Regression anatomy, revealed
2017
Filoso, Valerio
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.
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