16 Multiple Linear Regression Viewpoints

This paper analyzes two methods for testing moderation effects in regression models that contain a continuous dependent variable, a continuous independent variable, and a dichotomized grouped moderator; a test of the interaction term in the full regression model and a test of the difference between the simple slopes. Typically, researchers test the significance of the interaction term. Based on mathematical equations and empirical examples, we argue that the test for the difference between the simple slopes should be utilized when researchers are interested in testing for moderation effects. By decomposing the test statistics for these two methods, we demonstrate that the test for the difference between the simple slopes has increased power and less Type II error, while retaining equivalent Type I error rates. oderated relationships in social science research exist when the relationship between two variables, X and Y, varies depending on the value of a third variable Z. This study examines a specific type of moderated relationship with a continuous dependent variable (Y), a continuous independent variable (X), and an independent dichotomous categorical variable (Z). Given these variables, a moderated relationship exists if the relationship between X and Y is different for both levels of Z. This can be estimated with an interaction term using the following regression equatio