Regression anatomy, revealed
Valerio Filoso
Department of Economics
University of Naples "Federico II"
Naples, Italy
[email protected]
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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.
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Valerio Filoso
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reganat, regression anatomy, Frisch–Waugh–Lovell theorem, linear models, partial correlation, semipartial correlation
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