Introduction

This Chapter reviews methods for studying the relationship between two or more variables. We begin with a brief description of scatterplots and simple summary statistics commonly calculated from them. Emphasis is given to examining the effect of outliers and influential points and to recognizing that measures of association such as the correlation coefficient only describe the linear (i.e., straight line) relationship. Simple linear regression is then described including the meaning of the slope, the basic assumptions needed, and the effects of violating the assumptions. Multiple regression is then introduced, again with emphasis on quantities of direct value to behavioral ecologists rather than on the analytical methods used to obtain these results.

We make a slight notational change in this Chapter. In prior Chapters, we have used lower-case letters for quantities associated with the sample and upper-case letters for quantities associated with the population. In discussions of regression, upper-case letters are generally used for individual values and their means regardless of whether they are associated with the sample or population. Regression coefficients for the population are generally identified by the symbols β (e.g., β0, β1 …) and the corresponding sample estimates are denoted b0, b1 and so on. These practices are so well established in the statistical literature that we follow them in this Chapter even though it introduces some inconsistency with other Chapters.

Scatterplots and correlation

Among the simplest and most commonly used methods for studying the relationship between two quantitative variables are scatterplots and correlations.