ABSTRACT
This chapter marks the transition from descriptive to model-based methods. We shall begin by treating regression descriptively and then introduce probability assumptions. In the last chapter all the variables had an equal status and PCA provided one way of looking at their interrelationships, beginning with the correlations. Regression looks at things differently, in an asymmetrical way, by asking how well one of the variables (usually denoted by y) can be predicted or estimated from the others (usually denoted by x1, x2, . . . , xk). Regression analysis is an important topic in its own right and it is very widely used in social science, including economics. It is also important as an ingredient of the techniques to which we come later in the book. Regression ideas lie at the heart of factor analysis and latent variable modelling in Chapters 7, 8, and 9, of structural equation modelling in Chapter 11 and of multilevel modelling in Chapter 12.
