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-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px;\">\n",
-    "    <strong>CS411 - Autumn 2019-2020</strong><br/>\n",
-    "    Patrick Jermann<br/><br/>\n",
-    "    <span style=\"text-decoration:underline;font-weight:bold;\">How to use this notebook?</span>\n",
-    "    <ul style=\"margin:0;padding:0 0 0 20px;\">\n",
-    "    <li>This notebook is made of text cells and code cells. The code cells have to be <strong>executed</strong> to see the result of the program. To execute a cell, simply select it and click on the \"play\" button (&#11208;) in the tool bar just above the notebook, or type <code>shift + enter</code>. It is important to execute the code cells in their order of appearance in the notebook.</li>\n",
-    "    <li>To improve readability, it can be useful to <strong>hide</strong> cells from the notebook (e.g. long code cells). To hide a cell, select it and click on the blue bar which appears on its left. To make the cell visible again, just click again on the blue bar, or on the three \"dots\" which represent the collapsed cell.</li></ul>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# The MOOC dataset\n",
-    "The data we use in this document to demonstrate the use of basic statistics is about students' performance in academic exams (e.g. the algebra course taken at the university) and their activitiy online in a related Massive Open Online Course (e.g. the algebra MOOC). The general question we try to answer is: what is the relation between the use of the MOOC by students and their academic achievement. \n",
-    "\n",
-    "**Question**: Does the use of MOOCs help succeed in courses ? Do only good students use the MOOCs ? Are MOOCs more helpful for better students ?\n",
-    "\n",
-    "As a general remark, we should note that because we did not conduct a controlled experiment with random assignment of subjects to experimental groups, we cannot establish any causal relationships between MOOC use and academic performance. Rather, we use statistical tools to \"explore\" data.\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Loading libraries\n",
-    "Some extra libraries are needed to perform some operations. We collect the commands to load the libraries in this cell. Executing this cell first ensures that all the necessary libraries are loaded. If one library is missing it can be installed via the install.packages() command. Simply add the line to the cell and re-execute."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "gdata: read.xls support for 'XLS' (Excel 97-2004) files ENABLED.\n",
-      "\n",
-      "gdata: Unable to load perl libaries needed by read.xls()\n",
-      "gdata: to support 'XLSX' (Excel 2007+) files.\n",
-      "\n",
-      "gdata: Run the function 'installXLSXsupport()'\n",
-      "gdata: to automatically download and install the perl\n",
-      "gdata: libaries needed to support Excel XLS and XLSX formats.\n",
-      "\n",
-      "Attaching package: ‘gdata’\n",
-      "\n",
-      "The following object is masked from ‘package:stats’:\n",
-      "\n",
-      "    nobs\n",
-      "\n",
-      "The following object is masked from ‘package:utils’:\n",
-      "\n",
-      "    object.size\n",
-      "\n",
-      "The following object is masked from ‘package:base’:\n",
-      "\n",
-      "    startsWith\n",
-      "\n",
-      "\n",
-      "Attaching package: ‘gplots’\n",
-      "\n",
-      "The following object is masked from ‘package:stats’:\n",
-      "\n",
-      "    lowess\n",
-      "\n",
-      "\n",
-      "Attaching package: ‘dplyr’\n",
-      "\n",
-      "The following objects are masked from ‘package:plyr’:\n",
-      "\n",
-      "    arrange, count, desc, failwith, id, mutate, rename, summarise,\n",
-      "    summarize\n",
-      "\n",
-      "The following objects are masked from ‘package:gdata’:\n",
-      "\n",
-      "    combine, first, last\n",
-      "\n",
-      "The following objects are masked from ‘package:stats’:\n",
-      "\n",
-      "    filter, lag\n",
-      "\n",
-      "The following objects are masked from ‘package:base’:\n",
-      "\n",
-      "    intersect, setdiff, setequal, union\n",
-      "\n",
-      "Loading required package: magrittr\n",
-      "\n",
-      "Attaching package: ‘ggpubr’\n",
-      "\n",
-      "The following object is masked from ‘package:plyr’:\n",
-      "\n",
-      "    mutate\n",
-      "\n",
-      "Loading required package: carData\n",
-      "\n",
-      "Attaching package: ‘car’\n",
-      "\n",
-      "The following object is masked from ‘package:dplyr’:\n",
-      "\n",
-      "    recode\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "\n",
-    "# Uncomment and run once if these packages are not installed yet.\n",
-    "# install.packages(\"gdata\")\n",
-    "# install.packages(\"gplots\")\n",
-    "# install.packages(\"car\")\n",
-    "# install.packages(\"ggpubr\")\n",
-    "\n",
-    "library(gdata) # reorder\n",
-    "library(gplots) # plotmeans\n",
-    "library(plyr) # ddply\n",
-    "library(dplyr) # summarySE\n",
-    "library(ggplot2) # plotting library\n",
-    "library(ggpubr) # plotting\n",
-    "library(car) # Anova\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "## Loading Data\n",
-    "Let's load data. The first step is to read a CSV file into a dataframe, which is the data structure used by R to store data."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "\n",
-    "# TODO: Adapt the path to your own installation.\n",
-    "# Set the working directory\n",
-    "setwd(\"./\")\n",
-    "\n",
-    "# Read a csv file (header = T signals that the first line of the file contains the names of the variables).\n",
-    "# The <- operator assigns the result of read.csv to the variable moocs.\n",
-    "# moocs is a dataframe, similar to an excel worksheet or a DataFrame in pandas.\n",
-    "\n",
-    "moocs <- read.csv(file=\"moocs.basic.csv\", header = T)\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<table>\n",
-       "<caption>A data.frame: 6 × 18</caption>\n",
-       "<thead>\n",
-       "\t<tr><th scope=col>EPFL_AcademicYear</th><th scope=col>EPFL_IsRepeating</th><th scope=col>EPFL_PropaedeuticGPA</th><th scope=col>EPFL_CourseGrade</th><th scope=col>EPFL_StudentSection</th><th scope=col>MOOC_NVideosWatched</th><th scope=col>MOOC_AverageMaxVideosWatched</th><th scope=col>MOOC_PercentageVideosWatched</th><th scope=col>MOOC_NProblemsSolved</th><th scope=col>MOOC_AverageMaxProblemsSolved</th><th scope=col>MOOC_PercentageProblemsSolved</th><th scope=col>MOOC_Grade</th><th scope=col>EPFL_Topic</th><th scope=col>EPFL_BacGrade</th><th scope=col>EPFL_BacLevel</th><th scope=col>EPFL_CourseType</th><th scope=col>EPFL_UniqueTopicID_Anonymous</th><th scope=col>EPFL_AnonymousUserID</th></tr>\n",
-       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
-       "</thead>\n",
-       "<tbody>\n",
-       "\t<tr><td>2015-2016</td><td>0</td><td>  NA</td><td>3.5</td><td>IN</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>-Inf</td><td>MATH-111</td><td>0.8142857</td><td>HI</td><td>MATH</td><td>MATH-111 2015-2016 T19</td><td>3824714ee78feab0dbfcf503ca2f4982</td></tr>\n",
-       "\t<tr><td>2015-2016</td><td>0</td><td>4.51</td><td>3.5</td><td>SV</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>   0</td><td>MATH-111</td><td>0.6833333</td><td>LO</td><td>MATH</td><td>MATH-111 2015-2016 T19</td><td>07bea1a899d08b881015ae1018d6778b</td></tr>\n",
-       "\t<tr><td>2015-2016</td><td>1</td><td>4.43</td><td>4.5</td><td>SV</td><td> 1</td><td>29</td><td> 0</td><td>NA</td><td>NA</td><td>NA</td><td>   0</td><td>MATH-111</td><td>0.8571429</td><td>HI</td><td>MATH</td><td>MATH-111 2015-2016 T19</td><td>ba2579f42a4d5cee4fcea913fbff0a1e</td></tr>\n",
-       "\t<tr><td>2015-2016</td><td>0</td><td>4.75</td><td>5.0</td><td>EL</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>-Inf</td><td>MATH-111</td><td>0.8500000</td><td>HI</td><td>MATH</td><td>MATH-111 2015-2016 T19</td><td>b9a3e806bc1104c6dace2e2393ef19ab</td></tr>\n",
-       "\t<tr><td>2015-2016</td><td>0</td><td>3.62</td><td>3.0</td><td>GM</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>-Inf</td><td>MATH-111</td><td>0.7750000</td><td>LO</td><td>MATH</td><td>MATH-111 2015-2016 T19</td><td>b01e6559a855cf4c774ac9a6193d4268</td></tr>\n",
-       "\t<tr><td>2015-2016</td><td>0</td><td>2.95</td><td>3.0</td><td>GC</td><td> 2</td><td>29</td><td>10</td><td>NA</td><td>NA</td><td>NA</td><td>   0</td><td>MATH-111</td><td>0.6666667</td><td>LO</td><td>MATH</td><td>MATH-111 2015-2016 T19</td><td>15917ccf6bfad439511f4a1276500b40</td></tr>\n",
-       "</tbody>\n",
-       "</table>\n"
-      ],
-      "text/latex": [
-       "A data.frame: 6 × 18\n",
-       "\\begin{tabular}{r|llllllllllllllllll}\n",
-       " EPFL\\_AcademicYear & EPFL\\_IsRepeating & EPFL\\_PropaedeuticGPA & EPFL\\_CourseGrade & EPFL\\_StudentSection & MOOC\\_NVideosWatched & MOOC\\_AverageMaxVideosWatched & MOOC\\_PercentageVideosWatched & MOOC\\_NProblemsSolved & MOOC\\_AverageMaxProblemsSolved & MOOC\\_PercentageProblemsSolved & MOOC\\_Grade & EPFL\\_Topic & EPFL\\_BacGrade & EPFL\\_BacLevel & EPFL\\_CourseType & EPFL\\_UniqueTopicID\\_Anonymous & EPFL\\_AnonymousUserID\\\\\n",
-       " <fct> & <int> & <dbl> & <dbl> & <fct> & <int> & <int> & <int> & <int> & <int> & <int> & <dbl> & <fct> & <dbl> & <fct> & <fct> & <fct> & <fct>\\\\\n",
-       "\\hline\n",
-       "\t 2015-2016 & 0 &   NA & 3.5 & IN & NA & NA & NA & NA & NA & NA & -Inf & MATH-111 & 0.8142857 & HI & MATH & MATH-111 2015-2016 T19 & 3824714ee78feab0dbfcf503ca2f4982\\\\\n",
-       "\t 2015-2016 & 0 & 4.51 & 3.5 & SV & NA & NA & NA & NA & NA & NA &    0 & MATH-111 & 0.6833333 & LO & MATH & MATH-111 2015-2016 T19 & 07bea1a899d08b881015ae1018d6778b\\\\\n",
-       "\t 2015-2016 & 1 & 4.43 & 4.5 & SV &  1 & 29 &  0 & NA & NA & NA &    0 & MATH-111 & 0.8571429 & HI & MATH & MATH-111 2015-2016 T19 & ba2579f42a4d5cee4fcea913fbff0a1e\\\\\n",
-       "\t 2015-2016 & 0 & 4.75 & 5.0 & EL & NA & NA & NA & NA & NA & NA & -Inf & MATH-111 & 0.8500000 & HI & MATH & MATH-111 2015-2016 T19 & b9a3e806bc1104c6dace2e2393ef19ab\\\\\n",
-       "\t 2015-2016 & 0 & 3.62 & 3.0 & GM & NA & NA & NA & NA & NA & NA & -Inf & MATH-111 & 0.7750000 & LO & MATH & MATH-111 2015-2016 T19 & b01e6559a855cf4c774ac9a6193d4268\\\\\n",
-       "\t 2015-2016 & 0 & 2.95 & 3.0 & GC &  2 & 29 & 10 & NA & NA & NA &    0 & MATH-111 & 0.6666667 & LO & MATH & MATH-111 2015-2016 T19 & 15917ccf6bfad439511f4a1276500b40\\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/markdown": [
-       "\n",
-       "A data.frame: 6 × 18\n",
-       "\n",
-       "| EPFL_AcademicYear &lt;fct&gt; | EPFL_IsRepeating &lt;int&gt; | EPFL_PropaedeuticGPA &lt;dbl&gt; | EPFL_CourseGrade &lt;dbl&gt; | EPFL_StudentSection &lt;fct&gt; | MOOC_NVideosWatched &lt;int&gt; | MOOC_AverageMaxVideosWatched &lt;int&gt; | MOOC_PercentageVideosWatched &lt;int&gt; | MOOC_NProblemsSolved &lt;int&gt; | MOOC_AverageMaxProblemsSolved &lt;int&gt; | MOOC_PercentageProblemsSolved &lt;int&gt; | MOOC_Grade &lt;dbl&gt; | EPFL_Topic &lt;fct&gt; | EPFL_BacGrade &lt;dbl&gt; | EPFL_BacLevel &lt;fct&gt; | EPFL_CourseType &lt;fct&gt; | EPFL_UniqueTopicID_Anonymous &lt;fct&gt; | EPFL_AnonymousUserID &lt;fct&gt; |\n",
-       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
-       "| 2015-2016 | 0 |   NA | 3.5 | IN | NA | NA | NA | NA | NA | NA | -Inf | MATH-111 | 0.8142857 | HI | MATH | MATH-111 2015-2016 T19 | 3824714ee78feab0dbfcf503ca2f4982 |\n",
-       "| 2015-2016 | 0 | 4.51 | 3.5 | SV | NA | NA | NA | NA | NA | NA |    0 | MATH-111 | 0.6833333 | LO | MATH | MATH-111 2015-2016 T19 | 07bea1a899d08b881015ae1018d6778b |\n",
-       "| 2015-2016 | 1 | 4.43 | 4.5 | SV |  1 | 29 |  0 | NA | NA | NA |    0 | MATH-111 | 0.8571429 | HI | MATH | MATH-111 2015-2016 T19 | ba2579f42a4d5cee4fcea913fbff0a1e |\n",
-       "| 2015-2016 | 0 | 4.75 | 5.0 | EL | NA | NA | NA | NA | NA | NA | -Inf | MATH-111 | 0.8500000 | HI | MATH | MATH-111 2015-2016 T19 | b9a3e806bc1104c6dace2e2393ef19ab |\n",
-       "| 2015-2016 | 0 | 3.62 | 3.0 | GM | NA | NA | NA | NA | NA | NA | -Inf | MATH-111 | 0.7750000 | LO | MATH | MATH-111 2015-2016 T19 | b01e6559a855cf4c774ac9a6193d4268 |\n",
-       "| 2015-2016 | 0 | 2.95 | 3.0 | GC |  2 | 29 | 10 | NA | NA | NA |    0 | MATH-111 | 0.6666667 | LO | MATH | MATH-111 2015-2016 T19 | 15917ccf6bfad439511f4a1276500b40 |\n",
-       "\n"
-      ],
-      "text/plain": [
-       "  EPFL_AcademicYear EPFL_IsRepeating EPFL_PropaedeuticGPA EPFL_CourseGrade\n",
-       "1 2015-2016         0                  NA                 3.5             \n",
-       "2 2015-2016         0                4.51                 3.5             \n",
-       "3 2015-2016         1                4.43                 4.5             \n",
-       "4 2015-2016         0                4.75                 5.0             \n",
-       "5 2015-2016         0                3.62                 3.0             \n",
-       "6 2015-2016         0                2.95                 3.0             \n",
-       "  EPFL_StudentSection MOOC_NVideosWatched MOOC_AverageMaxVideosWatched\n",
-       "1 IN                  NA                  NA                          \n",
-       "2 SV                  NA                  NA                          \n",
-       "3 SV                   1                  29                          \n",
-       "4 EL                  NA                  NA                          \n",
-       "5 GM                  NA                  NA                          \n",
-       "6 GC                   2                  29                          \n",
-       "  MOOC_PercentageVideosWatched MOOC_NProblemsSolved\n",
-       "1 NA                           NA                  \n",
-       "2 NA                           NA                  \n",
-       "3  0                           NA                  \n",
-       "4 NA                           NA                  \n",
-       "5 NA                           NA                  \n",
-       "6 10                           NA                  \n",
-       "  MOOC_AverageMaxProblemsSolved MOOC_PercentageProblemsSolved MOOC_Grade\n",
-       "1 NA                            NA                            -Inf      \n",
-       "2 NA                            NA                               0      \n",
-       "3 NA                            NA                               0      \n",
-       "4 NA                            NA                            -Inf      \n",
-       "5 NA                            NA                            -Inf      \n",
-       "6 NA                            NA                               0      \n",
-       "  EPFL_Topic EPFL_BacGrade EPFL_BacLevel EPFL_CourseType\n",
-       "1 MATH-111   0.8142857     HI            MATH           \n",
-       "2 MATH-111   0.6833333     LO            MATH           \n",
-       "3 MATH-111   0.8571429     HI            MATH           \n",
-       "4 MATH-111   0.8500000     HI            MATH           \n",
-       "5 MATH-111   0.7750000     LO            MATH           \n",
-       "6 MATH-111   0.6666667     LO            MATH           \n",
-       "  EPFL_UniqueTopicID_Anonymous EPFL_AnonymousUserID            \n",
-       "1 MATH-111 2015-2016 T19       3824714ee78feab0dbfcf503ca2f4982\n",
-       "2 MATH-111 2015-2016 T19       07bea1a899d08b881015ae1018d6778b\n",
-       "3 MATH-111 2015-2016 T19       ba2579f42a4d5cee4fcea913fbff0a1e\n",
-       "4 MATH-111 2015-2016 T19       b9a3e806bc1104c6dace2e2393ef19ab\n",
-       "5 MATH-111 2015-2016 T19       b01e6559a855cf4c774ac9a6193d4268\n",
-       "6 MATH-111 2015-2016 T19       15917ccf6bfad439511f4a1276500b40"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "head(moocs)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Our dataset contains variables which name starts with *EPFL* and other variables starting with *MOOC*. The variables with EPFL come from the academic database and describe student's performance in their EPFL exams. The variables starting with MOOC conern their online activity in the MOOC."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<ol class=list-inline>\n",
-       "\t<li>'EPFL_AcademicYear'</li>\n",
-       "\t<li>'EPFL_IsRepeating'</li>\n",
-       "\t<li>'EPFL_PropaedeuticGPA'</li>\n",
-       "\t<li>'EPFL_CourseGrade'</li>\n",
-       "\t<li>'EPFL_StudentSection'</li>\n",
-       "\t<li>'MOOC_NVideosWatched'</li>\n",
-       "\t<li>'MOOC_AverageMaxVideosWatched'</li>\n",
-       "\t<li>'MOOC_PercentageVideosWatched'</li>\n",
-       "\t<li>'MOOC_NProblemsSolved'</li>\n",
-       "\t<li>'MOOC_AverageMaxProblemsSolved'</li>\n",
-       "\t<li>'MOOC_PercentageProblemsSolved'</li>\n",
-       "\t<li>'MOOC_Grade'</li>\n",
-       "\t<li>'EPFL_Topic'</li>\n",
-       "\t<li>'EPFL_BacGrade'</li>\n",
-       "\t<li>'EPFL_BacLevel'</li>\n",
-       "\t<li>'EPFL_CourseType'</li>\n",
-       "\t<li>'EPFL_UniqueTopicID_Anonymous'</li>\n",
-       "\t<li>'EPFL_AnonymousUserID'</li>\n",
-       "</ol>\n"
-      ],
-      "text/latex": [
-       "\\begin{enumerate*}\n",
-       "\\item 'EPFL\\_AcademicYear'\n",
-       "\\item 'EPFL\\_IsRepeating'\n",
-       "\\item 'EPFL\\_PropaedeuticGPA'\n",
-       "\\item 'EPFL\\_CourseGrade'\n",
-       "\\item 'EPFL\\_StudentSection'\n",
-       "\\item 'MOOC\\_NVideosWatched'\n",
-       "\\item 'MOOC\\_AverageMaxVideosWatched'\n",
-       "\\item 'MOOC\\_PercentageVideosWatched'\n",
-       "\\item 'MOOC\\_NProblemsSolved'\n",
-       "\\item 'MOOC\\_AverageMaxProblemsSolved'\n",
-       "\\item 'MOOC\\_PercentageProblemsSolved'\n",
-       "\\item 'MOOC\\_Grade'\n",
-       "\\item 'EPFL\\_Topic'\n",
-       "\\item 'EPFL\\_BacGrade'\n",
-       "\\item 'EPFL\\_BacLevel'\n",
-       "\\item 'EPFL\\_CourseType'\n",
-       "\\item 'EPFL\\_UniqueTopicID\\_Anonymous'\n",
-       "\\item 'EPFL\\_AnonymousUserID'\n",
-       "\\end{enumerate*}\n"
-      ],
-      "text/markdown": [
-       "1. 'EPFL_AcademicYear'\n",
-       "2. 'EPFL_IsRepeating'\n",
-       "3. 'EPFL_PropaedeuticGPA'\n",
-       "4. 'EPFL_CourseGrade'\n",
-       "5. 'EPFL_StudentSection'\n",
-       "6. 'MOOC_NVideosWatched'\n",
-       "7. 'MOOC_AverageMaxVideosWatched'\n",
-       "8. 'MOOC_PercentageVideosWatched'\n",
-       "9. 'MOOC_NProblemsSolved'\n",
-       "10. 'MOOC_AverageMaxProblemsSolved'\n",
-       "11. 'MOOC_PercentageProblemsSolved'\n",
-       "12. 'MOOC_Grade'\n",
-       "13. 'EPFL_Topic'\n",
-       "14. 'EPFL_BacGrade'\n",
-       "15. 'EPFL_BacLevel'\n",
-       "16. 'EPFL_CourseType'\n",
-       "17. 'EPFL_UniqueTopicID_Anonymous'\n",
-       "18. 'EPFL_AnonymousUserID'\n",
-       "\n",
-       "\n"
-      ],
-      "text/plain": [
-       " [1] \"EPFL_AcademicYear\"             \"EPFL_IsRepeating\"             \n",
-       " [3] \"EPFL_PropaedeuticGPA\"          \"EPFL_CourseGrade\"             \n",
-       " [5] \"EPFL_StudentSection\"           \"MOOC_NVideosWatched\"          \n",
-       " [7] \"MOOC_AverageMaxVideosWatched\"  \"MOOC_PercentageVideosWatched\" \n",
-       " [9] \"MOOC_NProblemsSolved\"          \"MOOC_AverageMaxProblemsSolved\"\n",
-       "[11] \"MOOC_PercentageProblemsSolved\" \"MOOC_Grade\"                   \n",
-       "[13] \"EPFL_Topic\"                    \"EPFL_BacGrade\"                \n",
-       "[15] \"EPFL_BacLevel\"                 \"EPFL_CourseType\"              \n",
-       "[17] \"EPFL_UniqueTopicID_Anonymous\"  \"EPFL_AnonymousUserID\"         "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# List the names of the variables\n",
-    "names(moocs)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Descriptive Statistics\n",
-    "\n",
-    "## Summary for variables"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       " EPFL_AcademicYear EPFL_IsRepeating EPFL_PropaedeuticGPA EPFL_CourseGrade\n",
-       " 2013-2014:2749    Min.   :0.0000   Min.   :1.690        Min.   :0.000   \n",
-       " 2014-2015:2694    1st Qu.:0.0000   1st Qu.:3.680        1st Qu.:3.000   \n",
-       " 2015-2016:3871    Median :0.0000   Median :4.250        Median :4.000   \n",
-       "                   Mean   :0.1846   Mean   :4.133        Mean   :3.719   \n",
-       "                   3rd Qu.:0.0000   3rd Qu.:4.630        3rd Qu.:5.000   \n",
-       "                   Max.   :1.0000   Max.   :5.890        Max.   :6.000   \n",
-       "                                    NA's   :1833                         \n",
-       " EPFL_StudentSection MOOC_NVideosWatched MOOC_AverageMaxVideosWatched\n",
-       " SV     :2199        Min.   : 1.00       Min.   :14.00               \n",
-       " GM     :1157        1st Qu.: 7.50       1st Qu.:44.00               \n",
-       " MT     :1128        Median :28.00       Median :45.00               \n",
-       " MA     :1040        Mean   :24.46       Mean   :48.95               \n",
-       " GC     : 970        3rd Qu.:39.00       3rd Qu.:58.00               \n",
-       " PH     : 649        Max.   :85.00       Max.   :85.00               \n",
-       " (Other):2171        NA's   :6339        NA's   :6339                \n",
-       " MOOC_PercentageVideosWatched MOOC_NProblemsSolved\n",
-       " Min.   :  0.00               Min.   :  1.00      \n",
-       " 1st Qu.: 20.00               1st Qu.:  3.00      \n",
-       " Median : 60.00               Median :  7.00      \n",
-       " Mean   : 54.28               Mean   : 10.67      \n",
-       " 3rd Qu.: 80.00               3rd Qu.: 14.00      \n",
-       " Max.   :100.00               Max.   :144.00      \n",
-       " NA's   :6339                 NA's   :7440        \n",
-       " MOOC_AverageMaxProblemsSolved MOOC_PercentageProblemsSolved   MOOC_Grade  \n",
-       " Min.   : 17.00                Min.   :  0.00                Min.   :-Inf  \n",
-       " 1st Qu.: 17.00                1st Qu.: 10.00                1st Qu.:-Inf  \n",
-       " Median : 20.00                Median : 30.00                Median :-Inf  \n",
-       " Mean   : 36.44                Mean   : 37.27                Mean   :-Inf  \n",
-       " 3rd Qu.: 25.00                3rd Qu.: 60.00                3rd Qu.:   0  \n",
-       " Max.   :142.00                Max.   :100.00                Max.   : 100  \n",
-       " NA's   :7440                  NA's   :7440                                \n",
-       "    EPFL_Topic   EPFL_BacGrade    EPFL_BacLevel EPFL_CourseType\n",
-       " CS-111  :1631   Min.   :0.1260   HI  :4346     CS  :2947      \n",
-       " CS-112  :1316   1st Qu.:0.7500   LO  :4249     EE  : 797      \n",
-       " EE-102  : 797   Median :0.8083   NA's: 719     MATH:1404      \n",
-       " MATH-111:1404   Mean   :0.8062                 PHYS:4166      \n",
-       " PHYS-101:4166   3rd Qu.:0.8536                                \n",
-       "                 Max.   :1.0000                                \n",
-       "                 NA's   :719                                   \n",
-       "         EPFL_UniqueTopicID_Anonymous\n",
-       " PHYS-101 2014-2015 T63: 336         \n",
-       " EE-102 2015-2016 T29  : 300         \n",
-       " MATH-111 2015-2016 T18: 295         \n",
-       " PHYS-101 2015-2016 T46: 295         \n",
-       " PHYS-101 2013-2014 T15: 288         \n",
-       " EE-102 2014-2015 T29  : 281         \n",
-       " (Other)               :7519         \n",
-       "                       EPFL_AnonymousUserID\n",
-       " e2e988bc1a66ae2f50330fd60a0c2367:   8     \n",
-       " 16af0f5438b6f7983392ab058a7e4eeb:   7     \n",
-       " 29e1b05939960835d785c0aaa20ae388:   7     \n",
-       " 35ad976f794b6523fe4dd3388b02ff5b:   7     \n",
-       " 4abf1bcbc3198f4f3c2feba5bca4f6e6:   7     \n",
-       " 4c46db8f7de7dd9b3521efad9efe0aa9:   7     \n",
-       " (Other)                         :9271     "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# For each variable, print some information about the distribution (if the variable is quantitative) \n",
-    "# or about the distinct values taken by the variable (if the variable is categorical). \n",
-    "\n",
-    "summary(moocs)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<dl class=dl-horizontal>\n",
-       "\t<dt>AUDIT</dt>\n",
-       "\t\t<dd>7</dd>\n",
-       "\t<dt>CGC</dt>\n",
-       "\t\t<dd>513</dd>\n",
-       "\t<dt>EDBB</dt>\n",
-       "\t\t<dd>1</dd>\n",
-       "\t<dt>EL</dt>\n",
-       "\t\t<dd>129</dd>\n",
-       "\t<dt>GC</dt>\n",
-       "\t\t<dd>970</dd>\n",
-       "\t<dt>GM</dt>\n",
-       "\t\t<dd>1157</dd>\n",
-       "\t<dt>IN</dt>\n",
-       "\t\t<dd>535</dd>\n",
-       "\t<dt>MA</dt>\n",
-       "\t\t<dd>1040</dd>\n",
-       "\t<dt>MT</dt>\n",
-       "\t\t<dd>1128</dd>\n",
-       "\t<dt>MX</dt>\n",
-       "\t\t<dd>168</dd>\n",
-       "\t<dt>PH</dt>\n",
-       "\t\t<dd>649</dd>\n",
-       "\t<dt>SC</dt>\n",
-       "\t\t<dd>346</dd>\n",
-       "\t<dt>SIE</dt>\n",
-       "\t\t<dd>472</dd>\n",
-       "\t<dt>SV</dt>\n",
-       "\t\t<dd>2199</dd>\n",
-       "</dl>\n"
-      ],
-      "text/latex": [
-       "\\begin{description*}\n",
-       "\\item[AUDIT] 7\n",
-       "\\item[CGC] 513\n",
-       "\\item[EDBB] 1\n",
-       "\\item[EL] 129\n",
-       "\\item[GC] 970\n",
-       "\\item[GM] 1157\n",
-       "\\item[IN] 535\n",
-       "\\item[MA] 1040\n",
-       "\\item[MT] 1128\n",
-       "\\item[MX] 168\n",
-       "\\item[PH] 649\n",
-       "\\item[SC] 346\n",
-       "\\item[SIE] 472\n",
-       "\\item[SV] 2199\n",
-       "\\end{description*}\n"
-      ],
-      "text/markdown": [
-       "AUDIT\n",
-       ":   7CGC\n",
-       ":   513EDBB\n",
-       ":   1EL\n",
-       ":   129GC\n",
-       ":   970GM\n",
-       ":   1157IN\n",
-       ":   535MA\n",
-       ":   1040MT\n",
-       ":   1128MX\n",
-       ":   168PH\n",
-       ":   649SC\n",
-       ":   346SIE\n",
-       ":   472SV\n",
-       ":   2199\n",
-       "\n"
-      ],
-      "text/plain": [
-       "AUDIT   CGC  EDBB    EL    GC    GM    IN    MA    MT    MX    PH    SC   SIE \n",
-       "    7   513     1   129   970  1157   535  1040  1128   168   649   346   472 \n",
-       "   SV \n",
-       " 2199 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# To get information about only one variable, use the $ sign to separate the name of \n",
-    "# the dataframe and the name of the variable like so: <name_dataframe>$<name_variable>\n",
-    "\n",
-    "# For nominal variables we get the count for the different categories \n",
-    "summary(moocs$EPFL_StudentSection)\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's \n",
-       "   0.00   20.00   60.00   54.28   80.00  100.00    6339 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# For a quantitative variable we get the ususal central tendency and dispersion indicators\n",
-    "summary(moocs$MOOC_PercentageVideosWatched)\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "54.2823529411765"
-      ],
-      "text/latex": [
-       "54.2823529411765"
-      ],
-      "text/markdown": [
-       "54.2823529411765"
-      ],
-      "text/plain": [
-       "[1] 54.28235"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "34.6713012975899"
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-      "text/latex": [
-       "34.6713012975899"
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-      "text/markdown": [
-       "34.6713012975899"
-      ],
-      "text/plain": [
-       "[1] 34.6713"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "60"
-      ],
-      "text/latex": [
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-      ],
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-       "[1] 60"
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-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
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-      ],
-      "text/latex": [
-       "100"
-      ],
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-       "100"
-      ],
-      "text/plain": [
-       "[1] 100"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "0"
-      ],
-      "text/latex": [
-       "0"
-      ],
-      "text/markdown": [
-       "0"
-      ],
-      "text/plain": [
-       "[1] 0"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# We can also compute these separately.\n",
-    "mean(moocs$MOOC_PercentageVideosWatched, na.rm=T) # na.rm removes missing values\n",
-    "sd(moocs$MOOC_PercentageVideosWatched, na.rm=T) # standard deviation\n",
-    "median(moocs$MOOC_PercentageVideosWatched, na.rm=T) # median (50% observations below and 50% observations above)\n",
-    "max(moocs$MOOC_PercentageVideosWatched, na.rm=T) # maximum\n",
-    "min(moocs$MOOC_PercentageVideosWatched, na.rm=T) # minimum"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
-    "    <strong>TODO</strong> : What is the mean and the standard deviation of the EPFL_CourseGrade ?\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
-       "  0.000   3.000   4.000   3.719   5.000   6.000 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "################\n",
-    "# Begin solution\n",
-    "\n",
-    "mean(moocs$EPFL_CourseGrade, na.rm=T) # na.rm removes missing values\n",
-    "sd(moocs$EPFL_CourseGrade, na.rm=T) # standard deviation\n",
-    "\n",
-    "\n",
-    "summary(moocs$EPFL_CourseGrade)\n",
-    "\n",
-    "# End solution\n",
-    "###############"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Defining new categorical variables\n",
-    "It is sometimes useful to transform a quantitative variable into a categorical variable. \n",
-    "\n",
-    "For example, below we create a variable that reflects whether students used the MOOC or not based on the number of videos they watched and the number of problems they attempted in the MOOC. In R, categorical variables are created with the function `factor`. The variable `didMOOC` is given the value `NO.MOOC` whenever the values for the number of videos watched and the number of problems attempted is missin. In other cases, the value is `MOOC`.   \n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<dl class=dl-horizontal>\n",
-       "\t<dt>MOOC</dt>\n",
-       "\t\t<dd>3004</dd>\n",
-       "\t<dt>NO.MOOC</dt>\n",
-       "\t\t<dd>6310</dd>\n",
-       "</dl>\n"
-      ],
-      "text/latex": [
-       "\\begin{description*}\n",
-       "\\item[MOOC] 3004\n",
-       "\\item[NO.MOOC] 6310\n",
-       "\\end{description*}\n"
-      ],
-      "text/markdown": [
-       "MOOC\n",
-       ":   3004NO.MOOC\n",
-       ":   6310\n",
-       "\n"
-      ],
-      "text/plain": [
-       "   MOOC NO.MOOC \n",
-       "   3004    6310 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "moocs$didMOOC = factor(\n",
-    "  ifelse(\n",
-    "      is.na(moocs$MOOC_NVideosWatched) & \n",
-    "      is.na(moocs$MOOC_NProblemsSolved), \n",
-    "    \"NO.MOOC\", \n",
-    "    \"MOOC\")\n",
-    ")\n",
-    "\n",
-    "summary(moocs$didMOOC)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<dl class=dl-horizontal>\n",
-       "\t<dt>NO.VIDEO</dt>\n",
-       "\t\t<dd>6591</dd>\n",
-       "\t<dt>SOME.VIDEO</dt>\n",
-       "\t\t<dd>2723</dd>\n",
-       "</dl>\n"
-      ],
-      "text/latex": [
-       "\\begin{description*}\n",
-       "\\item[NO.VIDEO] 6591\n",
-       "\\item[SOME.VIDEO] 2723\n",
-       "\\end{description*}\n"
-      ],
-      "text/markdown": [
-       "NO.VIDEO\n",
-       ":   6591SOME.VIDEO\n",
-       ":   2723\n",
-       "\n"
-      ],
-      "text/plain": [
-       "  NO.VIDEO SOME.VIDEO \n",
-       "      6591       2723 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# We consider that not taking the MOOC is like not watching videos\n",
-    "moocs$watched_videos = factor(\n",
-    "                          ifelse(\n",
-    "                            moocs$MOOC_PercentageVideosWatched == 0 |\n",
-    "                            is.na(moocs$MOOC_PercentageVideosWatched),\n",
-    "                            \"NO.VIDEO\",\n",
-    "                            \"SOME.VIDEO\")\n",
-    "                          )\n",
-    "\n",
-    "summary(moocs$watched_videos)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<dl class=dl-horizontal>\n",
-       "\t<dt>NO.PROBLEM</dt>\n",
-       "\t\t<dd>7621</dd>\n",
-       "\t<dt>SOME.PROBLEM</dt>\n",
-       "\t\t<dd>1693</dd>\n",
-       "</dl>\n"
-      ],
-      "text/latex": [
-       "\\begin{description*}\n",
-       "\\item[NO.PROBLEM] 7621\n",
-       "\\item[SOME.PROBLEM] 1693\n",
-       "\\end{description*}\n"
-      ],
-      "text/markdown": [
-       "NO.PROBLEM\n",
-       ":   7621SOME.PROBLEM\n",
-       ":   1693\n",
-       "\n"
-      ],
-      "text/plain": [
-       "  NO.PROBLEM SOME.PROBLEM \n",
-       "        7621         1693 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# We consider that not taking the MOOC is like not solving any problems\n",
-    "moocs$solved_problems = factor(\n",
-    "                          ifelse(\n",
-    "                            moocs$MOOC_PercentageProblemsSolved == 0 |\n",
-    "                              is.na(moocs$MOOC_PercentageProblemsSolved),\n",
-    "                            \"NO.PROBLEM\",\n",
-    "                            \"SOME.PROBLEM\")\n",
-    "                          )\n",
-    "\n",
-    "summary(moocs$solved_problems)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Checking activity types\n",
-    "Do people who solve problems also watch videos ? When using a MOOC, some students only watch videos and don't do exercices. But most of the students who do exercices also watch videos. It appears that almost nobody is *only* solving problems. \n",
-    "> **Problem**: If we use these variables as two factors to analyse our data set we'll have very uneven groups.     \n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "            \n",
-       "             NO.PROBLEM SOME.PROBLEM\n",
-       "  NO.VIDEO         6555           36\n",
-       "  SOME.VIDEO       1066         1657"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# With two arguments, the table command cross-tabulates the number of observations per category.\n",
-    "table(moocs$watched_videos, moocs$solved_problems)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
-    "    <strong>TODO</strong> : To fix this problem we qualify MOOC usage with three categories: \n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "* `NONE` corresponds to no use of MOOCs, \n",
-    "* `WATCH` corresponds to students mainly watching videos and \n",
-    "* `DO` corresponds to students doing some exercices."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<dl class=dl-horizontal>\n",
-       "\t<dt>DO</dt>\n",
-       "\t\t<dd>1693</dd>\n",
-       "\t<dt>NONE</dt>\n",
-       "\t\t<dd>6555</dd>\n",
-       "\t<dt>WATCH</dt>\n",
-       "\t\t<dd>1066</dd>\n",
-       "</dl>\n"
-      ],
-      "text/latex": [
-       "\\begin{description*}\n",
-       "\\item[DO] 1693\n",
-       "\\item[NONE] 6555\n",
-       "\\item[WATCH] 1066\n",
-       "\\end{description*}\n"
-      ],
-      "text/markdown": [
-       "DO\n",
-       ":   1693NONE\n",
-       ":   6555WATCH\n",
-       ":   1066\n",
-       "\n"
-      ],
-      "text/plain": [
-       "   DO  NONE WATCH \n",
-       " 1693  6555  1066 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "#################\n",
-    "# Begin Solution:\n",
-    "\n",
-    "moocs$MOOC <-     factor(\n",
-    "        ifelse(moocs$watched_videos == \"NO.VIDEO\" & moocs$solved_problems == \"NO.PROBLEM\", \n",
-    "               \"NONE\", \n",
-    "               \n",
-    "              ifelse(moocs$solved_problems == \"SOME.PROBLEM\",\n",
-    "                    \"DO\",\n",
-    "                    \"WATCH\")\n",
-    "              \n",
-    "              )\n",
-    "    )\n",
-    "\n",
-    "\n",
-    "\n",
-    "# End Solution \n",
-    "###############\n",
-    "\n",
-    "summary(moocs$MOOC)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The order of the categories is a bit 'unlogical'. We'd like to have them appear in outputs and graphs sorted by increasing level of involvement: NONE, WATCH and DO. Let's fix this problem by reordering the levels of the factor."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "install.packages(\"gdata\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       " NONE WATCH    DO \n",
-       " 6555  1066  1693 "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "library(gdata)\n",
-    "# put the levels into a convenient order (for graphing, etc.)\n",
-    "moocs$MOOC <- reorder(moocs$MOOC, new.order=c(\"NONE\", \"WATCH\", \"DO\"))\n",
-    "table(moocs$MOOC)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Do people who use the MOOC get better grades ?\n",
-    "\n",
-    "## Looking at the means.\n",
-    "Let's start by looking at the mean grade for the three groups of our variable `MOOC`. The `ddply` function allows to apply a function to a subset of the data defined by a categorical variable (`MOOC` in our case). The ddply returns a new data frame with the category and the result."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "library(plyr)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<table>\n",
-       "<caption>A data.frame: 3 × 2</caption>\n",
-       "<thead>\n",
-       "\t<tr><th scope=col>MOOC</th><th scope=col>grp.mean</th></tr>\n",
-       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
-       "</thead>\n",
-       "<tbody>\n",
-       "\t<tr><td>NONE </td><td>3.513959</td></tr>\n",
-       "\t<tr><td>WATCH</td><td>3.828799</td></tr>\n",
-       "\t<tr><td>DO   </td><td>4.445363</td></tr>\n",
-       "</tbody>\n",
-       "</table>\n"
-      ],
-      "text/latex": [
-       "A data.frame: 3 × 2\n",
-       "\\begin{tabular}{r|ll}\n",
-       " MOOC & grp.mean\\\\\n",
-       " <fct> & <dbl>\\\\\n",
-       "\\hline\n",
-       "\t NONE  & 3.513959\\\\\n",
-       "\t WATCH & 3.828799\\\\\n",
-       "\t DO    & 4.445363\\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/markdown": [
-       "\n",
-       "A data.frame: 3 × 2\n",
-       "\n",
-       "| MOOC &lt;fct&gt; | grp.mean &lt;dbl&gt; |\n",
-       "|---|---|\n",
-       "| NONE  | 3.513959 |\n",
-       "| WATCH | 3.828799 |\n",
-       "| DO    | 4.445363 |\n",
-       "\n"
-      ],
-      "text/plain": [
-       "  MOOC  grp.mean\n",
-       "1 NONE  3.513959\n",
-       "2 WATCH 3.828799\n",
-       "3 DO    4.445363"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "mu <- ddply(moocs, \"MOOC\", summarise, grp.mean=mean(EPFL_CourseGrade))\n",
-    "mu\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Looking at the variance ?\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<table>\n",
-       "<caption>A data.frame: 3 × 3</caption>\n",
-       "<thead>\n",
-       "\t<tr><th scope=col>MOOC</th><th scope=col>grp.sd</th><th scope=col>grp.mean</th></tr>\n",
-       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
-       "</thead>\n",
-       "<tbody>\n",
-       "\t<tr><td>DO   </td><td>1.197095</td><td>4.445363</td></tr>\n",
-       "\t<tr><td>NONE </td><td>1.490969</td><td>3.513959</td></tr>\n",
-       "\t<tr><td>WATCH</td><td>1.325802</td><td>3.828799</td></tr>\n",
-       "</tbody>\n",
-       "</table>\n"
-      ],
-      "text/latex": [
-       "A data.frame: 3 × 3\n",
-       "\\begin{tabular}{r|lll}\n",
-       " MOOC & grp.sd & grp.mean\\\\\n",
-       " <fct> & <dbl> & <dbl>\\\\\n",
-       "\\hline\n",
-       "\t DO    & 1.197095 & 4.445363\\\\\n",
-       "\t NONE  & 1.490969 & 3.513959\\\\\n",
-       "\t WATCH & 1.325802 & 3.828799\\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/markdown": [
-       "\n",
-       "A data.frame: 3 × 3\n",
-       "\n",
-       "| MOOC &lt;fct&gt; | grp.sd &lt;dbl&gt; | grp.mean &lt;dbl&gt; |\n",
-       "|---|---|---|\n",
-       "| DO    | 1.197095 | 4.445363 |\n",
-       "| NONE  | 1.490969 | 3.513959 |\n",
-       "| WATCH | 1.325802 | 3.828799 |\n",
-       "\n"
-      ],
-      "text/plain": [
-       "  MOOC  grp.sd   grp.mean\n",
-       "1 DO    1.197095 4.445363\n",
-       "2 NONE  1.490969 3.513959\n",
-       "3 WATCH 1.325802 3.828799"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "sigma <- ddply(moocs, \"MOOC\", summarise, grp.sd=sd(EPFL_CourseGrade))\n",
-    "#head(sigma)\n",
-    "\n",
-    "info <- merge(sigma, mu)\n",
-    "info\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Plotting\n",
-    "To further investigate the difference between the ghree groups, let's plot the grade of the students `EPFL_CourseGrade` against the categorical variable `MOOC` that we just defined.  We'll use three different plots: \n",
-    "\n",
-    "* boxplot, \n",
-    "* histogram and \n",
-    "* mean plots.\n",
-    "\n",
-    "### Boxplots\n",
-    "\n",
-    "Boxplots allow to visualise the distribution of the variable. The central line in the box shows the median and the edges of the boxes show the interquartiles. A simple tutorial for variations of this type of plot is available here: http://www.sthda.com/english/wiki/ggplot2-box-plot-quick-start-guide-r-software-and-data-visualization.\n",
-    "\n",
-    "From the plot below, it seems that the distribution of grades for people who did not use the MOOC (`NONE`) tends to be lower in the grade scale than the grades of people who `WATCH` videos or people who `DO` assignments. From the shape of the boxesm we also see that the distributions for `NONE` and `WATCH` are more symmetric than for `DO`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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9bR/MD7dONMiJUCYgUJxDKAWEECsQwg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\n+tiyjMql2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-      "text/plain": [
-       "Plot with title “Grade by Activity Level”"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# Setting the size of plots generated with ggplot below. \n",
-    "options(repr.plot.width = 5, repr.plot.height = 5)\n",
-    "\n",
-    "# Quick and simple boxplot\n",
-    "boxplot(moocs$EPFL_CourseGrade ~ moocs$MOOC, main=\"Grade by Activity Level\", xlab=\"Activity Level\", ylab=\"Grade\")\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "install.packages(ggplot2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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HkHDhx455136ow7HI533303MzPTnZ4VTz31lCRJK1asaMxJmpKnFWiF0WicNm3a\ntGnTmqAaAAAANAGbzSaEWFdUsq6o5FrOU1ZW1vjJnTp1mjFjxuzZs++55x6LxeIeP3XqlM1m\nS09PrzM/Kiqqffv2hw8fbsxJFIWFhbVXpsPCwpQmZN+6eoBWHD9+fN++fVarNTo6ulevXp07\nd/Z5KQAAAGgaBoNBCNHKaOgUUTeDNtKpKvtZe7XZbFZ11OzZs99+++158+Y9/fTT7kGlPbje\nlgzlqcacRJGQkLBhwwb3w3rPee2uHqBzcnIef/zx3bt31x7s06fP/PnzR44c6Y+aAAAA4FdK\ngL6hVcsne3T17gyvHj3x7skzagN0VFTU//3f/82YMeOXv/ylezA5Odlisezbt6/OZKvVeurU\nqUmTJjXmJIqA6IFesmTJmDFjdu/e3bdv34ceemjmzJkPPfRQ3759d+/efcsttyxZssTf9QEA\nACCYTJs2LSUlZfbs2e4Ro9E4ceLEZcuWFRQU1J45d+5cWZbvu+++xpykKXlagT5w4EBWVlan\nTp1WrVo1YMCA2k/t3Llz8uTJWVlZgwYN8sfmIAAAAAhKOp1uwYIFo0aNqr2Z27x583Jzc4cO\nHTpnzpz+/ftbrdaVK1cuWrToxRdfrDdq1nsSIYTD4dizZ0/tkU6dOkVHR/v4LXh4bsGCBSaT\nKScnp056FkIMGDAgJyfHZDItWLDAtwUBAAAguI0YMeKOO+6orq52j8TFxeXl5d17771z587t\n06fPrbfeeujQoY8//vixxx5r/EmEECUlJX3+2+eff+7z+j2tQG/atGnixIkdO3as99mOHTtO\nmDDhiy++8HlNAAAACCYLFy6sM7JmzZo6IzExMS+88MILL7zg9UkWLlx45Rx/8BSgi4qK3NtW\n16tHjx6rVq3ydUkAAABoCl+eL532Vd1L9xrprL366pOClKcAbTabKysrPUyorKxUe+klAAAA\nNNeqVat27dpZrdbCeraJE0KImpqaqqoqs9ms7NdRD5M5IaZlYmKi/4oMWJ4CdFpa2oYNG/70\npz81NGHDhg1paWl+qAoAAAB+FBER4flmfjk5OXPnzn3wwQfHjRvXZFU1F54uIhw/fvy///3v\nN954o95nFy1atH379vHjx/unMAAAACAQeQrQWVlZaWlpWVlZmZmZeXl5yo0Qa2pq8vLyMjMz\nf/3rX/fo0eNXv/pVU5UKAAAAaM9TC0d4ePinn346duzY5cuXL1++XJIki8Vis89SgzgAACAA\nSURBVNmUeyr27t177dq14eHhDR2ek5Pz6quvLl++3L333rPPPrtz586FCxe67wT+17/+dfv2\n7W+//bbysKqqasqUKU6n86233oqMjLTb7RMmTGjo/GvXrq2url6zZk1ubu6ZM2f0en1SUlL/\n/v3Hjh0bERGxZMmSf//732+99VbtQx588MGMjIysrKxGfW0AAABCVUREhPvfqOMqt/Ju3779\nzp07V6xY8cEHH+zfv99qtSYlJaWnp48fP/7++++vs3N1HRkZGbIs79mzZ+jQoUIIp9N54MCB\nhISEPXv2uAP03r17a99ucfPmzZ06dTIYDDk5OePGjTOZTO69SL777rvXXnvt0UcfTU5OVkYq\nKytnzZp17ty58ePHp6SkREREnDp16rPPPjObzTTrAAAAXIuBAwe+/vrr3bp107qQQHSVAC2E\nMBqNU6dOnTp1qtpTx8XFtW3bdu/evUqAPnr0qBDijjvuyM/Pv/vuu4UQpaWlp0+frr3GvH79\n+rFjx+r1+r///e933XWXJEnuqK3sB9K2bVv3yGuvvXbmzJlXX301KSlJGencufPQoUOtVqva\nUgEAAEJHI9eV+/fv38gTSpJ0DeU0P1cP0Irjx4/v27fParVGR0f36tXLnWI9y8jIyMvLU/68\nd+/e9PT0Pn36vPPOOw6Hw2AwKDdadK9AHzp0qLi4+KabbtLpdIsXL66zOF2H0+ncunXryJEj\n3enZTdXdGquqqkpLS90PTSZTWFhY4w9XS6fT2Wy24uJiu93uv1cJHSaTyeVyORwOrQsJBpWV\nlXq9vqKiwuVyaV1Ls1dRUaF1CUCDZFkuKSnRuopgYDabExMTdTqdX5ODn4KpTufpKjhc1dUD\ndE5OzuOPP7579+7ag3369Jk/f/7IkSM9H5uRkfHJJ58UFha2bdt2z549gwcPbt++vcViOXTo\nUK9evfbs2dOxY8eYmBhl8vr16wcPHqxsLD1kyJD169d7CNDnzp2z2+0dOnTw8OoXLlwYO3as\n5wp37NhR+xaRixYtuvK+5b61bt06DzsDAgDgV9XV1Q888IDWVQSJZ5999tZbb/XrSyhbOPic\n5xt9eMFisYTUIvRVAvSSJUsefvhhl8vVt2/ffv36xcTElJWV7dq1Kz8//5Zbblm8ePH06dM9\nHJ6enh4WFrZ37964uLjDhw8rV++lp6fv2bOnV69e7u4OIUR5eXlubu4zzzyjPBw1atTMmTNL\nS0tjY2O9fm/R0dFz5sypPfLss8/WmZOQkDBq1Cj3w6ioqDp3VPctnU6XmJg4cuRI5UJMXCPl\n/1W+mD4hSZIkSSw/+8SZM2e+/fZbrasA6qfT6dzffHEtJElKTEx0OBx+/eSUZVmvb2y/QOM1\npuaSkpLXX3/9l7/8pfvyM7h5+is5cOBAVlZWp06dVq1aVWdddufOnZMnT87Kyho0aFDPnj0b\nOoPFYklJSdm7d29iYmJkZKTyF9C7d+8NGzacPHny4sWL7jXmnJwch8Px5JNPuo91uVyfffbZ\nvffeW++Z4+LizGZzQUGBp/em19dpNbnyP8GePXvWvuW61Wr16+9eDQbD9ddfn5aW5vOf/EKT\nxWJxOp1+/ZkndERFRRmNxtLSUjL0tVu/fj0BGgHLaDQ+/vjjWlcRDCIiIsLDw61Wq187CQ0G\ng1Z3fd6/f//WrVv79OlDgL6SpwC9YMECk8mUk5PTsWPHOk8NGDAgJyfnuuuuW7BgQXZ2toeT\n9OnTZ+3atfHx8b1791ZGevXq9frrr3/55Zd6vV4J37Isf/rpp3feeWftxeCtW7d+9tlnEyZM\nqLdNR6/X33zzzRs3brzrrrvqtEErjdqe3jQAAAA8Un7By6956+WphXzTpk0TJ068Mj0rOnbs\nOGHChC+++MLzC2RkZFRWVn7++efuAJ2YmBgfH79mzZq0tDSTySSE2L17d3Fx8a233tqhlttu\nu+3ChQtfffVVQ2eeMmVKYmLi73//+w8//PDAgQPHjx/fsmXLk08+uWnTJs8lAQAAAF7ztAJd\nVFTUo0cPDxN69OixatUqzy+Qmpqq3H7FHaCFEL169crJyXH3b6xfv75z585t27atfWBcXFz3\n7t3Xr19/ww031HvmyMjIl156ac2aNZs3b161apXBYGjTps2QIUPGjBnjuSQAAAB8+eWXFy9e\nbOjZQ4cOCSEOHDjgoQm7RYsWw4YNC6nLBxWSh5X56OjoRx991MOWEXPmzHn55ZfLysr8U5sG\nmqCTKTo6uqqqih5on6AH2ofogfah9evXv/LKKwU/Czvfj42irlXf2Q4hCyHE2cG60z/142Zh\nIaLHKzWxVvM///lPrQsJBk3WA+2PxtSKiori4uJJkyZd+6n+9re/paSktGjRIqRitKcV6LS0\ntA0bNngI0Bs2bEhLS/NDVQAAAPCjy5cvCyEqO+jOX+9l8G253xX1naycJ9R4CtDjx4//wx/+\n8MYbb/zqV7+68tlFixZt3779z3/+s99qAwAAgB/Z48T5AV7+rsx8To76LkQvMfT0JcvKykpL\nS8vKysrMzMzLy1O28q6pqcnLy8vMzPz1r3/do0ePerM1AAAAoHjzzTd1Ol3tW2COHTtWkqTa\n9+n7zW9+U/tyuIqKiqioKIvFcuHCBSHEpUuXpIYJIWw229y5czMyMiIiIlq2bNm/f/+nn35a\naTOeMWNGu3bt6pTUtWvXhx9+2Ot35GkFOjw8/NNPPx07duzy5cuXL18uSZJyOaDSNt27d++1\na9eGh4d7/doAAAAIeqNHj5ZlOScnZ/LkyUKImpqaLVu2dOjQ4fPPP+/Tp48yJycnZ/To0e5D\nVqxY0bt3b5PJ9NZbb/3hD3+wWCzutL1r167p06evXLnSvddFWVnZ0KFDT548OWvWrAEDBsTE\nxBw8eHDp0qUtWrT4wx/+4I93dJV727Rv337nzp0rVqz44IMP9u/fb7Vak5KS0tPTx48ff//9\n9xuNRn/UBAAAgKCRnJzcrVs3d4DeuXOnJEm/+93v1q9fr9zWR7mB6x//+Ef3IYsXL/7d735n\nMpmefvrpRx99VKfTuXdvU9aVU1NT3SPTp08/evTovn37unbtqoxkZGRMnjz53LlzfnpHV785\npNFonDp16tSpU/1UAQAAADSht8mWQi/7mPWXVBw4evToNWvWKH/euHHjsGHDbrnllieffLK6\nutpkMn3++edCCPcN9XJzc48dOzZhwoSwsLBf//rXdRan63A4HH//+98zMzPd6dktPj5e3Vtq\nNN/fXR0AAAABrry8XAgRfUiOPlRzLecpKSlRbizt2ahRo1577bUjR46kpqbm5OTcc889PXv2\njIqKys3NHTFiRE5OTq9evVq3bq1MfuONN8aPH9+iRQshxL333rt48WIPAfrUqVOVlZXp6eke\nXr2wsPDKXfZq3wBbLU8B2m63N+YUWt2iHQAAAN5R4mlVomTt5uU2dpHH5IjTcqtWrRozefjw\n4Xq9Picnp127djt27HjjjTeUwZycnBEjRmzcuNG9KfX58+dXr16trEkLIaZOnTp48OAzZ860\nadOm3jM35mbjCQkJGzZsqD0yduzYxpTdkKtcRNiYU3CTdAAAgOZFp9MJIWxtpcJbvbxFUbtP\nnBGn5bCwRh0eFRU1YMCAnJyczp07t2rVSrn+b+TIkX/729/uu+++oqIi9xrzW2+9VV1dPXz4\ncPexTqdz6dKlDd2ZJDk5OSIiYv/+/R5e3WAwuBumFdd4Id9VWjjMZvPAgQMb+aUBAAAA6jV6\n9OhXXnmlQ4cOI0eOVEZGjBjx0EMPvf/++0ajcciQIUIIWZb/+te/PvLII7Wvvvv73/++ZMmS\nJ598st5EajQa77333rfffvvRRx+t0wZ97tw5P7VBewrQXbp0OXbs2JEjR6ZMmTJ16tQuXbr4\nowIAAAAEvdGjR8+ZMyc7O/svf/mLMtK5c+f27du//PLLgwcPtlgsQojPPvvs2LFjDz30ULdu\n3dwHPvzww88///zHH39855131nvmefPm7dixo3///rNmzbrhhhuio6OVbex+8pOf+GkbO083\nUjl69OimTZuGDx/+8ssvp6SkjBgxYuXKlVVVVf6oAwAAAEHshhtuiIqKqqiocK9ACyFGjBhR\nUVHhvp7vjTfeyMjIqJ2ehRDJycmDBg1avHhxQ2eOjY3Ny8v7/e9/v3Llyttuu2348OELFy68\n4447ruVWKZ55WoGWJGn48OHDhw8vKytbtWpVdnb2z3/+85iYmMmTJ0+bNu3666/3U00AAAAI\nMnq93mq11hnMzs7Ozs52P/zXv/5V77Fffvml+8/Dhg278gK8iIiIp5566qmnnrry2IULFy5c\nuLDO4Hfffdf4yq/UqG3sYmJisrKysrKy9uzZk52dvXLlykWLFs2fP99Pq+IAAADwK2Vbt1b5\nrlb5Lq1raX7U7QPdtWvXjIyMHTt27Nq169KlS36qCQAAAH7VunXrESNGXLkk7HbhwoUTJ04k\nJycnJCQ0NMdisXTq1Mk/BQa0xgbo3Nzc7Ozs999/v7Ky8sYbb1y6dOnEiRP9WhkAAAD8xGg0\n1tvw4JaTkzN37txx48aNGzeuyapqLq4SoIuLi5cvX/7mm28ePnw4ISHh4YcfnjZtWlpaWtMU\nBwAAAAQaTwH6zjvvXLdunSzLt9xyy9y5c8eOHWswGJqsMgAAACAAeQrQa9euNZvNd911V9u2\nbbdv3759+/Z6p7300kv+qQ0AAADaaN26tU6nS0xM1LqQQHSVFg673f7uu+96nkOABgAACDLp\n6enr1q0zmUxaFxKIPAXor776qsnqAAAAQNNo0aKFD6eJHzfFCx2eAnS/fv2arA4AAACgWVC3\nDzQAAACaO5/fzaNFixYhtQit07oAAAAABJxjx47de++9+/fv17qQQESABgAAQF3ff//92bNn\nv/vuO60LCUQEaABA4CoaqhNC2FuJi+kh9NthAAGOAA0ACFw6lxBCmEuFI5oADSBQcBEhACBQ\nyaLlfvmHP3wjnx1MhgZ8xuVyvf3222VlZQ1NKCwsFEJs2rTp+++/b2hORETEL37xC6PR6JcS\nAxgBGgAQoCJOuowX5X79+n399dct97rODua3poDPnDlz5p133rnqtAMHDhw4cMDDhJtvvrlH\njx6+q6t5IEADAAJU7H5ZCDF58mSn07l7927TBbm6FYvQgG+4XC4hRHTnEUk3/s67M5zNz774\n7VpZln1aV/PAT/MAgIAki5YHZIvFMnDgwFGjRgkhWh4Ixe/TgF+FGSOMUW29+yfMFNn4F5ox\nY4YkSZIkhYWFxcTE9O3b97HHHisoKKg9p7y8fPbs2d26dTObzTExMaNGjVq/fr2v37FvEKAB\nAIEo8oRssMqDBw82Go3Dhw8PCwtruc+ldVEAvNe6detDhw4dOHDgs88+e/jhhz///POePXtu\n2rRJeba0tPSGG25YuXLlrFmz8vPz161b171799tvv33+/Pnall0vWjgAAIFIicvDhg0TQkRH\nR2dkZOTn55vPyfZ4ujiAZkmv13fv3l3584ABAzIzM4cPH/7AAw8cO3bMZDIpC9KHDh3q0KGD\nMmfQoEHh4eFPPPHE7bffHmht1qxAAwACjiSLmAOuyMjIjIwMZWTo0KFC/LgpB4Dmz2g0PvHE\nE4WFhV9++aXD4Xj33XczMzPd6Vnx1FNPSZK0YsUKrYpsCCvQAICAE3lMNlwSN912k8FgUEYG\nDRr06quvxu6pKRrB0g/gM/ayggsHP/Ty2AtHhRDXchFhenq6EOLYsWOdOnWy2WzKw9qioqLa\nt29/+PBhr1/CTwjQAICA03KvSwgxZMgQ90iLFi369Omzc+fO8BJRlaBdZUCwKC8vF0LYivfZ\nivddy3nOnj173XXXeXesEr4lSXL/oaE5gYYADQAILJJTxBx0RUdH9+rVq/b40KFDd+7c2XKv\ns2p0mFa1AUEjKipKCNGibd9WPcd7d4bSw59UFGxLTEz0uoZ9+/YJIbp06ZKcnGyxWJSHtVmt\n1lOnTk2aNMnrl/ATAjQAILBEHZX1NjF07NCwsP8KyoMGDTIajbF7HWdGa1UaEGyMkW2iu4zy\n7tjKs/srCq4+rSGXL19+8cUX27Vrd9NNNxmNxokTJy5btuyJJ56o3QY9d+5cWZbvu+8+71/G\nPwjQAIDA0nKfU/x3/4YiPDy8f//+ubm5ljOyrQ17cQDNTE1NzbfffiuEqKio2Lt372uvvfbd\nd9+tXbtWuRP4vHnzcnNzhw4dOmfOnP79+1ut1pUrVy5atOjFF1/s2bOn1rXXRYAGAAQQqUaO\nOSTHxsbWu2vVkCFDcnNzW+5z2drQxQE0M2fPnk1LS9PpdC1atOjcufOoUaPWrFnjXm+Oi4vL\ny8t74YUX5s6dW1BQYDab+/Xr9/HHH//kJz/Rtux6EaABAAEk+ogcZhdDbxuq09Wz28bAgQPD\nw8Nj99oLxwjBGjTQfCxcuHDhwoWe58TExLzwwgsvvPBC05R0LQjQAIAAouy/oez6fCWTyTRg\nwIAtW7ZEnJYrk0nQwLWqqSqrOnfIu2OdVaW+LaYZIUADAAKFziFiDouEhIRu3bo1NGfIkCFb\ntmxpuddVmUwXB+A95Zc85QXbygu2Xct56lzsGyII0ACAQBF9yKWrlocOHVrvdrCKAQMGRERE\nxO63nb6dLg7Ae23atHn44YetVmtDE06cOLF9+/a+ffumpqY2NMdisXTt2tU/BQY0AjQAIFDE\n7pdFw/0bCoPBMHDgwI0bN7YokC91JEEDXtLpdBMnTvQwIScnZ/v27YMHDx43blyTVdVccENU\nAEBACLssog67kpKSrrqgpSTslvtcTVIXANRFgAYABITob1w6hxg2bNhVZ15//fWRkZGx+2SJ\nCA1ACwRoAEBAiN139f4NhV6vv/HGG/WVcovvZf/XBYSolJSULl26pKWlaV1IICJAAwC0F1Yl\nR30nJycnd+zYsTHzlZwdSxcH4DcdOnRYunRp9+7dtS4kEHERIQBAey0PylKNPHz48EbO79On\nT0xMTM03ZSfHhsmhuIkWcE0iIyO1LqF5YwUaAKA95f4pN910UyPn63S6wYMH6ytF5HcsQgNo\nagRoAIDG9JUi8pjcuXPn9u3bN/6oH7o49tMGDaCpEaABABpr+Y1LcjXq8sHarrvuuri4uJiD\nslRDhgbQpAjQAACNKf0bQ4YMUXWU0sURViVHH/VPWQDQAAI0AEBLhgrR4nu5W7duSUlJao9V\nNo3mjioAmhgBGgCgpZb7XZKsun9D0b1799atW8ccknUOn9cFAA1iGzsA8Ivktc5261gZvTqd\nQ0iSdPPNN3txrCRJN9100z/+8Y9ecx1CJ/m8tuCjs8vCrHURQPNHgAYAH+vevXunTp2qqqq0\nLqTZ6Nu3b3x8vHfH/uQnP8nPz7fb7b4tKVhJMVJ6errWVQDNniTLXLz8H1ar1eHw4y8CDQZD\ndHR0VVVVZWWl/14ldFgsFqfTWV1drXUhwSAqKspoNJaWlrpcLJr6QGxsbGlpqdZVBAOdThcb\nG1tdXV1RUaF1LcHAbDbrdDqbzaZ1IcEgIiIiPDy8aZKD/84P79ADDQAAAKhAgAYAAABUIEAD\nAAAAKhCgAQAAABUI0AAAAIAKBGgAAABABQI0AAAAoAIBGgAAAFCBAA0AAACoQIAGAAAAVCBA\nAwAAACoQoAEAAAAVCNAAAACACgRoAAAAQAUCNAAAAKACARoAAABQgQANAAAAqECABgAAAFQg\nQAMAAAAqEKABAAAAFQjQAAAAgAoEaAAAAEAFAjQAAACgAgEaAAAAUIEADQAAAKhAgAYAAABU\nIEADAAAAKhCgAQAAABUI0AAAAIAKBGgAAABABQI0AAAAoAIBGgAAAFCBAA0AAACoQIAGAAAA\nVCBAAwAAACoQoAEAAAAVCNAAAACACgRoAAAAQAUCNAAAAKCCXusCAECF+fPnnzx5Uusqrk6v\n19fU1GhdRf3GjRs3YsSIOoMFBQWvvPKKw+HQpCTP9Hq9LMtOp1PrQq7CbDbPnDkzLi5O60IA\n+B0BGkCzUV1dvXHjRq2raPY+/fTTKwP09u3bDx48qEk9weTIkSMEaCAUEKABNDN9Y6P/0qen\n1lU0V7dv+6q4uPjK8aKiIiHE2wN6p0RGNHlRwWBFQeEb3xXIsqx1IQCaAj3QABBC2oabz58/\nf2WrxpkzZ4QQbS1mLYoCgGaGAA0AIaRtuNnlcl25CF1UVNTSaLCEhWlSFQA0LwRoAAghyRaz\n+LFhw83hcJSWlrYNZ/kZABqFAA0AIURJyXUCdFFRkcvlIkADQCMRoAEghCgpWel4dvuhAZoA\nDQCNQ4AGgBBSb4BWFqTbEaABoHEI0AAQQpQrBa9s4RBswQEAjUaABoDQ0tZiPnv2rMvlco/Q\nwgEAqhCgASC0tA03OxyO8+fPu0eKioos+rCWRoOGVQFAM0KABoDQUmcjDpfLVVJS0tbM8jMA\nNBYBGgBCS53rCM+dO+dwONqGmzQtCgCaEwI0AISWtv99LxVu4g0AahGgASC01FmB/mELDq4g\nBIBGI0ADQGhpbTYZdDr3CjQBGgDUIkADQGjRCZFoNtVp4WhnCde0KABoTgjQABBy2oabbTab\n1WoVQhQVFRl0ugQzFxECQGMRoAEg5CiXDCprz8XFxYlmI98MAKDx+MwEgJDj3gq6rKzMZrPR\nAA0AqhCgASDkuAP0Dw3Q4TRAA4AKeq0LAAA0NeW2KUVFRYmJiYJNoAFAJQI0AISctuHhOkk6\nc+bMDwGaFg4AUIMWDgAIOUad1MpoPHPmzI+bQLMFBwCoQIAGgFDU1mIqKys7duyYJEQSK9AA\noAYBGgBCUVuzWQhRUFAQZzKadHwvAAAV+NAEgFCkXDgoy3I7riAEAJUI0AAQitwXDnIFIQCo\nRYAGgFBEgAYArxGgASAUuTs3CNAAoBYBGgBCUaReH2XQCwI0AKhHgAaAUHS80tbSaJSEKL18\nWetaAKCZIUADQChaUVBYUGmThXju0DGtawGAZoYADQAAAKhAgAYAAABUIEADAAAAKhCgAQAA\nABUI0AAAAIAKBGgAAABABQI0AAAAoAIBGgAAAFCBAA0AAACoQIAGAAAAVCBAAwAAACoQoAEA\nAAAVCNAAAACACgRoAAAAQAUCNAAAAKACARoAAABQgQANAAAAqECABgAAAFQgQAMAAAAqEKAB\nAAAAFQjQAAAAgAoEaAAAAEAFAjQAAACgAgEaAAAAUIEADQAAAKig1+qFlyxZ8tFHHw0ePHjm\nzJnuwV/+8pc333xzZmam8tBms61evXr79u0lJSUGgyElJeWuu+7q27dv40+iTKjz0gsWLOja\ntasf3xsAAACCl2YBWghhNBpzc3O/+eabnj17XvlsRUXFzJkzq6urJ0+enJKSYrPZtmzZ8swz\nz2RmZt59992NPIkQIjo6es6cObVH2rVr59s3AgAAgNChZYCOj4/v2LFjdnb2n//8Z0mS6jz7\n1ltvlZSULFq0KCEhQRnp3r270WhctmxZ//79k5OTG3MSIYRer+/cubNf3wgAAABCh8Y90FOm\nTCkoKPjiiy/qjDudzm3bto0cOdKdnhUTJ06UJKnO/IZOAgAAAPiclivQQojWrVuPHTv2nXfe\nGTx4sMlkco+fO3euurq6Q4cOdeZbLJb4+PjCwsLGnERx4cKFsWPHuh/qdLp//etf7odHjhxZ\nvXq1++H48ePda9v+oNPp9u/fv2bNGlmW/fcqoUP5nQNfTJ/Q6XSSJDmdTq0L8STAywM2bNiw\nb98+ravwhI9NH5Ikady4cSkpKVdmDwQ9jQO0EGL8+PEbN2788MMPJ02aVOepelsy6v3f3sNJ\n6vRA1zlnYWHhhx9+6H44atSolJQUtW9BlVOnTtVO8ACAoLFz506tS0CT6tevX0OXYPlKTU2N\nX88P72gfoC0Wy3333bd06dLRo0e7B+Pi4kwm04kTJ+pMttls58+fHzJkSGNOovDcA92vX793\n3nnH/bBVq1ZlZWXevZHG0Ov1gwcPzs7Orq6u9t+rhA6TyeRyuRwOh9aFBIPw8HC9Xl9ZWely\nubSupUGXL1+eMWOG1lUADXrwwQczMjK0rsITg8Gg0+n4HuQTJpOpU6dOly5d8mvGDQsLi4yM\n9N/54R3tA7QQ4pZbblm3bl3tIKvX62+++eaNGzf+7Gc/q90G/f7778uyPGzYsMacpDEiIyPT\n0tLcD61Wq1/TmCRJ0dHRqamplZWV/nuV0GGxWJxOJ98JfCIqKspoNJaWlgZygObvGgGudevW\nAX7Zutls1ul0NptN60KCQURERHh4uNVq9WuArve38dBcQARoSZKmTZv21FNP6fX/qWfKlCmH\nDh2aPXu2so1dZWXlli1b1q1bl5mZ2b59+0aeRAhRU1Nz/Pjx2iOJiYkWi8VP7wUAAADBLSAC\ntBCiV69e/fv3r909FhUV9dJLL61evfr9998vKSkxGo1du3Z96qmn+vXr1/iTCCGsVmud3/nO\nnDlz8ODBPn8LAAAACAWaBejp06fXGfnjH/9YZyQiIiIzM9N9Y0IvTjJ9+vQr5wAAAABe03gf\naAAAAKB5IUADAAAAKhCgAQAAABUI0AAAAIAKBGgAAABABQI0AAAAoAIBGgAAAFCBAA0AAACo\nQIAGAAAAVCBAAwAAACoQoAEAAAAVCNAAAACACgRoAAAAQAUCNAAAAKACARoAAABQgQANAAAA\nqECABgAAAFQgQAMAAAAqEKABAAAAFQjQAAAAgAoEaAAAAEAFAjQAAACgAgEaAAAAUIEADQAA\nAKhAgAYAAABUIEADQCiK0esj9GF6SWptMmpdCwA0MwRoAAhFv03t1MporJHl53p117oWAGhm\nCNAAEIpcslxsrxZCFFbZta4FAJoZAjQAhKKS6suXXS5BgAYA9QjQABCKCm0/5GYCNACoRYAG\ngFDkzs3uJA0AaCQCNACEov8EaFagAUAlAjQAhCIlN5vN5tOsQAOASgRoTC09RQAAEq9JREFU\nAAhFp212vV6flpZW6XRaHQ6tywGA5oQADQCh6EyVvXXr1snJyYIuDgBQiQANACGn7LKj0ulM\nSkpKSkoSQpy2VWtdEQA0JwRoAAg5ypJzmzZtlADNCjQAqEKABoCQo1w46F6BJkADgCoEaAAI\nOaer/hOgJUk6bavSuiIAaE4I0AAQcgp/DNBGo7FVq1asQAOAKgRoAAg5hVV2SZKU/o2kpKTS\nyw5bjVProgCg2SBAA0DIKayyt2rVymg0CiGUGF1kZyMOAGgsAjQAhBZbjbPsskPJzUKINm3a\nCCFOV9EGDQCNRYAGgNBSWGWXf1x4Fj/+oZAbegNAoxGgASC0uDeBVh6ykx0AqEWABoDQ4t6C\nQ3lIgAYAtQjQABBa6qxAR0ZGRkZGFlZxESEANBYBGgBCi9LunJiY6B5JSkoqrrI7XC7tigKA\n5oQADQChpdBeraw6u0eSkpJcQpy1X9awKgBoRgjQABBCamT5bJXd3QCtoA0aAFQhQANACCmq\nsrtqNUArlIcEaABoJAI0AISQOltwKFiBBgBVCNAAEEKU3TbqrEAToAFAFQI0AISQelegW7Vq\nZTQaT9u4mzcANAoBGgBCSL0BWpKkpKSkM1XVskZVAUDzQoAGgBBSaLObTKbY2Ng640lJSdUu\n14VqdrIDgKvTa10AAKhzzn55TWGx1lU0V2eq7InJyZIk1RlX1qRXny5KMpu0qKvZO1R+SesS\nADQdAjSAZkOn04WFhZ20Vc379rjWtTRj7dq1u3IwOTlZCPH/7d13UBTnA8bx9ygH0lQUC0xA\nYDAWIIrRqJPEEizYQAIYxEY0sU0siONYMhF/SiaxRCMq9oJmsASCmlEjFmIEFQbBrihIsMQS\nxaPkOMr9/rjM5TwR3CSyBr+fv273Xt599pzBx3X3vbibt+s8Tr1iYcE/P4DXAgUawH+Gubn5\nl19+eevWLbmD1M7a2rqkpETuFNVQKBSdO3d+dn+fPn2USqVG88rdwqFQKKytrSsqKtTqV32R\nECsrKx8fH7lTAKgLFGgA/yXe3t7e3t5yp6idvb39o0eP5E4hgbm5ua+vr9wpqmFiYmJvb19W\nVlZUVCR3FgD4Ew8RAgAAABJQoAEAAAAJKNAAAACABBRoAAAAQAIKNAAAACABBRoAAACQgAIN\nAAAASECBBgAAACSgQAMAAAASUKABAAAACSjQAAAAgAQUaAAAAEACCjQAAAAgAQUaAAAAkIAC\nDQAAAEhAgQYAAAAkoEADAAAAElCgAQAAAAko0AAAAIAEFGgAAABAAgo0AAAAIAEFGgAAAJCA\nAg0AAABIQIEGAAAAJKBAAwAAABJQoAEAAAAJKNAAAACABBRoAAAAQAIKNAAAACABBRoAAACQ\ngAINAAAASECBBgAAACSgQAMAAAASUKABAAAACSjQAAAAgAQKrVYrd4bXSH5+/o4dO7p169ar\nVy+5swBP2bNnz7Vr16ZMmWJjYyN3FuAvKpUqJiamTZs2gYGBcmcBnnL06NFTp06NGDHC2dlZ\n7iyoa1yBrlMPHjxISEi4dOmS3EEAY6dPn05ISFCr1XIHAZ6iVqsTEhJOnz4tdxDA2IULFxIS\nEh4+fCh3EMiAAg0AAABIQIEGAAAAJKBAAwAAABLwECEAAAAgAVegAQAAAAko0AAAAIAEFGgA\nAABAAjO5A7xGMjIy4uLibt261bBhQ19f39DQUIVCIXcoQCQnJ6ekpNy8ebOsrMzR0XHgwIF9\n+vSROxTwlytXrsyePVur1f7www9yZwH+VFpaumPHjrS0tMLCQnt7+759+4aEhMgdCnWHAl1H\nrl69unDhQj8/v4iIiBs3bqxevbqqqmrEiBFy5wLE0aNH27dv7+/vb2VllZqaunLlyoqKCj8/\nP7lzAUIIoVKpFi9e3LFjx8zMTLmzAH/SaDRz5syprKwcNWqUo6NjUVHRH3/8IXco1CkKdB1J\nSEhwcnIaP368EMLFxeXu3btJSUnBwcEWFhZyR8PrLjo6Wv+6Xbt2eXl5J0+epEDjVaDVapcu\nXerr62tpaUmBxqtj7969Dx48iI2NtbW1lTsL5ME90HXk8uXLPj4++k0fHx+1Wp2bmytjJKBa\nGo2mYcOGcqcAhBAiPj6+oqLio48+kjsI8JTU1FRvb+/t27ePHj16/Pjxq1atKioqkjsU6hQF\nui5otdrCwsLGjRvr9+heP3r0SL5QQDWSk5OvX78eEBAgdxBAZGdnHzx4MDIyksdF8Kq5e/fu\n6dOni4uL582b9+mnn54/fz4qKoov1nitcAsHgD+dOHEiNjZ2+vTpHh4ecmfB6+7x48dLly6d\nNm2a4aUH4BVRVVVlbW09ffp0MzMzIYRSqZw7d+6lS5fat28vdzTUEQp0XVAoFI0aNXr8+LF+\nj+61vb29fKGApxw4cGDjxo2RkZFdu3aVOwsg8vLyCgsLFyxYoNvUarVarTYgICAkJGT48OHy\nZgPs7e3t7Ox07VkI4ezsLIS4f/8+Bfr1QYGuI23bts3MzBw7dqxuMzMz09LS0s3NTd5UgE58\nfHxCQsLnn3/+1ltvyZ0FEEKIdu3arVy5Ur955MiRvXv3rlixolGjRjKmAnQ8PT3PnDlTWVlp\namoqhCgoKBBCNG/eXO5cqDvcA11HAgMDb9++vXbt2vz8/GPHjiUmJg4ZMoQlOPAqWL9+/c6d\nO8PDw21tbXNzc3Nzc3V/GQAysrS0dDGgu5HDxcWFJ1zxKggICCgpKVm5cmV+fv758+fXrFnT\nunXrtm3byp0LdUfBPe91Jj09ffv27QUFBbovUhk+fDhPxuBVEBYWZvT8eIsWLdatWydXHuBZ\niYmJW7du5YtU8Oq4cuXK5s2bb9y4YWNj4+PjM2bMGDs7O7lDoe5QoAEAAAAJuIUDAAAAkIAC\nDQAAAEhAgQYAAAAkoEADAAAAElCgAQAAAAko0AAAAIAEFGgAwIsKCgqytLSUOwUAyIwCDeDf\nl5GRoXiO48ePVzvGysrK09Nz/vz5paWlNU+ycOFCwwHjxo37eyE1Gs369ev79Onj4OCgVCqb\nNm3q6+sbGxurVqv/8QdQR8rLy7ds2TJgwICWLVsqlUo7OzsfH5+IiIhz587JHQ0A6jMzuQMA\nqLc6deoUEBBgtNPV1dVws0uXLsHBwUKIBw8eJCUlRUVFpaSkHD16VP89nc9O0rNnz3+e7dat\nW4MHD87KyvLw8AgNDW3ZsqVKpTp16tSkSZN279595MiRf36Il+3OnTv+/v4ZGRnu7u5Dhw51\ncnLSaDTXrl2Li4tbvnz5jz/+6OfnJ3dGAKifKNAAXpYOHTrMmzev5jFeXl6RkZG61//73/86\nd+58/PjxlJQUfUt+kUmkKi8v17Xn6OjoWbNmmZj89X9xly5dWr169b97OCOlpaVWVlb/cBLd\nKWRmZi5evDgiIsLwFMrKyjZv3my452UEAIDXGbdwAHhVKJXK/v37CyFycnJe6oG2bduWlZUV\nFhY2e/Zso6LZrl27mJgY/WZhYeGMGTNcXV0tLCyaN28eFhZ2/fp1/bvLly9XKBQZGRmGMwQE\nBNjY2Og39+zZo1Aodu3aFRUV5eHhoVQqFyxYIISoqKj4+uuvvby8bG1tbW1tPTw8xowZU1RU\npP/BioqKZcuWdejQoUGDBra2tj179vzpp5/078bFxWVmZoaHh0dGRhqdgoWFxYQJE/r161dz\ngCdPnsybN++dd95p2rSphYWFm5tbZGRkcXGx4VT37t0bPXq0vb29tbV1jx49UlNTn/0wa84J\nAPUSV6ABvCwqlcqwbgohTExM3NzcaviRa9euCSGaNGnyvEnMzMxatWr1D4Pt3r1bCPHZZ5/V\nPKykpOT9998/f/58WFhY9+7dc3Jy1qxZc+DAgbS0tDfffFPSEWfNmuXk5BQdHd2iRQtzc3Mh\nxOzZs5csWTJ8+PApU6aYmJjk5+fv379fpVLZ2toKISorK4cMGXLo0KHg4OBx48ap1ert27f3\n799/x44doaGhQohdu3YJISZNmvS3AxQUFKxbty4oKCg0NFSpVP7888/Lli07c+ZMSkqK7v6Z\n4uLiHj165OTkfPLJJ506dTp79mzfvn2dnZ0Np601JwDUT1oA+Lelp6dX+wvHwsLCaMywYcPy\n8vLy8vLS09N193I4ODg8efLkeZM0b97caIaxY8dKjefo6KhQKMrLy2seFhUVJYRYtGiRfs+h\nQ4eEEP369dNtfvPNN0KI9PR0w5/y9/e3trbWb+rKeuvWrY0O5+rq2qtXr+cdetWqVUKITZs2\n6fdoNBofH5/mzZvr5nFycjI6haqqqjwD9+7dqzmAWq3WaDSGexYtWiSEOHz4sOHpr1mzRj9g\n/fr1Rn+IteYEgHqJK9AAXpYPPvhgwoQJhntMTU2NxuzcuXPnzp36TS8vr82bN9vZ2T1vkn9l\nDTWVSmVlZWVmVssvwO+//97GxiYiIkK/p2/fvt26dTt8+LBKpTIMWavw8HCjwzVq1Ojy5cvp\n6emdO3d+dvy2bduaNWsWGhpquCRIaGjozJkzs7OzO3Xq9OTJE6NTKCkpMXxAc+DAgfv3768h\ngIWFhf51eXl5ZWXl0KFD586de+rUKV9fX93pN2nSxHCRk48//nj+/PkPHz588Zwv9OkAwH8N\nBRrAy9KqVaugoKCax/j6+k6ePFmhUFhaWrq5uXl4ePyNSaSys7O7e/duRUVFzR06NzfX3d3d\nqLJ7eXmlpaXdvHnT29v7xY9otPaIEGLJkiUhISFdunRxdnZ+9913fX19hw0bpn+27/LlyyqV\nqkGDBs9Odf/+fSFEw4YN79y5Y3gKDRo0SExMFEIUFhaGh4fXGkAIsWXLlnXr1mVnZ+uXDhRC\nPHr0SPfixo0bXl5ehh+RiYlJmzZtfvnlF/2eWnMCQL1EgQYgJxcXl2eXunvZvLy87ty5k5mZ\n2aVLlxqGabVa/Wp61ar23YqKimd3Gl7u1endu3deXt7BgwePHTuWkpLy3XffffHFF2lpaU5O\nTkKIqqoqDw+Pbdu2PTtVmzZthBCenp63b9/Oysp6++23dftNTU11n+Rvv/32IgGWLVs2Y8aM\nwYMHb9iwwdHR0cLC4vfffx80aFBVVVUNJ6jVag03a80JAPUSBRrAayc4OPjQoUMxMTHVNj89\nd3f369evq9Vqw4vQFy5cMDEx0T3IaG9vLwwu2eoYPTdZA1tb2+DgYN0y2PHx8aGhod9+++1X\nX30lhGjduvWFCxc8PT0NF/R49hRiY2M3bNjwgoczsnHjRldX16SkJH1LPnHihOEAd3f3nJwc\nw4vcVVVVV69eNRxTa04AqJdYxg7Aa2fkyJEdOnSIi4tbsmSJ0SXVq1evTps2Tfc6MDCwuLh4\n+fLl+neTk5NTU1N9fX11N0Dr1uI4ePCgfkBCQoJRxXweo9rdtWtXw52jRo3SaDSRkZFG8e7c\nuaMf0LFjx40bN65YscJoTGVl5YsEMDEx0Wq1+sGVlZXR0dGGAwIDAx8+fLhp0yb9nq1bt96+\nfdtwTK05AaBe4go0gJclKytL/7XbegMGDPDx8XnZR5k6dapuPbhqKZXKffv2DRo0aObMmZs2\nbfLz82vRooVKpTp9+vSRI0f03+ESGRm5Z8+e2bNnX7x4Ub+MXePGjVesWKEb0KVLl65du65Y\nsaKoqMjT0/PcuXNJSUleXl65ubm1xnZ0dBw0aFCnTp2cnJzu37+/YcMGU1PTkSNH6t6dPHly\ncnLy2rVrz5496+/v7+DgUFBQkJaWlp2drbu32NzcfN++ff7+/tOmTVu9enX//v2dnJzUanV+\nfn5SUpIQwsvLq+YAQUFB8+fP9/PzCwkJKSoqio+PNyrBERERO3bsmDhxYlZWVseOHbOzs7du\n3dq2bVvDs6s1JwDUT/ItAAKg3nreMnbCYFm0Whehe8EB1SooKKg1pFqtXrt2be/evZs0aWJm\nZta4ceOePXvGxMSUlpbqxzx+/Hj69OkuLi7m5uYODg6hoaE5OTmGk/z666+6b06xtrbu06fP\nuXPnql3GLjEx0ejoc+bM6d69e9OmTc3NzZ2cnAICAlJTUw0HVFZWxsbGdu3a1cbGxtLSslWr\nVgEBAXFxcYZjNBrNpk2b+vXr16xZMzMzMxsbG09Pz4kTJxqurPe8AOXl5QsXLnR3d1cqlW+8\n8cb06dPz8vKEEFOnTtWPuXv37ogRIxo1amRlZfXee++dPHnyww8/NFzG7gVzAkA9o9A+fckB\nAAAAQA24BxoAAACQgHugAdQ3Wq22rKzsee8qlUoTE64dAAD+Pv4WAVDfXLx4scHz7dq1S+6A\nAID/Nu6BBlDfqNXqCxcuPO9dd3f3xo0b12UeAEA9Q4EGAAAAJOAWDgAAAEACCjQAAAAgAQUa\nAAAAkIACDQAAAEhAgQYAAAAkoEADAAAAEvwfc2pkE9y+b6oAAAAASUVORK5CYII=",
-      "text/plain": [
-       "plot without title"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# Setting the size of plots generated with ggplot below. \n",
-    "options(repr.plot.width = 8, repr.plot.height = 5)\n",
-    "\n",
-    "# More sophisticated plots with GGPLOT.\n",
-    "# Tutorial: http://www.sthda.com/english/wiki/ggplot2-box-plot-quick-start-guide-r-software-and-data-visualization\n",
-    "ggplot(moocs, aes(x=MOOC, y=EPFL_CourseGrade, fill=MOOC)) +\n",
-    "    geom_boxplot(notch=TRUE) + coord_flip() "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Histograms\n",
-    "\n",
-    "Histograms give a more precise representation of the actual grade distribution. Below, we define bins of 0.5 to represent the frequency of the different grades. The vertical dashed lines represent the means of the distributions. Notice that we reuse the dataframe `mu` that we defined above. We see indeed that the `DO` group is less symmetric than the others."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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j172k5RFOWFF15wOp1vvfXWkiVL2s56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\nAABIQAENAAAASEABDQAAAEjwv5SmMHADP5xgAAAAAElFTkSuQmCC",
-      "text/plain": [
-       "plot without title"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# Tutorial about generating such a figure\n",
-    "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
-    "options(repr.plot.width = 8, repr.plot.height = 5)\n",
-    "\n",
-    "ggplot(moocs, aes(x=EPFL_CourseGrade, fill=MOOC)) +\n",
-    "    geom_histogram(binwidth=.5, alpha=.5, position=\"dodge\") + \n",
-    "    geom_vline(data=mu, aes(xintercept=grp.mean, color=MOOC), linetype=\"dashed\") \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Mean plots\n",
-    "Mean plots represent the mean along with the confidence interval for the mean. There is a 95% chance that the confidence interval contains the true mean of `EPFL_CourseGrade` for the population. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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HPCrFmzeFMl3717FxkZuWDBAmVl5Q0b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\nIOYNGx8k4AAAAABJRU5ErkJggg==",
-      "text/plain": [
-       "Plot with title “Grade given MOOC activity”"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# library(gplots)\n",
-    "\n",
-    "options(repr.plot.width = 5, repr.plot.height = 5)\n",
-    "\n",
-    "# plotmeans is defined in the gplots library \n",
-    "# make sure to load the library by executing > library(gplots) before. \n",
-    "plotmeans(moocs$EPFL_CourseGrade ~ moocs$MOOC, main=\"Grade given MOOC activity\", ylab=\"Grade\", xlab=\"Activity Level\")\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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715R4iNELGm16qc4VJnvRDLEMrbuL/h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\nrkJggg==",
-      "text/plain": [
-       "plot without title"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "options(repr.plot.width = 5, repr.plot.height = 5)\n",
-    "\n",
-    "# Alternate form using the package ggpubr\n",
-    "# See examples here: http://www.sthda.com/english/articles/24-ggpubr-publication-ready-plots/79-plot-meansmedians-and-error-bars/\n",
-    "\n",
-    "ggline(moocs, x = \"MOOC\", y = \"EPFL_CourseGrade\", \n",
-    "            add = c(\"mean_ci\"))\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# ANOVA - Analysis of Variance"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
-    "    <strong>Test</strong>: ANOVA a.k.a. ANalysis Of VAriance \n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "ANOVA allows comparing whether one variable has the same mean in different groups ? The formula to specify the test is done in tow steps. First we define a linear model with  `m <- lm(quantitative ~  categorical)` and then we do the Anova of the model `Anova(m)`.\n",
-    "\n",
-    "* H0: mean_1 = mean_2 = ...= Mean_n\n",
-    "* H1: mean_1 != mean_2 != ... != mean_n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We use the Analysis of Variance (ANOVA) to compare the mean of a variable across several modalities of a categorical variable. In the example below, we compare the course grade (`EPFL_CourseGrade`) across different modalities of MOOC usage (the `MOOC` variable takes three possible values: `NONE`, `WATCH` and `DO`). "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<table>\n",
-       "<caption>A anova: 2 × 4</caption>\n",
-       "<thead>\n",
-       "\t<tr><th></th><th scope=col>Sum Sq</th><th scope=col>Df</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
-       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
-       "</thead>\n",
-       "<tbody>\n",
-       "\t<tr><th scope=row>moocs$MOOC</th><td> 1181.668</td><td>   2</td><td>291.5936</td><td>1.479869e-123</td></tr>\n",
-       "\t<tr><th scope=row>Residuals</th><td>18866.175</td><td>9311</td><td>      NA</td><td>           NA</td></tr>\n",
-       "</tbody>\n",
-       "</table>\n"
-      ],
-      "text/latex": [
-       "A anova: 2 × 4\n",
-       "\\begin{tabular}{r|llll}\n",
-       "  & Sum Sq & Df & F value & Pr(>F)\\\\\n",
-       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
-       "\\hline\n",
-       "\tmoocs\\$MOOC &  1181.668 &    2 & 291.5936 & 1.479869e-123\\\\\n",
-       "\tResiduals & 18866.175 & 9311 &       NA &            NA\\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/markdown": [
-       "\n",
-       "A anova: 2 × 4\n",
-       "\n",
-       "| <!--/--> | Sum Sq &lt;dbl&gt; | Df &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
-       "|---|---|---|---|---|\n",
-       "| moocs$MOOC |  1181.668 |    2 | 291.5936 | 1.479869e-123 |\n",
-       "| Residuals | 18866.175 | 9311 |       NA |            NA |\n",
-       "\n"
-      ],
-      "text/plain": [
-       "           Sum Sq    Df   F value  Pr(>F)       \n",
-       "moocs$MOOC  1181.668    2 291.5936 1.479869e-123\n",
-       "Residuals  18866.175 9311       NA            NA"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# needs library(car)\n",
-    "\n",
-    "m <- lm(moocs$EPFL_CourseGrade ~ moocs$MOOC)  \n",
-    "Anova(m)\n",
-    "\n",
-    "r <- residuals(m)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
-    "    <strong>Reporting</strong>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "This is the way you report the ANOVA in an article.\n",
-    "\n",
-    "> We conducted a one-way ANOVA to test whether the course grades differ for different categories of MOOC usage. There is a significant difference of course grades across different types of MOOC use (F[2,9311]=291.6, p<.001). \n",
-    "\n",
-    "Beware, that since we did not randomly assign subjects to experimental groups, but rather students chose whether they use the MOOC or not, we can't conclude about any causal effect. It is possible that better students are inclided to use MOOCs more than weaker students. Hence, the \"effect of\" the MOOC would be due to this hidden variable which actually explains the difference."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightBlue;\">\n",
-    "    <strong>Advanced topic</strong> : There are different ways to run anovas in R. They differ with regards to the type of Sum of Square that they report.  \n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Following http://goanna.cs.rmit.edu.au/~fscholer/anova.php the Type III Sum of Square is more adapted  to interpret the contributions of the differnt variables. R and anova report Type I sums of square.\n",
-    "\n",
-    "Here is an explanation about how to obtain Type III sums of squares: https://www.r-bloggers.com/anova-%E2%80%93-type-iiiiii-ss-explained/\n",
-    "And some explanations here: prometheus.scp.rochester.edu/zlab/sites/default/files/InteractionsAndTypesOfSS.pdf\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Which groups differ among each other ?"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
-    "    <strong>Test</strong>: Pair-wise t-test\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "A pairwise test allows to know which groups differ from each other. Because of repeated testing, we have to adjust the p-value by dividing the .05 value by the number of tests. In our case, the tests show that all groups differ from each other when taken 2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "\tPairwise comparisons using t tests with pooled SD \n",
-       "\n",
-       "data:  moocs$EPFL_CourseGrade and moocs$MOOC \n",
-       "\n",
-       "      NONE    WATCH  \n",
-       "WATCH 6.7e-11 -      \n",
-       "DO    < 2e-16 < 2e-16\n",
-       "\n",
-       "P value adjustment method: bonferroni "
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# Checks which group is different from what other group in doing 2 by 2 tests.\n",
-    "pairwise.t.test(moocs$EPFL_CourseGrade, moocs$MOOC, p.adj = \"bonf\") \n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "\n",
-    "cat(\"Means\")\n",
-    "tapply(moocs$EPFL_CourseGrade, moocs$MOOC, mean)\n",
-    "\n",
-    "cat(\"Standard Deviations\")\n",
-    "tapply(moocs$EPFL_CourseGrade, moocs$MOOC, sd)\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
-    "    <strong>Reporting</strong>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And here is the wording for the article. \n",
-    "\n",
-    "> A series of pair-wise t-tests with bonferonni adjusment for repeated testing, shows that the average grade for students who did not use the MOOC (m=3.5, sd=2.5) is smaller than the average grade of students who watched videos (m=3.8, sd=1.3) and smaller than the average grade of students who did the assignments (m=4.4, sd=1.2)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Assumptions\n",
-    "Is it ok to run an ANOVA blindly as we did just before ? \n",
-    "\n",
-    "Not really, we should have checked the assumptions for ANOVA first.\n",
-    "\n",
-    "* Normality of the residuals\n",
-    "* Homoscedasticity of the residuals = the error distribution should be the same regardless of the category.\n",
-    "\n",
-    "### Visually inspecting normality Assumption\n",
-    "Testing normality visually with quantile plots. If the variable is normally distributed, the observations would follow the line drawn by qqline.  We see from the plots below that the distribution of the residuals of our model used for the Anova departs very strongly from a normal distribution.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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OoKsJ+ENZ6j0TvZhiVo7TFTuc+AfniQkBWKxlBXgN0krBQraOc79HGYOj9hKiAh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\nNaTf6KuTRhkAAAAASUVORK5CYII=",
-      "text/plain": [
-       "Plot with title “Residuals”"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# split the plotting area into 2 lines and 2 columns\n",
-    "par(mfrow=c(2,2))\n",
-    "\n",
-    "# Setting the size of plots below. \n",
-    "options(repr.plot.width = 7.5, repr.plot.height = 7.5)\n",
-    "\n",
-    "v <- rnorm(1000)\n",
-    "hist(v, main=\"Normal variable\")\n",
-    "qqnorm(v, main=\"Normal variable\");\n",
-    "qqline(v);\n",
-    "\n",
-    "# The residuals of the model we used to run the Anova\n",
-    "# r <- residuals(m)\n",
-    "hist(r, main=\"Residuals\")\n",
-    "qqnorm(r, main=\"Residuals\");\n",
-    "qqline(r)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Normality tests"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
-    "    <strong>Test</strong>: Shapiro-Wilks Test\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "Normality can also be tested statistically, however the normality tests are rather sensitive to small deviations, especially when sample sizes are large. For example, the Shapiro-Wilks test, is testing the null hypothesis that the variable is normally distributed. In this case the adequate p.value is .1. Hence, with p <<.1 we have to reject the null hypothesis and conclude that the variable is not normally distributed. This test work with samples smaller than 5000 observations.  \n",
-    "\n",
-    "* H0: variable is normally distributed\n",
-    "* H1: variable is not normally distributed\n",
-    "\n",
-    "We see below that for our variable `v` that we generated to be normally distributed, p = 0.47, far greater than 0.1, hence we cannot reject H0.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "\tShapiro-Wilk normality test\n",
-       "\n",
-       "data:  v\n",
-       "W = 0.99838, p-value = 0.4792\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "shapiro.test(v)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "However, for the residuals of our Anova, we have to reject H0, and conclude that they are not normally distributed.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "\tShapiro-Wilk normality test\n",
-       "\n",
-       "data:  sample(r, 1500)\n",
-       "W = 0.9573, p-value < 2.2e-16\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# taking a sample of 1500 residuals for illustrating the output of the shapiro test\n",
-    "shapiro.test(sample(r,1500)) \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Testing Homoscedasticity assumption\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
-    "    <strong>Test</strong>: Bartlett test\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "* H0: variances are the same\n",
-    "* H1: variances are different\n",
-    "\n",
-    "We see below, that the p-value is much smaller than .05 and therefore we reject H0. \n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "\tBartlett test of homogeneity of variances\n",
-       "\n",
-       "data:  r by moocs$MOOC\n",
-       "Bartlett's K-squared = 130, df = 2, p-value < 2.2e-16\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "bartlett.test(r ~ moocs$MOOC)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "\n",
-    "\n",
-    "The difference in variuance is also appararent in a boxplot, where we see that the variance for the DO group is smaller. We also see that the residuals for WATCH tend to be slightly more positive than negative (their median is above 0) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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zB5D08Kwnr7a/eWN1tuvdrjQCbvIUpB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\nYUEFYUEFYUEFYUEFYUHF/wOCQirlK83Q8wAAAABJRU5ErkJggg==",
-      "text/plain": [
-       "plot without title"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "options(repr.plot.width = 5, repr.plot.height = 5)\n",
-    "boxplot(r ~ moocs$MOOC)\n",
-    "abline(h=0)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## If variances are unequal or residuals are not normally distributed\n",
-    "\n",
-    "If variances are unequal we can either \n",
-    "\n",
-    "* adapt the oneway test by stating that `var.equal = F` \n",
-    "* or use a non parametric alternative to ANOVA like the Kruskal Wallis test. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "\tOne-way analysis of means (not assuming equal variances)\n",
-       "\n",
-       "data:  moocs$EPFL_CourseGrade and moocs$MOOC\n",
-       "F = 366.38, num df = 2.0, denom df = 2495.4, p-value < 2.2e-16\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "# adapt the caluclations to take unequal variances into account \n",
-    "oneway.test(moocs$EPFL_CourseGrade ~ moocs$MOOC, var.equal = F)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
-    "    <strong>Test</strong>: Kruskal test\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Tests the null hypothesis that the location parameters are the same in each of the groups. This test does not make assumptions about the distribution of the residuals, nor about the variances.\n",
-    "\n",
-    "* H0: the mean ranks of observations are the same in all groups\n",
-    "* H1: the mean ranks of observations are different."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "\n",
-       "\tKruskal-Wallis rank sum test\n",
-       "\n",
-       "data:  moocs$EPFL_CourseGrade by moocs$MOOC\n",
-       "Kruskal-Wallis chi-squared = 608.7, df = 2, p-value < 2.2e-16\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "\n",
-    "kruskal.test(moocs$EPFL_CourseGrade ~ moocs$MOOC)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
-    "    <strong>Reporting</strong>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "> Because the assumption of equal variances was not respected (K2[2]=130, p< .001) in our sample, we conducted a non-parametric Kruskal-Wallis test that showed that the mean rank of course grades differs significantly across groups (X2[2]=608.7, p < .001).  "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Exercise : analyse the effect of prior knowlege on the grades.\n",
-    "Students' baccalaureat grade is given by the variable `EPFL_BacGrade`. In the plot below we see the distribution of the grades at the baccalaureat and display the median and quartiles as vertical bars.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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Dwez8TExNbW1svLy8LCQiUTVwN9fX0P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\nAEBwSDgAAABAcH8Bi5BQsX3Dww4AAAAASUVORK5CYII=",
-      "text/plain": [
-       "Plot with title “Histogram of moocs.bac$EPFL_BacGrade”"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "options(repr.plot.width = 6, repr.plot.height = 4)\n",
-    "\n",
-    "# Remove observations for which we do not have a EPFL_BacGrade\n",
-    "moocs.bac <- subset(moocs, ! is.na(moocs$EPFL_BacGrade))\n",
-    "\n",
-    "# Draw a histogram with 50 bins\n",
-    "hist(moocs.bac$EPFL_BacGrade, breaks=50)\n",
-    "\n",
-    "# Draw a vertical line at the median\n",
-    "abline(v=median(moocs.bac$EPFL_BacGrade, na.rm=T), col=\"red\", lwd=3) \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
-    "    <strong>Task 1</strong> : Define two categorical variables named prior and prior4 that distinguish students given their baccalaureat grade. \n",
-    "    <ul>\n",
-    "        <li>prior : The values of the variable are HI for strong students and LO for weakers students. use median() to define high and low levels of ability</li>\n",
-    "    </ul>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# TODO: Define two categorical variables named moocs$prior and moocs$prior4 that distinguishstudents given at their baccalaureat grade.\n",
-    "\n",
-    "# 1) moocs$prior. \n",
-    "# The values of the variable are \"HI\"\" for strong students and \"LO\"\" for weakers students.\n",
-    "# => use median() to define high and low levels of ability\n",
-    "\n",
-    "################\n",
-    "# Begin solution\n",
-    "moocs.bac$prior <- ...\n",
-    "\n",
-    "\n",
-    "# end solution\n",
-    "##############\n",
-    "\n",
-    "\n",
-    "# count the number of observations in LO and HI \n",
-    "table(moocs.bac$prior)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
-    "    <strong>Task 2</strong> : Plot the means for the EPFL_CourseGrade given the prior grade level. \n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "################\n",
-    "# Begin Solution\n",
-    "\n",
-    "\n",
-    "\n",
-    "# end Solution\n",
-    "################\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
-    "    <strong>Task 3</strong> : Compare the means of EPFL_CourseGrade. \n",
-    "    <ul>\n",
-    "        <li>Check assumptions to run an ANOVA </li>\n",
-    "        <li>Run an ANOVA or a replacement if the assumptions are not set </li>\n",
-    "    </ul>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "################\n",
-    "# Begin Solution\n",
-    "\n",
-    "# Build model\n",
-    "\n",
-    "# Check normality of residuals\n",
-    "\n",
-    "# Check homoscedasticity \n",
-    "\n",
-    "# Plots\n",
-    "\n",
-    "# Make the test\n",
-    "\n",
-    "# end Solution\n",
-    "################\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Two factor ANOVA"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can add more than one categorical predictor and also model the interaction of two factors. When there is an interaction, the effect of one variable is conditional on the effect of another variable  \n",
-    "\n",
-    "Interaction between two terms is represented by a `:`. A syntaxic equivalent for the model that contains single and interaction effects is `A * B == A + B + A:B`"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "ERROR",
-     "evalue": "Error in model.frame.default(formula = moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + : invalid type (NULL) for variable 'moocs.bac$prior'\n",
-     "output_type": "error",
-     "traceback": [
-      "Error in model.frame.default(formula = moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + : invalid type (NULL) for variable 'moocs.bac$prior'\nTraceback:\n",
-      "1. lm(moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + moocs.bac$prior + \n .     moocs.bac$MOOC:moocs.bac$prior)",
-      "2. eval(mf, parent.frame())",
-      "3. eval(mf, parent.frame())",
-      "4. stats::model.frame(formula = moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + \n .     moocs.bac$prior + moocs.bac$MOOC:moocs.bac$prior, drop.unused.levels = TRUE)",
-      "5. model.frame.default(formula = moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + \n .     moocs.bac$prior + moocs.bac$MOOC:moocs.bac$prior, drop.unused.levels = TRUE)"
-     ]
-    }
-   ],
-   "source": [
-    "\n",
-    "m3  <- lm(moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + moocs.bac$prior + moocs.bac$MOOC:moocs.bac$prior)\n",
-    "print(Anova(m3, type=3))\n",
-    "\n",
-    "r3 <- residuals(m3)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
-    "    <strong>Reporting</strong>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "> We conducted a 3 x 2 factorial ANOVA with prior performance and MOOC useage as factors. The results indicate a main effect of MOOC usage (F[2,374]=102.40, p<.001), as well as a main effect of prior knowledge (F[1,1179]=645.78, p<.001). There is also an interaction effect between the two factors (F[20,2]=5.3, p<.01).    "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Plotting\n",
-    "\n",
-    "The ggline package comes in handy to plot interactions between variables. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
-    "    <strong>Reporting</strong>\n",
-    "</div>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "> In our case here, we see that the relation between the different types of MOOC activity is not the same from strong or weaker students. It seems that for strong students, watching videos does not increase the score compared to doing nothing. However, doing exercices is beneficial for both strong and weak students. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "ggline(moocs.bac, x = \"MOOC\", y = \"EPFL_CourseGrade\", \n",
-    "       add = c(\"mean_ci\"),\n",
-    "       color = \"prior\", palette = \"jco\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Testing Assumptions"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "options(repr.plot.width = 8, repr.plot.height = 4)\n",
-    "par(mfrow=c(1,3))\n",
-    "qqnorm(r3)\n",
-    "qqline(r3)\n",
-    "\n",
-    "boxplot(r3 ~ moocs.bac$MOOC)\n",
-    "boxplot(r3 ~ moocs.bac$prior)\n",
-    "\n",
-    "bartlett.test(r3 ~ moocs.bac$MOOC)\n",
-    "bartlett.test(r3 ~ moocs.bac$prior)\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "options(repr.plot.width = 8, repr.plot.height = 8)\n",
-    "par(mfrow=c(2,2))\n",
-    "plot(m3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Choosing a non parametric version of the 2-way ANOVA"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "friedman.test(moocs.bac$EPFL_CourseGrade, moocs.bac$MOOC, moocs.bac$prior)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "table( moocs.bac$MOOC, moocs.bac$prior)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "R",
-   "language": "R",
-   "name": "ir"
-  },
-  "language_info": {
-   "codemirror_mode": "r",
-   "file_extension": ".r",
-   "mimetype": "text/x-r-source",
-   "name": "R",
-   "pygments_lexer": "r",
-   "version": "3.6.1"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
diff --git a/CS411-stats-solutions.ipynb b/CS411-stats-solutions.ipynb
index 476afd3..af0dacb 100644
--- a/CS411-stats-solutions.ipynb
+++ b/CS411-stats-solutions.ipynb
@@ -1,3039 +1,3511 @@
 {
  "cells": [
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px;\">\n",
     "    <strong>CS411 - Autumn 2019-2020</strong><br/>\n",
     "    Patrick Jermann<br/><br/>\n",
     "    <span style=\"text-decoration:underline;font-weight:bold;\">How to use this notebook?</span>\n",
     "    <ul style=\"margin:0;padding:0 0 0 20px;\">\n",
     "    <li>This notebook is made of text cells and code cells. The code cells have to be <strong>executed</strong> to see the result of the program. To execute a cell, simply select it and click on the \"play\" button (&#11208;) in the tool bar just above the notebook, or type <code>shift + enter</code>. It is important to execute the code cells in their order of appearance in the notebook.</li>\n",
     "    <li>To improve readability, it can be useful to <strong>hide</strong> cells from the notebook (e.g. long code cells). To hide a cell, select it and click on the blue bar which appears on its left. To make the cell visible again, just click again on the blue bar, or on the three \"dots\" which represent the collapsed cell.</li></ul>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# The MOOC dataset\n",
     "The data we use in this document to demonstrate the use of basic statistics is about students' performance in academic exams (e.g. the algebra course taken at the university) and their activitiy online in a related Massive Open Online Course (e.g. the algebra MOOC). The general question we try to answer is: what is the relation between the use of the MOOC by students and their academic achievement. \n",
     "\n",
     "**Question**: Does the use of MOOCs help succeed in courses ? Do only good students use the MOOCs ? Are MOOCs more helpful for better students ?\n",
     "\n",
     "As a general remark, we should note that because we did not conduct a controlled experiment with random assignment of subjects to experimental groups, we cannot establish any causal relationships between MOOC use and academic performance. Rather, we use statistical tools to \"explore\" data.\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Loading libraries\n",
     "Some extra libraries are needed to perform some operations. We collect the commands to load the libraries in this cell. Executing this cell first ensures that all the necessary libraries are loaded. If one library is missing it can be installed via the install.packages() command. Simply add the line to the cell and re-execute."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 79,
    "metadata": {},
    "outputs": [],
    "source": [
     "# Uncomment and run once if these packages are not installed yet.\n",
     "# install.packages(\"gdata\")\n",
     "# install.packages(\"gplots\")\n",
     "# install.packages(\"plyr\")\n",
     "# install.packages(\"dplyr\")\n",
     "# install.packages(\"ggplot2\")\n",
     "# install.packages(\"ggpubr\")\n",
     "# install.packages(\"car\")\n",
     "\n",
     "library(gdata) # reorder\n",
     "library(gplots) # plotmeans\n",
     "library(plyr) # ddply\n",
     "library(dplyr) # summarySE\n",
     "library(ggplot2) # plotting library\n",
     "library(ggpubr) # plotting\n",
     "library(car) # Anova\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "\n",
     "## Loading Data\n",
     "Let's load data. The first step is to read a CSV file into a dataframe, which is the data structure used by R to store data."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 80,
    "metadata": {},
    "outputs": [],
    "source": [
     "\n",
     "# TODO: Adapt the path to your own installation.\n",
     "# Set the working directory\n",
     "setwd(\"./\")\n",
     "\n",
     "# Read a csv file (header = T signals that the first line of the file contains the names of the variables).\n",
     "# The <- operator assigns the result of read.csv to the variable moocs.\n",
     "# moocs is a dataframe, similar to an excel worksheet or a DataFrame in pandas.\n",
     "moocs <- read.csv(file=\"moocs.basic.csv\", header = T)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Our dataset contains variables which name starts with *EPFL* and other variables starting with *MOOC*. The variables with EPFL come from the academic database and describe student's performance in their EPFL exams. The variables starting with MOOC conern their online activity in the MOOC."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 81,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<ol class=list-inline>\n",
        "\t<li>'EPFL_AcademicYear'</li>\n",
        "\t<li>'EPFL_IsRepeating'</li>\n",
        "\t<li>'EPFL_PropaedeuticGPA'</li>\n",
        "\t<li>'EPFL_CourseGrade'</li>\n",
        "\t<li>'EPFL_StudentSection'</li>\n",
        "\t<li>'MOOC_NVideosWatched'</li>\n",
        "\t<li>'MOOC_AverageMaxVideosWatched'</li>\n",
        "\t<li>'MOOC_PercentageVideosWatched'</li>\n",
        "\t<li>'MOOC_NProblemsSolved'</li>\n",
        "\t<li>'MOOC_AverageMaxProblemsSolved'</li>\n",
        "\t<li>'MOOC_PercentageProblemsSolved'</li>\n",
        "\t<li>'MOOC_Grade'</li>\n",
        "\t<li>'EPFL_Topic'</li>\n",
        "\t<li>'EPFL_BacGrade'</li>\n",
        "\t<li>'EPFL_BacLevel'</li>\n",
        "\t<li>'EPFL_CourseType'</li>\n",
        "\t<li>'EPFL_UniqueTopicID_Anonymous'</li>\n",
        "\t<li>'EPFL_AnonymousUserID'</li>\n",
        "</ol>\n"
       ],
       "text/latex": [
        "\\begin{enumerate*}\n",
        "\\item 'EPFL\\_AcademicYear'\n",
        "\\item 'EPFL\\_IsRepeating'\n",
        "\\item 'EPFL\\_PropaedeuticGPA'\n",
        "\\item 'EPFL\\_CourseGrade'\n",
        "\\item 'EPFL\\_StudentSection'\n",
        "\\item 'MOOC\\_NVideosWatched'\n",
        "\\item 'MOOC\\_AverageMaxVideosWatched'\n",
        "\\item 'MOOC\\_PercentageVideosWatched'\n",
        "\\item 'MOOC\\_NProblemsSolved'\n",
        "\\item 'MOOC\\_AverageMaxProblemsSolved'\n",
        "\\item 'MOOC\\_PercentageProblemsSolved'\n",
        "\\item 'MOOC\\_Grade'\n",
        "\\item 'EPFL\\_Topic'\n",
        "\\item 'EPFL\\_BacGrade'\n",
        "\\item 'EPFL\\_BacLevel'\n",
        "\\item 'EPFL\\_CourseType'\n",
        "\\item 'EPFL\\_UniqueTopicID\\_Anonymous'\n",
        "\\item 'EPFL\\_AnonymousUserID'\n",
        "\\end{enumerate*}\n"
       ],
       "text/markdown": [
        "1. 'EPFL_AcademicYear'\n",
        "2. 'EPFL_IsRepeating'\n",
        "3. 'EPFL_PropaedeuticGPA'\n",
        "4. 'EPFL_CourseGrade'\n",
        "5. 'EPFL_StudentSection'\n",
        "6. 'MOOC_NVideosWatched'\n",
        "7. 'MOOC_AverageMaxVideosWatched'\n",
        "8. 'MOOC_PercentageVideosWatched'\n",
        "9. 'MOOC_NProblemsSolved'\n",
        "10. 'MOOC_AverageMaxProblemsSolved'\n",
        "11. 'MOOC_PercentageProblemsSolved'\n",
        "12. 'MOOC_Grade'\n",
        "13. 'EPFL_Topic'\n",
        "14. 'EPFL_BacGrade'\n",
        "15. 'EPFL_BacLevel'\n",
        "16. 'EPFL_CourseType'\n",
        "17. 'EPFL_UniqueTopicID_Anonymous'\n",
        "18. 'EPFL_AnonymousUserID'\n",
        "\n",
        "\n"
       ],
       "text/plain": [
        " [1] \"EPFL_AcademicYear\"             \"EPFL_IsRepeating\"             \n",
        " [3] \"EPFL_PropaedeuticGPA\"          \"EPFL_CourseGrade\"             \n",
        " [5] \"EPFL_StudentSection\"           \"MOOC_NVideosWatched\"          \n",
        " [7] \"MOOC_AverageMaxVideosWatched\"  \"MOOC_PercentageVideosWatched\" \n",
        " [9] \"MOOC_NProblemsSolved\"          \"MOOC_AverageMaxProblemsSolved\"\n",
        "[11] \"MOOC_PercentageProblemsSolved\" \"MOOC_Grade\"                   \n",
        "[13] \"EPFL_Topic\"                    \"EPFL_BacGrade\"                \n",
        "[15] \"EPFL_BacLevel\"                 \"EPFL_CourseType\"              \n",
        "[17] \"EPFL_UniqueTopicID_Anonymous\"  \"EPFL_AnonymousUserID\"         "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# List the names of the variables\n",
     "names(moocs)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Descriptive Statistics\n",
     "\n",
     "## Summary for variables"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 82,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        " EPFL_AcademicYear EPFL_IsRepeating EPFL_PropaedeuticGPA EPFL_CourseGrade\n",
        " 2013-2014:2749    Min.   :0.0000   Min.   :1.690        Min.   :0.000   \n",
        " 2014-2015:2694    1st Qu.:0.0000   1st Qu.:3.680        1st Qu.:3.000   \n",
        " 2015-2016:3871    Median :0.0000   Median :4.250        Median :4.000   \n",
        "                   Mean   :0.1846   Mean   :4.133        Mean   :3.719   \n",
        "                   3rd Qu.:0.0000   3rd Qu.:4.630        3rd Qu.:5.000   \n",
        "                   Max.   :1.0000   Max.   :5.890        Max.   :6.000   \n",
        "                                    NA's   :1833                         \n",
        " EPFL_StudentSection MOOC_NVideosWatched MOOC_AverageMaxVideosWatched\n",
        " SV     :2199        Min.   : 1.00       Min.   :14.00               \n",
        " GM     :1157        1st Qu.: 7.50       1st Qu.:44.00               \n",
        " MT     :1128        Median :28.00       Median :45.00               \n",
        " MA     :1040        Mean   :24.46       Mean   :48.95               \n",
        " GC     : 970        3rd Qu.:39.00       3rd Qu.:58.00               \n",
        " PH     : 649        Max.   :85.00       Max.   :85.00               \n",
        " (Other):2171        NA's   :6339        NA's   :6339                \n",
        " MOOC_PercentageVideosWatched MOOC_NProblemsSolved\n",
        " Min.   :  0.00               Min.   :  1.00      \n",
        " 1st Qu.: 20.00               1st Qu.:  3.00      \n",
        " Median : 60.00               Median :  7.00      \n",
        " Mean   : 54.28               Mean   : 10.67      \n",
        " 3rd Qu.: 80.00               3rd Qu.: 14.00      \n",
        " Max.   :100.00               Max.   :144.00      \n",
        " NA's   :6339                 NA's   :7440        \n",
        " MOOC_AverageMaxProblemsSolved MOOC_PercentageProblemsSolved   MOOC_Grade  \n",
        " Min.   : 17.00                Min.   :  0.00                Min.   :-Inf  \n",
        " 1st Qu.: 17.00                1st Qu.: 10.00                1st Qu.:-Inf  \n",
        " Median : 20.00                Median : 30.00                Median :-Inf  \n",
        " Mean   : 36.44                Mean   : 37.27                Mean   :-Inf  \n",
        " 3rd Qu.: 25.00                3rd Qu.: 60.00                3rd Qu.:   0  \n",
        " Max.   :142.00                Max.   :100.00                Max.   : 100  \n",
        " NA's   :7440                  NA's   :7440                                \n",
        "    EPFL_Topic   EPFL_BacGrade    EPFL_BacLevel EPFL_CourseType\n",
        " CS-111  :1631   Min.   :0.1260   HI  :4346     CS  :2947      \n",
        " CS-112  :1316   1st Qu.:0.7500   LO  :4249     EE  : 797      \n",
        " EE-102  : 797   Median :0.8083   NA's: 719     MATH:1404      \n",
        " MATH-111:1404   Mean   :0.8062                 PHYS:4166      \n",
        " PHYS-101:4166   3rd Qu.:0.8536                                \n",
        "                 Max.   :1.0000                                \n",
        "                 NA's   :719                                   \n",
        "         EPFL_UniqueTopicID_Anonymous\n",
        " PHYS-101 2014-2015 T63: 336         \n",
        " EE-102 2015-2016 T29  : 300         \n",
        " MATH-111 2015-2016 T18: 295         \n",
        " PHYS-101 2015-2016 T46: 295         \n",
        " PHYS-101 2013-2014 T15: 288         \n",
        " EE-102 2014-2015 T29  : 281         \n",
        " (Other)               :7519         \n",
        "                       EPFL_AnonymousUserID\n",
        " e2e988bc1a66ae2f50330fd60a0c2367:   8     \n",
        " 16af0f5438b6f7983392ab058a7e4eeb:   7     \n",
        " 29e1b05939960835d785c0aaa20ae388:   7     \n",
        " 35ad976f794b6523fe4dd3388b02ff5b:   7     \n",
        " 4abf1bcbc3198f4f3c2feba5bca4f6e6:   7     \n",
        " 4c46db8f7de7dd9b3521efad9efe0aa9:   7     \n",
        " (Other)                         :9271     "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# For each variable, print some information about the distribution (if the variable is quantitative) \n",
     "# or about the distinct values taken by the variable (if the variable is categorical). \n",
     "\n",
     "summary(moocs)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 83,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<dl class=dl-horizontal>\n",
        "\t<dt>AUDIT</dt>\n",
        "\t\t<dd>7</dd>\n",
        "\t<dt>CGC</dt>\n",
        "\t\t<dd>513</dd>\n",
        "\t<dt>EDBB</dt>\n",
        "\t\t<dd>1</dd>\n",
        "\t<dt>EL</dt>\n",
        "\t\t<dd>129</dd>\n",
        "\t<dt>GC</dt>\n",
        "\t\t<dd>970</dd>\n",
        "\t<dt>GM</dt>\n",
        "\t\t<dd>1157</dd>\n",
        "\t<dt>IN</dt>\n",
        "\t\t<dd>535</dd>\n",
        "\t<dt>MA</dt>\n",
        "\t\t<dd>1040</dd>\n",
        "\t<dt>MT</dt>\n",
        "\t\t<dd>1128</dd>\n",
        "\t<dt>MX</dt>\n",
        "\t\t<dd>168</dd>\n",
        "\t<dt>PH</dt>\n",
        "\t\t<dd>649</dd>\n",
        "\t<dt>SC</dt>\n",
        "\t\t<dd>346</dd>\n",
        "\t<dt>SIE</dt>\n",
        "\t\t<dd>472</dd>\n",
        "\t<dt>SV</dt>\n",
        "\t\t<dd>2199</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description*}\n",
        "\\item[AUDIT] 7\n",
        "\\item[CGC] 513\n",
        "\\item[EDBB] 1\n",
        "\\item[EL] 129\n",
        "\\item[GC] 970\n",
        "\\item[GM] 1157\n",
        "\\item[IN] 535\n",
        "\\item[MA] 1040\n",
        "\\item[MT] 1128\n",
        "\\item[MX] 168\n",
        "\\item[PH] 649\n",
        "\\item[SC] 346\n",
        "\\item[SIE] 472\n",
        "\\item[SV] 2199\n",
        "\\end{description*}\n"
       ],
       "text/markdown": [
        "AUDIT\n",
        ":   7CGC\n",
        ":   513EDBB\n",
        ":   1EL\n",
        ":   129GC\n",
        ":   970GM\n",
        ":   1157IN\n",
        ":   535MA\n",
        ":   1040MT\n",
        ":   1128MX\n",
        ":   168PH\n",
        ":   649SC\n",
        ":   346SIE\n",
        ":   472SV\n",
        ":   2199\n",
        "\n"
       ],
       "text/plain": [
        "AUDIT   CGC  EDBB    EL    GC    GM    IN    MA    MT    MX    PH    SC   SIE \n",
        "    7   513     1   129   970  1157   535  1040  1128   168   649   346   472 \n",
        "   SV \n",
        " 2199 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# To get information about only one variable, use the $ sign to separate the name of \n",
     "# the dataframe and the name of the variable like so: <name_dataframe>$<name_variable>\n",
     "\n",
     "# For nominal variables we get the count for the different categories \n",
     "summary(moocs$EPFL_StudentSection)\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 84,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's \n",
        "   0.00   20.00   60.00   54.28   80.00  100.00    6339 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# For a quantitative variable we get the ususal central tendency and dispersion indicators\n",
     "summary(moocs$MOOC_PercentageVideosWatched)\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 85,
    "metadata": {},
    "outputs": [
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    "source": [
     "# We can also compute these separately.\n",
     "mean(moocs$MOOC_PercentageVideosWatched, na.rm=T) # na.rm removes missing values\n",
     "sd(moocs$MOOC_PercentageVideosWatched, na.rm=T) # standard deviation\n",
     "median(moocs$MOOC_PercentageVideosWatched, na.rm=T) # median (50% observations below and 50% observations above)\n",
     "max(moocs$MOOC_PercentageVideosWatched, na.rm=T) # maximum\n",
     "min(moocs$MOOC_PercentageVideosWatched, na.rm=T) # minimum"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
     "    <strong>TODO</strong> : What is the mean and the standard deviation of the EPFL_CourseGrade ?\n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 86,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
        "  0.000   3.000   4.000   3.719   5.000   6.000 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "################\n",
     "# Begin solution\n",
     "\n",
     "summary(moocs$EPFL_CourseGrade)\n",
     "\n",
     "# End solution\n",
     "###############"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Defining new categorical variables\n",
     "It is sometimes useful to transform a quantitative variable into a categorical variable. \n",
     "\n",
     "For example, below we create a variable that reflects whether students used the MOOC or not based on the number of videos they watched and the number of problems they attempted in the MOOC. In R, categorical variables are created with the function `factor`. The variable `didMOOC` is given the value `NO.MOOC` whenever the values for the number of videos watched and the number of problems attempted is missin. In other cases, the value is `MOOC`.   \n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 87,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<dl class=dl-horizontal>\n",
        "\t<dt>MOOC</dt>\n",
        "\t\t<dd>3004</dd>\n",
        "\t<dt>NO.MOOC</dt>\n",
        "\t\t<dd>6310</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description*}\n",
        "\\item[MOOC] 3004\n",
        "\\item[NO.MOOC] 6310\n",
        "\\end{description*}\n"
       ],
       "text/markdown": [
        "MOOC\n",
        ":   3004NO.MOOC\n",
        ":   6310\n",
        "\n"
       ],
       "text/plain": [
        "   MOOC NO.MOOC \n",
        "   3004    6310 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "moocs$didMOOC = factor(\n",
     "  ifelse(\n",
     "      is.na(moocs$MOOC_NVideosWatched) & \n",
     "      is.na(moocs$MOOC_NProblemsSolved), \n",
     "    \"NO.MOOC\", \n",
     "    \"MOOC\")\n",
     ")\n",
     "\n",
     "summary(moocs$didMOOC)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 88,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<dl class=dl-horizontal>\n",
        "\t<dt>NO.VIDEO</dt>\n",
        "\t\t<dd>6591</dd>\n",
        "\t<dt>SOME.VIDEO</dt>\n",
        "\t\t<dd>2723</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description*}\n",
        "\\item[NO.VIDEO] 6591\n",
        "\\item[SOME.VIDEO] 2723\n",
        "\\end{description*}\n"
       ],
       "text/markdown": [
        "NO.VIDEO\n",
        ":   6591SOME.VIDEO\n",
        ":   2723\n",
        "\n"
       ],
       "text/plain": [
        "  NO.VIDEO SOME.VIDEO \n",
        "      6591       2723 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# We consider that not taking the MOOC is like not watching videos\n",
     "moocs$watched_videos = factor(\n",
     "                          ifelse(\n",
     "                            moocs$MOOC_PercentageVideosWatched == 0 |\n",
     "                            is.na(moocs$MOOC_PercentageVideosWatched),\n",
     "                            \"NO.VIDEO\",\n",
     "                            \"SOME.VIDEO\")\n",
     "                          )\n",
     "\n",
     "summary(moocs$watched_videos)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 89,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<dl class=dl-horizontal>\n",
        "\t<dt>NO.PROBLEM</dt>\n",
        "\t\t<dd>7621</dd>\n",
        "\t<dt>SOME.PROBLEM</dt>\n",
        "\t\t<dd>1693</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description*}\n",
        "\\item[NO.PROBLEM] 7621\n",
        "\\item[SOME.PROBLEM] 1693\n",
        "\\end{description*}\n"
       ],
       "text/markdown": [
        "NO.PROBLEM\n",
        ":   7621SOME.PROBLEM\n",
        ":   1693\n",
        "\n"
       ],
       "text/plain": [
        "  NO.PROBLEM SOME.PROBLEM \n",
        "        7621         1693 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# We consider that not taking the MOOC is like not solving any problems\n",
     "moocs$solved_problems = factor(\n",
     "                          ifelse(\n",
     "                            moocs$MOOC_PercentageProblemsSolved == 0 |\n",
     "                              is.na(moocs$MOOC_PercentageProblemsSolved),\n",
     "                            \"NO.PROBLEM\",\n",
     "                            \"SOME.PROBLEM\")\n",
     "                          )\n",
     "\n",
     "summary(moocs$solved_problems)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Checking activity types\n",
     "Do people who solve problems also watch videos ? When using a MOOC, some students only watch videos and don't do exercices. But most of the students who do exercices also watch videos. It appears that almost nobody is *only* solving problems. \n",
     "> **Problem**: If we use these variables as two factors to analyse our data set we'll have very uneven groups.     \n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 90,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "            \n",
        "             NO.PROBLEM SOME.PROBLEM\n",
        "  NO.VIDEO         6555           36\n",
        "  SOME.VIDEO       1066         1657"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# With two arguments, the table command cross-tabulates the number of observations per category.\n",
     "table(moocs$watched_videos, moocs$solved_problems)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
     "    <strong>TODO</strong> : To fix this problem we qualify MOOC usage with three categories: \n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "* `NONE` corresponds to no use of MOOCs, \n",
     "* `WATCH` corresponds to students mainly watching videos and \n",
     "* `DO` corresponds to students doing some exercices."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 91,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<dl class=dl-horizontal>\n",
        "\t<dt>DO</dt>\n",
        "\t\t<dd>1693</dd>\n",
        "\t<dt>NONE</dt>\n",
        "\t\t<dd>6555</dd>\n",
        "\t<dt>WATCH</dt>\n",
        "\t\t<dd>1066</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description*}\n",
        "\\item[DO] 1693\n",
        "\\item[NONE] 6555\n",
        "\\item[WATCH] 1066\n",
        "\\end{description*}\n"
       ],
       "text/markdown": [
        "DO\n",
        ":   1693NONE\n",
        ":   6555WATCH\n",
        ":   1066\n",
        "\n"
       ],
       "text/plain": [
        "   DO  NONE WATCH \n",
        " 1693  6555  1066 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "#################\n",
     "# Begin Solution:\n",
     "moocs$MOOC <- factor(\n",
     "  ifelse(moocs$watched_videos == \"NO.VIDEO\" & moocs$solved_problems == \"NO.PROBLEM\",\n",
     "       \"NONE\",\n",
     "       ifelse(moocs$solved_problems == \"SOME.PROBLEM\",\n",
     "              \"DO\",\n",
     "              \"WATCH\")\n",
     "       )\n",
     ")\n",
     "# End Solution \n",
     "###############\n",
     "\n",
     "summary(moocs$MOOC)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The order of the categories is a bit 'unlogical'. We'd like to have them appear in outputs and graphs sorted by increasing level of involvement: NONE, WATCH and DO. Let's fix this problem by reordering the levels of the factor."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 92,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        " NONE WATCH    DO \n",
        " 6555  1066  1693 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "library(gdata)\n",
     "# put the levels into a convenient order (for graphing, etc.)\n",
     "moocs$MOOC <- reorder(moocs$MOOC, new.order=c(\"NONE\", \"WATCH\", \"DO\"))\n",
     "table(moocs$MOOC)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Do people who use the MOOC get better grades ?\n",
     "\n",
     "## Looking at the means.\n",
     "Let's start by looking at the mean grade for the three groups of our variable `MOOC`. The `ddply` function allows to apply a function to a subset of the data defined by a categorical variable (`MOOC` in our case). The ddply returns a new data frame with the category and the result."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 93,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<table>\n",
        "<caption>A data.frame: 3 × 2</caption>\n",
        "<thead>\n",
        "\t<tr><th scope=col>MOOC</th><th scope=col>grp.mean</th></tr>\n",
        "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
        "</thead>\n",
        "<tbody>\n",
        "\t<tr><td>NONE </td><td>3.513959</td></tr>\n",
        "\t<tr><td>WATCH</td><td>3.828799</td></tr>\n",
        "\t<tr><td>DO   </td><td>4.445363</td></tr>\n",
        "</tbody>\n",
        "</table>\n"
       ],
       "text/latex": [
        "A data.frame: 3 × 2\n",
        "\\begin{tabular}{r|ll}\n",
        " MOOC & grp.mean\\\\\n",
        " <fct> & <dbl>\\\\\n",
        "\\hline\n",
        "\t NONE  & 3.513959\\\\\n",
        "\t WATCH & 3.828799\\\\\n",
        "\t DO    & 4.445363\\\\\n",
        "\\end{tabular}\n"
       ],
       "text/markdown": [
        "\n",
        "A data.frame: 3 × 2\n",
        "\n",
        "| MOOC &lt;fct&gt; | grp.mean &lt;dbl&gt; |\n",
        "|---|---|\n",
        "| NONE  | 3.513959 |\n",
        "| WATCH | 3.828799 |\n",
        "| DO    | 4.445363 |\n",
        "\n"
       ],
       "text/plain": [
        "  MOOC  grp.mean\n",
        "1 NONE  3.513959\n",
        "2 WATCH 3.828799\n",
        "3 DO    4.445363"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "mu <- ddply(moocs, \"MOOC\", summarise, grp.mean=mean(EPFL_CourseGrade))\n",
     "mu\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Looking at the variance ?\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 94,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<table>\n",
        "<caption>A data.frame: 3 × 3</caption>\n",
        "<thead>\n",
        "\t<tr><th scope=col>MOOC</th><th scope=col>grp.sd</th><th scope=col>grp.mean</th></tr>\n",
        "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
        "</thead>\n",
        "<tbody>\n",
        "\t<tr><td>DO   </td><td>1.197095</td><td>4.445363</td></tr>\n",
        "\t<tr><td>NONE </td><td>1.490969</td><td>3.513959</td></tr>\n",
        "\t<tr><td>WATCH</td><td>1.325802</td><td>3.828799</td></tr>\n",
        "</tbody>\n",
        "</table>\n"
       ],
       "text/latex": [
        "A data.frame: 3 × 3\n",
        "\\begin{tabular}{r|lll}\n",
        " MOOC & grp.sd & grp.mean\\\\\n",
        " <fct> & <dbl> & <dbl>\\\\\n",
        "\\hline\n",
        "\t DO    & 1.197095 & 4.445363\\\\\n",
        "\t NONE  & 1.490969 & 3.513959\\\\\n",
        "\t WATCH & 1.325802 & 3.828799\\\\\n",
        "\\end{tabular}\n"
       ],
       "text/markdown": [
        "\n",
        "A data.frame: 3 × 3\n",
        "\n",
        "| MOOC &lt;fct&gt; | grp.sd &lt;dbl&gt; | grp.mean &lt;dbl&gt; |\n",
        "|---|---|---|\n",
        "| DO    | 1.197095 | 4.445363 |\n",
        "| NONE  | 1.490969 | 3.513959 |\n",
        "| WATCH | 1.325802 | 3.828799 |\n",
        "\n"
       ],
       "text/plain": [
        "  MOOC  grp.sd   grp.mean\n",
        "1 DO    1.197095 4.445363\n",
        "2 NONE  1.490969 3.513959\n",
        "3 WATCH 1.325802 3.828799"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "sigma <- ddply(moocs, \"MOOC\", summarise, grp.sd=sd(EPFL_CourseGrade))\n",
     "#head(sigma)\n",
     "\n",
     "info <- merge(sigma, mu)\n",
     "info\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Plotting\n",
     "To further investigate the difference between the ghree groups, let's plot the grade of the students `EPFL_CourseGrade` against the categorical variable `MOOC` that we just defined.  We'll use three different plots: \n",
     "\n",
     "* boxplot, \n",
     "* histogram and \n",
     "* mean plots.\n",
     "\n",
     "### Boxplots\n",
     "\n",
     "Boxplots allow to visualise the distribution of the variable. The central line in the box shows the median and the edges of the boxes show the interquartiles. A simple tutorial for variations of this type of plot is available here: http://www.sthda.com/english/wiki/ggplot2-box-plot-quick-start-guide-r-software-and-data-visualization.\n",
     "\n",
     "From the plot below, it seems that the distribution of grades for people who did not use the MOOC (`NONE`) tends to be lower in the grade scale than the grades of people who `WATCH` videos or people who `DO` assignments. From the shape of the boxesm we also see that the distributions for `NONE` and `WATCH` are more symmetric than for `DO`."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 95,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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       "text/plain": [
        "Plot with title “Grade by Activity Level”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# Setting the size of plots generated with ggplot below. \n",
     "options(repr.plot.width = 5, repr.plot.height = 5)\n",
     "\n",
     "# Quick and simple boxplot\n",
     "boxplot(moocs$EPFL_CourseGrade ~ moocs$MOOC, main=\"Grade by Activity Level\", xlab=\"Activity Level\", ylab=\"Grade\")\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 96,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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HkHDhx455136ow7HI533303MzPTnZ4VTz31lCRJK1asaMxJmpKnFWiF0WicNm3a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",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# Setting the size of plots generated with ggplot below. \n",
     "options(repr.plot.width = 8, repr.plot.height = 5)\n",
     "\n",
     "# More sophisticated plots with GGPLOT.\n",
     "# Tutorial: http://www.sthda.com/english/wiki/ggplot2-box-plot-quick-start-guide-r-software-and-data-visualization\n",
     "ggplot(moocs, aes(x=MOOC, y=EPFL_CourseGrade, fill=MOOC)) +\n",
     "    geom_boxplot(notch=TRUE) + coord_flip() "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Histograms\n",
     "\n",
     "Histograms give a more precise representation of the actual grade distribution. Below, we define bins of 0.5 to represent the frequency of the different grades. The vertical dashed lines represent the means of the distributions. Notice that we reuse the dataframe `mu` that we defined above. We see indeed that the `DO` group is less symmetric than the others."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 97,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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j172k5RFOWFF15wOp1vvfXWkiVL2s56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\nAABIQAENAAAASEABDQAAAEjwv5SmMHADP5xgAAAAAElFTkSuQmCC",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# Tutorial about generating such a figure\n",
     "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n",
     "options(repr.plot.width = 8, repr.plot.height = 5)\n",
     "\n",
     "ggplot(moocs, aes(x=EPFL_CourseGrade, fill=MOOC)) +\n",
     "    geom_histogram(binwidth=.5, alpha=.5, position=\"dodge\") + \n",
     "    geom_vline(data=mu, aes(xintercept=grp.mean, color=MOOC), linetype=\"dashed\") \n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Mean plots\n",
     "Mean plots represent the mean along with the confidence interval for the mean. There is a 95% chance that the confidence interval contains the true mean of `EPFL_CourseGrade` for the population. "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 98,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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HPCrFmzeFMl3717FxkZuWDBAmVl5Q0b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\nIOYNGx8k4AAAAABJRU5ErkJggg==",
       "text/plain": [
        "Plot with title “Grade given MOOC activity”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "options(repr.plot.width = 5, repr.plot.height = 5)\n",
     "\n",
     "# plotmeans is defined in the gplots library \n",
     "# make sure to load the library by executing > library(gplots) before. \n",
     "plotmeans(moocs$EPFL_CourseGrade ~ moocs$MOOC, main=\"Grade given MOOC activity\", ylab=\"Grade\", xlab=\"Activity Level\")\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 99,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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715R4iNELGm16qc4VJnvRDLEMrbuL/h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\nrkJggg==",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "options(repr.plot.width = 5, repr.plot.height = 5)\n",
     "\n",
     "# Alternate form using the package ggpubr\n",
     "# See examples here: http://www.sthda.com/english/articles/24-ggpubr-publication-ready-plots/79-plot-meansmedians-and-error-bars/\n",
     "\n",
     "ggline(moocs, x = \"MOOC\", y = \"EPFL_CourseGrade\", \n",
     "            add = c(\"mean_ci\"))\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# ANOVA - Analysis of Variance"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
     "    <strong>Question</strong>: Does the grade of students (EPFL_CourseGrade) depend on students' type of MOOC interaction (MOOC, a categorical variable).\n",
     "</div>\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Test</strong>: ANOVA a.k.a. ANalysis Of VAriance \n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "ANOVA allows comparing whether one variable has the same mean in different groups ? The formula to specify the test is done in tow steps. First we define a linear model with  `m <- lm(quantitative ~  categorical)` and then we do the Anova of the model `Anova(m)`.\n",
     "\n",
     "* H0: mean_1 = mean_2 = ...= Mean_n\n",
     "* H1: mean_1 != mean_2 != ... != mean_n\n",
     "    "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We use the Analysis of Variance (ANOVA) to compare the mean of a variable across several modalities of a categorical variable. In the example below, we compare the course grade (`EPFL_CourseGrade`) across different modalities of MOOC usage (the `MOOC` variable takes three possible values: `NONE`, `WATCH` and `DO`). "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 100,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<table>\n",
        "<caption>A anova: 2 × 4</caption>\n",
        "<thead>\n",
        "\t<tr><th></th><th scope=col>Sum Sq</th><th scope=col>Df</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
        "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
        "</thead>\n",
        "<tbody>\n",
        "\t<tr><th scope=row>moocs$MOOC</th><td> 1181.668</td><td>   2</td><td>291.5936</td><td>1.479869e-123</td></tr>\n",
        "\t<tr><th scope=row>Residuals</th><td>18866.175</td><td>9311</td><td>      NA</td><td>           NA</td></tr>\n",
        "</tbody>\n",
        "</table>\n"
       ],
       "text/latex": [
        "A anova: 2 × 4\n",
        "\\begin{tabular}{r|llll}\n",
        "  & Sum Sq & Df & F value & Pr(>F)\\\\\n",
        "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
        "\\hline\n",
        "\tmoocs\\$MOOC &  1181.668 &    2 & 291.5936 & 1.479869e-123\\\\\n",
        "\tResiduals & 18866.175 & 9311 &       NA &            NA\\\\\n",
        "\\end{tabular}\n"
       ],
       "text/markdown": [
        "\n",
        "A anova: 2 × 4\n",
        "\n",
        "| <!--/--> | Sum Sq &lt;dbl&gt; | Df &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
        "|---|---|---|---|---|\n",
        "| moocs$MOOC |  1181.668 |    2 | 291.5936 | 1.479869e-123 |\n",
        "| Residuals | 18866.175 | 9311 |       NA |            NA |\n",
        "\n"
       ],
       "text/plain": [
        "           Sum Sq    Df   F value  Pr(>F)       \n",
        "moocs$MOOC  1181.668    2 291.5936 1.479869e-123\n",
        "Residuals  18866.175 9311       NA            NA"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# needs library(car)\n",
     "\n",
     "m <- lm(moocs$EPFL_CourseGrade ~ moocs$MOOC)  \n",
     "Anova(m)\n",
     "\n",
     "r <- residuals(m)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
     "    <strong>Reporting</strong>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "\n",
     "This is the way you report the ANOVA in an article.\n",
     "\n",
     "> We conducted a one-way ANOVA to test whether the course grades differ for different categories of MOOC usage. There is a significant difference of course grades across different types of MOOC use (F[2,9311]=291.6, p<.001). \n",
     "\n",
     "Beware, that since we did not randomly assign subjects to experimental groups, but rather students chose whether they use the MOOC or not, we can't conclude about any causal effect. It is possible that better students are inclided to use MOOCs more than weaker students. Hence, the \"effect of\" the MOOC would be due to this hidden variable which actually explains the difference."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightBlue;\">\n",
     "    <strong>Advanced topic</strong> : There are different ways to run anovas in R. They differ with regards to the type of Sum of Square that they report.  \n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Following http://goanna.cs.rmit.edu.au/~fscholer/anova.php the Type III Sum of Square is more adapted  to interpret the contributions of the differnt variables. R and anova report Type I sums of square.\n",
     "\n",
     "Here is an explanation about how to obtain Type III sums of squares: https://www.r-bloggers.com/anova-%E2%80%93-type-iiiiii-ss-explained/\n",
     "And some explanations here: http://prometheus.scp.rochester.edu/zlab/sites/default/files/InteractionsAndTypesOfSS.pdf\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
     "    <strong>Question</strong>: Which groups differ among each other ? Now that the ANOVA tells us that the three types of MOOC useage do not lead to the same grade, we want to know more precisely which categories are different from others.\n",
     "</div>\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Test</strong>: Pair-wise t-test\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "A pairwise test allows to know which groups differ from each other. Because of repeated testing, we have to adjust the p-value by dividing the .05 value by the number of tests. In our case, the tests show that all groups differ from each other when taken 2"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 122,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tPairwise comparisons using t tests with pooled SD \n",
        "\n",
        "data:  moocs$EPFL_CourseGrade and moocs$MOOC \n",
        "\n",
        "      NONE    WATCH  \n",
        "WATCH 6.7e-11 -      \n",
        "DO    < 2e-16 < 2e-16\n",
        "\n",
        "P value adjustment method: bonferroni "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# Checks which group is different from what other group in doing 2 by 2 tests.\n",
     "pairwise.t.test(moocs$EPFL_CourseGrade, moocs$MOOC, p.adj = \"bonf\") \n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 123,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Means"
      ]
     },
     {
      "data": {
       "text/html": [
        "<dl class=dl-horizontal>\n",
        "\t<dt>NONE</dt>\n",
        "\t\t<dd>3.51395881006865</dd>\n",
        "\t<dt>WATCH</dt>\n",
        "\t\t<dd>3.82879924953096</dd>\n",
        "\t<dt>DO</dt>\n",
        "\t\t<dd>4.44536326048435</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description*}\n",
        "\\item[NONE] 3.51395881006865\n",
        "\\item[WATCH] 3.82879924953096\n",
        "\\item[DO] 4.44536326048435\n",
        "\\end{description*}\n"
       ],
       "text/markdown": [
        "NONE\n",
        ":   3.51395881006865WATCH\n",
        ":   3.82879924953096DO\n",
        ":   4.44536326048435\n",
        "\n"
       ],
       "text/plain": [
        "    NONE    WATCH       DO \n",
        "3.513959 3.828799 4.445363 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Standard Deviations"
      ]
     },
     {
      "data": {
       "text/html": [
        "<dl class=dl-horizontal>\n",
        "\t<dt>NONE</dt>\n",
        "\t\t<dd>1.49096929439005</dd>\n",
        "\t<dt>WATCH</dt>\n",
        "\t\t<dd>1.32580239254368</dd>\n",
        "\t<dt>DO</dt>\n",
        "\t\t<dd>1.19709461657678</dd>\n",
        "</dl>\n"
       ],
       "text/latex": [
        "\\begin{description*}\n",
        "\\item[NONE] 1.49096929439005\n",
        "\\item[WATCH] 1.32580239254368\n",
        "\\item[DO] 1.19709461657678\n",
        "\\end{description*}\n"
       ],
       "text/markdown": [
        "NONE\n",
        ":   1.49096929439005WATCH\n",
        ":   1.32580239254368DO\n",
        ":   1.19709461657678\n",
        "\n"
       ],
       "text/plain": [
        "    NONE    WATCH       DO \n",
        "1.490969 1.325802 1.197095 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "cat(\"Means\")\n",
     "tapply(moocs$EPFL_CourseGrade, moocs$MOOC, mean)\n",
     "\n",
     "cat(\"Standard Deviations\")\n",
     "tapply(moocs$EPFL_CourseGrade, moocs$MOOC, sd)\n",
     "\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
     "    <strong>Reporting</strong>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "And here is the wording for the article. \n",
     "\n",
     "> A series of pair-wise t-tests with bonferonni adjusment for repeated testing, shows that the average grade for students who did not use the MOOC (m=3.5, sd=2.5) is smaller than the average grade of students who watched videos (m=3.8, sd=1.3) and smaller than the average grade of students who did the assignments (m=4.4, sd=1.2)."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Assumptions\n",
     "Is it ok to run an ANOVA blindly as we did just before ? \n",
     "\n",
     "Not really, we should have checked the assumptions for ANOVA first.\n",
     "\n",
     "* Normality of the residuals\n",
     "* Homoscedasticity of the residuals = the error distribution should be the same regardless of the category.\n",
     "\n",
     "### Visually inspecting normality Assumption\n",
     "Testing normality visually with quantile plots. If the variable is normally distributed, the observations would follow the line drawn by qqline.  We see from the plots below that the distribution of the residuals of our model used for the Anova departs very strongly from a normal distribution.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 127,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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El4poKDsXoxtjoGjk8YH5CQCrOi0JgVNQnfECuISE/L2QLjxieUAUhod2hJeEqs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\nAZj9AVD8Frn2ZE60AAAAAElFTkSuQmCC",
       "text/plain": [
        "Plot with title “Residuals from ANOVA”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# split the plotting area into 2 lines and 2 columns\n",
     "par(mfrow=c(2,2))\n",
     "\n",
     "# Setting the size of plots below. \n",
     "options(repr.plot.width = 7.5, repr.plot.height = 7.5)\n",
     "\n",
     "# we generate 1000 data points from a normally distributed variable (by default average = 0 and standard deviation = 1)\n",
     "v <- rnorm(1000) \n",
     "hist(v, main=\"Normal variable (generated)\")\n",
     "qqnorm(v, main=\"Normal variable (generated)\");\n",
     "qqline(v);\n",
     "\n",
     "# The residuals of the model we used to run the Anova\n",
     "# r <- residuals(m)\n",
     "hist(r, main=\"Residuals from ANOVA\")\n",
     "qqnorm(r, main=\"Residuals from ANOVA\");\n",
     "qqline(r)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
     "    <strong>Question</strong>: Are the residuals normally distributed ?\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Test</strong>: Shapiro-Wilks Test\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "\n",
     "Normality can also be tested statistically, however the normality tests are rather sensitive to small deviations, especially when sample sizes are large. For example, the Shapiro-Wilks test, is testing the null hypothesis that the variable is normally distributed. In this case the adequate p.value is .1. Hence, with p <<.1 we have to reject the null hypothesis and conclude that the variable is not normally distributed. This test work with samples smaller than 5000 observations.  \n",
     "\n",
     "* H0: variable is normally distributed\n",
     "* H1: variable is not normally distributed\n",
     "\n",
     "We see below that for our variable `v` that we generated to be normally distributed, p = 0.47, far greater than 0.1, hence we cannot reject H0.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 125,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tShapiro-Wilk normality test\n",
        "\n",
        "data:  v\n",
        "W = 0.99838, p-value = 0.4792\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "shapiro.test(v)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "\n",
     "However, for the residuals of our Anova, we have to reject H0, and conclude that they are not normally distributed.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 126,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tShapiro-Wilk normality test\n",
        "\n",
        "data:  sample(r, 1500)\n",
        "W = 0.9573, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# taking a sample of 1500 residuals for illustrating the output of the shapiro test\n",
     "shapiro.test(sample(r,1500)) \n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
     "    <strong>Question</strong>: Are the residuals homoscedastic ? In other terms, is the variance of the residuals the same for the different groups ?\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Test</strong>: Bartlett test\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "* H0: variances are the same\n",
     "* H1: variances are different\n",
     "\n",
     "We see below, that the p-value is much smaller than .05 and therefore we reject H0 (and conclude that variances are different). \n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 106,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tBartlett test of homogeneity of variances\n",
        "\n",
        "data:  r by moocs$MOOC\n",
        "Bartlett's K-squared = 130, df = 2, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "bartlett.test(r ~ moocs$MOOC)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "\n",
     "\n",
     "The difference in variuance is also appararent in a boxplot, where we see that the variance for the DO group is smaller. We also see that the residuals for WATCH tend to be slightly more positive than negative (their median is above 0) "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 107,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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zB5D08Kwnr7a/eWN1tuvdrjQCbvIUpB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\nYUEFYUEFYUEFYUEFYUHF/wOCQirlK83Q8wAAAABJRU5ErkJggg==",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "options(repr.plot.width = 5, repr.plot.height = 5)\n",
     "boxplot(r ~ moocs$MOOC)\n",
     "abline(h=0)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## If variances are unequal or residuals are not normally distributed\n",
     "\n",
     "If variances are unequal we can either \n",
     "\n",
     "* adapt the oneway test by stating that `var.equal = F` \n",
     "* or use a non parametric alternative to ANOVA like the Kruskal Wallis test. "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 108,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tOne-way analysis of means (not assuming equal variances)\n",
        "\n",
        "data:  moocs$EPFL_CourseGrade and moocs$MOOC\n",
        "F = 366.38, num df = 2.0, denom df = 2495.4, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "# adapt the caluclations to take unequal variances into account \n",
     "oneway.test(moocs$EPFL_CourseGrade ~ moocs$MOOC, var.equal = F)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
     "    <strong>Question</strong>: Are samples from the different groups stemming from the same distribution ?\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Test</strong>: Kruskal test, a non-parametric alternative to ANOVA which does not pressupose normally distributed residuals.\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Tests the null hypothesis that the location parameters are the same in each of the groups. This test does not make assumptions about the distribution of the residuals, nor about the variances.\n",
     "\n",
     "* H0: the mean ranks of observations are the same in all groups\n",
     "* H1: the mean ranks of observations are different."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 128,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tKruskal-Wallis rank sum test\n",
        "\n",
        "data:  moocs$EPFL_CourseGrade by moocs$MOOC\n",
        "Kruskal-Wallis chi-squared = 608.7, df = 2, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "\n",
     "kruskal.test(moocs$EPFL_CourseGrade ~ moocs$MOOC)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
     "    <strong>Reporting</strong>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "> Because the assumption of normality of residuals was not respected (W = 0.94655, p-value < .001) in our sample, we conducted a non-parametric Kruskal-Wallis test that showed that the mean rank of course grades differs significantly across groups (X2[2]=608.7, p < .001).  "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Exercise : analyse the effect of prior knowlege on the grades.\n",
     "Students' baccalaureat grade is given by the variable `EPFL_BacGrade`. In the plot below we see the distribution of the grades at the baccalaureat and display the median and quartiles as vertical bars.\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 129,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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Dwez8TExNbW1svLy8LCQiUTVwN9fX0P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\nAEBwSDgAAABAcH8Bi5BQsX3Dww4AAAAASUVORK5CYII=",
       "text/plain": [
        "Plot with title “Histogram of moocs.bac$EPFL_BacGrade”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "options(repr.plot.width = 6, repr.plot.height = 4)\n",
     "\n",
     "# Remove observations for which we do not have a EPFL_BacGrade\n",
     "moocs.bac <- subset(moocs, ! is.na(moocs$EPFL_BacGrade))\n",
     "\n",
     "# Draw a histogram with 50 bins\n",
     "hist(moocs.bac$EPFL_BacGrade, breaks=50)\n",
     "\n",
     "# Draw a vertical line at the median\n",
     "abline(v=median(moocs.bac$EPFL_BacGrade, na.rm=T), col=\"red\", lwd=3) \n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
     "    <strong>Task 1</strong> : Define two categorical variables named prior and prior4 that distinguish students given their baccalaureat grade. \n",
     "    <ul>\n",
     "        <li>prior : The values of the variable are HI for strong students and LO for weakers students. use median() to define high and low levels of ability</li>\n",
     "    </ul>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 130,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "  LO   HI \n",
        "4318 4277 "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# TODO: Define two categorical variables named moocs$prior and moocs$prior4 that distinguishstudents given at their baccalaureat grade.\n",
     "\n",
     "# 1) moocs$prior. \n",
     "# The values of the variable are \"HI\"\" for strong students and \"LO\"\" for weakers students.\n",
     "# => use median() to define high and low levels of ability\n",
     "\n",
     "################\n",
     "# Begin solution\n",
     "moocs.bac$prior <- factor(\n",
     "                  ifelse(moocs.bac$EPFL_BacGrade > median(moocs.bac$EPFL_BacGrade, na.rm=T),\n",
     "                         \"HI\",\n",
     "                         \"LO\"\n",
     "                         )\n",
     ")\n",
     "\n",
     "# reorder the levels of prior so that low comes before hi in the graphs\n",
     "moocs.bac$prior <- reorder(moocs.bac$prior, new.order=c(\"LO\", \"HI\"))\n",
     "\n",
     "\n",
     "# end solution\n",
     "##############\n",
     "\n",
     "\n",
     "# count the number of observations in LO and HI \n",
     "table(moocs.bac$prior)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
     "    <strong>Task 2</strong> : Plot the means for the EPFL_CourseGrade given the prior grade level. \n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 131,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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XmkgwD0M85FuHv37i63y8jIuLq67tixo78jAQDfKSoqcnd39/f3HzVqFOksAP2M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",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "################\n",
     "# Begin Solution\n",
     "\n",
     "options(repr.plot.width = 5, repr.plot.height = 5)\n",
     "plotmeans(moocs.bac$EPFL_CourseGrade ~ moocs.bac$prior)\n",
     "\n",
     "# end Solution\n",
     "################\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
     "    <strong>Task 3</strong> : Compare the means of EPFL_CourseGrade. \n",
     "    <ul>\n",
     "        <li>Check assumptions to run an ANOVA </li>\n",
     "        <li>Run an ANOVA or a replacement if the assumptions are not set </li>\n",
     "    </ul>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 132,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tShapiro-Wilk normality test\n",
        "\n",
        "data:  sample(r2, 2000)\n",
        "W = 0.95358, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "\tBartlett test of homogeneity of variances\n",
        "\n",
        "data:  r2 by moocs.bac$prior\n",
        "Bartlett's K-squared = 114.6, df = 1, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "\tKruskal-Wallis rank sum test\n",
        "\n",
        "data:  moocs.bac$EPFL_CourseGrade by moocs.bac$prior\n",
        "Kruskal-Wallis chi-squared = 867.09, df = 1, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "image/png": 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IWmn2eOZwqtkPye1ZujNyAdh3+EPlF1Bm4VRGEpNP088ztsZwnT96wm0LfrIA9w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\nRK5CYII=",
       "text/plain": [
        "Plot with title “Normal Q-Q Plot”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "################\n",
     "# Begin Solution\n",
     "\n",
     "# Build model\n",
     "m2 <- lm(moocs.bac$EPFL_CourseGrade ~ moocs.bac$prior)\n",
     "r2 <- residuals(m2)\n",
     "\n",
     "# Check normality of residuals\n",
     "shapiro.test(sample(r2, 2000))\n",
     "\n",
     "# Check homoscedasticity \n",
     "bartlett.test(r2 ~ moocs.bac$prior)\n",
     "\n",
     "# Plots\n",
     "options(repr.plot.width = 6, repr.plot.height = 4)\n",
     "par(mfrow=c(1,2))\n",
     "qqnorm(r2)\n",
     "qqline(r2)\n",
     "\n",
     "boxplot(r2 ~ moocs.bac$prior)\n",
     "\n",
     "# The variances appear to be different across the levels of prior experience\n",
     "# => Kruskal test instead\n",
     "\n",
     "kruskal.test(moocs.bac$EPFL_CourseGrade ~ moocs.bac$prior)\n",
     "\n",
     "# end Solution\n",
     "################\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Two factor ANOVA"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We can add more than one categorical predictor and also model the interaction of two factors. When there is an interaction, the effect of one variable is conditional on the effect of another variable  \n",
     "\n",
     "Interaction between two terms is represented by a `:`. A syntaxic equivalent for the model that contains single and interaction effects is `A * B == A + B + A:B`"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 133,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Anova Table (Type III tests)\n",
       "\n",
       "Response: moocs.bac$EPFL_CourseGrade\n",
       "                               Sum Sq   Df    F value    Pr(>F)    \n",
       "(Intercept)                     31721    1 17373.5762 < 2.2e-16 ***\n",
       "moocs.bac$MOOC                    374    2   102.4039 < 2.2e-16 ***\n",
       "moocs.bac$prior                  1179    1   645.7809 < 2.2e-16 ***\n",
       "moocs.bac$MOOC:moocs.bac$prior     20    2     5.3793  0.004626 ** \n",
       "Residuals                       15682 8589                         \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n"
      ]
     }
    ],
    "source": [
     "\n",
     "m3  <- lm(moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + moocs.bac$prior + moocs.bac$MOOC:moocs.bac$prior)\n",
     "print(Anova(m3, type=3))\n",
     "\n",
     "r3 <- residuals(m3)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
     "    <strong>Reporting</strong>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "> We conducted a 3 x 2 factorial ANOVA with prior performance and MOOC useage as factors. The results indicate a main effect of MOOC usage (F[2,374]=102.40, p<.001), as well as a main effect of prior knowledge (F[1,1179]=645.78, p<.001). There is also an interaction effect between the two factors (F[20,2]=5.3, p<.01).    "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Plotting\n",
     "\n",
     "The ggline package comes in handy to plot interactions between variables. "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
     "    <strong>Reporting</strong>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "> In our case here, we see that the relation between the different types of MOOC activity is not the same from strong or weaker students. It seems that for strong students, watching videos does not increase the score compared to doing nothing. However, doing exercices is beneficial for both strong and weak students. "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 115,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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VM+XKVrGyp0fUkWul7g1MHaRUEDg8AB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\n",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "ggline(moocs.bac, x = \"MOOC\", y = \"EPFL_CourseGrade\", \n",
     "       add = c(\"mean_ci\"),\n",
     "       color = \"prior\", palette = \"jco\")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Testing Assumptions"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightBlue;\">\n",
     "    <strong>Advanced topic</strong> : With relatively large samples, normality and variance tests tend to produce small p-values and force us to reject the null hypotheses for normality and homoscedasticity. Instead of systematically (and somewhat blindly) using normality and homoscedasticity tests, we suggest that you explore visually the distribution of residuals to judge whether there are strong deviations from normality and whether there are large variance disparities.\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 116,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tBartlett test of homogeneity of variances\n",
        "\n",
        "data:  r3 by moocs.bac$MOOC\n",
        "Bartlett's K-squared = 116.22, df = 2, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "\tBartlett test of homogeneity of variances\n",
        "\n",
        "data:  r3 by moocs.bac$prior\n",
        "Bartlett's K-squared = 131.29, df = 1, p-value < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "image/png": 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gIqIzD/SiwG1BdYyphYeVuNV5uFXk3jhurDjjRrN7REV3AEUSkBlRGYAJXiZyOJ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\nAElFTkSuQmCC",
       "text/plain": [
        "Plot with title “Normal Q-Q Plot”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "options(repr.plot.width = 8, repr.plot.height = 4)\n",
     "par(mfrow=c(1,3))\n",
     "qqnorm(r3)\n",
     "qqline(r3)\n",
     "\n",
     "boxplot(r3 ~ moocs.bac$MOOC)\n",
     "boxplot(r3 ~ moocs.bac$prior)\n",
     "\n",
     "bartlett.test(r3 ~ moocs.bac$MOOC)\n",
     "bartlett.test(r3 ~ moocs.bac$prior)\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Linear regression\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
     "    <strong>Question</strong>: In our example data set, we want to know whether the EPFL course grade can be predicted by the percentage of videos that were watched by students.\n",
     "</div>\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Linear Model</strong>: The null model\n",
     "    <br/>The resulting model indicates that the average EPFL_Course_Grade is 3.74. \n",
     "</div>\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Test</strong>: t-test on Estimate\n",
     "    <br/>The resulting model indicates that the average EPFL_Course_Grade is 3.74. The t-test in addition tests whether this value can be considered larger than zero. From observing the statistics reported for the residuals, it appears that the median is larger than zerp (we would expext a median of zero if the residuals were normally distributed and if there were as many positive as negative error terms). \n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 118,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "Call:\n",
        "lm(formula = EPFL_CourseGrade ~ 1, data = moocs.bac)\n",
        "\n",
        "Residuals:\n",
        "    Min      1Q  Median      3Q     Max \n",
        "-3.7433 -0.7433  0.2567  1.2567  2.2567 \n",
        "\n",
        "Coefficients:\n",
        "            Estimate Std. Error t value Pr(>|t|)    \n",
        "(Intercept)  3.74328    0.01572   238.1   <2e-16 ***\n",
        "---\n",
        "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
        "\n",
        "Residual standard error: 1.457 on 8594 degrees of freedom\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# lm estimates the parameters of y = ax + b so as to minimise the Error. \n",
     "# In this model, we use a = 0 and estimate only b (represented as the constant term ~1)\n",
     "m0 <- lm(EPFL_CourseGrade ~ 1, data=moocs.bac)\n",
     "\n",
     "summary(m0)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Linear Model</strong>: The model with one predictor\n",
     "    <br/>The resulting model indicates that the average EPFL_Course_Grade is 3.62 + 0,01 for each percentage of videos watched. \n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Tests</strong>: Again, the  t-tests check whether the Estimates can be considered larger than zero. Additionally, a F-statistic is computed to compare the new model with the null model. This test checker whether we have reduced the residuals, and augmented the variance explained by the model by adding a term (in our case MOOC_PercentageVideosWatched. This indicates that this model m1 is better (accounts for more variance of the response variable) than model m0. \n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 119,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "Call:\n",
        "lm(formula = EPFL_CourseGrade ~ MOOC_PercentageVideosWatched, \n",
        "    data = moocs.bac)\n",
        "\n",
        "Residuals:\n",
        "    Min      1Q  Median      3Q     Max \n",
        "-4.6502 -0.7257  0.2607  0.8770  2.3770 \n",
        "\n",
        "Coefficients:\n",
        "                              Estimate Std. Error t value Pr(>|t|)    \n",
        "(Intercept)                  3.6230215  0.0433419   83.59   <2e-16 ***\n",
        "MOOC_PercentageVideosWatched 0.0102719  0.0006735   15.25   <2e-16 ***\n",
        "---\n",
        "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
        "\n",
        "Residual standard error: 1.23 on 2766 degrees of freedom\n",
        "  (5827 observations deleted due to missingness)\n",
        "Multiple R-squared:  0.07756,\tAdjusted R-squared:  0.07723 \n",
        "F-statistic: 232.6 on 1 and 2766 DF,  p-value: < 2.2e-16\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# lm estimates the parameters of y = ax + b so as to minimise the Error. \n",
     "m1 <- lm(EPFL_CourseGrade ~ MOOC_PercentageVideosWatched, data=moocs.bac)\n",
     "\n",
     "# The adjusted R^2 is interpreted as the proportion of variance explained.# \n",
     "# The F-statistic indicates whereh this model is better than the null model that would include only one parameter (the mean).\n",
     "summary(m1)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
     "    <strong>Question</strong>: Is the model satisfying the assumptions for regression ? \n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Assumptions for linear regression :\n",
     " * Linearity: The relationship between X and the mean of Y is linear.\n",
     " * Homoscedasticity: The variance of residual is the same for any value of X.\n",
     " * Independence: Observations are independent of each other.\n",
     " * Normality: For any fixed value of X, Y, and the residuals are normally distributed.\n",
     " "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Linear Model</strong>: Checking linearity\n",
     "    <br/>A simple way to check whether the relation between the dependent variable and predictors is linear consists of plotting one against he other.  \n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "From the plot below, we see there is clearly a problem. because the cloud of points does not seem to be well summarised by a line."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 162,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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W/ePK1LYxghRVEJCQmKZ4x0AsDMzEz2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cCxcuFBUV8Xg8TU1NKyurhQsXDh8+nKJQ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",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "options(repr.plot.width = 5, repr.plot.height = 5)\n",
     "\n",
     "# Simple plot with basic R plotting. Use the command plot(y ~ x).  \n",
     "# pch means plotting character, 20 is a small dot, 1 is a circle, etc.\n",
     "# jitter allows to add a little bit of noise so that the points do not overlap in the plot.\n",
     "\n",
     "plot(jitter(EPFL_CourseGrade) ~ jitter(MOOC_PercentageVideosWatched), pch = 20, data=moocs.bac)\n",
     "\n",
     "# also plot the regression line that corresponds to model m0\n",
     "abline(m0, col=\"blue\", lwd=3)\n",
     "\n",
     "# also plot the regression line that corresponds to model m1\n",
     "abline(m1, col=\"red\", lwd=3)\n",
     "\n",
     "# See https://rpkgs.datanovia.com/ggpubr/reference/ggscatter.html for more sophisticated plotting.\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Linear Model</strong>: Checking normality and homoscedasticity of the residuals.\n",
     "    <br/>A simple way to check these assumptions consists of plotting a QQ plot for residuals and investigating whether there is a \"trend\" in th residuals with th fitted values. \n",
     "</div>"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 158,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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mrVqrVq1aooHeLTTz/Nzc3Vb0lNTUVbtenBBUFwdnZev3798OHDS0vm8kk5chot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\nAf/a6AMZcNctlu0TgwcPVnhuIIR69uzJsgx43iQjI6OgoCB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OMsC7YwsKYuL6KwAAIABJREFUeMv8ksxMKCj4z4WdnMDBARwdwdERHBze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\nYII=",
       "text/plain": [
        "Plot with title “”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "options(repr.plot.width = 6, repr.plot.height = 6)\n",
     "par(mfrow=c(2,2))\n",
     "\n",
     "plot(m1)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Part of our trouble comes from thre asymetric distribution of the variable MOOC_PercentageVideosWatched"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 170,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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nsLBFbE4lK/MhA4KAIXqXGoVwgs47PAHiQYAmvxTOCCpoSQPOFf0wKGQ71CYBmf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\nAElFTkSuQmCC",
       "text/plain": [
        "Plot with title “Course Grade”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "par(mfrow=c(1,2))\n",
     "options(repr.plot.width = 8, repr.plot.height = 4)\n",
     "hist(moocs.bac$MOOC_PercentageVideosWatched, main=\"Percentage Videos Watched\", xlab=\"Percentage\")\n",
     "hist(moocs.bac$EPFL_CourseGrade, main=\"Course Grade\", xlab=\"Grade\")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Anscombe's dataset\n",
     "Anscombe, Francis J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17–21. doi: 10.2307/2682899."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 171,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<table>\n",
        "<caption>A data.frame: 11 × 8</caption>\n",
        "<thead>\n",
        "\t<tr><th scope=col>x1</th><th scope=col>x2</th><th scope=col>x3</th><th scope=col>x4</th><th scope=col>y1</th><th scope=col>y2</th><th scope=col>y3</th><th scope=col>y4</th></tr>\n",
        "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
        "</thead>\n",
        "<tbody>\n",
        "\t<tr><td>10</td><td>10</td><td>10</td><td> 8</td><td> 8.04</td><td>9.14</td><td> 7.46</td><td> 6.58</td></tr>\n",
        "\t<tr><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 6.95</td><td>8.14</td><td> 6.77</td><td> 5.76</td></tr>\n",
        "\t<tr><td>13</td><td>13</td><td>13</td><td> 8</td><td> 7.58</td><td>8.74</td><td>12.74</td><td> 7.71</td></tr>\n",
        "\t<tr><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8.81</td><td>8.77</td><td> 7.11</td><td> 8.84</td></tr>\n",
        "\t<tr><td>11</td><td>11</td><td>11</td><td> 8</td><td> 8.33</td><td>9.26</td><td> 7.81</td><td> 8.47</td></tr>\n",
        "\t<tr><td>14</td><td>14</td><td>14</td><td> 8</td><td> 9.96</td><td>8.10</td><td> 8.84</td><td> 7.04</td></tr>\n",
        "\t<tr><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 7.24</td><td>6.13</td><td> 6.08</td><td> 5.25</td></tr>\n",
        "\t<tr><td> 4</td><td> 4</td><td> 4</td><td>19</td><td> 4.26</td><td>3.10</td><td> 5.39</td><td>12.50</td></tr>\n",
        "\t<tr><td>12</td><td>12</td><td>12</td><td> 8</td><td>10.84</td><td>9.13</td><td> 8.15</td><td> 5.56</td></tr>\n",
        "\t<tr><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 4.82</td><td>7.26</td><td> 6.42</td><td> 7.91</td></tr>\n",
        "\t<tr><td> 5</td><td> 5</td><td> 5</td><td> 8</td><td> 5.68</td><td>4.74</td><td> 5.73</td><td> 6.89</td></tr>\n",
        "</tbody>\n",
        "</table>\n"
       ],
       "text/latex": [
        "A data.frame: 11 × 8\n",
        "\\begin{tabular}{r|llllllll}\n",
        " x1 & x2 & x3 & x4 & y1 & y2 & y3 & y4\\\\\n",
        " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
        "\\hline\n",
        "\t 10 & 10 & 10 &  8 &  8.04 & 9.14 &  7.46 &  6.58\\\\\n",
        "\t  8 &  8 &  8 &  8 &  6.95 & 8.14 &  6.77 &  5.76\\\\\n",
        "\t 13 & 13 & 13 &  8 &  7.58 & 8.74 & 12.74 &  7.71\\\\\n",
        "\t  9 &  9 &  9 &  8 &  8.81 & 8.77 &  7.11 &  8.84\\\\\n",
        "\t 11 & 11 & 11 &  8 &  8.33 & 9.26 &  7.81 &  8.47\\\\\n",
        "\t 14 & 14 & 14 &  8 &  9.96 & 8.10 &  8.84 &  7.04\\\\\n",
        "\t  6 &  6 &  6 &  8 &  7.24 & 6.13 &  6.08 &  5.25\\\\\n",
        "\t  4 &  4 &  4 & 19 &  4.26 & 3.10 &  5.39 & 12.50\\\\\n",
        "\t 12 & 12 & 12 &  8 & 10.84 & 9.13 &  8.15 &  5.56\\\\\n",
        "\t  7 &  7 &  7 &  8 &  4.82 & 7.26 &  6.42 &  7.91\\\\\n",
        "\t  5 &  5 &  5 &  8 &  5.68 & 4.74 &  5.73 &  6.89\\\\\n",
        "\\end{tabular}\n"
       ],
       "text/markdown": [
        "\n",
        "A data.frame: 11 × 8\n",
        "\n",
        "| x1 &lt;dbl&gt; | x2 &lt;dbl&gt; | x3 &lt;dbl&gt; | x4 &lt;dbl&gt; | y1 &lt;dbl&gt; | y2 &lt;dbl&gt; | y3 &lt;dbl&gt; | y4 &lt;dbl&gt; |\n",
        "|---|---|---|---|---|---|---|---|\n",
        "| 10 | 10 | 10 |  8 |  8.04 | 9.14 |  7.46 |  6.58 |\n",
        "|  8 |  8 |  8 |  8 |  6.95 | 8.14 |  6.77 |  5.76 |\n",
        "| 13 | 13 | 13 |  8 |  7.58 | 8.74 | 12.74 |  7.71 |\n",
        "|  9 |  9 |  9 |  8 |  8.81 | 8.77 |  7.11 |  8.84 |\n",
        "| 11 | 11 | 11 |  8 |  8.33 | 9.26 |  7.81 |  8.47 |\n",
        "| 14 | 14 | 14 |  8 |  9.96 | 8.10 |  8.84 |  7.04 |\n",
        "|  6 |  6 |  6 |  8 |  7.24 | 6.13 |  6.08 |  5.25 |\n",
        "|  4 |  4 |  4 | 19 |  4.26 | 3.10 |  5.39 | 12.50 |\n",
        "| 12 | 12 | 12 |  8 | 10.84 | 9.13 |  8.15 |  5.56 |\n",
        "|  7 |  7 |  7 |  8 |  4.82 | 7.26 |  6.42 |  7.91 |\n",
        "|  5 |  5 |  5 |  8 |  5.68 | 4.74 |  5.73 |  6.89 |\n",
        "\n"
       ],
       "text/plain": [
        "   x1 x2 x3 x4 y1    y2   y3    y4   \n",
        "1  10 10 10  8  8.04 9.14  7.46  6.58\n",
        "2   8  8  8  8  6.95 8.14  6.77  5.76\n",
        "3  13 13 13  8  7.58 8.74 12.74  7.71\n",
        "4   9  9  9  8  8.81 8.77  7.11  8.84\n",
        "5  11 11 11  8  8.33 9.26  7.81  8.47\n",
        "6  14 14 14  8  9.96 8.10  8.84  7.04\n",
        "7   6  6  6  8  7.24 6.13  6.08  5.25\n",
        "8   4  4  4 19  4.26 3.10  5.39 12.50\n",
        "9  12 12 12  8 10.84 9.13  8.15  5.56\n",
        "10  7  7  7  8  4.82 7.26  6.42  7.91\n",
        "11  5  5  5  8  5.68 4.74  5.73  6.89"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# library(datasets)\n",
     "anscombe"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 174,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tPearson's product-moment correlation\n",
        "\n",
        "data:  anscombe$x1 and anscombe$y1\n",
        "t = 4.2415, df = 9, p-value = 0.00217\n",
        "alternative hypothesis: true correlation is not equal to 0\n",
        "95 percent confidence interval:\n",
        " 0.4243912 0.9506933\n",
        "sample estimates:\n",
        "      cor \n",
        "0.8164205 \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "\tPearson's product-moment correlation\n",
        "\n",
        "data:  anscombe$x2 and anscombe$y2\n",
        "t = 4.2386, df = 9, p-value = 0.002179\n",
        "alternative hypothesis: true correlation is not equal to 0\n",
        "95 percent confidence interval:\n",
        " 0.4239389 0.9506402\n",
        "sample estimates:\n",
        "      cor \n",
        "0.8162365 \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "\tPearson's product-moment correlation\n",
        "\n",
        "data:  anscombe$x3 and anscombe$y3\n",
        "t = 4.2394, df = 9, p-value = 0.002176\n",
        "alternative hypothesis: true correlation is not equal to 0\n",
        "95 percent confidence interval:\n",
        " 0.4240623 0.9506547\n",
        "sample estimates:\n",
        "      cor \n",
        "0.8162867 \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "\tPearson's product-moment correlation\n",
        "\n",
        "data:  anscombe$x4 and anscombe$y4\n",
        "t = 4.243, df = 9, p-value = 0.002165\n",
        "alternative hypothesis: true correlation is not equal to 0\n",
        "95 percent confidence interval:\n",
        " 0.4246394 0.9507224\n",
        "sample estimates:\n",
        "      cor \n",
        "0.8165214 \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# x and y are correlated with r = 0.81\n",
     "cor.test(anscombe$x1, anscombe$y1)\n",
     "cor.test(anscombe$x2, anscombe$y2)\n",
     "cor.test(anscombe$x3, anscombe$y3)\n",
     "cor.test(anscombe$x4, anscombe$y4)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 175,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "Call:\n",
        "lm(formula = anscombe$y1 ~ anscombe$x1)\n",
        "\n",
        "Coefficients:\n",
        "(Intercept)  anscombe$x1  \n",
        "     3.0001       0.5001  \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "Call:\n",
        "lm(formula = anscombe$y2 ~ anscombe$x2)\n",
        "\n",
        "Coefficients:\n",
        "(Intercept)  anscombe$x2  \n",
        "      3.001        0.500  \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "Call:\n",
        "lm(formula = anscombe$y3 ~ anscombe$x3)\n",
        "\n",
        "Coefficients:\n",
        "(Intercept)  anscombe$x3  \n",
        "     3.0025       0.4997  \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "text/plain": [
        "\n",
        "Call:\n",
        "lm(formula = anscombe$y4 ~ anscombe$x4)\n",
        "\n",
        "Coefficients:\n",
        "(Intercept)  anscombe$x4  \n",
        "     3.0017       0.4999  \n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# the parameters for a linear model y~x are the same\n",
     "m1 <- lm(anscombe$y1 ~ anscombe$x1)\n",
     "m1\n",
     "\n",
     "m2 <- lm(anscombe$y2 ~ anscombe$x2)\n",
     "m2\n",
     "\n",
     "m3 <- lm(anscombe$y3 ~ anscombe$x3)\n",
     "m3\n",
     "\n",
     "m4 <- lm(anscombe$y4 ~ anscombe$x4)\n",
     "m4"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 177,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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PLCWh0+o8tqWKT609UK74p6w+UirW7Z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\ngAEQCQAGQCQAGACRAGAARAKAAf8fF+gXjXXW/y0AAAAASUVORK5CYII=",
       "text/plain": [
        "plot without title"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# Plot the relation between y and x for the four datasets (y1~x1; y2~x2; y3~x3 and y4~x4) \n",
     "# What do you observe ?\n",
     "options(repr.plot.width = 7, repr.plot.height = 7)\n",
     "par(mfrow=c(2,2))\n",
     "\n",
     "plot(anscombe$y1~anscombe$x1, pch=19)\n",
     "abline(m1)\n",
     "\n",
     "plot(anscombe$y2~anscombe$x2, pch=19)\n",
     "abline(m2)\n",
     "\n",
     "plot(anscombe$y3~anscombe$x3, pch=19)\n",
     "abline(m3)\n",
     "\n",
     "plot(anscombe$y4~anscombe$x4, pch=19)\n",
     "abline(m4)\n",
     "par(mfrow=c(1,1))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Homoscedasticity"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 179,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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PUIjR0AgEAtXLgwJiamsgua9O/fv1ob7YAdDEPBwTRsGM2aRaGh1bpoMGtUVenS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       "text/plain": [
        "Plot with title “Model 4”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# linearity (there should not be huge residuals) \n",
     "# and homoscedasticity (there should not be a trend for residuals as we increase the fitted values)\n",
     "par(mfrow=c(2,2))\n",
     "plot(m1, which=1, main=\"Model 1\") # \n",
     "plot(m2, which=1, main=\"Model 2\") # Looks like there is a pattern\n",
     "plot(m3, which=1, main=\"Model 3\") # There is a trend downwards, the error becomes larger and more negative as we predict larger values. This means we surestimate more and more the predicted values.  \n",
     "plot(m4, which=1, main=\"Model 4\")\n",
     "par(mfrow=c(1,1))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Normality"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 180,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
       "Warning message:\n",
       "“not plotting observations with leverage one:\n",
       "  8”"
      ]
     },
     {
      "data": {
       "image/png": 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p/cEeiFxkX/Uz+4vdOVok4fcIsRUicISEK2RGMoCeN1QbFdO0eF7OOpovY/O70g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\nXRxljMt1NgI4P9Kj8Tglcen96D80d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       "text/plain": [
        "Plot with title “Model 4”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# Assumption: normality of residuals. \n",
     "par(mfrow=c(2,2))\n",
     "plot(m1, which=2, main=\"Model 1\") # \n",
     "plot(m2, which=2, main=\"Model 2\") # Looks like there is a pattern\n",
     "plot(m3, which=2, main=\"Model 3\") # There is an outlier (observation 3)  \n",
     "plot(m4, which=2, main=\"Model 4\")\n",
     "par(mfrow=c(1,1))"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 181,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
       "Warning message:\n",
       "“not plotting observations with leverage one:\n",
       "  8”"
      ]
     },
     {
      "data": {
       "image/png": 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RyUpKQkqn2j6hiJECJiVOtAta5JosZO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HR+fGjRuampp0BwEAQlDrRAa1roNCY8dYe/fuvZPGsyEAACAASURBVHnzpqOj4/nz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\nN7e///7b29u7e/fuRNSrV68VK1b4+/vr6emxH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       "text/plain": [
        "Plot with title “Model 4”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# Fitted agains standardised residuals. there shoudl be no trend in the data \n",
     "par(mfrow=c(2,2))\n",
     "plot(m1, which=3, main=\"Model 1\") # \n",
     "plot(m2, which=3, main=\"Model 2\") # Looks like there is a pattern\n",
     "plot(m3, which=3, main=\"Model 3\") # There is an outlier (observation 3)  \n",
     "plot(m4, which=3, main=\"Model 4\")\n",
     "par(mfrow=c(1,1))"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 182,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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VU3EGVTbO/bNBApAohEwwGRNm8Oe/nx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\nAAAAAElFTkSuQmCC",
       "text/plain": [
        "Plot with title “Model 4”"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# Cook's distance. Measures the influence of one particular observation on the parameters of the regression. Values close and above 1 have a too large influence and should be observed.  \n",
     "par(mfrow=c(2,2))\n",
     "plot(m1, which=4, main=\"Model 1\") # \n",
     "plot(m2, which=4, main=\"Model 2\") # Looks like observations 6 and 8 are quite large\n",
     "plot(m3, which=4, main=\"Model 3\") # There is an outlier (observation 3)  \n",
     "plot(m4, which=4, main=\"Model 4\")\n",
     "par(mfrow=c(1,1))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Exercise : analyse the effect of prior knowlege on the grades using a linear regression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
+    "    <strong>Task 1</strong> : Build a regression model that predicts the results of students in the EPFL course (EPFL_CourseGrade) with their score in highschool (EPFL_BacGrade).\n",
+    "    <ul>\n",
+    "        <li>Is the high school grade contributing to better course grades ?</li>\n",
+    "        <li>What can you say about the the intercept, and how can you interpret the value of the Estimates ?</li>\n",
+    "    </ul>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 189,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "Call:\n",
+       "lm(formula = EPFL_CourseGrade ~ EPFL_BacGrade, data = moocs.bac)\n",
+       "\n",
+       "Residuals:\n",
+       "    Min      1Q  Median      3Q     Max \n",
+       "-4.9422 -0.7805  0.1753  0.9947  5.7297 \n",
+       "\n",
+       "Coefficients:\n",
+       "              Estimate Std. Error t value Pr(>|t|)    \n",
+       "(Intercept)    -1.8190     0.1612  -11.29   <2e-16 ***\n",
+       "EPFL_BacGrade   6.8992     0.1991   34.66   <2e-16 ***\n",
+       "---\n",
+       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
+       "\n",
+       "Residual standard error: 1.365 on 8593 degrees of freedom\n",
+       "Multiple R-squared:  0.1226,\tAdjusted R-squared:  0.1225 \n",
+       "F-statistic:  1201 on 1 and 8593 DF,  p-value: < 2.2e-16\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "################\n",
+    "# Begin Solution\n",
+    "\n",
+    "m0 <- lm(EPFL_CourseGrade ~ 1, data = moocs.bac)\n",
+    "\n",
+    "m1 <- lm(EPFL_CourseGrade ~ EPFL_BacGrade, data = moocs.bac)\n",
+    "summary(m1)\n",
+    "\n",
+    "# End Solution\n",
+    "################\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
+    "    <strong>Task 2</strong> : Check normality and homoscedasticity assumptions\n",
+    "    <ul>\n",
+    "        <li>What can you say about the normality of the residuals ?</li>\n",
+    "        <li>What can you say about the variance of the error ?</li>\n",
+    "        <li>Are there outliers ?</li>    \n",
+    "    </ul>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 190,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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EZHR0dqH2Nj4/fv3588eXL27NkC2hHqGCorK7+5D7eQgKipqKhQn02ExKWysvL0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\nHAAAAACg3f8DlA+6ZMHIntIAAAAASUVORK5CYII=",
+      "text/plain": [
+       "Plot with title “”"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "################\n",
+    "# Begin Solution\n",
+    "\n",
+    "options(repr.plot.width = 6, repr.plot.height = 6)\n",
+    "par(mfrow=c(2,2))\n",
+    "\n",
+    "plot(m1)\n",
+    "\n",
+    "# End Solution\n",
+    "################"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
+    "    <strong>Task 3</strong> : Check assumptions\n",
+    "    <ul>\n",
+    "        <li>Are there outliers ? What observations could we get rid of to get a better model ?</li>    \n",
+    "    </ul>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 208,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
+       " 0.1260  0.7500  0.8083  0.8062  0.8536  1.0000 "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "Call:\n",
+       "lm(formula = EPFL_CourseGrade ~ EPFL_BacGrade, data = moocs.bac.bis)\n",
+       "\n",
+       "Residuals:\n",
+       "    Min      1Q  Median      3Q     Max \n",
+       "-5.0000 -0.7777  0.1685  0.9871  3.5970 \n",
+       "\n",
+       "Coefficients:\n",
+       "              Estimate Std. Error t value Pr(>|t|)    \n",
+       "(Intercept)    -2.1091     0.1645  -12.82   <2e-16 ***\n",
+       "EPFL_BacGrade   7.2541     0.2031   35.73   <2e-16 ***\n",
+       "---\n",
+       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
+       "\n",
+       "Residual standard error: 1.36 on 8583 degrees of freedom\n",
+       "Multiple R-squared:  0.1295,\tAdjusted R-squared:  0.1294 \n",
+       "F-statistic:  1276 on 1 and 8583 DF,  p-value: < 2.2e-16\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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liu9c7T+zrEihyIFRaIFQ0QKywQKxogVlggljG1WyqWPF2xpdY8F8QKC8Qyonpu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\nQmCC",
+      "text/plain": [
+       "Plot with title “Histogram of moocs.bac$EPFL_BacGrade”"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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dzxyy+/pCgqIyODpumUlBSBQLB48eJr165RFNW4cWONjwpFUR4eHnv37n379m31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\nlXz8+LGudng8ntQt7/hKszyRI4Q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RcX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\nFqseYVK1lJcAAAAASUVORK5CYII=",
+      "text/plain": [
+       "Plot with title “”"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "################\n",
+    "# Begin Solution\n",
+    "\n",
+    "summary(moocs.bac$EPFL_BacGrade)\n",
+    "\n",
+    "options(repr.plot.width = 5, repr.plot.height = 5)\n",
+    "par(mfrow=c(1,1))\n",
+    "\n",
+    "hist(moocs.bac$EPFL_BacGrade, breaks=50)\n",
+    "\n",
+    "moocs.bac.bis <- subset(moocs.bac, subset=EPFL_BacGrade > 0.5)\n",
+    "\n",
+    "m1.bis <- lm(EPFL_CourseGrade ~ EPFL_BacGrade, data = moocs.bac.bis)\n",
+    "summary(m1.bis)\n",
+    "\n",
+    "options(repr.plot.width = 6, repr.plot.height = 6)\n",
+    "par(mfrow=c(2,2))\n",
+    "plot(m1.bis)\n",
+    "# End Solution\n",
+    "################\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightPink;\">\n",
+    "    <strong>Task 4</strong> : Check linear dependence\n",
+    "    <ul>\n",
+    "        <li>Plot the variables against each other</li>\n",
+    "    </ul>\n",
+    "</div>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 211,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+sPHDjAMMyuXbtuM71BMOBACCGEfuLu6B9vc3Z2LigoeOKJJ5qamj744IMzZ85k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YLC4vL/fy8iotLVWr1XK5XKVSabVa2H3B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\n9tpr5I3YrVu3SMlnn33G4XBYljU+tW/duhUh1NzcTP784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6eoqLi4OCglTdbt26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\nEEJI77DgQAghhJDeYcGBEEIIIb37D7X0uLO6P6J9AAAAAElFTkSuQmCC",
+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ggscatter(moocs.bac.bis, x = \"EPFL_BacGrade\", y = \"EPFL_CourseGrade\",\n",
+    "   color = \"black\", shape = 21, size = 1, # Points color, shape and size\n",
+    "   add = \"reg.line\",  # Add regressin line\n",
+    "   add.params = list(color = \"blue\", fill = \"lightgray\"), # Customize reg. line\n",
+    "   conf.int = TRUE, # Add confidence interval\n",
+    "   cor.coef = TRUE, # Add correlation coefficient. see ?stat_cor\n",
+    "   cor.coeff.args = list(method = \"pearson\", label.x = 1, label.sep = \"\\n\")\n",
+    "   )"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Categorical variables"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"border:1px solid black; padding:10px 10px; background-color: Yellow;\">\n",
+    "    <strong>Question</strong>:  Do people with higher prior ability (the prior variable) use the MOOC differently (the MOOC variable) ? This question asks about the relationship of two categorical variables (prior and MOOC both have a set of distinct nominal values).  \n",
+    "</div>"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "\n",
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightYellow;\">\n",
     "    <strong>Test</strong>: Chi-square test\n",
     "</div>\n",
     "    "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Do people with higher prior ability (the `prior` variable) use the MOOC differently (the `MOOC` variable) ? This question asks about the relationship of two categorical variables (`prior` and `MOOC` both have a set of distinct nominal values). \n",
     "\n",
     "The chi-square tests whether the observations in two categorical variables can be considered independent. It does this by comparing the observed number of cases and the expected number of cases under the assumption of independence. \n",
     "\n",
     "* H0: the variables are independent.\n",
     "* H1: the variables are not independent.\n",
     "\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 213,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "       \n",
+      "          LO   HI\n",
+      "  NONE  3235 2798\n",
+      "  WATCH  477  509\n",
+      "  DO     606  970\n"
+     ]
+    }
+   ],
    "source": [
     "tt <- table( moocs.bac$MOOC, moocs.bac$prior)\n",
     "print(tt)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 214,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "\tPearson's Chi-squared test\n",
+      "\n",
+      "data:  tt\n",
+      "X-squared = 116.57, df = 2, p-value < 2.2e-16\n",
+      "\n"
+     ]
+    }
+   ],
    "source": [
     "tt.chisq <- chisq.test(tt)\n",
     "print(tt.chisq)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 215,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "       \n",
+      "          LO   HI\n",
+      "  NONE  3235 2798\n",
+      "  WATCH  477  509\n",
+      "  DO     606  970\n",
+      "       \n",
+      "               LO        HI\n",
+      "  NONE  3030.8894 3002.1106\n",
+      "  WATCH  495.3517  490.6483\n",
+      "  DO     791.7589  784.2411\n"
+     ]
+    }
+   ],
    "source": [
     "print(tt.chisq$obs)\n",
     "print(tt.chisq$exp)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 216,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "       \n",
+      "                LO         HI\n",
+      "  NONE   3.7074954 -3.7252233\n",
+      "  WATCH -0.8245554  0.8284981\n",
+      "  DO    -6.6016609  6.6332277\n"
+     ]
+    }
+   ],
    "source": [
     "# pearson residuals larger than 1.96 are significantly different from 0 with p<.05\n",
     "# the Pearson residuals, (observed - expected) / sqrt(expected).\n",
     "print(tt.chisq$res)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 217,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "3.70749449574115"
+      ],
+      "text/latex": [
+       "3.70749449574115"
+      ],
+      "text/markdown": [
+       "3.70749449574115"
+      ],
+      "text/plain": [
+       "[1] 3.707494"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "# Compute residual for cell 1,1\n",
     "(3235-3030.8894) / sqrt(3030.8894)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div style=\"border:1px solid black; padding:10px 10px; background-color: LightGreen;\">\n",
     "    <strong>Reporting</strong>\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "> A test of independence shows that the students with high prior ability do not have the same pattern of MOOC useage compared to the students of low ability ($\\chi^2$[2]=116.57, p<.001). A closer inspection of the Pearson residuals shows that low ability students are more likely to not use the MOOC and that high ability students are more likey to do the exercices. "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 218,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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U16mdd4/wJAzTk6Ol64cAF3G+cIPT09Qsi9e/cOHjwYExMjEAhevXoVFxc3ceJE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\nQgBCE0IAQvsXmEMVHPlQ4BUAAAAASUVORK5CYII=",
+      "text/plain": [
+       "Plot with title “MOOC Usage and Prior Ability”"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "# Setting the size of plots generated with ggplot below. \n",
     "options(repr.plot.width = 5, repr.plot.height = 5)\n",
     "\n",
     "mosaicplot(tt, shade = TRUE, las=2, main = \"MOOC Usage and Prior Ability\")"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 183,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<ol class=list-inline>\n",
+       "\t<li>'EPFL_AcademicYear'</li>\n",
+       "\t<li>'EPFL_IsRepeating'</li>\n",
+       "\t<li>'EPFL_PropaedeuticGPA'</li>\n",
+       "\t<li>'EPFL_CourseGrade'</li>\n",
+       "\t<li>'EPFL_StudentSection'</li>\n",
+       "\t<li>'MOOC_NVideosWatched'</li>\n",
+       "\t<li>'MOOC_AverageMaxVideosWatched'</li>\n",
+       "\t<li>'MOOC_PercentageVideosWatched'</li>\n",
+       "\t<li>'MOOC_NProblemsSolved'</li>\n",
+       "\t<li>'MOOC_AverageMaxProblemsSolved'</li>\n",
+       "\t<li>'MOOC_PercentageProblemsSolved'</li>\n",
+       "\t<li>'MOOC_Grade'</li>\n",
+       "\t<li>'EPFL_Topic'</li>\n",
+       "\t<li>'EPFL_BacGrade'</li>\n",
+       "\t<li>'EPFL_BacLevel'</li>\n",
+       "\t<li>'EPFL_CourseType'</li>\n",
+       "\t<li>'EPFL_UniqueTopicID_Anonymous'</li>\n",
+       "\t<li>'EPFL_AnonymousUserID'</li>\n",
+       "\t<li>'didMOOC'</li>\n",
+       "\t<li>'watched_videos'</li>\n",
+       "\t<li>'solved_problems'</li>\n",
+       "\t<li>'MOOC'</li>\n",
+       "\t<li>'prior'</li>\n",
+       "</ol>\n"
+      ],
+      "text/latex": [
+       "\\begin{enumerate*}\n",
+       "\\item 'EPFL\\_AcademicYear'\n",
+       "\\item 'EPFL\\_IsRepeating'\n",
+       "\\item 'EPFL\\_PropaedeuticGPA'\n",
+       "\\item 'EPFL\\_CourseGrade'\n",
+       "\\item 'EPFL\\_StudentSection'\n",
+       "\\item 'MOOC\\_NVideosWatched'\n",
+       "\\item 'MOOC\\_AverageMaxVideosWatched'\n",
+       "\\item 'MOOC\\_PercentageVideosWatched'\n",
+       "\\item 'MOOC\\_NProblemsSolved'\n",
+       "\\item 'MOOC\\_AverageMaxProblemsSolved'\n",
+       "\\item 'MOOC\\_PercentageProblemsSolved'\n",
+       "\\item 'MOOC\\_Grade'\n",
+       "\\item 'EPFL\\_Topic'\n",
+       "\\item 'EPFL\\_BacGrade'\n",
+       "\\item 'EPFL\\_BacLevel'\n",
+       "\\item 'EPFL\\_CourseType'\n",
+       "\\item 'EPFL\\_UniqueTopicID\\_Anonymous'\n",
+       "\\item 'EPFL\\_AnonymousUserID'\n",
+       "\\item 'didMOOC'\n",
+       "\\item 'watched\\_videos'\n",
+       "\\item 'solved\\_problems'\n",
+       "\\item 'MOOC'\n",
+       "\\item 'prior'\n",
+       "\\end{enumerate*}\n"
+      ],
+      "text/markdown": [
+       "1. 'EPFL_AcademicYear'\n",
+       "2. 'EPFL_IsRepeating'\n",
+       "3. 'EPFL_PropaedeuticGPA'\n",
+       "4. 'EPFL_CourseGrade'\n",
+       "5. 'EPFL_StudentSection'\n",
+       "6. 'MOOC_NVideosWatched'\n",
+       "7. 'MOOC_AverageMaxVideosWatched'\n",
+       "8. 'MOOC_PercentageVideosWatched'\n",
+       "9. 'MOOC_NProblemsSolved'\n",
+       "10. 'MOOC_AverageMaxProblemsSolved'\n",
+       "11. 'MOOC_PercentageProblemsSolved'\n",
+       "12. 'MOOC_Grade'\n",
+       "13. 'EPFL_Topic'\n",
+       "14. 'EPFL_BacGrade'\n",
+       "15. 'EPFL_BacLevel'\n",
+       "16. 'EPFL_CourseType'\n",
+       "17. 'EPFL_UniqueTopicID_Anonymous'\n",
+       "18. 'EPFL_AnonymousUserID'\n",
+       "19. 'didMOOC'\n",
+       "20. 'watched_videos'\n",
+       "21. 'solved_problems'\n",
+       "22. 'MOOC'\n",
+       "23. 'prior'\n",
+       "\n",
+       "\n"
+      ],
+      "text/plain": [
+       " [1] \"EPFL_AcademicYear\"             \"EPFL_IsRepeating\"             \n",
+       " [3] \"EPFL_PropaedeuticGPA\"          \"EPFL_CourseGrade\"             \n",
+       " [5] \"EPFL_StudentSection\"           \"MOOC_NVideosWatched\"          \n",
+       " [7] \"MOOC_AverageMaxVideosWatched\"  \"MOOC_PercentageVideosWatched\" \n",
+       " [9] \"MOOC_NProblemsSolved\"          \"MOOC_AverageMaxProblemsSolved\"\n",
+       "[11] \"MOOC_PercentageProblemsSolved\" \"MOOC_Grade\"                   \n",
+       "[13] \"EPFL_Topic\"                    \"EPFL_BacGrade\"                \n",
+       "[15] \"EPFL_BacLevel\"                 \"EPFL_CourseType\"              \n",
+       "[17] \"EPFL_UniqueTopicID_Anonymous\"  \"EPFL_AnonymousUserID\"         \n",
+       "[19] \"didMOOC\"                       \"watched_videos\"               \n",
+       "[21] \"solved_problems\"               \"MOOC\"                         \n",
+       "[23] \"prior\"                        "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "names(moocs.bac)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 185,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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EHblKiy7qMXboo/pOIhddz+P65qNJiN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\nAABJRU5ErkJggg==",
+      "text/plain": [
+       "Plot with title “Histogram of moocs.bac$EPFL_BacGrade”"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
    "display_name": "R",
    "language": "R",
    "name": "ir"
   },
   "language_info": {
    "codemirror_mode": "r",
    "file_extension": ".r",
    "mimetype": "text/x-r-source",
    "name": "R",
    "pygments_lexer": "r",
    "version": "3.6.1"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 4
 }