><li>3</li><li>3</li><li>2</li><li>3</li><li>3</li><li>1</li><li>1</li><li>1</li><li>1</li><li>2</li><li>1</li><li>3</li><li>3</li><li>3</li><li>3</li><li>2</li><li>1</li><li>1</li><li>1</li></ol>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<style>\n",
       "\t.list-inline {list-style: none; margin:0; padding: 0}\n",
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       "\t.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "\t</style>\n",
       "\t<ol class=list-inline><li>'1'</li><li>'2'</li><li>'3'</li></ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3\n",
       "\\item 3\n",
       "\\item 3\n",
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       "\\item 2\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\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. 3\n",
       "2. 3\n",
       "3. 3\n",
       "4. 1\n",
       "5. 2\n",
       "6. 3\n",
       "7. 1\n",
       "8. 3\n",
       "9. 2\n",
       "10. 1\n",
       "11. 2\n",
       "12. 3\n",
       "13. 2\n",
       "14. 1\n",
       "15. 1\n",
       "16. 2\n",
       "17. 2\n",
       "18. 3\n",
       "19. 3\n",
       "20. 3\n",
       "21. 3\n",
       "22. 2\n",
       "23. 1\n",
       "24. 2\n",
       "25. 3\n",
       "26. 3\n",
       "27. 2\n",
       "28. 1\n",
       "29. 2\n",
       "30. 3\n",
       "31. 3\n",
       "32. 3\n",
       "33. 2\n",
       "34. 1\n",
       "35. 1\n",
       "36. 3\n",
       "37. 2\n",
       "38. 2\n",
       "39. 2\n",
       "40. 3\n",
       "41. 1\n",
       "42. 2\n",
       "43. 3\n",
       "44. 3\n",
       "45. 3\n",
       "46. 3\n",
       "47. 3\n",
       "48. 3\n",
       "49. 2\n",
       "50. 3\n",
       "51. 3\n",
       "52. 1\n",
       "53. 1\n",
       "54. 1\n",
       "55. 1\n",
       "56. 2\n",
       "57. 1\n",
       "58. 3\n",
       "59. 3\n",
       "60. 3\n",
       "61. 3\n",
       "62. 2\n",
       "63. 1\n",
       "64. 1\n",
       "65. 1\n",
       "\n",
       "\n",
       "\n",
       "**Levels**: 1. '1'\n",
       "2. '2'\n",
       "3. '3'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 3 3 3 1 2 3 1 3 2 1 2 3 2 1 1 2 2 3 3 3 3 2 1 2 3 3 2 1 2 3 3 3 2 1 1 3 2 2\n",
       "[39] 2 3 1 2 3 3 3 3 3 3 2 3 3 1 1 1 1 2 1 3 3 3 3 2 1 1 1\n",
       "Levels: 1 < 2 < 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       " 1  2  3 \n",
       "18 18 29 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a factor\n",
    "cereals$shelf <- factor(cereals$shelf, levels = 1:3, ordered = TRUE)\n",
    "cereals$shelf\n",
    "table(cereals$shelf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# if you want to name the factor levels instead of numbering them, package car, function recode\n",
    "cereals$shelfC <-\n",
    "  recode(cereals$shelf, \" 1='low'; 2='medium'; 3='high' \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     name               mfr                type              calories    \n",
       " Length:65          Length:65          Length:65          Min.   : 50.0  \n",
       " Class :character   Class :character   Class :character   1st Qu.:100.0  \n",
       " Mode  :character   Mode  :character   Mode  :character   Median :110.0  \n",
       "                                                          Mean   :107.4  \n",
       "                                                          3rd Qu.:110.0  \n",
       "                                                          Max.   :160.0  \n",
       "    protein           fat             sodium          fiber       \n",
       " Min.   :1.000   Min.   :0.0000   Min.   :  0.0   Min.   : 0.000  \n",
       " 1st Qu.:2.000   1st Qu.:0.0000   1st Qu.:140.0   1st Qu.: 0.000  \n",
       " Median :2.000   Median :1.0000   Median :190.0   Median : 1.500  \n",
       " Mean   :2.462   Mean   :0.9385   Mean   :175.4   Mean   : 2.185  \n",
       " 3rd Qu.:3.000   3rd Qu.:1.0000   3rd Qu.:220.0   3rd Qu.: 3.000  \n",
       " Max.   :6.000   Max.   :3.0000   Max.   :320.0   Max.   :14.000  \n",
       "     carbo           sugars       shelf      potass          vitamins     \n",
       " Min.   : 5.00   Min.   : 0.000   1:18   Min.   : 15.00   Min.   :  0.00  \n",
       " 1st Qu.:12.00   1st Qu.: 3.000   2:18   1st Qu.: 40.00   1st Qu.: 25.00  \n",
       " Median :14.00   Median : 7.000   3:29   Median : 90.00   Median : 25.00  \n",
       " Mean   :14.74   Mean   : 7.385          Mean   : 97.46   Mean   : 29.62  \n",
       " 3rd Qu.:17.00   3rd Qu.:11.000          3rd Qu.:120.00   3rd Qu.: 25.00  \n",
       " Max.   :23.00   Max.   :15.000          Max.   :330.00   Max.   :100.00  \n",
       "     weight           cups           shelfC  \n",
       " Min.   :0.500   Min.   :0.2500   high  :29  \n",
       " 1st Qu.:1.000   1st Qu.:0.6700   low   :18  \n",
       " Median :1.000   Median :0.7500   medium:18  \n",
       " Mean   :1.045   Mean   :0.7969              \n",
       " 3rd Qu.:1.000   3rd Qu.:1.0000              \n",
       " Max.   :1.500   Max.   :1.5000              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Basic statistical summary of the data set\n",
    "summary(cereals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining a function to calculate coefficient of variation:\n",
    "cv = function(x) {\n",
    "  sd = sqrt(var(x))\n",
    "  mu = abs(mean(x))\n",
    "  sd / mu\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>sodium</dt><dd>0.428678816381526</dd><dt>fiber</dt><dd>1.1695296780008</dd><dt>carbo</dt><dd>0.270277154639366</dd><dt>sugars</dt><dd>0.586709560791333</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[sodium] 0.428678816381526\n",
       "\\item[fiber] 1.1695296780008\n",
       "\\item[carbo] 0.270277154639366\n",
       "\\item[sugars] 0.586709560791333\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "sodium\n",
       ":   0.428678816381526fiber\n",
       ":   1.1695296780008carbo\n",
       ":   0.270277154639366sugars\n",
       ":   0.586709560791333\n",
       "\n"
      ],
      "text/plain": [
       "   sodium     fiber     carbo    sugars \n",
       "0.4286788 1.1695297 0.2702772 0.5867096 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# using it\n",
    "apply(cereals[, 7:10], 2, cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "#other function\n",
    "cereal_stats = data.frame(\n",
    "  cv = apply(cereals[, c(4:10, 12:15)], 2, cv),\n",
    "  kurtosis = apply(cereals[, c(4:10, 12:15)], 2, kurtosis),\n",
    "  skew = apply(cereals[, c(4:10, 12:15)], 2, skewness)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                cv kurtosis        skew\n",
      "calories 0.1656678 6.005008 -0.62341330\n",
      "protein  0.4431485 4.526630  0.82696035\n",
      "fat      0.9009638 2.685449  0.58514557\n",
      "sodium   0.4286788 3.363517 -0.71731751\n",
      "fiber    1.1695297 9.802591  2.27434460\n",
      "carbo    0.2702772 2.575780  0.20539196\n",
      "sugars   0.5867096 1.817431  0.01802315\n",
      "potass   0.7599692 4.557778  1.39032104\n",
      "vitamins 0.7139905 9.926056  2.76463813\n",
      "weight   0.1402434 7.373096  0.84731167\n",
      "cups     0.3029334 3.285915  0.13353101\n"
     ]
    }
   ],
   "source": [
    "#using it\n",
    "print(cereal_stats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`summarise()` ungrouping output (override with `.groups` argument)\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 6 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>mfr</th><th scope=col>mean(sugars)</th><th scope=col>sd(sugars)</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>G</td><td>7.954545</td><td>3.872704</td></tr>\n",
       "\t<tr><td>K</td><td>7.904762</td><td>4.526641</td></tr>\n",
       "\t<tr><td>N</td><td>2.000000</td><td>3.464102</td></tr>\n",
       "\t<tr><td>P</td><td>8.777778</td><td>4.576510</td></tr>\n",
       "\t<tr><td>Q</td><td>7.000000</td><td>4.795832</td></tr>\n",
       "\t<tr><td>R</td><td>3.800000</td><td>1.643168</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 3\n",
       "\\begin{tabular}{lll}\n",
       " mfr & mean(sugars) & sd(sugars)\\\\\n",
       " <chr> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t G & 7.954545 & 3.872704\\\\\n",
       "\t K & 7.904762 & 4.526641\\\\\n",
       "\t N & 2.000000 & 3.464102\\\\\n",
       "\t P & 8.777778 & 4.576510\\\\\n",
       "\t Q & 7.000000 & 4.795832\\\\\n",
       "\t R & 3.800000 & 1.643168\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 6 × 3\n",
       "\n",
       "| mfr &lt;chr&gt; | mean(sugars) &lt;dbl&gt; | sd(sugars) &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| G | 7.954545 | 3.872704 |\n",
       "| K | 7.904762 | 4.526641 |\n",
       "| N | 2.000000 | 3.464102 |\n",
       "| P | 8.777778 | 4.576510 |\n",
       "| Q | 7.000000 | 4.795832 |\n",
       "| R | 3.800000 | 1.643168 |\n",
       "\n"
      ],
      "text/plain": [
       "  mfr mean(sugars) sd(sugars)\n",
       "1 G   7.954545     3.872704  \n",
       "2 K   7.904762     4.526641  \n",
       "3 N   2.000000     3.464102  \n",
       "4 P   8.777778     4.576510  \n",
       "5 Q   7.000000     4.795832  \n",
       "6 R   3.800000     1.643168  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summarise(group_by(cereals, mfr), mean(sugars), sd(sugars))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cFj3L+yIW/vHq5sQHXjdkh7t0TOgO/7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\nOHjFiQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Basic plot: relationship between fiber and calories\n",
    "plot(cereals$fiber, cereals$calories)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KDArpAGh0XCg33fvFkfXHhc5xG/4ieH3WwKqSBFUnv0SJWUAt8nYNCzaSNue/Ka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\n/52utr0LJYkHAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Basic plot: relationship between fat and calories\n",
    "plot(cereals$fat, cereals$calories)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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guEm3VBCTVMP3k/6bX3XMhb5vfqj4L/MA0ulZqSfcIfK7IAVmiqKu/n+5nle6yN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\nEECQAAggSAAE/h+ZVEdvcseM6wAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(jitter(cereals$fat), jitter(cereals$calories))"
   ]
  },
  {
   "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
}