The main CAST e-books cover topics that are usually taught in introductory statistical methods courses. The material in this CAST e-book is more advanced and is usually left until a second statistics course or later.

This e-book shows how to model variation in a 'response' variable in terms of one or more 'explanatory' variables.

The e-book starts by revising simple linear regression (with a single numerical explanatory variable). Regression diagnostics include material about the concepts of leverage, outliers and influence.

These ideas are extended to multiple linear regression (in which variation in a response variable is explaned by two or more explanatory variables). Matrix notation is a concise way to describe these models. The concept of interaction is also explained.

Analysis of variance is a powerful technique for analysing multiple regression models. In particular, it helps to explain the consequences of multicollinearity in data. Analysis of variance is used to test hypotheses about the models.

The multiple regression model (which is also called a General Linear Model) can also model situations involving categorical explanatory variables. A chapter describes modelling and inference for these models.

Finally, an optional chapter explains some of the statistical theory behind analysis of variance.

The material assumes a good understanding of basic statistical concepts and methods. You are therefore strongly advised to revise the basics from one of the main CAST e-books before studying the material here.