Statistical Applications for Environmental Analysis and Risk Assessment

Chapter 12Simple Linear Regression

12.1 Introduction and Overview

Regression analysis is a multifaceted statistical tool for exploring the unknown relationship between two or more variables using techniques that can be simple or complex, depending on the nature of the data being analyzed. The analysis is described as a “regression” because although data values are typically variable, they tend to regress or fall off toward the mean or center. Regression may be viewed as an extension of correlation (Chapter 11) in that it normally involves the quantification of a relationship between variables that are believed to be correlated. For instance, if correlation tests indicate that two variables, X and Y, are correlated and it is desired to estimate or predict values of Y corresponding to specified values of X, a regression of Y on X is performed, resulting in the desired predictive equation or relationship for predicting Y from X. The dependent or response variable is usually referred to as the Y variable and the predictor (i.e., independent or explanatory) variable as the X.

This chapter focuses primarily on conventional linear regression, which assumes that the data satisfy certain requirements. Chapter 13 describes standard methods for transforming nonconforming data so that conventional linear regression may be used, as well as alternative parametric (i.e., associated with a known data distribution) methods that avoid transformation, namely, the generalized linear model (GLM). ...