Regression Anatomy, Revealed

Filoso, Valerio (2010): Regression Anatomy, Revealed.

Abstract

The Regression Anatomy (RA) theorem (Angrist and Pischke 2009) is an alternative formulation of the Frisch-Waugh-Lovell (FWL) theorem (Frisch and Waugh 1933; Lovell 1963), a key finding in the algebra of OLS multiple regression models. In this paper, we present a command, reganat, to implement graphically the method of RA. This addition complements the built-in Stata command avplot in the validation of linear models, producing bidimensional scatterplots and regression lines obtained controlling for the other covariates, along with several fine-tuning options. Moreover, the article provides (1) a fully worked-out proof of the RA theorem and (2) an explanation of how the RA and FWL theorems relate to partial and semipartial correlations, whose coefficients are informative when evaluating relevant variables in a linear regression model.

• Item Type: MPRA Paper
• Language: English
• Keywords: Regression anatomy, Frisch-Waugh-Lovell theorem, Linear models, Partial correlation, Semipartial correlation
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General

References

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Frisch, R., and F. V. Waugh. 1933. Partial Time Regressions as Compared with Individual Trends. Econometrica 1(4): 387–401.

Lovell, M. C. 1963. Seasonal Adjustment of Economic Time Series. Journal of the American Statistical Association 58: 993–1010.

Ruud, P. A. 2000. An Introduction to Classical Econometric Theory. New York: Oxford University Press.