Statistics in a Nutshell

Chapter 14. Multiple Linear Regression

In Chapter 12, you learned how to use bivariate linear regression to build simple linear models suitable for characterization of the relationship between two variables (typically one dependent variable and one independent variable). Clearly, many variables in the physical world can have multiple IVs independently, accounting for some portion of variance in the DV. Note the difference between “single linear regression” and “multiple linear regression”—the former refers to a setting in which there are multiple responses in a response vector emphasizing that we are in the setting with a single outcome but multiple predictors. This chapter discusses multiple linear regression as an extension of simple linear regression. Assumptions specific to multivariate regression, such as multicollinearity among predictor variables, are discussed and methods for model-building are presented.

Multiple Regression Models

The use of simple linear regression models and the bivariate correlation coefficient and its square (the coefficient of determination) are useful for illustrating simple examples; in reality, very few physical systems or fields of interest rely on a single independent and dependent variable pair. Consider models used to study climate change, such as General Circulation Models (GCMs) and even more sophisticated Atmosphere-Ocean General Circulation Models (AOGCMs). These models have been developed over the past 30 years to allow the increasingly accurate ...