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<h1>#Reproducible Research Peer Assessment 1</h1>
<p>This script loads activity.csv to variable, activity, then
performs analysis on steps variable based on different categories.</p>
<p>First, let's load activity.csv and check its structure.</p>
<pre><code class="r">activity = read.csv(unz("activity.zip", "activity.csv"), stringsAsFactor = F)
str(activity)
</code></pre>
<pre><code>## 'data.frame': 17568 obs. of 3 variables:
## $ steps : int NA NA NA NA NA NA NA NA NA NA ...
## $ date : chr "2012-10-01" "2012-10-01" "2012-10-01" "2012-10-01" ...
## $ interval: int 0 5 10 15 20 25 30 35 40 45 ...
</code></pre>
<p>We have to convert date character to date type.</p>
<pre><code class="r">activity$date = as.Date(activity$date, format = "%Y-%m-%d")
</code></pre>
<p>Now compute total number of steps for each day and plot histogram.</p>
<pre><code class="r">activity.dailyTotalSteps = tapply(activity$steps, activity$date, sum)
hist(activity.dailyTotalSteps)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-3"/> </p>
<p>The mean and median of activity.dailyTotalSteps.</p>
<pre><code class="r">mean(activity.dailyTotalSteps, na.rm = T)
</code></pre>
<pre><code>## [1] 10766
</code></pre>
<pre><code class="r">median(activity.dailyTotalSteps, na.rm = T)
</code></pre>
<pre><code>## [1] 10765
</code></pre>
<p>Plot the number of steps per 5-minute, averaged across all days.</p>
<pre><code class="r">steps.mean = tapply(activity$steps, activity$interval, mean, na.rm = T)
plot(steps.mean, type = "l", xaxt = "n", xlab = "Hour of day", ylab = "Average number of steps")
xtk = seq(0, 288, 12)
axis(1, at = xtk, labels = xtk/12)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-5"/> </p>
<p>Report which 5-minute interval, on average, has the maximum steps and the index of that max in steps.mean array.</p>
<pre><code class="r">which.max(steps.mean)
</code></pre>
<pre><code>## 835
## 104
</code></pre>
<p>How many missing values (NA) do we have in this activity?</p>
<pre><code class="r">sum(is.na(activity$steps))
</code></pre>
<pre><code>## [1] 2304
</code></pre>
<p>Replace NA with last known value in time series of the new data frame, imputedActivity.</p>
<p>If the very first value is NA, we set it to mean value of steps in the entire dataset.</p>
<pre><code class="r">na.location = is.na(activity$steps)
imputedActivity = activity
if (na.location[1]) {
lastSteps = 0
imputedActivity$steps[1] = mean(imputedActivity$steps, na.rm = T)
} else {
lastSteps = imputedActivity$steps[1]
}
</code></pre>
<p>Now we look each steps variable and replace it with lastSteps if it's NA.</p>
<pre><code class="r">for (i in seq(2, nrow(imputedActivity))) {
if (na.location[i]) {
imputedActivity$steps[i] = lastSteps
} else {
lastSteps = imputedActivity$steps[i]
}
}
</code></pre>
<p>The final number of NA in imputedActivity$steps should be zero.</p>
<pre><code class="r">sum(is.na(imputedActivity$steps))
</code></pre>
<pre><code>## [1] 0
</code></pre>
<p>Now compute total number of steps for each day and plot histogram for imputedActivity.</p>
<pre><code class="r">imputedActivity.dailyTotalSteps = tapply(imputedActivity$steps, imputedActivity$date,
sum)
hist(imputedActivity.dailyTotalSteps)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-11"/> </p>
<p>The mean and median of activity.dailyTotalSteps.</p>
<pre><code class="r">mean(imputedActivity.dailyTotalSteps, na.rm = T)
</code></pre>
<pre><code>## [1] 9355
</code></pre>
<pre><code class="r">median(imputedActivity.dailyTotalSteps, na.rm = T)
</code></pre>
<pre><code>## [1] 10395
</code></pre>
<p>We can clearly see mean and median values change after we impute.</p>
<p>Let's compare activities between weekdays and weekends.
First, partition days into weekday and weekend.</p>
<pre><code class="r">imputedActivity$day = weekdays(imputedActivity$date)
imputedActivity$day[imputedActivity$day == "Sunday" | imputedActivity$day ==
"Saturday"] = "weekend"
imputedActivity$day[imputedActivity$day != "weekend"] = "weekday"
imputedActivity$day = as.factor(imputedActivity$day)
</code></pre>
<p>Plot average number of steps for each 5-min interval, averaging over weekdays, and over weekends.
Note that we need to load lattice plotting system library.</p>
<pre><code class="r">library(lattice)
weekdayActivity = subset(imputedActivity, imputedActivity$day == "weekday")
weekendActivity = subset(imputedActivity, imputedActivity$day == "weekend")
s1 = tapply(weekdayActivity$steps, weekdayActivity$interval, mean)
s2 = tapply(weekendActivity$steps, weekendActivity$interval, mean)
meanSteps = c(s1, s2)
interval = c(seq(0, 1435, 5), seq(0, 1435, 5))
day = c(rep("weekday", 288), rep("weekend", 288))
plotData = data.frame(meanSteps, interval, day)
plotData$day = as.factor(plotData$day)
xyplot(meanSteps ~ interval | day, data = plotData, type = "l", ylab = "Average number of steps in 5-min interval",
xlab = "index of 5-min intervals", layout = c(1, 2))
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-14"/> </p>
<p>We can clearly see the difference between these two plots.</p>
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