Statistics in a Nutshell, 2nd Edition

Chapter 8. Introduction to Regression and ANOVA

Regression and analysis of variance (ANOVA) are two techniques within the general linear model (GLM). If you’re not comfortable with the concept of a linear function, you should review the discussion of the Pearson correlation coefficient in Chapter 7. In Chapters 8 through 11, we cover a number of statistical techniques, some of them fairly complex but all built on this basic principle of the linear relationship among two or more variables. This chapter presents the most basic linear models, simple regression and one-way ANOVA; Chapters 9 through 11 present more complex techniques within the GLM family. The types of analysis presented in these chapters are nearly always performed using computer software; fortunately, most of them are common enough to be included in any statistical computing package. Also fortunately, it’s usually not difficult to figure out how to use a given package if you understand the theory underlying the model. For this reason, we concentrate on explaining how these models work and keep our advice sufficiently broad that it should apply to most systems.

The General Linear Model

Underlying all techniques within the GLM family is the assumption that a dependent variable is the function of one or more independent variables. We often speak in terms of predicting or explaining a dependent variable, using a set of independent variables, but step back for a minute to consider what it means for one variable to be a function ...