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PA1_template.html
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<title>Loading and preprocessing the data</title>
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<h2>Loading and preprocessing the data</h2>
<pre><code class="r">library(dplyr)
library(xtable)
library(lattice)
library(lubridate)
data <- read.csv("activity.csv")
</code></pre>
<h2>What is mean total number of steps taken per day?</h2>
<pre><code class="r">stepsPerDay <- data %>%
group_by(date) %>%
summarize(tot = sum(steps, na.rm = T))
hist(stepsPerDay$tot, main = "Histogram of Steps per Day", xlab = "Steps per Day")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-2"/> </p>
<pre><code class="r">dtMean <- round(mean(stepsPerDay$tot),digits = 2)
dtMedian <- median(stepsPerDay$tot)
</code></pre>
<h4>Mean: 9354.23</h4>
<h4>Median: 10395</h4>
<h2>What is the average daily activity pattern?</h2>
<pre><code class="r">stepsPerTime <- data %>%
group_by(interval) %>%
summarize(avg = mean(steps, na.rm=T))
plot(stepsPerTime$interval,stepsPerTime$avg,type = "l",main="Avg Steps per Interval",xlab="5 min interval",ylab="Avg Steps")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-3"/> </p>
<pre><code class="r">dtMax <- filter(stepsPerTime, avg == max(stepsPerTime$avg)) %>% select(interval)
</code></pre>
<h4>Interval with highest average steps: 835</h4>
<h2>Imputing missing values</h2>
<p>I took the interval's average in order to fill in NA values. A better method might be
to break intervals down by day type</p>
<pre><code class="r">NArows <- data %>%
filter(is.na(steps))
naRowCount <- count(NArows)
</code></pre>
<h4>Rows with NA: 2304</h4>
<pre><code class="r">nonNArows <- data %>%
filter(!is.na(steps))
nonNArows$steps <- as.numeric(nonNArows$steps)
avgData <- select(NArows, -steps) %>%
inner_join(stepsPerTime) %>%
select(avg, date, interval)
</code></pre>
<pre><code>## Joining by: "interval"
</code></pre>
<pre><code class="r">colnames(avgData) <- colnames(nonNArows)
fullData <- dplyr::union(nonNArows,avgData)
stepsPerDayFull <- fullData %>%
group_by(date) %>%
summarize(tot = sum(steps, na.rm = T))
hist(stepsPerDayFull$tot, main = "Histogram of Steps per Day w/ Avg for NAs", xlab = "Steps per Day")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-5"/> </p>
<pre><code class="r">dtMean <- round(mean(stepsPerDay$tot),digits = 2)
dtMedian <- median(stepsPerDay$tot)
</code></pre>
<h4>Mean w/ Interval Avg for NAs: 9354.23</h4>
<h4>Median w/ Interval Avg for NAs: 10395</h4>
<h2>Are there differences in activity patterns between weekdays and weekends?</h2>
<pre><code class="r">fullData <- mutate(fullData,dayType = ifelse(wday(as.Date(fullData$date),T) == c("Sun","Sat"),"Weekend","Weekday")) %>%
group_by(dayType, interval) %>%
summarize(avg = mean(steps)) %>%
arrange(interval)
xyplot(avg ~ interval | dayType, fullData, type="l", layout = c(1,2), xlab = "Interval", ylab="Average Steps",main="Average Steps by Day Type")
</code></pre>
<p><img 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" alt="plot of chunk unnamed-chunk-6"/> </p>
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