O'Reilly logo

The R Book, 2nd Edition by Michael J. Crawley

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 7

Mathematics

You can do a lot of maths in R. Here we concentrate on the kinds of mathematics that find most frequent application in scientific work and statistical modelling:

  • functions;
  • continuous distributions;
  • discrete distributions;
  • matrix algebra;
  • calculus;
  • differential equations.

7.1 Mathematical functions

For the kinds of functions you will meet in statistical computing there are only three mathematical rules that you need to learn: these are concerned with powers, exponents and logarithms. In the expression xb the explanatory variable is raised to the power b. In ex the explanatory variable appears as a power – in this special case, of e = 2.718 28, of which x is the exponent. The inverse of ex is the logarithm of x, denoted by log(x) – note that all our logs are to the base e and that, for us, writing log(x) is the same as ln(x).

It is also useful to remember a handful of mathematical facts that are useful for working out behaviour at the limits. We would like to know what happens to y when x gets very large (e.g. x → ∞) and what happens to y when x goes to 0 (i.e. what the intercept is, if there is one). These are the most important rules:

  • Anything to the power zero is 1: x0 = 1.
  • One raised to any power is still 1: 1x = 1.
  • Infinity plus 1 is infinity: ∞ + 1 = ∞.
  • One over infinity (the reciprocal of infinity, ∞–1) is zero: inline.
  • A number > 1 raised to the power infinity ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required