Regressions are Commonly Misinterpreted

Abstract

Much literature misinterprets results of fitting multivariable models for linear regression, logistic regression, and other generalized linear models, as well as for survival, longitudinal, and hierarchical regressions. For the leading case of multiple regression, regression coefficients can be accurately interpreted via the added-variable plot. However, a common interpretation does not reflect the way regression methods actually work. Additional support for the correct interpretation comes from examining regression coefficients in multivariate normal distributions and from the geometry of least squares. To properly implement multivariable models, one must be cautious when calculating predictions that average over other variables, as in the Stata command margins.