In this chapter we once again take up the subject of regression, first introduced in chapter 4, and this will now be our central theme for the remainder of this book. In chapter 4 we dealt only with simple regression, with one dependent and one explanatory variable. In the present chapter we will extend the model to see what happens when there is more than one explanatory variable. We introduce this idea in §8.1, and explain various aspects of the concept of multiple regression in §8.2. The related concepts of partial and multiple correlation are covered in §8.3.

In chapter 9 we will examine some of the underlying ideas in more depth, and will also deal with some of the issues arising from the fact that the data underlying our regressions are typically drawn from samples and so are subject to sampling error. Two further extensions of the basic linear regression model, the use of dummy variables and of lagged values, are then introduced in chapter 10.

The inclusion of additional explanatory variables

Extension of a regression to include several explanatory variables is frequently desirable, because it is usually appropriate to formulate and discuss relationships in which the behaviour of the dependent variable is explained by more than one factor.

The basic idea is very simple. In the initial treatment of the relationship between two variables (bivariate regression) in §4.2.1 there was one dependent variable (Y), which was influenced by one explanatory variable (X).