Germán Rodríguez

Introducing R
Princeton University
Obviously the first thing you need to do is download a copy of R. The current version is 3.5.1 and was released in February 2018. New releases occur every six months or so, often around April and October. You will find binaries for Windows, Mac OS X and Linux in the Comprehensive R Archive Network. Find the mirror nearest you and follow the links. The Windows installer is fairly easy to use and, after agreeing to the license terms, lets you choose which components you want to install. Additional packages can always be installed directly from R at a later time.

*Local Notes.* R has been installed on OPR's Windows
and Unix servers. Just logon to coale or lotka and compute away.

We recommend that you create a shortcut to start R as part of the
installation. If you skipped that step just right clicking on the executable
`RGui.exe`

, drag it to your desktop, and choose 'Create a shotcut here'.
It is also a good idea to set R's working directory at this time.
Right click on the shortcut, choose 'Properties' and enter your
default working directory on the 'Start in' field.
The working directory can also be set from within R as explained later.
It's a good idea to have a separate folder for each research project.

All you need to follow along is the R console as described below, but I strongly recommend that you install R Studio from www.rstudio.com, which provides a nice integrated development environment (IDE) and is available for Linux, Max OS X, and Windows.

When R starts you will see a window called the RConsole. This is where you type your commands and see the text results. (Graphs appear in a separate window.) You are prompted to type commands with the greater than symbol. To quit R type

> q()

Note the parentheses after the q; this is because in R you don't type commands
but rather call *functions* to achieve results, even quit!
To call a function you type the name followed by the arguments in parentheses.
If the function takes no arguments you just type the
name followed by left and right parenthesis.
(If you forget the parentheses and type just the name of the function,
R will list it.)

You should also know about the `help`

function,
which opens a help window.
This function can be called with arguments to obtain help about
specific features of R, for example `help(plot)`

.
A shortcut for help on a topic is a question mark followed by the topic
as in `?plot`

.
If you picked compiled html help during the installation you should get
that by default; if not you can always type `options(chmhelp=TRUE)`

.

The RConsole allows command editing. You will find that the left and right arrow keys, home, end, backspace, insert, and delete work exactly as you would expect. You also get a command history: the up and down arrow keys can be used to scroll through recent commands. Thus, if you make a mistake all you need to do is press the up key to recall your last command and edit it.

It is possible to prepare commands in a file and then
have R execute them using the `source`

function.
You can send the output to a file instead of the RConsole by
using the `sink`

function.
Both functions take a filename (in quotes) as argument.

*Warning: *
The backslash character has a special meaning to R.
When you specify a Windows path in the RConsole you have to:
(1) double-up your backslashes, or
(2) use forward slashes instead.
Thus, if you want to read R code (or data) from a USB drive available as drive E,
say, do not type E:\myprogram.r. You have to type E:\\myprogram.r or E:/myprogram.r.
(However, when you specify a path in a file open or file save dialog you have to
use the native format, with a single backward slash.)

Alternatively, you may prefer to use R interactively and rely on cut and paste to transfer output from the RConsole to a word processing document.

R works like a calculator, you type an expression and get the answer:

> 1+2 [1] 3

The standard arithmetic operators are
`+, -, *,`

and `/`

for add, subtract, multiply and divide,
and `^`

for exponentiation, so 2^3=8.
These operators have the standard precedence, with exponentiation
highest and addition/subtraction lowest,
but you can always control the order of evaluation with parentheses.
You can use mathematical functions, such as `sqrt`

,
`exp`

, and `log`

. For example

> log(0.3/(1-0.3)) [1] -0.8472979

R also understands the relational operators `<=, <, ==, >, >=`

and
`!=`

for less than or equal, less than, equal, greater than, greater than or
equal, and not equal.
These can be used to create logical expressions that take values TRUE and FALSE
(or T and F for short).
Logical expressions may be combined with the logical operators
`|`

for OR and `&`

for AND, as shown further below.

The results of a calculation may be assigned to a named object.
The assignment operator in R is `<-`

, read as "gets",
but by popular demand R now accepts the equal sign as well,
so ` x <- 2`

and `x = 2`

both assign the
value 2 to a variable (technically an object) named `x`

.

Typing a name prints its contents.
The name `pi`

is used for the constant
p. Thus,

> s <- pi/sqrt(3) > s [1] 1.813799

assigns π/√3 to the variable
`s`

and then prints the result.

Names may contain letters, numbers or periods, and (starting with 1.9.0)
the underscore character, but must start with a letter or period.
(I recommend you always start names with a letter.)
Thus, `v.one`

and `v_one`

are valid names
but `v one`

is not (because it includes a space).

*Warning:*R is *case sensitive*,
`v.one`

, `V.one`

and `v.One`

are all
different names.

R objects exist during your session but vanish when you exit.
However, you will be asked if you want to save an image of your workspace
before you leave.
You can also save individual objects to disk, see `help(save)`

.
(In contrast, S-Plus objects are permanent; they populate--and often
overpopulate--your hard disk, staying there until you explicitly remove them.)

Note that assignments are expressions too, you can type
`x <- y <- 2`

and both x and y will get 2.
This works because the assignment `y <- 2`

is
also an expression that takes the value 2.

*Exercise*: What's the difference between `x == 2`

and
`x = 2`

? Use the console to find out.

So far we have worked with scalars (single numbers) but R is designed to work with
vectors as well. The function `c`

, which is
short for catenate (or concatenate if you prefer) can be used to create vectors
from scalars or other vectors:

> x <- c(1,3,5,7) > x [1] 1 3 5 7

The colon operator `:`

can be used to generate a sequence of numbers

> x <- 1:10 > x [1] 1 2 3 4 5 6 7 8 9 10

You can also use the `seq`

function to create a sequence
given the starting and stopping points and an increment.
For example here are eleven values between 0 and 1 in steps of 0.1:

> seq(0, 1, 0.1) [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Another function that is useful in creating vectors is `rep`

for repeat
or replicate. For example `rep(3,4)`

replicates the number three four
times. The first argument can be a vector, so `rep(x,3)`

replicates the
entire vector x three times. If both arguments are vectors of the *same*
size, then each element of the first vector is replicated the number or times
indicated by the corresponding element in the second vector. Consider this
example:

> rep(1:3, 2) [1] 1 2 3 1 2 3 > rep(1:3, c(2,2,2)) [1] 1 1 2 2 3 3

The first call repeats the vector 1:3 twice. The second call repeats each
element of 1:3 twice, and could have been written
`rep(1:3, rep(2,3))`

,
a common R idiom.

R operations are *vectorized*. If x is a vector, then
`log(x)`

is a vector with the logs of the elements of x.
Arithmetic and relational operators also work element by element.
If x and y are vectors of the same length, then `x + y`

is a vector with elements equal to the sum of the corresponding elements
of x and y.
If y is a scalar it is added to each element of x.
If x and y are vectors of different lengths, the shorter one is
recycled as needed, perhaps a fractional number of times
(in which case you get a warning).

The logical operators `|`

for *or* and
`&`

for *and* also work element by element.
(The double operators `||`

for *or* and
`&&`

for *and* work only on the first element
of each vector and use shortcut evaluation;
they are used mostly in writing R functions and will not be discussed further.)

> a = c(TRUE, TRUE, FALSE, FALSE) > b = c(TRUE, FALSE, TRUE, FALSE) > a & b [1] TRUE FALSE FALSE FALSE

The number of elements of a vector is returned by the function `length`

.
Individual elements are addressed using *subscripts* in square brackets,
so `x[1] `

is the first element of x, `x[2]`

is the second,
and `x[length(x)]`

is the last.

The subscript can be a vector itself, so `x[1:3]`

is a vector consisting
of the first three elements of x.
A negative subscript excludes the corresponding element, so `x[-1]`

returns a vector with all elements of x except the first one.

Interestingly, a subscript can also be a logical expression, in which case you get the elements for which the expression is TRUE. For example to list the elements of x that are less than 5 we use

> x[x < 5] 1] 1 2 3 4

I read this expression 'x such that x is less than 5'.
This works because the subcript `x < 5`

is this vector:

> x < 5 [1] TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE FALSE

R's (and of course S-Plus's) subscripting facility is extremely powerful. You may find that it takes a while to get used to it, but eventually the language becomes natural.

R also understands matrices and higher dimensional arrays. The following function creates a 3 by 4 matrix and fills it by columns with the numbers 1 to 12:

> M = matrix(1:12, 3, 4) > M [,1] [,2] [,3] [,4] [1,] 1 4 7 10 [2,] 2 5 8 11 [3,] 3 6 9 12

The elements of a matrix may be addressed using the row and
column subscripts in square brackets, separated by a comma.
Thus, `M[1,1]`

is the first element of `M`

.

`M[1,]`

is the first row and
`M[,1]`

is the first column of `M`

.
Any of the subscripts can be a vector, so
`M[1:2,1:2]`

is the
upper-left 2 by 2 corner of `M`

. Try it.
The number of rows and columns of a matrix are returned by
the functions `nrow`

and `ncol`

.
To transpose a matrix use the function `t`

.
The matrix multiplication operator is `%*%`

.
Matrix inversion is done by the function `solve`

.
See the linear regression section for an example.

*Exercise*:
How do you list the last element of a matrix?

R has very extensive and powerful graphic facilities.
In the example below we use `seq`

to create equally spaced points
between -3 and 3 in steps of 0.1 (that's 61 points).
Then we call the function `dnorm`

to calculate the standard normal density
evaluated at those points, we plot it, and add a title in a nice shade of blue.
Note that we are able to add the title to the current plot in a separate call.

> z <- seq(-3,3,.1) > d <- dnorm(z) > plot(z,d,type="l") > title("The Standard Normal Density",col.main="cornflowerblue")

Arguments to a function can be specified by position or by name. The
plot function expects the first two arguments to be vectors giving the x and y
coordinates of the points to be plotted. We also specified the type of
plot. Since this is one of many optional parameters (type `?plot`

for
details), we specified it by name as` type="l"`

(the letter el).
This indicates that we want the points joined to form a line, rather than the
default which is to plot discrete points. Note that R uses the
equal sign to specify named arguments to a function.

The title function expects a character string with the
title as the first argument. We also specified the optional argument
`col.main="cornflowerblue"`

to set the color of the title.
There are 657 named colors to choose from,
type `colors()`

to see their names.

The next example is based on a demo included in the R distribution and is
simply meant to show off R's use of colors. We use the `pie`

function
to create a chart with 16 slices. The slices are all the same width, but we fill them
with different colors obtained using the `rainbow`

function.

> pie(rep(1,16),col=rainbow(16))

Note the use of the `rep`

function to replicate the number one 16 times.
To see how one can specify colors and labels for the slices, try calling
`pie`

with arguments
`1:4, c("r", "g", "b","w")`

and `col=c("red,"green","blue","white")`

.

To save a graph make sure the focus is on the graph window
and choose __F__ile | __S__ave as, from the menu.
You get several choices of format, including postcript, which is
good for printing, and windows metafile, which is ideal for
embedding your graph in another Windows document.

Most remarkably, you also get the png format, which makes it easy to include R graphs in web pages such as this, particularly now that this format is supported by all major browsers. R also supports jpeg, but I think png is better than jpeg for statistical plots. All graphs on these pages are in png format.

Alternatively, you can copy the graph to the clipboard by choosing
__F__ile | __C__opy to clipboard. You get a choice of two formats.
I recommend that you use the metafile format because it's more flexible.
You can then paste the graph into a word processing or spreadsheet document.
You can also print the graph using __F__ile | __P__rint.

*Exercise*: Simulate 20 observations from the regression model
Y = a+b x + e
using the x vector generated above.
Set a = 1 and b = 2.
Use standard normal errors generated as
`rnorm(20)`

, where 20 is the number of observations.

Continue with Reading Data