Experimental Design and Data Analysis for Biologists

In Chapter 5, we examined linear models with a single continuous predictor variable. In this chapter, we will discuss more complex models, including linear models with multiple predictor variables and models where one predictor interacts with itself in a polynomial term, and also nonlinear models. Note that this chapter will assume that you have read the previous chapter on bivariate relationships because many aspects of multiple regression are simply extensions from bivariate (simple) regression.

Multiple linear regression analysis

A common extension of simple linear regression is the case where we have recorded more than one predictor variable. When all the predictor variables are continuous, the models are referred to as multiple regression models. When all the predictor variables are categorical (grouping variables), then we are dealing with analysis of variance (ANOVA) models (Chapters 8–11). The distinction between regression and ANOVA models is not always helpful as general linear models can include both continuous and categorical predictors (Chapter 12). Nonetheless, the terminology is entrenched in the applied statistics, and the biological, literature. We will demonstrate multiple regression with two published examples.

Relative abundance of C3 and C4 plants

Paruelo & Lauenroth (1996) analyzed the geographic distribution and the effects of climate variables on the relative abundance of a number of plant functional types (PFTs) including shrubs, forbs, succulents (e.g. cacti), C3 grasses and C4 grasses. The latter PFTs represent grasses that utilize the C from the atmosphere differently in photosynthesis and are expected to have different responses to CO2 and climate change.