Much of statistics relies on being able to evaluate expectations of random variables, and finding quantiles of distributions.

As of this writing, there are more than 3000 objects in the R base packages, and more than 15,000 other packages available on CRAN, most containing dozens of objects of their own. This represents a huge amount of functionality, and nobody could be expected to remember it all. The best we can hope for is that people should be able to discover it, using the help system and other resources, as well as judicious guesses about where to look. Guessing is made easier when consistent principles are followed as code is written. For example, names should reflect the purpose of packages and functions. Guessing is made harder by inconsistency, for example when names are poorly chosen, or conventions for forming names are inconsistent.

Programming involves writing relatively complex systems of instructions. There are two broad styles of programming: the imperative style (used in R, for example) involves stringing together instructions telling the computer what to do. The declarative style (used in HTML in web pages, for example, and to some extent in ggplot2, as described in Section 3.4) involves writing a description of the end result, without giving the details about how to get there. Within each of these broad styles, there are many subdivisions, and a given program may involve aspects of several of them. For example, R programs may be procedural (describing what steps to take to achieve a task), modular (broken up into self-contained packages), object-oriented (organized to describe operations on complex objects), and/or functional (organized as a collection of functions which do specific calculations without having external side-effects), among other possibilities. In this book we will concentrate on the procedural aspects of programming.

Having installed the R and RStudio systems, you are now ready to begin to learn the art of statistical programming. The first step is to learn the syntax of the language that you will be programming in; you need to know the rules of the language. This chapter will give you an introduction to the syntax of R. Most of what we discuss here relates to what you would type into the R console or into the RStudio script window.

Welcome to the world of statistical programming. We will start in this chapter by giving you an idea of what statistical programming is all about. We will also tell you what to expect as you proceed through the rest of the book. The chapter will finish with some instructions about how to download and install R, the software package and language on which we base our programming examples, and RStudio, an “integrated development environment” (or “IDE”) for R.

Linear algebra deals with vector spaces and linear operations on them. In mathematics, we usually represent vectors as column vectors of numbers, and linear operations as matrices. Applying a linear operation to a vector becomes multiplication of a column vector by a matrix, and composition of operations is matrix multiplication.

In statistical modeling, we may want to find a set of parameters for a model which minimize the expected prediction errors for the model.