Statistics in a Nutshell, 2nd Edition

Chapter 10. Multiple Linear Regression

In Chapter 8, we introduced simple linear regression, in which one independent variable is used to predict or explain the value of one dependent variable. This model is useful for introducing the principles of linear regression, but in real-world situations, simple regression is rarely used. Multiple linear regression, in which two or more independent variables are related to a single dependent variable, is much more common. Multiple regression is a common research technique used in many fields, including the sciences, medicine, the social sciences, and education. One attraction of multiple regression is flexibility; predictor variables can be continuous, categorical, or dichotomous, and any combination of these variable types can be used in a single equation. If a categorical variable is used, it must be recoded into dichotomous dummy variables. We cover this technique also in this chapter. With the additional complication of multiple predictor variables, additional assumptions must be met, and these are discussed in this chapter as well. Finally, the ability to use multiple predictors means that model-building strategies are useful to build the best model for a particular purpose; these strategies are also discussed in this chapter.

Multiple Regression Models

The study of simple linear regression models and the bivariate correlation coefficient and its square (the coefficient of determination) are useful as an introduction to the concepts of ...