Pillai N., Vijayamohanan
(2016):
*How Do You Interpret Your Regression Coefficients?*

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## Abstract

This note is in response to David C. Hoaglin’s provocative statement in The Stata Journal (2016) that “Regressions are commonly misinterpreted”. “Citing the preliminary edition of Tukey’s classic Exploratory Data Analysis (1970, chap. 23), Hoaglin argues that the correct interpretation of a regression coefficient is that it “tells us how Y responds to change in X2 after adjusting for simultaneous linear change in the other predictors in the data at hand”. He contrasts this with what he views as the common misinterpretation of the coefficient as “the average change in Y for a 1-unit increase in X2 when the other Xs are held constant”. He asserts that this interpretation is incorrect because “[i]t does not accurately reflect how multiple regression works”. We find that Hoaglin’s characterization of common practice is often inaccurate and that his narrow view of proper interpretation is too limiting to fully exploit the potential of regression models. His article rehashes debates that were settled long ago, confuses the estimator of an effect with what is estimated, ignores modern approaches, and rejects a basic goal of applied research.” (Long and Drukker, 2016:25). This note broadly agrees with the comments that followed his article in the same issue of The Stata Journal (2016) and seeks to present an argument in favour of the commonly held interpretation that Hoaglin unfortunately marks as misinterpretation.

Item Type: | MPRA Paper |
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Original Title: | How Do You Interpret Your Regression Coefficients? |

Language: | English |

Keywords: | Regression, Partial regression coefficients, interpretation, partial correlation |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General |

Item ID: | 76867 |

Depositing User: | Vijayamohanan Pillai N |

Date Deposited: | 20 Feb 2017 09:49 |

Last Modified: | 26 Sep 2019 12:53 |

References: | Hoaglin, David C. (2016) “Regressions are commonly misinterpreted”. The Stata Journal Vol. 16, Number 1, pp. 5–22. Johnston, J. (1972) Econometric Methods. Second edition. McGraw-Hill. Long, J. Scott and Drukker, David M. (2016) “Regressions are commonly misinterpreted: Comments on the article”. The Stata Journal Vol. 16, Number 1, pp. 25–29. Davidson, R. and J. G. MacKinnon. 2004. Econometric theory and methods. New York: Oxford University Press. Frisch, R. and F.V.Waugh. 1933. .Partial time regression as compared with individual trends. Econometrica 1 (October): 387-401. Green, W. H. 2003. Econometric Analysis. 5th ed., Upper Saddle River: Prentice Hall. Johnston, J. and J. Dinardo.1997. Econometric methods. 4th ed. New York: McGraw Hill/Irwin. Lovell, M. C. 1963. Seasonal adjustment of economic time series and multiple regression analysis. Journal of the American Statistical Association 58 (December): 993-l0l0. Goldberger, A., 1991, A Course in Econometrics, Harvard University Press,Cambridge. Davidson, R. and MacKinnon, R., 1993, Estimation and Inference in Econometrics, Oxford University Press, Oxford. Fiebig, D., Bartels, R. and Kramer, W., 1996, The Frisch-Waugh Theorem and Generalized Least Squares, Econometric Reviews, 15(4), pp. 431-443. Ruud, P., 2000, An Introduction to Classical Econometric Theory, Oxford University Press, Oxford. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/76867 |