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<title>Course 5 assignment week 2</title>
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<h1>Course 5 assignment week 2</h1>
<h2>Loading and preprocessing the data</h2>
<p>Data from a personal activity monitoring device. Includes the steps, the date
and the interval.</p>
<pre><code class="r">library(data.table)
setwd("C:/frodriguezp/DataScience/Rprojects");
fname<-"./data/activity.csv"
md0<-read.csv(fname)
md0<-as.data.table(md0)
md0$date<-as.Date(md0$date,"%Y-%m-%d")
md<-md0[!is.na(steps), ]
print(head(md),10)
</code></pre>
<pre><code>## steps date interval
## 1: 0 2012-10-02 0
## 2: 0 2012-10-02 5
## 3: 0 2012-10-02 10
## 4: 0 2012-10-02 15
## 5: 0 2012-10-02 20
## 6: 0 2012-10-02 25
</code></pre>
<h2>Processing</h2>
<h3>Mean of total steps taken per day</h3>
<p>Total number of steps per day and its histogram</p>
<pre><code class="r">mddate<-md[,.(sum=sum(steps)),by=date]
hist(mddate[,sum],breaks=8
,main="Histogram",xlab="steps")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-2"/></p>
<p>Mean and median of the total number of steps taken per day</p>
<pre><code class="r">stats_mddate<-mddate[,.(mean=mean(sum),median=median(sum))]
print(stats_mddate)
</code></pre>
<pre><code>## mean median
## 1: 10766.19 10765
</code></pre>
<h2>Average daily activity pattern</h2>
<p>Time series plot of the 5-minute interval (x-axis) and the average number of steps taken, averaged across all days (y-axis)</p>
<pre><code class="r">mdint<-md[,.(mean=mean(steps)),by=interval]
with(mdint,plot(interval,mean,type = "l",
ylab="average number of steps"))
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-4"/></p>
<pre><code class="r">intmax<-mdint$interval[which.max(mdint$mean)]
</code></pre>
<p>The 5-minute interval that contains the maximum number of steps
is the 835 identifier.</p>
<h2>Imputing missing values</h2>
<p>Total number of missing values in the dataset</p>
<pre><code class="r">totalna<-sum(is.na(md0$steps))
totaldays<-dim(md0[,.(.N),by=date])[1]
nadays<-totalna/dim(mdint)[1]
print(totalna)
</code></pre>
<pre><code>## [1] 2304
</code></pre>
<p>The data includes the record form 61 days, but 8 days contain
<em>NA</em> values.</p>
<p>Missing values in the dataset will be replaced for the averaged number of steps
for that 5-minute interval</p>
<pre><code class="r">md<-md0
md$steps[is.na(md$steps)]<-rep(mdint$mean,nadays)
</code></pre>
<p>Histogram of the total number of steps taken each day.</p>
<pre><code class="r">mddate<-md[,.(sum=sum(steps)),by=date]
hist(mddate[,sum],breaks=8
,main="Histogram",xlab="steps")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-7"/></p>
<pre><code class="r">stats_mddate<-rbind(stats_mddate,mddate[,.(mean=mean(sum),median=median(sum))])
print(stats_mddate)
</code></pre>
<pre><code>## mean median
## 1: 10766.19 10765.00
## 2: 10766.19 10766.19
</code></pre>
<p>Mainly there is no difference between removing the missing values and replce
them.</p>
<h2>Differences in activity patterns between weekdays and weekends</h2>
<pre><code class="r">weekdays<-weekdays.Date(md$date) %in% c("Saturday","Sunday")
weekdays<-factor(weekdays); levels(weekdays)<-c("weekday","weekend")
md$weekdays<-weekdays
mdint<-md[,.(mean=mean(steps)),by=.(interval,weekdays)]
par(mfrow=c(2,1), oma = c(5,4,0,0)+0.1, mar=c(0,0,2,1)+0.1)
with(subset(mdint,weekdays=="weekday"),
plot(interval,mean, type = "l", col="blue"))
legend("topright", lty = 1,col = c("blue"), legend = c("Weekday"))
with(subset(mdint,weekdays=="weekend"),
plot(interval,mean, type = "l", col="red"))
legend("topright", lty = 1,col = c("red"), legend = c("Weekend"))
title(xlab = "interval",
ylab = "steps",
outer = TRUE)
</code></pre>
<p><img src="data:image/png;base64,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" 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