Statistical Power, Reliability, and Model Assumptions in Multiple Linear Regression: Assessing and Addressing Common Issues

Multiple linear regression analysis is one of the most frequently used strategies among counseling researchers and evaluators. While providing a robust strategy to test theories, identify associations between client and intervention characteristics with treatment outcomes, and explore the relationships between program features and intended impacts, the analyses depend on points of scientific rigor and a series of statistical model assumptions. This article reviews two points of scientific rigor and six model assumptions: (a) measurement precision; (b) sufficiency of statistical power; (c) absence of influential cases, outliers, and leverage points; (d) linearity between predictor and criterion variables; (e) normality of residuals; (f) independence of observations; (g) absence of multicollinearity; and (h) homoskedasticity. In each instance, we provide background information and related strategies for assessing and addressing violations. Implications for scientist-practitioners and researchers are discussed.