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<title>Reproducible Research - Peer Assessment 1</title>
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<body>
<h1>Reproducible Research - Peer Assessment 1</h1>
<p>Created by: Ankush Jindal</p>
<p>Created on: 13/12/14</p>
<h2>Loading and preprocessing the data</h2>
<p>The report requires <code>activity.csv</code> to be present in the same folder as <code>PA1_template.Rmd</code>. </p>
<h3>Loading the data</h3>
<pre><code class="r">df <- read.csv("activity.csv")
</code></pre>
<h3>Preprocessing the data</h3>
<pre><code class="r">df$date <- as.Date(df$date, format = "%Y-%m-%d") # convert date to column with date type
# create dataframe with total steps per day
df.day <- aggregate(df$steps, by = list(df$date), sum)
names(df.day)[1] <- "day"
names(df.day)[2] <- "steps"
# create dataframe with total steps per interval
df.interval <- aggregate(df$steps, by = list(df$interval), sum, na.rm = TRUE,
na.action = NULL)
names(df.interval)[1] <- "interval"
names(df.interval)[2] <- "steps"
# create dataframe with mean steps per interval
df.mean.interval <- aggregate(df$steps, by = list(df$interval), mean, na.rm = TRUE,
na.action = NULL)
names(df.mean.interval)[1] <- "interval"
names(df.mean.interval)[2] <- "mean.steps"
</code></pre>
<h2>What is mean total number of steps taken per day?</h2>
<h3>Histogram of the total number of steps taken each day</h3>
<pre><code class="r">
hist(df.day$steps, main = "Histogram of the total number of steps taken each day",
xlab = "total number of steps taken each day")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-3"/> </p>
<h3>The mean and median total number of steps taken per day</h3>
<p>Mean number of steps per day:</p>
<pre><code class="r">mean(df.day$steps, na.rm = TRUE)
</code></pre>
<pre><code>## [1] 10766
</code></pre>
<p>Median number of steps per day:</p>
<pre><code class="r">median(df.day$steps, na.rm = TRUE)
</code></pre>
<pre><code>## [1] 10765
</code></pre>
<h2>What is the average daily activity pattern?</h2>
<h3>Time series plot</h3>
<p><em>Make a time series plot (i.e. type = “l”) of the 5-minute interval (x-axis) and the average number of steps taken, averaged across all days (y-axis)</em></p>
<pre><code class="r">
plot(df.mean.interval$interval, df.mean.interval$mean.steps, type = "n", main = "Time Series Plot per 5-minute interval",
xlab = "5-minute intervals", ylab = "Average number of steps taken")
lines(df.mean.interval$interval, df.mean.interval$mean.steps, type = "l")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-6"/> </p>
<pre><code class="r">
</code></pre>
<h3>Maximum number of steps</h3>
<p><em>Which 5-minute interval, on average across all the days in the dataset, contains the maximum number of steps?</em>
5-minute interval with maximum number of steps:</p>
<pre><code class="r">
df.mean.interval[which.max(df.mean.interval$mean.steps), 1]
</code></pre>
<pre><code>## [1] 835
</code></pre>
<p>p.s. and the maximum number of steps = 206.1698</p>
<h2>Inputing missing values</h2>
<h3>Missing values</h3>
<p><em>Calculate and report the total number of missing values in the dataset (i.e. the total number of rows with NAs)</em>
Total number of missing values in the dataset:</p>
<pre><code class="r">sum(is.na(df$steps))
</code></pre>
<pre><code>## [1] 2304
</code></pre>
<h3>Fill in missing values</h3>
<p><em>Devise a strategy for filling in all of the missing values in the dataset. The strategy does not need to be sophisticated. For example, you could use the mean/median for that day, or the mean for that 5-minute interval, etc.</em>
I am going to use the mean for the interval as a replacement for missing values. The <code>df.mean.interval</code> dataframe (contains mean per interval) has been created during the preprocessing step (see above).</p>
<pre><code class="r">
df.missing <- merge(df, df.mean.interval, by = "interval", sort = FALSE) # merge df and df.mean.interval dataframes
df.missing <- df.missing[with(df.missing, order(date, interval)), ] # sort on date and interval (optional)
# replace in steps column NA with value in mean.steps column
df.missing$steps[is.na(df.missing$steps)] <- df.missing$mean.steps[is.na(df.missing$steps)]
df.missing$mean.steps <- NULL # remove the column with the mean since it is no longer needed
</code></pre>
<p>Note: the dataset now contains fractions for the number of steps:</p>
<pre><code class="r">head(df.missing)
</code></pre>
<pre><code>## interval steps date
## 1 0 1.71698 2012-10-01
## 63 5 0.33962 2012-10-01
## 128 10 0.13208 2012-10-01
## 205 15 0.15094 2012-10-01
## 264 20 0.07547 2012-10-01
## 327 25 2.09434 2012-10-01
</code></pre>
<p>The instructions don't list it as a requirement, but it would make sence to round the mean steps since fractions of steps per interval do not make sence. For the purpose of this report I have chosen to round them:</p>
<pre><code class="r">df.missing$steps <- round(df.missing$steps, digits = 0)
</code></pre>
<h3>New dataset with missing data filled in</h3>
<p><em>Create a new dataset that is equal to the original dataset but with the missing data filled in.</em></p>
<pre><code class="r">
df.new <- df.missing[, c(2, 3, 1)]
</code></pre>
<h3>Histogram of total number of steps</h3>
<p><em>Make a histogram of the total number of steps taken each day and Calculate and report the mean and median total number of steps taken per day. Do these values differ from the estimates from the first part of the assignment? What is the impact of imputing missing data on the estimates of the total daily number of steps?</em></p>
<pre><code class="r"># create dataframe with total steps per day different from before since this
# has NA replaced with mean steps per interval
df.day.new <- aggregate(df.new$steps, by = list(df.new$date), sum)
names(df.day.new)[1] <- "day"
names(df.day.new)[2] <- "steps"
</code></pre>
<h3>Histogram of the total number of steps taken each day</h3>
<pre><code class="r">hist(df.day.new$steps, main = "Histogram of the total number of steps taken each day (NA replaced)",
xlab = "total number of steps taken each day")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-14"/> </p>
<h3>The mean and median total number of steps taken per day</h3>
<p>Mean number of steps per day:</p>
<pre><code class="r"># na.rm now is optional since all NA have been replaced!
mean(df.day.new$steps, na.rm = TRUE)
</code></pre>
<pre><code>## [1] 10766
</code></pre>
<p>Median number of steps per day:</p>
<pre><code class="r"># na.rm now is optional since all NA have been replaced!
median(df.day.new$steps, na.rm = TRUE)
</code></pre>
<pre><code>## [1] 10762
</code></pre>
<p>The Mean is equal to the estimates from the first part of the assignment.</p>
<p>The Median is slightly lower when compared to the first part of the assignment. </p>
<p>The histogram shows a similar shape as before with overall higher frequencies due to the NA being replaced in the new histogram. See also this side by side plot:</p>
<pre><code class="r">par(mfrow = c(1, 2))
hist(df.day$steps, main = "(with NA)", xlab = "total number of steps taken each day")
hist(df.day.new$steps, main = "(NA replaced)", xlab = "total number of steps taken each day")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-17"/> </p>
<h3>Estimates of the total daily number of steps</h3>
<h2>Are there differences in activity patterns between weekdays and weekends?</h2>
<h3>new factor variable</h3>
<p><em>Create a new factor variable in the dataset with two levels – “weekday” and “weekend” indicating whether a given date is a weekday or weekend day.</em></p>
<pre><code class="r"># create copy of the dataframe
df.new.2 <- df.new
# make sure we use English date names
Sys.setlocale("LC_TIME", "English")
</code></pre>
<pre><code>## [1] "English_United States.1252"
</code></pre>
<pre><code class="r"># create a factor with the names of the days for all dates
df.new.2$weekdays <- factor(format(df.new.2$date, "%A"))
# the day names fe
levels(df.new.2$weekdays)
</code></pre>
<pre><code>## [1] "Friday" "Monday" "Saturday" "Sunday" "Thursday" "Tuesday"
## [7] "Wednesday"
</code></pre>
<pre><code class="r"># replace the levels
levels(df.new.2$weekdays) <- list(weekday = c("Monday", "Tuesday", "Wednesday",
"Thursday", "Friday"), weekend = c("Saturday", "Sunday"))
</code></pre>
<h3>panel plot</h3>
<p><em>Make a panel plot containing a time series plot (i.e. type = “l”) of the 5-minute interval (x-axis) and the average number of steps taken, averaged across all weekday days or weekend days (y-axis).</em></p>
<pre><code class="r">df.new.2.mean.interval <- aggregate(df.new.2$steps, by = list(df.new.2$weekdays,
df.new.2$interval), mean, na.rm = TRUE, na.action = NULL)
names(df.new.2.mean.interval)[1] <- "weekday"
names(df.new.2.mean.interval)[2] <- "interval"
names(df.new.2.mean.interval)[3] <- "mean.steps"
library(lattice)
xyplot(df.new.2.mean.interval$mean.steps ~ df.new.2.mean.interval$interval |
df.new.2.mean.interval$weekday, layout = c(1, 2), type = "l", xlab = "Interval",
ylab = "Number of steps")
</code></pre>
<p><img 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KKy/eXOyCw8TvWX6/9OGtKL9zp3/OzcNuFdvVA8xF9v/4hH6gmkw+Pmbvwf5maNtARIPYF0yP6YNFJPIB0ep/qr86gjLQFSTyAdPuJ5jd8wwq/xSD2DZAi/xiP1DJIh/BqP1DNIxoLvq5840hJQfLT2IXrGg+KjtQ/RMx4UP6M9T/WbxveIH3+HR/Grwlf8tt+IQfGz21/zVL9NvK/xm/5qEoqP1j5Ez3hQfLT2IXrGg+Int9/He+4ofm77K17jN4qX+E8PtOO9/GjN3bf1VxpZX2xE8avCR/xVpr96c31W+L6ovsTM/iqzVYqX+1YMn6dzrsv71UX1tYXqlxfOW4IhPhAtfqKUtuV15nqxtjjoqy8qtb+ulOJXRdi7+suz5otK7a8rpfhVEfJ5/O3T8hZ/O9d4ig/U/vhVdOfbuaun+IjtQ/SMBcVHbB+iZywoPmL7ED0jcbQu9iUcik89jURQfOppJILiU08jERSfehqJkC5e7G29aPHdVh4Un3QO6aD4pHNIB8UnnUM6KD7pHNIhXrxU8xQv1DzFCzVP8blM8xRvJKVA8VZaBhTvyEiA4h0ZCVC8IyMBindkJEDxjowEKN6RkQDFOzISoHhHRgIU78hIgOIdGQlQvCMjgbDij2shXGblJ6TX/zFp9GYkEFT8dbk+xu2zUvgGFkZAb0YCQVfE+Klc9ubTD/ezs3wDix+hNyOB2YsfOSnFl+tZX11sYPEj9GYkEPYa37i+Pt/A4kfozUggvPjr83K1u61d48WZj3DEX5YrIG3trp7iA7cP0TMSGMjtH4p35vYPxTtz+4finbn9Q/HO3P6heGdu/1C8M7d/KN6Z2z8U78ztH4p35vYPxTtz+4finbn9Q/HO3P6heGdu/1C8M7d/KN6Z2z8U78ztH4p35vYPxTtz+4finbn9Q/HO3P6heGcuLVhgDIp35tKCBcageGcuLVhgDIp35tKCBcag+J5sSrDAGHLF40Q+IVhgDIrvyydkia+/pPi+fEIoPiYw82ZBOrYnvl78qPyA9Oo/Jg0zbxYkA0ucfcIvflQtibD+hRFg5s2CZGxOfLX4UbUIyvoXP4KZNwuSsYz44IsfVcserX/xI5h5syAZmzvia/HWET9vpNjAzK/G/EbFb/YaH/XhnhJ7o+I3e1cfV/yE4BsUH6dnHGDlzZKgo00ITvFRgZU3S4KONiE4xUcFVt4sCTrahOBY4hkGxXd5syToaBOC49g+snyK7/JmSdDRJgRvmkZVT/FDJQFHGx8cjlR4KH6oJOBo44PDkQqPOPGwEnbV+CDje8wJPn2Y8YgV7zBhl5wKMmHYoS7QknCVB0eqeNdNs11yIsikYQf6QEvCWREaireqxgeZNOxAH2hJOCtCI1S88zUSu6Q3yPimbeyBLtCScFaEZt/i0Ve0YvFwV4RGpngM1I2KO7plF3qgC9Qk3BWhkSceOcXnOxfvPJ1DOeqtyvmBT/XoDw6KD80WxWuhJw8zHlHiUT3KcDRt6ucFPt1hILh2o0nxIdi8+Ijm9yzeUoye53FK/cjIo1sqkfv6GOKtfnHYu3io+eohhrt1nkg8KD40PeKHOoyNPLqlErmnD8UHB+atUijxg0/K+yO7O+mzpPgAwHgcceqNbIOVWrup6tEfnuKDg7x7na7KBxM/9WSP/vD6bxHMyljsXHz1D03+xIE6WKm3myPeHZ/ig4P2H7T8YIeRgSl+gZ6TgbJD++oJlKrBfgMN0Fw7tGvIpBmZnTTxdmUs9ike1a5OI5z4vJEfUnxO8YHQxaNOoy3r7XcysD7E+PM9up3ZRytzVcYhgvjLrPyEdMKPSUN9NNH+FmBMx7H188S3v39GFcx2Y2c0n/Dib5+VwlMujACX+DGWTrVQ6meLt/og34n4Tz/cz87ylIsfIVcOrTFHutpxqFap3774oIsflVzfKRdASrn4EfIA4u1eDvFTngA2/cwuyNOIj9L++jzl4keoNlCz4zv29oJV7xY/WLZj8dfneXHEJ77GTzvStY6OdF2iF6FnDDhKoSah10BtYPZENPdx7urPky5+hGqLmR3tdO4KCPVYhVZs9cVABmqZoyfiuN/j83hUW8zsaKedJW7xcJ4HMJCBWuboCYofC7TdpI5Q0u6oRmNjLOSWS6uvnoHV3x7FKg3AjsXP6QglfSKqKR5NI1u8fvLRM9DKHKOC4seC+R07Rc67b6NxVwzl7rx5kRhK095AFB8QzO/Y2MJU8Yqg9q8D6Jr2BmrEw9WymYhVGoAdiodHTy/xTd/2ItAG6w/UHvFwtMwpfgqY3xOKR9O8GbZt2/aEVoOqOLe8QUtD3ZtjUPwUML+nLl4PZIYdI75Kw+zoTCOneD8wv2d74DkebzOsJb79RdE6295gdu7KzTEofgrw6YpmN1p8c05XTxBqZ+fNQtMceoXZtGpoRQgBxetdkdeHHsxAZtix4u2OaC7+FB8U+HRFFQCwAplhR4u3BoEyjlnjaN0rvn+IEVC81RlNEJg1Rh5dhXqJ1ypdQyg9jVaOTkfvcDbqH2IEFG91RhME2mNshVUqkU8QrxzZI07i9t0GrMQcKN7sjDaIcpaFw1FbgOaKbYfpGaTrOmJC5m/dhM4DULzZGWqQ+t7Kec3uShwH7uCxPOVuDdZlp0163fRRvNEZjiDWZban03DRzAnZ4mEm5kDxRmc4gww/xjHF58pNhxGa4nUQorMR5MRjbNdSfICeE0GEzknFG2No4mcPQ/HjYg4HtWvDi1dORnVwnHjyMAjFj4s5NWgc8aj3zcHu8Wru/sRjFUEjiG+Ob9QDwBY/YVCKjxR0eo8RIaFGRm68vjDpxE/x2wHm34IM1xS/U06Id72s3A/Fbwj7T7SqbORTfniK3xDDfzJALlo8lhkmCRgsRW8LF9sXP/8ytxPUPy80yeqSgIFe0cSP/pg08u61CaXIbtTTWbnuwecVjQ3TvUsH7X0AThwGscRPWBhB+YM3UP8M2i0Luh8nV0QrbUf8hu+d9kHpCjD00l4s8ZMWP0Lzq1pl0BzIDfWP0+Sa34+qrA0i82g30G/yBwi/+FFFysWPyAiWOOLnjUSisoJrPElB+rt6koTtP48ns6B4oVC8UCheKBQvFIoXyoLiyapYTPwCEcOF4qQiDh4+4k4e4/iRKD5+pL1MiuLThaL4+KE4qYiDh4+4k8c4fqRViCebgOKFQvFCoXihULxQKF4oFC+U0OKt92TOC9J9Y71PwOMbwtUw84PVobzndfs0y+6+DTQpHwKLt9+FPQP1G+t9Al5nd15rYeYHO4YKMa/rs8L0RZhJeRFYvP25ixmo31jvEfD2p/KzP2qY2cGqUIHmVX4pe4hJ+RFavPVJqxmo31jvFfAoXgnjEazsF2hexUEfaFI+rPGIL2m+sd4rYLAjPm/d+M/r8iwPNSkf1niNV7+x3ivg8TANczk9hgowr9unF3kealI+rPWu/jzEPe/xMA1zA12H8p7XZfn2uPP93dWTrUDxQqF4oVC8UCheKBQvFIoXCsULheKFQvFCoXihULxQZIn/8PvXVqq/za6h+P42u0ac+A9f/3eWXXx6kN15fdzkH/7tr+XbH2+fvfhwv6ih+D1Sir9/Xr4PotR7eZ5fneUf7l+U76L88PU/vntxbEDx+6P2Wu0+FaI//flYcHVe/p/nTV4AksU/yMr3yR8Lvv7ns+N7YYpzP8XvEF189RbHsuD22f98/fbTgwue6neKJr68xtdX+/wqOz/+Bnz41xcUv0M68bdPj3f1n7+o7uIL4aX97F/+ekHxZM9QvFAoXigULxSKFwrFC4XihULxQqF4oVC8UCheKBQvlP8HgCUaxgGmPzUAAAAASUVORK5CYII=" 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