2. First steps with data frames.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First steps with DataFrames.jl\n",
    "\n",
    "### Bogumił Kamiński\n",
    "\n",
    "In this notebook we will reproduce the classical Anscombe's quartert plot.\n",
    "\n",
    "Our objective is to produce a figure similar to this one (the plot is taken from https://upload.wikimedia.org/wikipedia/commons/e/ec/Anscombe%27s_quartet_3.svg):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Anscombe's quartet](https://upload.wikimedia.org/wikipedia/commons/e/ec/Anscombe%27s_quartet_3.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with loading of the required packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m project at `~/JuliaAcademy-DataFrames`\n"
     ]
    }
   ],
   "source": [
    "] activate ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using DataFrames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    <p><b>PyPlot.jl configuration:</b></p>\n",
    "    <p>In some environments automatic installation of PyPlot.jl might fail. If you encounter this ussue please refer to <a href=\"https://github.com/JuliaPy/PyPlot.jl#installation\">the PyPlot.jl installation instructions</a>. </p>\n",
    "</div>\n",
    "\n",
    "In particular typically executing the following commands:\n",
    "\n",
    "```\n",
    "using Pkg\n",
    "ENV[\"PYTHON\"]=\"\"\n",
    "Pkg.build(\"PyCall\")\n",
    "```\n",
    "\n",
    "should resolve the PyPlot.jl installation issues. However, on OS X sometimes more configuration steps are required. You can find the detailed instructions [here](https://github.com/JuliaPy/PyPlot.jl#os-x)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "using GLM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a matrix in which we store 8 columns representing Anscombe's quartet data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11×8 Matrix{Float64}:\n",
       " 10.0   8.04  10.0  9.14  10.0   7.46   8.0   6.58\n",
       "  8.0   6.95   8.0  8.14   8.0   6.77   8.0   5.76\n",
       " 13.0   7.58  13.0  8.74  13.0  12.74   8.0   7.71\n",
       "  9.0   8.81   9.0  8.77   9.0   7.11   8.0   8.84\n",
       " 11.0   8.33  11.0  9.26  11.0   7.81   8.0   8.47\n",
       " 14.0   9.96  14.0  8.1   14.0   8.84   8.0   7.04\n",
       "  6.0   7.24   6.0  6.13   6.0   6.08   8.0   5.25\n",
       "  4.0   4.26   4.0  3.1    4.0   5.39  19.0  12.5\n",
       " 12.0  10.84  12.0  9.13  12.0   8.15   8.0   5.56\n",
       "  7.0   4.82   7.0  7.26   7.0   6.42   8.0   7.91\n",
       "  5.0   5.68   5.0  4.74   5.0   5.73   8.0   6.89"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aq = [10.0   8.04  10.0  9.14  10.0   7.46   8.0   6.58\n",
    "       8.0   6.95   8.0  8.14   8.0   6.77   8.0   5.76\n",
    "      13.0   7.58  13.0  8.74  13.0  12.74   8.0   7.71\n",
    "       9.0   8.81   9.0  8.77   9.0   7.11   8.0   8.84\n",
    "      11.0   8.33  11.0  9.26  11.0   7.81   8.0   8.47\n",
    "      14.0   9.96  14.0  8.1   14.0   8.84   8.0   7.04\n",
    "       6.0   7.24   6.0  6.13   6.0   6.08   8.0   5.25\n",
    "       4.0   4.26   4.0  3.1    4.0   5.39  19.0  12.50 \n",
    "      12.0  10.84  12.0  9.13  12.0   8.15   8.0   5.56\n",
    "       7.0   4.82   7.0  7.26   7.0   6.42   8.0   7.91\n",
    "       5.0   5.68   5.0  4.74   5.0   5.73   8.0   6.89]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can simply convert a maxtrx to a `DataFrame` by calling its constructor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>11×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">x5</th><th style = \"text-align: left;\">x6</th><th style = \"text-align: left;\">x7</th><th style = \"text-align: left;\">x8</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">8.04</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">9.14</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">7.46</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.58</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.95</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.14</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.77</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.76</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">7.58</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">8.74</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">12.74</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.71</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.81</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.77</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">7.11</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.84</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">8.33</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">9.26</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">7.81</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.47</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">9.96</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.1</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.04</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">7.24</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.08</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.25</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.26</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">5.39</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">12.5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">10.84</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">9.13</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">8.15</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.56</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">4.82</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.26</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">6.42</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.91</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">4.74</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.73</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.89</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & x5 & x6 & x7 & x8\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 10.0 & 8.04 & 10.0 & 9.14 & 10.0 & 7.46 & 8.0 & 6.58 \\\\\n",
       "\t2 & 8.0 & 6.95 & 8.0 & 8.14 & 8.0 & 6.77 & 8.0 & 5.76 \\\\\n",
       "\t3 & 13.0 & 7.58 & 13.0 & 8.74 & 13.0 & 12.74 & 8.0 & 7.71 \\\\\n",
       "\t4 & 9.0 & 8.81 & 9.0 & 8.77 & 9.0 & 7.11 & 8.0 & 8.84 \\\\\n",
       "\t5 & 11.0 & 8.33 & 11.0 & 9.26 & 11.0 & 7.81 & 8.0 & 8.47 \\\\\n",
       "\t6 & 14.0 & 9.96 & 14.0 & 8.1 & 14.0 & 8.84 & 8.0 & 7.04 \\\\\n",
       "\t7 & 6.0 & 7.24 & 6.0 & 6.13 & 6.0 & 6.08 & 8.0 & 5.25 \\\\\n",
       "\t8 & 4.0 & 4.26 & 4.0 & 3.1 & 4.0 & 5.39 & 19.0 & 12.5 \\\\\n",
       "\t9 & 12.0 & 10.84 & 12.0 & 9.13 & 12.0 & 8.15 & 8.0 & 5.56 \\\\\n",
       "\t10 & 7.0 & 4.82 & 7.0 & 7.26 & 7.0 & 6.42 & 8.0 & 7.91 \\\\\n",
       "\t11 & 5.0 & 5.68 & 5.0 & 4.74 & 5.0 & 5.73 & 8.0 & 6.89 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m11×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1      \u001b[0m\u001b[1m x2      \u001b[0m\u001b[1m x3      \u001b[0m\u001b[1m x4      \u001b[0m\u001b[1m x5      \u001b[0m\u001b[1m x6      \u001b[0m\u001b[1m x7      \u001b[0m\u001b[1m x8      \u001b[0m\n",
       "     │\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────────────\n",
       "   1 │    10.0     8.04     10.0     9.14     10.0     7.46      8.0     6.58\n",
       "   2 │     8.0     6.95      8.0     8.14      8.0     6.77      8.0     5.76\n",
       "   3 │    13.0     7.58     13.0     8.74     13.0    12.74      8.0     7.71\n",
       "   4 │     9.0     8.81      9.0     8.77      9.0     7.11      8.0     8.84\n",
       "   5 │    11.0     8.33     11.0     9.26     11.0     7.81      8.0     8.47\n",
       "   6 │    14.0     9.96     14.0     8.1      14.0     8.84      8.0     7.04\n",
       "   7 │     6.0     7.24      6.0     6.13      6.0     6.08      8.0     5.25\n",
       "   8 │     4.0     4.26      4.0     3.1       4.0     5.39     19.0    12.5\n",
       "   9 │    12.0    10.84     12.0     9.13     12.0     8.15      8.0     5.56\n",
       "  10 │     7.0     4.82      7.0     7.26      7.0     6.42      8.0     7.91\n",
       "  11 │     5.0     5.68      5.0     4.74      5.0     5.73      8.0     6.89"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = DataFrame(aq, :auto)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the auto-generated column names are `x1`, `x2`, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we replace automatically generated column names by proper ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Vector{String}:\n",
       " \"x1\"\n",
       " \"y1\"\n",
       " \"x2\"\n",
       " \"y2\"\n",
       " \"x3\"\n",
       " \"y3\"\n",
       " \"x4\"\n",
       " \"y4\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newnames = vec(string.([\"x\", \"y\"], [1 2 3 4]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>11×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">y1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">y2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">y3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">y4</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">8.04</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">9.14</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">7.46</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.58</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.95</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.14</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.77</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.76</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">7.58</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">8.74</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">12.74</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.71</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.81</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.77</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">7.11</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.84</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">8.33</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">9.26</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">7.81</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.47</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">9.96</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.1</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.04</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">7.24</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.08</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.25</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.26</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">5.39</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">12.5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">10.84</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">9.13</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">8.15</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.56</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">4.82</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.26</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">6.42</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.91</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">4.74</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.73</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.89</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& x1 & y1 & x2 & y2 & x3 & y3 & x4 & y4\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 10.0 & 8.04 & 10.0 & 9.14 & 10.0 & 7.46 & 8.0 & 6.58 \\\\\n",
       "\t2 & 8.0 & 6.95 & 8.0 & 8.14 & 8.0 & 6.77 & 8.0 & 5.76 \\\\\n",
       "\t3 & 13.0 & 7.58 & 13.0 & 8.74 & 13.0 & 12.74 & 8.0 & 7.71 \\\\\n",
       "\t4 & 9.0 & 8.81 & 9.0 & 8.77 & 9.0 & 7.11 & 8.0 & 8.84 \\\\\n",
       "\t5 & 11.0 & 8.33 & 11.0 & 9.26 & 11.0 & 7.81 & 8.0 & 8.47 \\\\\n",
       "\t6 & 14.0 & 9.96 & 14.0 & 8.1 & 14.0 & 8.84 & 8.0 & 7.04 \\\\\n",
       "\t7 & 6.0 & 7.24 & 6.0 & 6.13 & 6.0 & 6.08 & 8.0 & 5.25 \\\\\n",
       "\t8 & 4.0 & 4.26 & 4.0 & 3.1 & 4.0 & 5.39 & 19.0 & 12.5 \\\\\n",
       "\t9 & 12.0 & 10.84 & 12.0 & 9.13 & 12.0 & 8.15 & 8.0 & 5.56 \\\\\n",
       "\t10 & 7.0 & 4.82 & 7.0 & 7.26 & 7.0 & 6.42 & 8.0 & 7.91 \\\\\n",
       "\t11 & 5.0 & 5.68 & 5.0 & 4.74 & 5.0 & 5.73 & 8.0 & 6.89 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m11×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1      \u001b[0m\u001b[1m y1      \u001b[0m\u001b[1m x2      \u001b[0m\u001b[1m y2      \u001b[0m\u001b[1m x3      \u001b[0m\u001b[1m y3      \u001b[0m\u001b[1m x4      \u001b[0m\u001b[1m y4      \u001b[0m\n",
       "     │\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────────────\n",
       "   1 │    10.0     8.04     10.0     9.14     10.0     7.46      8.0     6.58\n",
       "   2 │     8.0     6.95      8.0     8.14      8.0     6.77      8.0     5.76\n",
       "   3 │    13.0     7.58     13.0     8.74     13.0    12.74      8.0     7.71\n",
       "   4 │     9.0     8.81      9.0     8.77      9.0     7.11      8.0     8.84\n",
       "   5 │    11.0     8.33     11.0     9.26     11.0     7.81      8.0     8.47\n",
       "   6 │    14.0     9.96     14.0     8.1      14.0     8.84      8.0     7.04\n",
       "   7 │     6.0     7.24      6.0     6.13      6.0     6.08      8.0     5.25\n",
       "   8 │     4.0     4.26      4.0     3.1       4.0     5.39     19.0    12.5\n",
       "   9 │    12.0    10.84     12.0     9.13     12.0     8.15      8.0     5.56\n",
       "  10 │     7.0     4.82      7.0     7.26      7.0     6.42      8.0     7.91\n",
       "  11 │     5.0     5.68      5.0     4.74      5.0     5.73      8.0     6.89"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rename!(df, newnames)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could have also assigned the names to columns at the moment of data frame creation like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>11×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">y1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">y2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">y3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">y4</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">8.04</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">9.14</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">7.46</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.58</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.95</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.14</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.77</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.76</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">7.58</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">8.74</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">12.74</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.71</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.81</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.77</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">7.11</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.84</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">8.33</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">9.26</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">7.81</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.47</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">9.96</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.1</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.04</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">7.24</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.08</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.25</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.26</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">5.39</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">12.5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">10.84</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">9.13</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">8.15</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.56</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">4.82</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.26</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">6.42</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.91</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">4.74</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.73</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.89</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& x1 & y1 & x2 & y2 & x3 & y3 & x4 & y4\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 10.0 & 8.04 & 10.0 & 9.14 & 10.0 & 7.46 & 8.0 & 6.58 \\\\\n",
       "\t2 & 8.0 & 6.95 & 8.0 & 8.14 & 8.0 & 6.77 & 8.0 & 5.76 \\\\\n",
       "\t3 & 13.0 & 7.58 & 13.0 & 8.74 & 13.0 & 12.74 & 8.0 & 7.71 \\\\\n",
       "\t4 & 9.0 & 8.81 & 9.0 & 8.77 & 9.0 & 7.11 & 8.0 & 8.84 \\\\\n",
       "\t5 & 11.0 & 8.33 & 11.0 & 9.26 & 11.0 & 7.81 & 8.0 & 8.47 \\\\\n",
       "\t6 & 14.0 & 9.96 & 14.0 & 8.1 & 14.0 & 8.84 & 8.0 & 7.04 \\\\\n",
       "\t7 & 6.0 & 7.24 & 6.0 & 6.13 & 6.0 & 6.08 & 8.0 & 5.25 \\\\\n",
       "\t8 & 4.0 & 4.26 & 4.0 & 3.1 & 4.0 & 5.39 & 19.0 & 12.5 \\\\\n",
       "\t9 & 12.0 & 10.84 & 12.0 & 9.13 & 12.0 & 8.15 & 8.0 & 5.56 \\\\\n",
       "\t10 & 7.0 & 4.82 & 7.0 & 7.26 & 7.0 & 6.42 & 8.0 & 7.91 \\\\\n",
       "\t11 & 5.0 & 5.68 & 5.0 & 4.74 & 5.0 & 5.73 & 8.0 & 6.89 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m11×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1      \u001b[0m\u001b[1m y1      \u001b[0m\u001b[1m x2      \u001b[0m\u001b[1m y2      \u001b[0m\u001b[1m x3      \u001b[0m\u001b[1m y3      \u001b[0m\u001b[1m x4      \u001b[0m\u001b[1m y4      \u001b[0m\n",
       "     │\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────────────\n",
       "   1 │    10.0     8.04     10.0     9.14     10.0     7.46      8.0     6.58\n",
       "   2 │     8.0     6.95      8.0     8.14      8.0     6.77      8.0     5.76\n",
       "   3 │    13.0     7.58     13.0     8.74     13.0    12.74      8.0     7.71\n",
       "   4 │     9.0     8.81      9.0     8.77      9.0     7.11      8.0     8.84\n",
       "   5 │    11.0     8.33     11.0     9.26     11.0     7.81      8.0     8.47\n",
       "   6 │    14.0     9.96     14.0     8.1      14.0     8.84      8.0     7.04\n",
       "   7 │     6.0     7.24      6.0     6.13      6.0     6.08      8.0     5.25\n",
       "   8 │     4.0     4.26      4.0     3.1       4.0     5.39     19.0    12.5\n",
       "   9 │    12.0    10.84     12.0     9.13     12.0     8.15      8.0     5.56\n",
       "  10 │     7.0     4.82      7.0     7.26      7.0     6.42      8.0     7.91\n",
       "  11 │     5.0     5.68      5.0     4.74      5.0     5.73      8.0     6.89"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DataFrame(aq, [:x1, :y1, :x2, :y2, :x3, :y3, :x4, :y4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> You might have noticed that in the first example we used a string (e.g. `\"x1\"`) as column name and in the second one we used a `Symbol` (e.g. `:x1`). This was intentional. DataFrames.jl allows you to use either of them for column indexing.\n",
    "\n",
    "To see the above rule at work let us extract the second column `:y1` from this data frame. Here are several options how you can do it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       "  8.04\n",
       "  6.95\n",
       "  7.58\n",
       "  8.81\n",
       "  8.33\n",
       "  9.96\n",
       "  7.24\n",
       "  4.26\n",
       " 10.84\n",
       "  4.82\n",
       "  5.68"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.y1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       "  8.04\n",
       "  6.95\n",
       "  7.58\n",
       "  8.81\n",
       "  8.33\n",
       "  9.96\n",
       "  7.24\n",
       "  4.26\n",
       " 10.84\n",
       "  4.82\n",
       "  5.68"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.\"y1\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       "  8.04\n",
       "  6.95\n",
       "  7.58\n",
       "  8.81\n",
       "  8.33\n",
       "  9.96\n",
       "  7.24\n",
       "  4.26\n",
       " 10.84\n",
       "  4.82\n",
       "  5.68"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[:, :y1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       "  8.04\n",
       "  6.95\n",
       "  7.58\n",
       "  8.81\n",
       "  8.33\n",
       "  9.96\n",
       "  7.24\n",
       "  4.26\n",
       " 10.84\n",
       "  4.82\n",
       "  5.68"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[:, \"y1\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume that now we want to reorder columns of the data frame `df` in-place by first grouping the \"x\"-columns and then \"y\" columns.\n",
    "\n",
    "This can be easily achieved with the `select!` function.\n",
    "\n",
    "Note that in column selection we can in particular use regular expressions like `r\"x\"` (matching all columns that have `\"x\"` in their name) and `:` which matches all columns (in this case only columns not having `\"x\"` in ther name are left)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>11×8 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">y1</th><th style = \"text-align: left;\">y2</th><th style = \"text-align: left;\">y3</th><th style = \"text-align: left;\">y4</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.04</td><td style = \"text-align: right;\">9.14</td><td style = \"text-align: right;\">7.46</td><td style = \"text-align: right;\">6.58</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.95</td><td style = \"text-align: right;\">8.14</td><td style = \"text-align: right;\">6.77</td><td style = \"text-align: right;\">5.76</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.58</td><td style = \"text-align: right;\">8.74</td><td style = \"text-align: right;\">12.74</td><td style = \"text-align: right;\">7.71</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.81</td><td style = \"text-align: right;\">8.77</td><td style = \"text-align: right;\">7.11</td><td style = \"text-align: right;\">8.84</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.33</td><td style = \"text-align: right;\">9.26</td><td style = \"text-align: right;\">7.81</td><td style = \"text-align: right;\">8.47</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">9.96</td><td style = \"text-align: right;\">8.1</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">7.04</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.24</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">6.08</td><td style = \"text-align: right;\">5.25</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">4.26</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">5.39</td><td style = \"text-align: right;\">12.5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">10.84</td><td style = \"text-align: right;\">9.13</td><td style = \"text-align: right;\">8.15</td><td style = \"text-align: right;\">5.56</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">4.82</td><td style = \"text-align: right;\">7.26</td><td style = \"text-align: right;\">6.42</td><td style = \"text-align: right;\">7.91</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">4.74</td><td style = \"text-align: right;\">5.73</td><td style = \"text-align: right;\">6.89</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & y1 & y2 & y3 & y4\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 10.0 & 10.0 & 10.0 & 8.0 & 8.04 & 9.14 & 7.46 & 6.58 \\\\\n",
       "\t2 & 8.0 & 8.0 & 8.0 & 8.0 & 6.95 & 8.14 & 6.77 & 5.76 \\\\\n",
       "\t3 & 13.0 & 13.0 & 13.0 & 8.0 & 7.58 & 8.74 & 12.74 & 7.71 \\\\\n",
       "\t4 & 9.0 & 9.0 & 9.0 & 8.0 & 8.81 & 8.77 & 7.11 & 8.84 \\\\\n",
       "\t5 & 11.0 & 11.0 & 11.0 & 8.0 & 8.33 & 9.26 & 7.81 & 8.47 \\\\\n",
       "\t6 & 14.0 & 14.0 & 14.0 & 8.0 & 9.96 & 8.1 & 8.84 & 7.04 \\\\\n",
       "\t7 & 6.0 & 6.0 & 6.0 & 8.0 & 7.24 & 6.13 & 6.08 & 5.25 \\\\\n",
       "\t8 & 4.0 & 4.0 & 4.0 & 19.0 & 4.26 & 3.1 & 5.39 & 12.5 \\\\\n",
       "\t9 & 12.0 & 12.0 & 12.0 & 8.0 & 10.84 & 9.13 & 8.15 & 5.56 \\\\\n",
       "\t10 & 7.0 & 7.0 & 7.0 & 8.0 & 4.82 & 7.26 & 6.42 & 7.91 \\\\\n",
       "\t11 & 5.0 & 5.0 & 5.0 & 8.0 & 5.68 & 4.74 & 5.73 & 6.89 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m11×8 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1      \u001b[0m\u001b[1m x2      \u001b[0m\u001b[1m x3      \u001b[0m\u001b[1m x4      \u001b[0m\u001b[1m y1      \u001b[0m\u001b[1m y2      \u001b[0m\u001b[1m y3      \u001b[0m\u001b[1m y4      \u001b[0m\n",
       "     │\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼────────────────────────────────────────────────────────────────────────\n",
       "   1 │    10.0     10.0     10.0      8.0     8.04     9.14     7.46     6.58\n",
       "   2 │     8.0      8.0      8.0      8.0     6.95     8.14     6.77     5.76\n",
       "   3 │    13.0     13.0     13.0      8.0     7.58     8.74    12.74     7.71\n",
       "   4 │     9.0      9.0      9.0      8.0     8.81     8.77     7.11     8.84\n",
       "   5 │    11.0     11.0     11.0      8.0     8.33     9.26     7.81     8.47\n",
       "   6 │    14.0     14.0     14.0      8.0     9.96     8.1      8.84     7.04\n",
       "   7 │     6.0      6.0      6.0      8.0     7.24     6.13     6.08     5.25\n",
       "   8 │     4.0      4.0      4.0     19.0     4.26     3.1      5.39    12.5\n",
       "   9 │    12.0     12.0     12.0      8.0    10.84     9.13     8.15     5.56\n",
       "  10 │     7.0      7.0      7.0      8.0     4.82     7.26     6.42     7.91\n",
       "  11 │     5.0      5.0      5.0      8.0     5.68     4.74     5.73     6.89"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select!(df, r\"x\", :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we could have used `select` instead of `select!` function to create a new data frame (instead of mutating the data frame in question in-place)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An interesting feature of Anscombe's quartet is that its variables have the same mean and variance.\n",
    "\n",
    "We can easily check this using the `describe` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">variable</th><th style = \"text-align: left;\">mean</th><th style = \"text-align: left;\">std</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Symbol\" style = \"text-align: left;\">Symbol</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">x1</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">x2</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">x3</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">x4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">y1</td><td style = \"text-align: right;\">7.50091</td><td style = \"text-align: right;\">2.03157</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">y2</td><td style = \"text-align: right;\">7.50091</td><td style = \"text-align: right;\">2.03166</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">y3</td><td style = \"text-align: right;\">7.5</td><td style = \"text-align: right;\">2.03042</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">y4</td><td style = \"text-align: right;\">7.50091</td><td style = \"text-align: right;\">2.03058</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& variable & mean & std\\\\\n",
       "\t\\hline\n",
       "\t& Symbol & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & x1 & 9.0 & 3.31662 \\\\\n",
       "\t2 & x2 & 9.0 & 3.31662 \\\\\n",
       "\t3 & x3 & 9.0 & 3.31662 \\\\\n",
       "\t4 & x4 & 9.0 & 3.31662 \\\\\n",
       "\t5 & y1 & 7.50091 & 2.03157 \\\\\n",
       "\t6 & y2 & 7.50091 & 2.03166 \\\\\n",
       "\t7 & y3 & 7.5 & 2.03042 \\\\\n",
       "\t8 & y4 & 7.50091 & 2.03058 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m variable \u001b[0m\u001b[1m mean    \u001b[0m\u001b[1m std     \u001b[0m\n",
       "     │\u001b[90m Symbol   \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼────────────────────────────\n",
       "   1 │ x1        9.0      3.31662\n",
       "   2 │ x2        9.0      3.31662\n",
       "   3 │ x3        9.0      3.31662\n",
       "   4 │ x4        9.0      3.31662\n",
       "   5 │ y1        7.50091  2.03157\n",
       "   6 │ y2        7.50091  2.03166\n",
       "   7 │ y3        7.5      2.03042\n",
       "   8 │ y4        7.50091  2.03058"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "describe(df, mean => :mean, std => :std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to practice the string/`Symbol` duality let us write the same using strings for column names:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>8×3 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">variable</th><th style = \"text-align: left;\">mean</th><th style = \"text-align: left;\">std</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Symbol\" style = \"text-align: left;\">Symbol</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">x1</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">x2</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">x3</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">x4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">3.31662</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">y1</td><td style = \"text-align: right;\">7.50091</td><td style = \"text-align: right;\">2.03157</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: left;\">y2</td><td style = \"text-align: right;\">7.50091</td><td style = \"text-align: right;\">2.03166</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: left;\">y3</td><td style = \"text-align: right;\">7.5</td><td style = \"text-align: right;\">2.03042</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: left;\">y4</td><td style = \"text-align: right;\">7.50091</td><td style = \"text-align: right;\">2.03058</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& variable & mean & std\\\\\n",
       "\t\\hline\n",
       "\t& Symbol & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & x1 & 9.0 & 3.31662 \\\\\n",
       "\t2 & x2 & 9.0 & 3.31662 \\\\\n",
       "\t3 & x3 & 9.0 & 3.31662 \\\\\n",
       "\t4 & x4 & 9.0 & 3.31662 \\\\\n",
       "\t5 & y1 & 7.50091 & 2.03157 \\\\\n",
       "\t6 & y2 & 7.50091 & 2.03166 \\\\\n",
       "\t7 & y3 & 7.5 & 2.03042 \\\\\n",
       "\t8 & y4 & 7.50091 & 2.03058 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m8×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m variable \u001b[0m\u001b[1m mean    \u001b[0m\u001b[1m std     \u001b[0m\n",
       "     │\u001b[90m Symbol   \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼────────────────────────────\n",
       "   1 │ x1        9.0      3.31662\n",
       "   2 │ x2        9.0      3.31662\n",
       "   3 │ x3        9.0      3.31662\n",
       "   4 │ x4        9.0      3.31662\n",
       "   5 │ y1        7.50091  2.03157\n",
       "   6 │ y2        7.50091  2.03166\n",
       "   7 │ y3        7.5      2.03042\n",
       "   8 │ y4        7.50091  2.03058"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "describe(df, mean => \"mean\", std => \"std\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us add a new column `id` to the data frame that will just index its rows from 1 to number of rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>11×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">y1</th><th style = \"text-align: left;\">y2</th><th style = \"text-align: left;\">y3</th><th style = \"text-align: left;\">y4</th><th style = \"text-align: left;\">id</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.04</td><td style = \"text-align: right;\">9.14</td><td style = \"text-align: right;\">7.46</td><td style = \"text-align: right;\">6.58</td><td style = \"text-align: right;\">1</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.95</td><td style = \"text-align: right;\">8.14</td><td style = \"text-align: right;\">6.77</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.58</td><td style = \"text-align: right;\">8.74</td><td style = \"text-align: right;\">12.74</td><td style = \"text-align: right;\">7.71</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.81</td><td style = \"text-align: right;\">8.77</td><td style = \"text-align: right;\">7.11</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.33</td><td style = \"text-align: right;\">9.26</td><td style = \"text-align: right;\">7.81</td><td style = \"text-align: right;\">8.47</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">9.96</td><td style = \"text-align: right;\">8.1</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">7.04</td><td style = \"text-align: right;\">6</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.24</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">6.08</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">7</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">4.26</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">5.39</td><td style = \"text-align: right;\">12.5</td><td style = \"text-align: right;\">8</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">10.84</td><td style = \"text-align: right;\">9.13</td><td style = \"text-align: right;\">8.15</td><td style = \"text-align: right;\">5.56</td><td style = \"text-align: right;\">9</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">4.82</td><td style = \"text-align: right;\">7.26</td><td style = \"text-align: right;\">6.42</td><td style = \"text-align: right;\">7.91</td><td style = \"text-align: right;\">10</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">4.74</td><td style = \"text-align: right;\">5.73</td><td style = \"text-align: right;\">6.89</td><td style = \"text-align: right;\">11</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & y1 & y2 & y3 & y4 & id\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 10.0 & 10.0 & 10.0 & 8.0 & 8.04 & 9.14 & 7.46 & 6.58 & 1 \\\\\n",
       "\t2 & 8.0 & 8.0 & 8.0 & 8.0 & 6.95 & 8.14 & 6.77 & 5.76 & 2 \\\\\n",
       "\t3 & 13.0 & 13.0 & 13.0 & 8.0 & 7.58 & 8.74 & 12.74 & 7.71 & 3 \\\\\n",
       "\t4 & 9.0 & 9.0 & 9.0 & 8.0 & 8.81 & 8.77 & 7.11 & 8.84 & 4 \\\\\n",
       "\t5 & 11.0 & 11.0 & 11.0 & 8.0 & 8.33 & 9.26 & 7.81 & 8.47 & 5 \\\\\n",
       "\t6 & 14.0 & 14.0 & 14.0 & 8.0 & 9.96 & 8.1 & 8.84 & 7.04 & 6 \\\\\n",
       "\t7 & 6.0 & 6.0 & 6.0 & 8.0 & 7.24 & 6.13 & 6.08 & 5.25 & 7 \\\\\n",
       "\t8 & 4.0 & 4.0 & 4.0 & 19.0 & 4.26 & 3.1 & 5.39 & 12.5 & 8 \\\\\n",
       "\t9 & 12.0 & 12.0 & 12.0 & 8.0 & 10.84 & 9.13 & 8.15 & 5.56 & 9 \\\\\n",
       "\t10 & 7.0 & 7.0 & 7.0 & 8.0 & 4.82 & 7.26 & 6.42 & 7.91 & 10 \\\\\n",
       "\t11 & 5.0 & 5.0 & 5.0 & 8.0 & 5.68 & 4.74 & 5.73 & 6.89 & 11 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m11×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1      \u001b[0m\u001b[1m x2      \u001b[0m\u001b[1m x3      \u001b[0m\u001b[1m x4      \u001b[0m\u001b[1m y1      \u001b[0m\u001b[1m y2      \u001b[0m\u001b[1m y3      \u001b[0m\u001b[1m y4      \u001b[0m\u001b[1m\u001b[0m ⋯\n",
       "     │\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │    10.0     10.0     10.0      8.0     8.04     9.14     7.46     6.58  ⋯\n",
       "   2 │     8.0      8.0      8.0      8.0     6.95     8.14     6.77     5.76\n",
       "   3 │    13.0     13.0     13.0      8.0     7.58     8.74    12.74     7.71\n",
       "   4 │     9.0      9.0      9.0      8.0     8.81     8.77     7.11     8.84\n",
       "   5 │    11.0     11.0     11.0      8.0     8.33     9.26     7.81     8.47  ⋯\n",
       "   6 │    14.0     14.0     14.0      8.0     9.96     8.1      8.84     7.04\n",
       "   7 │     6.0      6.0      6.0      8.0     7.24     6.13     6.08     5.25\n",
       "   8 │     4.0      4.0      4.0     19.0     4.26     3.1      5.39    12.5\n",
       "   9 │    12.0     12.0     12.0      8.0    10.84     9.13     8.15     5.56  ⋯\n",
       "  10 │     7.0      7.0      7.0      8.0     4.82     7.26     6.42     7.91\n",
       "  11 │     5.0      5.0      5.0      8.0     5.68     4.74     5.73     6.89\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.id = 1:nrow(df) # also writing axes(df, 1) on the right hand side would work\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly to `nrow` which gives us a number of rows in a data frame, one can use `ncol` function to get its number of columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ncol(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to practice what we have already learnt let us create a new data frame which will have `:id` coumn in front of the remaining columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>11×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">id</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">y1</th><th style = \"text-align: left;\">y2</th><th style = \"text-align: left;\">y3</th><th style = \"text-align: left;\">y4</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.04</td><td style = \"text-align: right;\">9.14</td><td style = \"text-align: right;\">7.46</td><td style = \"text-align: right;\">6.58</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.95</td><td style = \"text-align: right;\">8.14</td><td style = \"text-align: right;\">6.77</td><td style = \"text-align: right;\">5.76</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.58</td><td style = \"text-align: right;\">8.74</td><td style = \"text-align: right;\">12.74</td><td style = \"text-align: right;\">7.71</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.81</td><td style = \"text-align: right;\">8.77</td><td style = \"text-align: right;\">7.11</td><td style = \"text-align: right;\">8.84</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.33</td><td style = \"text-align: right;\">9.26</td><td style = \"text-align: right;\">7.81</td><td style = \"text-align: right;\">8.47</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">9.96</td><td style = \"text-align: right;\">8.1</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">7.04</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.24</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">6.08</td><td style = \"text-align: right;\">5.25</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">4.26</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">5.39</td><td style = \"text-align: right;\">12.5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">10.84</td><td style = \"text-align: right;\">9.13</td><td style = \"text-align: right;\">8.15</td><td style = \"text-align: right;\">5.56</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">4.82</td><td style = \"text-align: right;\">7.26</td><td style = \"text-align: right;\">6.42</td><td style = \"text-align: right;\">7.91</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">4.74</td><td style = \"text-align: right;\">5.73</td><td style = \"text-align: right;\">6.89</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& id & x1 & x2 & x3 & x4 & y1 & y2 & y3 & y4\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 10.0 & 10.0 & 10.0 & 8.0 & 8.04 & 9.14 & 7.46 & 6.58 \\\\\n",
       "\t2 & 2 & 8.0 & 8.0 & 8.0 & 8.0 & 6.95 & 8.14 & 6.77 & 5.76 \\\\\n",
       "\t3 & 3 & 13.0 & 13.0 & 13.0 & 8.0 & 7.58 & 8.74 & 12.74 & 7.71 \\\\\n",
       "\t4 & 4 & 9.0 & 9.0 & 9.0 & 8.0 & 8.81 & 8.77 & 7.11 & 8.84 \\\\\n",
       "\t5 & 5 & 11.0 & 11.0 & 11.0 & 8.0 & 8.33 & 9.26 & 7.81 & 8.47 \\\\\n",
       "\t6 & 6 & 14.0 & 14.0 & 14.0 & 8.0 & 9.96 & 8.1 & 8.84 & 7.04 \\\\\n",
       "\t7 & 7 & 6.0 & 6.0 & 6.0 & 8.0 & 7.24 & 6.13 & 6.08 & 5.25 \\\\\n",
       "\t8 & 8 & 4.0 & 4.0 & 4.0 & 19.0 & 4.26 & 3.1 & 5.39 & 12.5 \\\\\n",
       "\t9 & 9 & 12.0 & 12.0 & 12.0 & 8.0 & 10.84 & 9.13 & 8.15 & 5.56 \\\\\n",
       "\t10 & 10 & 7.0 & 7.0 & 7.0 & 8.0 & 4.82 & 7.26 & 6.42 & 7.91 \\\\\n",
       "\t11 & 11 & 5.0 & 5.0 & 5.0 & 8.0 & 5.68 & 4.74 & 5.73 & 6.89 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m11×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m id    \u001b[0m\u001b[1m x1      \u001b[0m\u001b[1m x2      \u001b[0m\u001b[1m x3      \u001b[0m\u001b[1m x4      \u001b[0m\u001b[1m y1      \u001b[0m\u001b[1m y2      \u001b[0m\u001b[1m y3      \u001b[0m\u001b[1m y\u001b[0m ⋯\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m F\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │     1     10.0     10.0     10.0      8.0     8.04     9.14     7.46    ⋯\n",
       "   2 │     2      8.0      8.0      8.0      8.0     6.95     8.14     6.77\n",
       "   3 │     3     13.0     13.0     13.0      8.0     7.58     8.74    12.74\n",
       "   4 │     4      9.0      9.0      9.0      8.0     8.81     8.77     7.11\n",
       "   5 │     5     11.0     11.0     11.0      8.0     8.33     9.26     7.81    ⋯\n",
       "   6 │     6     14.0     14.0     14.0      8.0     9.96     8.1      8.84\n",
       "   7 │     7      6.0      6.0      6.0      8.0     7.24     6.13     6.08\n",
       "   8 │     8      4.0      4.0      4.0     19.0     4.26     3.1      5.39\n",
       "   9 │     9     12.0     12.0     12.0      8.0    10.84     9.13     8.15    ⋯\n",
       "  10 │    10      7.0      7.0      7.0      8.0     4.82     7.26     6.42\n",
       "  11 │    11      5.0      5.0      5.0      8.0     5.68     4.74     5.73\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select(df, \"id\", :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this time `df` data frame was not changed, as `select` makes a copy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>11×9 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">x1</th><th style = \"text-align: left;\">x2</th><th style = \"text-align: left;\">x3</th><th style = \"text-align: left;\">x4</th><th style = \"text-align: left;\">y1</th><th style = \"text-align: left;\">y2</th><th style = \"text-align: left;\">y3</th><th style = \"text-align: left;\">y4</th><th style = \"text-align: left;\">id</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.04</td><td style = \"text-align: right;\">9.14</td><td style = \"text-align: right;\">7.46</td><td style = \"text-align: right;\">6.58</td><td style = \"text-align: right;\">1</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">6.95</td><td style = \"text-align: right;\">8.14</td><td style = \"text-align: right;\">6.77</td><td style = \"text-align: right;\">5.76</td><td style = \"text-align: right;\">2</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.58</td><td style = \"text-align: right;\">8.74</td><td style = \"text-align: right;\">12.74</td><td style = \"text-align: right;\">7.71</td><td style = \"text-align: right;\">3</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.81</td><td style = \"text-align: right;\">8.77</td><td style = \"text-align: right;\">7.11</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">8.33</td><td style = \"text-align: right;\">9.26</td><td style = \"text-align: right;\">7.81</td><td style = \"text-align: right;\">8.47</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">9.96</td><td style = \"text-align: right;\">8.1</td><td style = \"text-align: right;\">8.84</td><td style = \"text-align: right;\">7.04</td><td style = \"text-align: right;\">6</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">7.24</td><td style = \"text-align: right;\">6.13</td><td style = \"text-align: right;\">6.08</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">7</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">4.26</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">5.39</td><td style = \"text-align: right;\">12.5</td><td style = \"text-align: right;\">8</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">10.84</td><td style = \"text-align: right;\">9.13</td><td style = \"text-align: right;\">8.15</td><td style = \"text-align: right;\">5.56</td><td style = \"text-align: right;\">9</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">4.82</td><td style = \"text-align: right;\">7.26</td><td style = \"text-align: right;\">6.42</td><td style = \"text-align: right;\">7.91</td><td style = \"text-align: right;\">10</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">4.74</td><td style = \"text-align: right;\">5.73</td><td style = \"text-align: right;\">6.89</td><td style = \"text-align: right;\">11</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccccccccc}\n",
       "\t& x1 & x2 & x3 & x4 & y1 & y2 & y3 & y4 & id\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 10.0 & 10.0 & 10.0 & 8.0 & 8.04 & 9.14 & 7.46 & 6.58 & 1 \\\\\n",
       "\t2 & 8.0 & 8.0 & 8.0 & 8.0 & 6.95 & 8.14 & 6.77 & 5.76 & 2 \\\\\n",
       "\t3 & 13.0 & 13.0 & 13.0 & 8.0 & 7.58 & 8.74 & 12.74 & 7.71 & 3 \\\\\n",
       "\t4 & 9.0 & 9.0 & 9.0 & 8.0 & 8.81 & 8.77 & 7.11 & 8.84 & 4 \\\\\n",
       "\t5 & 11.0 & 11.0 & 11.0 & 8.0 & 8.33 & 9.26 & 7.81 & 8.47 & 5 \\\\\n",
       "\t6 & 14.0 & 14.0 & 14.0 & 8.0 & 9.96 & 8.1 & 8.84 & 7.04 & 6 \\\\\n",
       "\t7 & 6.0 & 6.0 & 6.0 & 8.0 & 7.24 & 6.13 & 6.08 & 5.25 & 7 \\\\\n",
       "\t8 & 4.0 & 4.0 & 4.0 & 19.0 & 4.26 & 3.1 & 5.39 & 12.5 & 8 \\\\\n",
       "\t9 & 12.0 & 12.0 & 12.0 & 8.0 & 10.84 & 9.13 & 8.15 & 5.56 & 9 \\\\\n",
       "\t10 & 7.0 & 7.0 & 7.0 & 8.0 & 4.82 & 7.26 & 6.42 & 7.91 & 10 \\\\\n",
       "\t11 & 5.0 & 5.0 & 5.0 & 8.0 & 5.68 & 4.74 & 5.73 & 6.89 & 11 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m11×9 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m x1      \u001b[0m\u001b[1m x2      \u001b[0m\u001b[1m x3      \u001b[0m\u001b[1m x4      \u001b[0m\u001b[1m y1      \u001b[0m\u001b[1m y2      \u001b[0m\u001b[1m y3      \u001b[0m\u001b[1m y4      \u001b[0m\u001b[1m\u001b[0m ⋯\n",
       "     │\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m\u001b[0m ⋯\n",
       "─────┼──────────────────────────────────────────────────────────────────────────\n",
       "   1 │    10.0     10.0     10.0      8.0     8.04     9.14     7.46     6.58  ⋯\n",
       "   2 │     8.0      8.0      8.0      8.0     6.95     8.14     6.77     5.76\n",
       "   3 │    13.0     13.0     13.0      8.0     7.58     8.74    12.74     7.71\n",
       "   4 │     9.0      9.0      9.0      8.0     8.81     8.77     7.11     8.84\n",
       "   5 │    11.0     11.0     11.0      8.0     8.33     9.26     7.81     8.47  ⋯\n",
       "   6 │    14.0     14.0     14.0      8.0     9.96     8.1      8.84     7.04\n",
       "   7 │     6.0      6.0      6.0      8.0     7.24     6.13     6.08     5.25\n",
       "   8 │     4.0      4.0      4.0     19.0     4.26     3.1      5.39    12.5\n",
       "   9 │    12.0     12.0     12.0      8.0    10.84     9.13     8.15     5.56  ⋯\n",
       "  10 │     7.0      7.0      7.0      8.0     4.82     7.26     6.42     7.91\n",
       "  11 │     5.0      5.0      5.0      8.0     5.68     4.74     5.73     6.89\n",
       "\u001b[36m                                                                1 column omitted\u001b[0m"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also easy to transform a data frame back to a matrix using the `Matrix` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11×9 Matrix{Float64}:\n",
       " 10.0  10.0  10.0   8.0   8.04  9.14   7.46   6.58   1.0\n",
       "  8.0   8.0   8.0   8.0   6.95  8.14   6.77   5.76   2.0\n",
       " 13.0  13.0  13.0   8.0   7.58  8.74  12.74   7.71   3.0\n",
       "  9.0   9.0   9.0   8.0   8.81  8.77   7.11   8.84   4.0\n",
       " 11.0  11.0  11.0   8.0   8.33  9.26   7.81   8.47   5.0\n",
       " 14.0  14.0  14.0   8.0   9.96  8.1    8.84   7.04   6.0\n",
       "  6.0   6.0   6.0   8.0   7.24  6.13   6.08   5.25   7.0\n",
       "  4.0   4.0   4.0  19.0   4.26  3.1    5.39  12.5    8.0\n",
       " 12.0  12.0  12.0   8.0  10.84  9.13   8.15   5.56   9.0\n",
       "  7.0   7.0   7.0   8.0   4.82  7.26   6.42   7.91  10.0\n",
       "  5.0   5.0   5.0   8.0   5.68  4.74   5.73   6.89  11.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matrix(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use this feature to determine a plotting range for our data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We take the extrema respectively of the \"x\" and \"y\" variables, add padding equal to 1, and finally collect them to vectors (without calling the `collect` our result would be a `Tuple`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       "  3.0\n",
       " 20.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xlims = collect(extrema(Matrix(select(df, r\"x\"))) .+ (-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Vector{Float64}:\n",
       "  2.1\n",
       " 13.74"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ylims = collect(extrema(Matrix(select(df, r\"y\"))) .+ (-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to produce the final plots.\n",
    "\n",
    "Note that the GLM.jl package is integrated with DataFrames.jl and in `lm` and `predict` functions we can use data frame objects to pass data.\n",
    "\n",
    "Note though that as GLM.jl in general supports other tabular types than just DataFrames.jl it is more strict and accepts only `Symbol`s as column names (this is required when we use the `term` function)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 4 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 2)\n",
    "fig.tight_layout(pad=4.0)\n",
    "for i in 1:4\n",
    "    x = Symbol(\"x\", i)\n",
    "    y = Symbol(\"y\", i)\n",
    "    model = lm(term(y)~term(x), df)\n",
    "    axs[i].plot(xlims, predict(model, DataFrame(x => xlims)), color=\"orange\")\n",
    "    axs[i].scatter(df[:, x], df[:, y])\n",
    "    axs[i].set_xlim(xlims)\n",
    "    axs[i].set_ylim(ylims)\n",
    "    axs[i].set_xlabel(\"x$i\")\n",
    "    axs[i].set_ylabel(\"y$i\")\n",
    "    a, b = round.(coef(model), digits=2)\n",
    "    c = round(100 * r2(model), digits=2)\n",
    "    axs[i].set_title(string(\"R²=$c%, $y=$a+$b$x\"))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note that in all cases the estimated models have exactly the same R² and estimated coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is worth to highlight several important features of DataFrames.jl package functionality that we used in the above example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, it is easy to create a data frame from variables holding column names and values using `=>`. Here is one more example how this functionality can be used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>3×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">var1</th><th style = \"text-align: left;\">var2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">6</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& var1 & var2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 4 \\\\\n",
       "\t2 & 2 & 5 \\\\\n",
       "\t3 & 3 & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m3×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m var1  \u001b[0m\u001b[1m var2  \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼──────────────\n",
       "   1 │     1      4\n",
       "   2 │     2      5\n",
       "   3 │     3      6"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = :var1\n",
    "y = :var2\n",
    "xc = 1:3\n",
    "yc = 4:6\n",
    "DataFrame(x => xc, y => yc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the same effect can be achieved with passing keyword arguments directly to `DataFrame` constructor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>3×2 DataFrame</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">var1</th><th style = \"text-align: left;\">var2</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">4</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">6</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& var1 & var2\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 4 \\\\\n",
       "\t2 & 2 & 5 \\\\\n",
       "\t3 & 3 & 6 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m3×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m var1  \u001b[0m\u001b[1m var2  \u001b[0m\n",
       "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼──────────────\n",
       "   1 │     1      4\n",
       "   2 │     2      5\n",
       "   3 │     3      6"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DataFrame(var1=xc, var2=yc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another thing you might have noticed is the use of `df[:, x]` and `df[:, y]` indexing expressions to get columns from a data frame. Let us comment on the differences between `df.col` and `df[:, col]` syntaxes that we discussed above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       " 10.0\n",
       "  8.0\n",
       " 13.0\n",
       "  9.0\n",
       " 11.0\n",
       " 14.0\n",
       "  6.0\n",
       "  4.0\n",
       " 12.0\n",
       "  7.0\n",
       "  5.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# gives you a direct access to the column stored in `df` but x1 is a literal\n",
    "df.x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       " 10.0\n",
       "  8.0\n",
       " 13.0\n",
       "  9.0\n",
       " 11.0\n",
       " 14.0\n",
       "  6.0\n",
       "  4.0\n",
       " 12.0\n",
       "  7.0\n",
       "  5.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now the column is copied, so this is the same as copy(df.x1)\n",
    "# in this case we could have used a variable instead of a literal for indexing\n",
    "df[:, :x1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what if you want to select a column without copying it but want to use a variable holding its name. There is a special `!` row selector for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":x1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = :x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11-element Vector{Float64}:\n",
       " 10.0\n",
       "  8.0\n",
       " 13.0\n",
       "  9.0\n",
       " 11.0\n",
       " 14.0\n",
       "  6.0\n",
       "  4.0\n",
       " 12.0\n",
       "  7.0\n",
       "  5.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = df[!, n]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check that `!` does not copy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v === df.x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indexing of a data frame is very flexible. All rules governing this functionality can be found at https://juliadata.github.io/DataFrames.jl/stable/lib/indexing/."
   ]
  }
 ],
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