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The preceding 2 articles have focused on the comparison of 2 or more samples for the purpose of testing for a difference among the samples with respect to 1 or more outcome variables. In contrast to outcome, it may be desirable to determine the relationship between 2 or more variables. The methods introduced in this article include correlation and regression. Correlation analysis assesses the linear relationship between 2 variables, providing a measure of both the strength and direction of the relationship. Correlation makes no assumption on causality in the relationship. It assumes only a linear relationship, and variables with a strong nonlinear relationship may show poor or absent correlation. To help identify the type of relationship between variables, visual inspection of a scatterplot is invaluable. Correlation can be performed on both parametric and nonparametric variables. The most commonly used parametric method is the Pearson product-moment correlation. Two nonparametric methods are in common use, including the Spearman rank order correlation and Kendall methods. Partial correlation provides for a measure of correlation after controlling for the effects of variables other than the 2 primary variables. In certain situations, the correlation relationship can be linear to a certain extent beyond which it may disappear or remain linear but at a different degree.

Regression analysis assesses the relationship between 1 dependent (observed) variable and 1 or more independent (explanatory) variables, with an implied causal relationship. Regression goes beyond correlation by inferring relationships between variables, allowing modeling of …