Chapter 3 - Correlation and Regression Analysis

Summary

Chapter 3 introduces readers to correlation and regression analysis. Methods of correlation answer the question concerning the portion of variance that two variables share. Regression uses, in most cases, metric dependent and metric or categorical independent variables. The OLS solution for the standard case of one predictor and one outcome variable is derived. Based on this derivation, characteristics of model parameters are explained. Real-world data examples are given for simple regression (one predictor and one outcome variable) and for multiple regression (multiple predictors and one outcome variable). In addition, this chapter describes GLM approaches to curvilinear regression (regression lines are curved rather than straight to approximate non-linear variable relations), to curvilinear regression of repeated observations, to symmetric regression (where the regression of Y on X results in the same solution as the regression of X on Y), to best subset and stepwise selection regression (which results in an optimal selection from multiple predictors), and the recently developed direction dependence analysis to evaluate hypotheses concerning the causal flow of a variable association