# Chapter 15 Appendix A A sample session

The following session is intended to introduce to you some features of the R environment by using them. Many features of the system will be unfamiliar and puzzling at first, but this puzzlement will soon disappear.

Start R appropriately for your platform (see Invoking R).

The R program begins, with a banner.

(Within R code, the prompt on the left hand side will not be shown to avoid confusion.)

help.start()

Start the HTML interface to on-line help (using a web browser available at your machine). You should briefly explore the features of this facility with the mouse.

Iconify the help window and move on to the next part.

x <- rnorm(50)
y <- rnorm(x)

Generate two pseudo-random normal vectors of x- and y-coordinates.

plot(x, y)

Plot the points in the plane. A graphics window will appear automatically.

ls()

See which R objects are now in the R workspace.

rm(x, y)

Remove objects no longer needed. (Clean up).

x <- 1:20

Make x = (1, 2, …, 20).

w <- 1 + sqrt(x)/2

A ‘weight’ vector of standard deviations.

dummy <- data.frame(x=x, y= x + rnorm(x)*w)
dummy

Make a data frame of two columns, x and y, and look at it.

fm <- lm(y ~ x, data=dummy)
summary(fm)

Fit a simple linear regression and look at the analysis. With y to the left of the tilde, we are modelling y dependent on x.

fm1 <- lm(y ~ x, data=dummy, weight=1/w^2)
summary(fm1)

Since we know the standard deviations, we can do a weighted regression.

attach(dummy)

Make the columns in the data frame visible as variables.

lrf <- lowess(x, y)

Make a nonparametric local regression function.

plot(x, y)

Standard point plot.

lines(x, lrf$$y)</code></dt> <dd><p>Add in the local regression.</p> </dd> <dt><code class="calibre2">abline(0, 1, lty=3)</code></dt> <dd><p>The true regression line: (intercept 0, slope 1).</p> </dd> <dt><code class="calibre2">abline(coef(fm))</code></dt> <dd><p>Unweighted regression line.</p> </dd> <dt><code class="calibre2">abline(coef(fm1), col = &quot;red&quot;)</code></dt> <dd><p>Weighted regression line.</p> </dd> <dt><code class="calibre2">detach()</code></dt> <dd><p>Remove data frame from the search path.</p> </dd> <dt><code class="calibre2">plot(fitted(fm), resid(fm),</code><br /> <code class="calibre2"> xlab=&quot;Fitted values&quot;,</code><br /> <code class="calibre2"> ylab=&quot;Residuals&quot;,</code><br /> <code class="calibre2"> main=&quot;Residuals vs Fitted&quot;)</code></dt> <dd><p>A standard regression diagnostic plot to check for heteroscedasticity. Can you see it?</p> </dd> <dt><code class="calibre2">qqnorm(resid(fm), main=&quot;Residuals Rankit Plot&quot;)</code></dt> <dd><p>A normal scores plot to check for skewness, kurtosis and outliers. (Not very useful here.)</p> </dd> <dt><code class="calibre2">rm(fm, fm1, lrf, x, dummy)</code></dt> <dd><p>Clean up again.</p> </dd> </dl> <p>The next section will look at data from the classical experiment of Michelson to measure the speed of light. This dataset is available in the <code class="calibre2">morley</code> object, but we will read it to illustrate the <code class="calibre2">read.table</code> function.</p> <dl> <dt><code class="calibre2">filepath &lt;- system.file(&quot;data&quot;, &quot;morley.tab&quot; , package=&quot;datasets&quot;)</code><br /> <code class="calibre2">filepath</code></dt> <dd><p>Get the path to the data file.</p> </dd> <dt><code class="calibre2">file.show(filepath)</code></dt> <dd><p>Optional. Look at the file.</p> </dd> <dt><code class="calibre2">mm &lt;- read.table(filepath)</code><br /> <code class="calibre2">mm</code></dt> <dd><p>Read in the Michelson data as a data frame, and look at it. There are five experiments (column <code class="calibre2">Expt</code>) and each has 20 runs (column <code class="calibre2">Run</code>) and <code class="calibre2">sl</code> is the recorded speed of light, suitably coded.</p> </dd> <dt><code class="calibre2">mm$$Expt <- factor(mm$$Expt)</code><br /> <code class="calibre2">mm$$Run <- factor(mm\$Run)

Change Expt and Run into factors.

attach(mm)

Make the data frame visible at position 3 (the default).

plot(Expt, Speed, main=“Speed of Light Data”, xlab=“Experiment No.”)

Compare the five experiments with simple boxplots.

fm <- aov(Speed ~ Run + Expt, data=mm)
summary(fm)

Analyze as a randomized block, with ‘runs’ and ‘experiments’ as factors.

fm0 <- update(fm, . ~ . - Run)
anova(fm0, fm)

Fit the sub-model omitting ‘runs’, and compare using a formal analysis of variance.

detach()
rm(fm, fm0)

Clean up before moving on.

We now look at some more graphical features: contour and image plots.

x <- seq(-pi, pi, len=50)
y <- x

x is a vector of 50 equally spaced values in the interval [-pi, pi]. y is the same.

f <- outer(x, y, function(x, y) cos(y)/(1 + x^2))

f is a square matrix, with rows and columns indexed by x and y respectively, of values of the function cos(y)/(1 + x^2).

oldpar <- par(no.readonly = TRUE)
par(pty=“s”)

Save the plotting parameters and set the plotting region to “square”.

contour(x, y, f)
contour(x, y, f, nlevels=15, add=TRUE)

Make a contour map of f; add in more lines for more detail.

fa <- (f-t(f))/2

fa is the “asymmetric part” of f. (t() is transpose).

contour(x, y, fa, nlevels=15)

Make a contour plot, …

par(oldpar)

… and restore the old graphics parameters.

image(x, y, f)
image(x, y, fa)

Make some high density image plots, (of which you can get hardcopies if you wish), …

objects(); rm(x, y, f, fa)

… and clean up before moving on.

R can do complex arithmetic, also.

th <- seq(-pi, pi, len=100)
z <- exp(1i*th)

1i is used for the complex number i.

par(pty=“s”)
plot(z, type=“l”)

Plotting complex arguments means plot imaginary versus real parts. This should be a circle.

w <- rnorm(100) + rnorm(100)*1i

Suppose we want to sample points within the unit circle. One method would be to take complex numbers with standard normal real and imaginary parts …

w <- ifelse(Mod(w) > 1, 1/w, w)

… and to map any outside the circle onto their reciprocal.

plot(w, xlim=c(-1,1), ylim=c(-1,1), pch=“+”,xlab=“x”, ylab=“y”)
lines(z)

All points are inside the unit circle, but the distribution is not uniform.

w <- sqrt(runif(100))exp(2pirunif(100)1i)
plot(w, xlim=c(-1,1), ylim=c(-1,1), pch=“+”, xlab=“x”, ylab=“y”)
lines(z)

The second method uses the uniform distribution. The points should now look more evenly spaced over the disc.

rm(th, w, z)

Clean up again.

q()

Quit the R program. You will be asked if you want to save the R workspace, and for an exploratory session like this, you probably do not want to save it.