Using Multiple Regression to Ascertain Group Differences in the Relationship of Predictors to a Criterion: Ethnic Group Differences in the Relationship between Course-taking and Achievement in Mathematics

Abstract

This study introduces an approach that utilizes ten regression models to assist in the study of the relationship between predictors and a criterion as it pertains to group differences. The models range in complexity from a simple multiple regression model that assumes one size fits all, to a full moderated multiple regression model, where each group has its own set of predictors. The different models arise via varying constraints that are theoretically meaningful and testable relative to equity of the groups. Data for mathematics achievement and course-taking for different ethnic groups obtained from the National Center for Education Statistics’ (NCES) High School Longitudinal Study of 2009 (HSLS: 09) are used to illustrate and explain the different models. This study is especially timely given the attention to achievement gaps and their causes and correlates.