1.1 GETTING STARTED

Programming, writing code, is an integral part of modern data analysis. This book assumes some experience with a programming language. R is simply a high level programming language with several functions that perform specialized statistical analysis. Any R programmer may also write their own functions, but the focus of this book is using functions already in R and writing some basic code using these functions.

In this book, R code is always shaded. Related R output that follows is always underlined or, if extensive, presented in a table. Comments in R code follow the pound sign, #. When R functions are discussed in the text, they will be italicized.

Some basic statistical analysis might involve inputting some values and performing some basic statistical analysis. Following the conventions already stated,

# this is a comment
x <- c(0.1,1.1,2.3,4.1, 5.6, 8.3) # create a vector of 6 values, these were just made up
y <- c(8.7, 6.5, 3.1, 3.3, −1.1, −0.9) #create a second vector
plot(x,y,xlab = “this places a label on the x axis”, ylab = “this labels the y axis”)
title(“this is a demo”)
# either “<-” or “=” can be used for assignments, but “<-” makes more sense.
# The reader should be aware that “=” and “<-” are not always interchangeable in R

(Figure 1.1).

The R code produces the data plotted in Figure 1.1.

[The commands for plots used in the book are simple commands that produce bitmap files that can easily be pasted into any report and resized. The actual graphs produced for the book use the slightly more complex tiff() function for better quality. For more information on better graphs check out help(tiff)].

Naming conventions used in this book:

A number of simple statistical operations are worth mentioning, using the data simulated for Figure 1.1.

• mean(x) produces the output: 3.583333 which is the mean of the x values.
• sum(x) produces the output: 21.5 as expected (21.5/6 is the mean).
• var(y) produces the output: 15.28667, the sample variance of y.

Incidentally, it is best to write code in notepad or some other text editor and then paste it in R. As the code gets longer, this becomes mandatory (more sophisticated environments exist for writing and debugging R code, such as RStudio, but they are not necessary).

1.2 SPECIAL R CONVENTIONS

Examples

2==2 will produce the output: TRUE

2=2 will produce an error, as this is an attempt to assign a value to a number

2==3 will produce the output: FALSE

1/0 will produce the output: Inf

Inf/Inf will produce the output: NaN

1 - NA will produce the output: NA

1.3 COMMON STRUCTURES

All programming languages have some looping feature and some conditional action feature. In R, the “if” statement is used for conditional action and the “for” statement for iterating a process several times. These are not the only structures in R for this purpose, but they are all that is required for this book.

The “if” statement allows an action when a condition is met:

x <- 2        y <- 3        z <- 2        c <- TRUE        d <- TRUE
if(x == y) {c <- 1-c}
if(x == z) {d <- 1-d}

Can you guess what the values of c and d will be at the end? The variable c still has the value TRUE; it was unchanged, but d has the value 0, because it is 1—TRUE, which is 0 (see Exercise 1). TRUE can be understood as 1 and FALSE can be understood as 0 in R.

The “for” statement allows an action to occur a pre-set number of times. With mathematics, the “for” statement is often a summation or multiplication action.

Consider the formula ∑¹⁰_{j = 1}j² which can be evaluated in closed form m(m + 1)(2m + 1)/6, where m = 10, is 385.

sum <- 0
for(j in 1:10) {sum <- sum + j^2}

In the end, the sum will have the value 385. As with summation in most textbooks, as far as possible the letters j,k,l, and m will be used when indexing summation (i and n are already used as mentioned previously), although any letter could be used. For example,

sum <- 0
for(z in 1:10) {sum <- sum + z^2}

gets the right answer but would be considered poor style.

1.4 COMMON FUNCTIONS

1.5 TIME SERIES FUNCTIONS

If what follows sounds like a foreign language, good, you are in the right class. Over the course of the book, these will all be introduced, but the students will learn to code primitive versions of these functions before they are allowed to use them.

In some sense, a substantial portion of this course is to learn these functions, and all the background associated with these functions. Throughout the book, the underlying formulas will be derived and some crude R code that produces the computations and/or plots will be presented. Only when this is done does the student know exactly what the function does and is the student permitted to use the function, which can be viewed as elegant, often cosmetic, improvements over the crude R code.

1.6 IMPORTING DATA

Obviously, data sets are often very long and manual entry is unrealistic. The functions scan() and read.table() allow for reading large files. These will be discussed in Chapter 3 when the first time series data are read in and plotted.

Only scan() and read.table() are required for this book. However, read.csv() and read.delim() can be useful for reading formats that use commas or tabs to separate items. Using library(foreign), it is possible to import data from several other software formats (SPSS, Minitab, etc.).

The next chapter is a review of simple regression and an introduction to more R code in that context.