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Assignment-1,-RMD.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="author" content="Bryan Murphy" />
<meta name="date" content="2023-04-03" />
<title>JHU5, Assignment 1</title>
<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
// be compatible with the behavior of Pandoc < 2.8).
document.addEventListener('DOMContentLoaded', function(e) {
var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
var i, h, a;
for (i = 0; i < hs.length; i++) {
h = hs[i];
if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6
a = h.attributes;
while (a.length > 0) h.removeAttribute(a[0].name);
}
});
</script>
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css" data-origin="pandoc">
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; }
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; }
code span.at { color: #7d9029; }
code span.bn { color: #40a070; }
code span.bu { color: #008000; }
code span.cf { color: #007020; font-weight: bold; }
code span.ch { color: #4070a0; }
code span.cn { color: #880000; }
code span.co { color: #60a0b0; font-style: italic; }
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; }
code span.do { color: #ba2121; font-style: italic; }
code span.dt { color: #902000; }
code span.dv { color: #40a070; }
code span.er { color: #ff0000; font-weight: bold; }
code span.ex { }
code span.fl { color: #40a070; }
code span.fu { color: #06287e; }
code span.im { color: #008000; font-weight: bold; }
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; }
code span.kw { color: #007020; font-weight: bold; }
code span.op { color: #666666; }
code span.ot { color: #007020; }
code span.pp { color: #bc7a00; }
code span.sc { color: #4070a0; }
code span.ss { color: #bb6688; }
code span.st { color: #4070a0; }
code span.va { color: #19177c; }
code span.vs { color: #4070a0; }
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; }
a.sourceLine {
pointer-events: auto;
}
</style>
<script>
// apply pandoc div.sourceCode style to pre.sourceCode instead
(function() {
var sheets = document.styleSheets;
for (var i = 0; i < sheets.length; i++) {
if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
try { var rules = sheets[i].cssRules; } catch (e) { continue; }
for (var j = 0; j < rules.length; j++) {
var rule = rules[j];
// check if there is a div.sourceCode rule
if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") continue;
var style = rule.style.cssText;
// check if color or background-color is set
if (rule.style.color === '' && rule.style.backgroundColor === '') continue;
// replace div.sourceCode by a pre.sourceCode rule
sheets[i].deleteRule(j);
sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
}
}
})();
</script>
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<h1 class="title toc-ignore entry-title">JHU5, Assignment 1</h1>
<h3 class="author">Bryan Murphy</h3>
<h3 class="date">2023-04-03</h3>
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<div class="entry-content">
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># This is our initial setup block, named setup, with include = TRUE so it will show up. </span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="co"># First we'll set any global variables we care about...</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span>opts_chunk<span class="sc">$</span><span class="fu">set</span>(<span class="at">echo =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="fu">options</span>(<span class="at">scipen=</span><span class="dv">999</span>) <span class="co"># This stops knitr from displaying 5 digit numbers as Scientific Notation.</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="co"># And then load our data. </span></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a>actdata <span class="ot"><-</span> <span class="fu">read.csv</span>(<span class="st">"repdata_data_activity/activity.csv"</span>)</span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="co"># And the only library call we'll need:</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tidyverse)</span></code></pre></div>
<pre><code>## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.4.0 ✔ purrr 1.0.1
## ✔ tibble 3.1.8 ✔ dplyr 1.0.10
## ✔ tidyr 1.3.0 ✔ stringr 1.5.0
## ✔ readr 2.1.3 ✔ forcats 0.5.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()</code></pre>
<h2 align="center">
<strong>Q1: What is the mean total number of steps taken per day?
</strong>
</h2>
<p>In order to answer this question, we first have to manipulate our
base dataset, which I’ve named <code>actdata</code> (for <em>“activity
data”</em>) to group by date, then summarize this group date by the
variable “steps”. This will give us our daily step count output, such as
might be tracked by a device like a Fitbit. We see the code to
accomplish this transformation below. In this variable, I’ve also
replaced all <code>NA</code> entries with the number <span class="math inline">\(0\)</span>, to make it possible to use this daily
step count data for subsequent transformations. I’ll thus call our
grouped, cleaned dataset <code>CleanDailySteps</code>. Notice this code
uses the piping operator, made possible because of our call
<code>library(tidyverse)</code> in the setup code chunk at the beginning
of this RMD file.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">group_by</span>(actdata, date) <span class="sc">%>%</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">summarize</span>(<span class="at">DailyStepCount =</span> <span class="fu">sum</span>(steps)) <span class="sc">%>%</span></span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">replace_na</span>(<span class="fu">list</span>(<span class="at">date =</span> <span class="dv">0</span>, <span class="at">DailyStepCount =</span> <span class="dv">0</span>)) <span class="ot">-></span> CleanDailySteps</span></code></pre></div>
<p>Looking at the structure of this file: <code>{r}</code> - we can see
that we have created a <span class="math inline">\(61 by 2\)</span>
tibble with two columns, <em>date</em> and <em>DailyStepCount.</em> This
lets us know that the dataset runs across 61 days, which will be
important when calculating any averages of the step data.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(CleanDailySteps)</span></code></pre></div>
<pre><code>## tibble [61 × 2] (S3: tbl_df/tbl/data.frame)
## $ date : chr [1:61] "2012-10-01" "2012-10-02" "2012-10-03" "2012-10-04" ...
## $ DailyStepCount: int [1:61] 0 126 11352 12116 13294 15420 11015 0 12811 9900 ...</code></pre>
<p>We can also look at the <code>head</code> of our dataset to see what
it looks like:</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(CleanDailySteps)</span></code></pre></div>
<pre><code>## # A tibble: 6 × 2
## date DailyStepCount
## <chr> <int>
## 1 2012-10-01 0
## 2 2012-10-02 126
## 3 2012-10-03 11352
## 4 2012-10-04 12116
## 5 2012-10-05 13294
## 6 2012-10-06 15420</code></pre>
<p>Let’s look at some descriptive statistics for
<code>DailyStepCount</code>, including, most importantly, <strong>the
mean total number of steps taken per day</strong> across the 61 days in
our dataset.</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">mean</span>(CleanDailySteps<span class="sc">$</span>DailyStepCount) <span class="co">#Mean total steps per day</span></span></code></pre></div>
<pre><code>## [1] 9354.23</code></pre>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sum</span>(CleanDailySteps<span class="sc">$</span>DailyStepCount)<span class="sc">/</span><span class="dv">61</span> <span class="co">#Calculating mean manually</span></span></code></pre></div>
<pre><code>## [1] 9354.23</code></pre>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">median</span>(CleanDailySteps<span class="sc">$</span>DailyStepCount) <span class="co">#Median total steps per day</span></span></code></pre></div>
<pre><code>## [1] 10395</code></pre>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(CleanDailySteps)</span></code></pre></div>
<pre><code>## date DailyStepCount
## Length:61 Min. : 0
## Class :character 1st Qu.: 6778
## Mode :character Median :10395
## Mean : 9354
## 3rd Qu.:12811
## Max. :21194</code></pre>
<p>We see that the mean number of steps per day is <span class="math inline">\(9,354\)</span>, while the median is <span class="math inline">\(10,395\)</span>, telling us that this data set is
<strong>skewed to the left</strong>, with a number of low or zero step
count days pulling down the mean of the column DailyStepCount.</p>
<div id="a-histogram-of-the-total-number-of-steps-taken-each-day." class="section level4">
<h4><strong>A histogram of the total number of steps taken each
day.</strong></h4>
<p>While we can make a histogram using the bar chart geometry with
ggplot2, we’re going to use <code>geom_histogram</code> to more clearly
demonstrate that we are creating a histogram specifically. We’re going
to use <code>+theme</code> modifiers to remove all vertical gridlines
and reformat the horizontal gridlines to make the chart a little easier
to look at.</p>
<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(CleanDailySteps, <span class="fu">aes</span>(<span class="at">x=</span>DailyStepCount)) <span class="sc">+</span></span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_histogram</span>(<span class="at">bins =</span> <span class="dv">20</span>, <span class="at">fill =</span> <span class="st">"navajowhite"</span>, <span class="at">color =</span> <span class="st">"midnightblue"</span>) <span class="sc">+</span></span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Daily Step Counts, 20 Bins"</span>, <span class="at">y =</span> <span class="st">"Count"</span>, <span class="at">x =</span> <span class="st">"Total Steps Taken / Day"</span>) <span class="sc">+</span></span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">plot.title =</span> <span class="fu">element_text</span>(<span class="at">hjust =</span> <span class="fl">0.5</span>)) <span class="sc">+</span> </span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lightskyblue1"</span>),</span>
<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a> <span class="at">plot.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lightskyblue1"</span>),</span>
<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.ontop =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb16-8"><a href="#cb16-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.grid.major.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb16-9"><a href="#cb16-9" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb16-10"><a href="#cb16-10" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.major.y =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"red4"</span>,</span>
<span id="cb16-11"><a href="#cb16-11" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.75</span>,</span>
<span id="cb16-12"><a href="#cb16-12" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">2</span>),</span>
<span id="cb16-13"><a href="#cb16-13" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.y =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"red4"</span>,</span>
<span id="cb16-14"><a href="#cb16-14" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.25</span>,</span>
<span id="cb16-15"><a href="#cb16-15" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">2</span>))</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<h2 align="center">
<strong>Q2: What is the average daily activity pattern?</strong>
</h2>
<p>Just from the histogram above, we can see that the daily activity
pattern follows a somewhat normal, albeit very left skewed,
distribution, with relatively fewer unusually high and unusually low
step count days, but a large number of 0 step count days (which could
possibly represent something like days where the person from whom the
data was being collected forgot to wear their Fitbit or other tracking
device).</p>
<p>But we can visualize the daily activity pattern across the hours of
an individual day, as well.</p>
<p><strong>Creating the dataset that will allow use to look at the
activity level across the span of a single day</strong></p>
<p>In order to be able to look at the average activity level per
5-minute interval for an average day, we need to group our original
dataset, <code>actdata</code>, by the variable <code>interval</code>,
sum the total steps for each <code>interval</code> across the 61 days of
the dataset, and then divide this sum by 61 to get the average number of
steps taken during that 5-minute interval on an average day.</p>
<p>The code below shows the steps we need to take to accomplish this
transformation,resulting in the creation of a data frame,
<code>interval_avgs</code>, that we can plot as a time series. Note that
the very first step is removing the <em>NAs</em> from
<code>actdata</code> and replacing them with <span class="math inline">\(0's\)</span> so as to prevent breaking any
subsequent operations.</p>
<p>We continue the practice of using the piping operator
<code>%>%</code> to make the linear nature of the transformation
operations more obvious, and to avoid creating unnecessary intermediate
variables that don’t actually need to exist permanently.</p>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>CleanActData <span class="ot"><-</span> <span class="fu">replace_na</span>(actdata,<span class="fu">list</span>(<span class="at">steps =</span> <span class="dv">0</span>, <span class="at">date =</span> <span class="dv">0</span>, <span class="at">interval =</span> <span class="dv">0</span> ))</span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>CleanActData <span class="sc">%>%</span> <span class="fu">select</span>(steps, interval) <span class="sc">%>%</span></span>
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">group_by</span>(interval) <span class="sc">%>%</span></span>
<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">summarize</span>(<span class="at">TotSteps =</span> <span class="fu">sum</span>(steps)) <span class="sc">%>%</span></span>
<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">AvgSteps =</span> TotSteps<span class="sc">/</span><span class="dv">61</span>) <span class="ot">-></span> interval_avgs </span>
<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb17-7"><a href="#cb17-7" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(interval_avgs)</span></code></pre></div>
<pre><code>## # A tibble: 6 × 3
## interval TotSteps AvgSteps
## <int> <int> <dbl>
## 1 0 91 1.49
## 2 5 18 0.295
## 3 10 7 0.115
## 4 15 8 0.131
## 5 20 4 0.0656
## 6 25 111 1.82</code></pre>
<p>Now we can use ggplot2 to plot <code>interval_avgs</code> with the
5-minute interval on the x-axis and the average number of steps taken
during that interval on the y-axis.</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(interval_avgs, <span class="fu">aes</span>(<span class="at">x =</span> interval, <span class="at">y =</span> AvgSteps)) <span class="sc">+</span></span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_line</span>(<span class="at">color =</span> <span class="st">"red2"</span>, <span class="at">linetype =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Average Steps Taken During Each </span><span class="sc">\n</span><span class="st">Five Minute Interval Across All Days"</span>, <span class="at">y =</span> <span class="st">"Average STeps Taken"</span>, <span class="at">x =</span> <span class="st">"Time of 5-Minute Interval During the Day"</span>) <span class="sc">+</span> </span>
<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lavenderblush1"</span>),</span>
<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a> <span class="at">plot.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lavenderblush1"</span>),</span>
<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.ontop =</span> <span class="cn">FALSE</span>) <span class="sc">+</span> </span>
<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">plot.title =</span> <span class="fu">element_text</span>(<span class="at">hjust =</span> <span class="fl">0.5</span>)) <span class="sc">+</span></span>
<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.grid.major.x =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"lightsteelblue4"</span>),</span>
<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb19-10"><a href="#cb19-10" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.major.y =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"lightsteelblue4"</span>,</span>
<span id="cb19-11"><a href="#cb19-11" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.75</span>,</span>
<span id="cb19-12"><a href="#cb19-12" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">2</span>),</span>
<span id="cb19-13"><a href="#cb19-13" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.y =</span> <span class="fu">element_blank</span>())</span></code></pre></div>
<p><img 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" /><!-- --></p>
<p>We can see that the user(s) this data was collected from tends to
wake up a little bit after 5 A.M. each day,their activity tends to peak
around 8 or 9 am, and they then remain fairly consistently active from
10 am until around 7 pm or so, and after 8 pm their activity drops
dramatically, possibly indicating they tend to go to sleep within a few
hours of that time.</p>
<p>The 5-minute interval, averaged across all the days in the dataset,
that tends to contain the maximum number of steps is 835 am,
corresponding to 179 steps taken during this 5 minute period, on
average. Maybe this time period represents part of the participant(s)
daily commute, for example.</p>
<h1 align="center">
<strong>Imputing missing values</strong>
</h1>
<p>This was the trickest part of the assignment, in my opinion.</p>
<p>Looking at the data, we can see that there are a significant number
of observations in the dataset, exclusively in the “steps” column.</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sapply</span>(actdata,<span class="cf">function</span>(x) <span class="fu">sum</span>(<span class="fu">is.na</span>(x)))</span></code></pre></div>
<pre><code>## steps date interval
## 2304 0 0</code></pre>
<p>In total, there are 2304 missing values in the dataset, making up
13.11% of the observations in our base dataset <code>actdata</code>.</p>
<p>In our calculations above, we simply replaced the missing values with
<span class="math inline">\(0's\)</span>. This might be a reasonable
assumption at some points, such as for the intervals representing the
times between 2 and 4 am, for example, but there are certainly missing
observations during intervals where the source of the data probably was
taking steps.</p>
<p>A more reasonable but still relatively simple method of filling in
these missing values is by replacing any missing step values with the
average number of steps taken during that 5-minute interval across the
entire dataset. As a bonus, this will replace missing values with <span class="math inline">\(0'\)</span> during intervals where the average
number of steps taken during that interval was <span class="math inline">\(0\)</span>, such as during time periods when the
data source was always asleep.</p>
<p>We can accomplish this with a <code>for</code> loop, creating a new
dataset called <code>imputed</code>. See below.</p>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a>imputed <span class="ot"><-</span> actdata</span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">17568</span>) {</span>
<span id="cb22-4"><a href="#cb22-4" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> ( <span class="fu">is.na</span>(actdata[i,<span class="dv">1</span>]) <span class="sc">==</span> <span class="cn">TRUE</span>) {</span>
<span id="cb22-5"><a href="#cb22-5" aria-hidden="true" tabindex="-1"></a> imputed[i,<span class="dv">1</span>] <span class="ot"><-</span> interval_avgs[interval_avgs<span class="sc">$</span>interval <span class="sc">==</span> actdata[i,<span class="dv">3</span>],<span class="dv">3</span>]</span>
<span id="cb22-6"><a href="#cb22-6" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb22-7"><a href="#cb22-7" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<p>If we look at our new dataset <code>imputed</code>, we can see that
the number of missing values is now 0, which is what we wanted. But if
we look at the summary of <code>imputed</code> and the summary of our
original <code>actdata</code>, we can see that while the mean and median
number of steps taken in a 5-minute interval in the original data was
<em>37.28</em> and <em><span class="math inline">\(0\)</span></em>,
respectively, in the new imputed dataset, the mean number of steps taken
in a 5-minute interval is 36.74, while the median number of steps taken
is still 0 steps. We can see these facts in the two outputs of a summary
function call, below.</p>
<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(imputed<span class="sc">$</span>steps)</span></code></pre></div>
<pre><code>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 0.00 36.74 26.00 806.00</code></pre>
<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(actdata<span class="sc">$</span>steps)</span></code></pre></div>
<pre><code>## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.00 0.00 0.00 37.38 12.00 806.00 2304</code></pre>
<p>This result seems confusing until we analyze it a little more
closely. In both datasets, the median is 0, implying that on average,
the source of the data does not move at all during any particular 5
minute interval. The means in both data sets are above 0, because the
source of the data obviously does move at some point, but substituting
imputed data in the place of missing observations brings down the mean
of the <code>steps</code> observations, implying that many of the
missing step values from <code>actdata</code> were replaced with low or
zero step counts.</p>
<p>Looking at the histograms of the step counts of the original dataset
alongside the imputed dataset makes the impact of filling in missing
values with imputed values more obvious.</p>
<p>But before we can do that, we need to replicate the process we used
to create <code>CleanDailySteps</code> to create an
<code>ImputedDailySteps</code> data frame.</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">group_by</span>(imputed, date) <span class="sc">%>%</span></span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">summarize</span>(<span class="at">DailyStepCount =</span> <span class="fu">sum</span>(steps)) <span class="sc">%>%</span></span>
<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">replace_na</span>(<span class="fu">list</span>(<span class="at">date =</span> <span class="dv">0</span>, <span class="at">DailyStepCount =</span> <span class="dv">0</span>)) <span class="ot">-></span> ImputedDailySteps</span>
<span id="cb27-4"><a href="#cb27-4" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(ImputedDailySteps)</span></code></pre></div>
<pre><code>## date DailyStepCount
## Length:61 Min. : 41
## Class :character 1st Qu.: 9354
## Mode :character Median :10395
## Mean :10581
## 3rd Qu.:12811
## Max. :21194</code></pre>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(CleanDailySteps)</span></code></pre></div>
<pre><code>## date DailyStepCount
## Length:61 Min. : 0
## Class :character 1st Qu.: 6778
## Mode :character Median :10395
## Mean : 9354
## 3rd Qu.:12811
## Max. :21194</code></pre>
<p>Comparing the summary() outputs for <code>CleanDailySteps</code> and
<code>ImputedDailySteps</code>, we can observe the facts.</p>
<ol style="list-style-type: decimal">
<li>In the original cleaned dataset,the mean number of daily steps taken
was <strong>9354.23 steps</strong>, while the median number of daily
steps taken was <strong>10395 steps.</strong></li>
<li>In the new dataset in which missing values were replaced by imputed
values,the mean number of daily steps taken was <strong>10581
steps</strong>, while the median number of daily steps taken was
<strong>10395 steps.</strong>
<ul>
<li>Thus, by substituting imputed values for missing values and then
calculating daily step counts, we can see that while the original data
set was skewed left, with a mean lower than the median, in the imputed
data set, the daily step counts are skewed right.</li>
<li>This tells us that including imputed values tends to increase the
daily step count values.</li>
</ul></li>
</ol>
<p>We can clearly see the effect of including imputed data on our daily
step counts by comparing the histogram of daily step counts for the
original data frame, <code>CleanDailySteps</code>, with the histogram
created using <code>ImputedDailySteps</code>. See below.</p>
<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a>p1 <span class="ot"><-</span> <span class="fu">ggplot</span>(CleanDailySteps, <span class="fu">aes</span>(<span class="at">x=</span>DailyStepCount)) <span class="sc">+</span></span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_histogram</span>(<span class="at">bins =</span> <span class="dv">20</span>, <span class="at">fill =</span> <span class="st">"navajowhite"</span>, <span class="at">color =</span> <span class="st">"midnightblue"</span>) <span class="sc">+</span></span>
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Daily Step Counts Using Cleaned Data, 20 Bins"</span>, <span class="at">y =</span> <span class="st">"Count"</span>, <span class="at">x =</span> <span class="st">"Total Steps Taken / Day"</span>) <span class="sc">+</span></span>
<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">plot.title =</span> <span class="fu">element_text</span>(<span class="at">hjust =</span> <span class="fl">0.5</span>)) <span class="sc">+</span> </span>
<span id="cb31-5"><a href="#cb31-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lightskyblue1"</span>),</span>
<span id="cb31-6"><a href="#cb31-6" aria-hidden="true" tabindex="-1"></a> <span class="at">plot.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lightskyblue1"</span>),</span>
<span id="cb31-7"><a href="#cb31-7" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.ontop =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb31-8"><a href="#cb31-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.grid.major.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb31-9"><a href="#cb31-9" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb31-10"><a href="#cb31-10" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.major.y =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"red4"</span>,</span>
<span id="cb31-11"><a href="#cb31-11" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.75</span>,</span>
<span id="cb31-12"><a href="#cb31-12" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">2</span>),</span>
<span id="cb31-13"><a href="#cb31-13" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.y =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"red4"</span>,</span>
<span id="cb31-14"><a href="#cb31-14" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.25</span>,</span>
<span id="cb31-15"><a href="#cb31-15" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">2</span>))</span>
<span id="cb31-16"><a href="#cb31-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-17"><a href="#cb31-17" aria-hidden="true" tabindex="-1"></a>p2 <span class="ot"><-</span> <span class="fu">ggplot</span>(ImputedDailySteps, <span class="fu">aes</span>(<span class="at">x=</span>DailyStepCount)) <span class="sc">+</span></span>
<span id="cb31-18"><a href="#cb31-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_histogram</span>(<span class="at">bins =</span> <span class="dv">20</span>, <span class="at">fill =</span> <span class="st">"navajowhite"</span>, <span class="at">color =</span> <span class="st">"midnightblue"</span>) <span class="sc">+</span></span>
<span id="cb31-19"><a href="#cb31-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Daily Step Counts Using Imputed Data, 20 Bins"</span>, <span class="at">y =</span> <span class="st">"Count"</span>, <span class="at">x =</span> <span class="st">"Total Steps Taken / Day"</span>) <span class="sc">+</span></span>
<span id="cb31-20"><a href="#cb31-20" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">plot.title =</span> <span class="fu">element_text</span>(<span class="at">hjust =</span> <span class="fl">0.5</span>)) <span class="sc">+</span> </span>
<span id="cb31-21"><a href="#cb31-21" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lightskyblue1"</span>),</span>
<span id="cb31-22"><a href="#cb31-22" aria-hidden="true" tabindex="-1"></a> <span class="at">plot.background =</span> <span class="fu">element_rect</span>(<span class="at">fill =</span> <span class="st">"lightskyblue1"</span>),</span>
<span id="cb31-23"><a href="#cb31-23" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.ontop =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb31-24"><a href="#cb31-24" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(<span class="at">panel.grid.major.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb31-25"><a href="#cb31-25" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.x =</span> <span class="fu">element_blank</span>(),</span>
<span id="cb31-26"><a href="#cb31-26" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.major.y =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"red4"</span>,</span>
<span id="cb31-27"><a href="#cb31-27" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.75</span>,</span>
<span id="cb31-28"><a href="#cb31-28" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">2</span>),</span>
<span id="cb31-29"><a href="#cb31-29" aria-hidden="true" tabindex="-1"></a> <span class="at">panel.grid.minor.y =</span> <span class="fu">element_line</span>(<span class="at">color =</span> <span class="st">"red4"</span>,</span>
<span id="cb31-30"><a href="#cb31-30" aria-hidden="true" tabindex="-1"></a> <span class="at">size =</span> <span class="fl">0.25</span>,</span>
<span id="cb31-31"><a href="#cb31-31" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">2</span>))</span>
<span id="cb31-32"><a href="#cb31-32" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb31-33"><a href="#cb31-33" aria-hidden="true" tabindex="-1"></a>gridExtra<span class="sc">::</span><span class="fu">grid.arrange</span>(p1, p2)</span></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<p>We can see that the <strong>impact of imputing missing data on the
estimates of the total daily number of steps</strong> is to decrease the
number of days in which the daily step count is <span class="math inline">\(0\)</span>, and instead many of these
formerly-<span class="math inline">\(0\)</span> days become days
clustered approximately aroun the center of the data.</p>
<h2 align="center">
<strong>Differences in activity patterns between weekdays and
weekends</strong>
</h2>
<p>First, we will create a new factor variable in our dataset with two
levels, weekday and weekend, indicating whether a given date is a
weekday or a weekend day.</p>
<p>First, looking at our dataset <code>imputed</code>, we see that the
<code>date</code> column is currently being considered a character
string column, and we want it as a dates column. Let’s create a new
dataset called imputed_dates in which <code>date</code> will be seen as
date data.</p>
<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(imputed)</span></code></pre></div>
<pre><code>## Rows: 17,568
## Columns: 3
## $ steps <dbl> 1.49180328, 0.29508197, 0.11475410, 0.13114754, 0.06557377, 1…
## $ date <chr> "2012-10-01", "2012-10-01", "2012-10-01", "2012-10-01", "2012…
## $ interval <int> 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 100, 105, 110, …</code></pre>
<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a>imputed_dates <span class="ot"><-</span> imputed</span>
<span id="cb34-2"><a href="#cb34-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb34-3"><a href="#cb34-3" aria-hidden="true" tabindex="-1"></a>imputed_dates <span class="ot"><-</span> imputed_dates <span class="sc">%>%</span></span>
<span id="cb34-4"><a href="#cb34-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate_at</span>(<span class="dv">2</span>,as.Date.character)</span>
<span id="cb34-5"><a href="#cb34-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb34-6"><a href="#cb34-6" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(imputed_dates)</span></code></pre></div>
<pre><code>## Rows: 17,568
## Columns: 3
## $ steps <dbl> 1.49180328, 0.29508197, 0.11475410, 0.13114754, 0.06557377, 1…
## $ date <date> 2012-10-01, 2012-10-01, 2012-10-01, 2012-10-01, 2012-10-01, …
## $ interval <int> 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 100, 105, 110, …</code></pre>
<p>Now that <code>date</code> is considered a date vector, we can create
a vector of the same number of rows as actdata (n = 17,568) telling us
the name of the day of the week associated with each row, then create a
logical vector for TRUE if the day of the week is a weekday and FALSE if
a weekend, convert that logical vector into a factor vector with
ifelse(), and finally bind that factor vector to
<code>imputed_dates</code>.</p>
<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb36-1"><a href="#cb36-1" aria-hidden="true" tabindex="-1"></a>daysoftheweek <span class="ot"><-</span> <span class="fu">weekdays</span>(imputed_dates[[<span class="dv">2</span>]])</span>
<span id="cb36-2"><a href="#cb36-2" aria-hidden="true" tabindex="-1"></a>day_type <span class="ot"><-</span> daysoftheweek <span class="sc">%in%</span> <span class="fu">c</span>(<span class="st">"Monday"</span>,<span class="st">"Tuesday"</span>,<span class="st">"Wednesday"</span>,<span class="st">"Thursday"</span>,<span class="st">"Friday"</span>)</span>
<span id="cb36-3"><a href="#cb36-3" aria-hidden="true" tabindex="-1"></a>day_type <span class="ot"><-</span> <span class="fu">as.factor</span>(<span class="fu">ifelse</span>(day_type, <span class="st">"weekday"</span>, <span class="st">"weekend"</span>))</span>
<span id="cb36-4"><a href="#cb36-4" aria-hidden="true" tabindex="-1"></a>imputed_dates <span class="ot"><-</span> <span class="fu">cbind</span>(imputed_dates, day_type)</span>
<span id="cb36-5"><a href="#cb36-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb36-6"><a href="#cb36-6" aria-hidden="true" tabindex="-1"></a><span class="fu">glimpse</span>(imputed_dates)</span></code></pre></div>
<pre><code>## Rows: 17,568
## Columns: 4
## $ steps <dbl> 1.49180328, 0.29508197, 0.11475410, 0.13114754, 0.06557377, 1…
## $ date <date> 2012-10-01, 2012-10-01, 2012-10-01, 2012-10-01, 2012-10-01, …
## $ interval <int> 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 100, 105, 110, …
## $ day_type <fct> weekday, weekday, weekday, weekday, weekday, weekday, weekday…</code></pre>
<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="fu">levels</span>(imputed_dates<span class="sc">$</span>day_type)</span></code></pre></div>
<pre><code>## [1] "weekday" "weekend"</code></pre>
<p>Having done that, we now have to process our new raw dataset
<code>imputed_dates</code> to collect and group the data by intervals,
and finally we can make a panel plot containing a time-series plot of
the 5-minute intervals on the x-axis and the average number of steps
taken, averaged across all weekdays or weekendays, on the y-axis.</p>
<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a>imputed_dates <span class="sc">%>%</span> <span class="fu">filter</span>(day_type <span class="sc">==</span> <span class="st">"weekday"</span>) <span class="sc">%>%</span></span>
<span id="cb40-2"><a href="#cb40-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(steps, interval) <span class="ot">-></span> imputed_weekdays</span>
<span id="cb40-3"><a href="#cb40-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb40-4"><a href="#cb40-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb40-5"><a href="#cb40-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb40-6"><a href="#cb40-6" aria-hidden="true" tabindex="-1"></a>imputed_dates <span class="sc">%>%</span> <span class="fu">filter</span>(day_type <span class="sc">==</span> <span class="st">"weekend"</span>) <span class="sc">%>%</span></span>
<span id="cb40-7"><a href="#cb40-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(steps, interval) <span class="ot">-></span> imputed_weekends</span>
<span id="cb40-8"><a href="#cb40-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb40-9"><a href="#cb40-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb40-10"><a href="#cb40-10" aria-hidden="true" tabindex="-1"></a><span class="fu">nrow</span>(imputed_weekdays) <span class="sc">+</span> <span class="fu">nrow</span>(imputed_weekends) <span class="sc">==</span> <span class="fu">nrow</span>(actdata)</span></code></pre></div>
<pre><code>## [1] TRUE</code></pre>
<p>Now we can finally create our plots.</p>
<div class="sourceCode" id="cb42"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a>p7 <span class="ot"><-</span> <span class="fu">ggplot</span>(imputed_weekdays, <span class="fu">aes</span>(<span class="at">x =</span> interval, <span class="at">y =</span> steps)) <span class="sc">+</span></span>
<span id="cb42-2"><a href="#cb42-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_smooth</span>(<span class="at">span =</span> <span class="fl">0.125</span>) <span class="sc">+</span></span>
<span id="cb42-3"><a href="#cb42-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Weekday Step Pattern, Averaged, Line"</span>)</span>
<span id="cb42-4"><a href="#cb42-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb42-5"><a href="#cb42-5" aria-hidden="true" tabindex="-1"></a>p8 <span class="ot"><-</span> <span class="fu">ggplot</span>(imputed_weekends, <span class="fu">aes</span>(<span class="at">x =</span> interval, <span class="at">y =</span> steps)) <span class="sc">+</span></span>
<span id="cb42-6"><a href="#cb42-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_smooth</span>(<span class="at">span =</span> <span class="fl">0.125</span>) <span class="sc">+</span></span>
<span id="cb42-7"><a href="#cb42-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Weekend Step Pattern, Averaged, Line"</span>)</span>
<span id="cb42-8"><a href="#cb42-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb42-9"><a href="#cb42-9" aria-hidden="true" tabindex="-1"></a>gridExtra<span class="sc">::</span><span class="fu">grid.arrange</span>(p7, p8)</span></code></pre></div>
<pre><code>## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'</code></pre>
<p><img src="data:image/png;base64,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" 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