Regression anatomy, revealed

Abstract

The regression anatomy theorem (Angrist and Pischke, 2009, Mostly Harmless Econometrics: An Empiricist's Companion [Princeton University Press]) is an alternative formulation of the Frisch-Waugh-Lovell theorem (Frisch and Waugh, 1933, Econometrica 1: 387-401; Lovell, 1963, Journal of the American Statistical Association 58: 993-1010), a key finding in the algebra of ordinary least-squares multiple regression models. In this article, I present a command, reganat, to implement graphically the method of regression anatomy. This addition complements the built-in Stata command avplot in the validation of linear models, producing bidimensional scatterplots and regression lines obtained by controlling for the other covariates, along with several fine-tuning options. Moreover, I provide 1) a fully worked-out proof of the regression anatomy theorem and 2) an explanation of how the regression anatomy and the Frisch-Waugh-Lovell theorems relate to partial and semipartial correlations, whose coefficients are informative when evaluating relevant variables in a linear regression model. © 2013 StataCorp LP.