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Regression anatomy, revealed

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  • Valerio Filoso

    () (University of Naples “Federico II”)

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. Copyright 2013 by StataCorp LP.

Suggested Citation

  • Valerio Filoso, 2013. "Regression anatomy, revealed," Stata Journal, StataCorp LP, vol. 13(1), pages 92-106, March.
  • Handle: RePEc:tsj:stataj:v:13:y:2013:i:1:p:92-106
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    References listed on IDEAS

    as
    1. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
    2. Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers 151, Cowles Foundation for Research in Economics, Yale University.
    3. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    4. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
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    More about this item

    Keywords

    reganat; regression anatomy; Frisch–Waugh–Lovell theorem; linear models; partial correlation; semipartial correlation;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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