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The Separation Principle in Linear Regression
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BibTeX
@MISC{Samaniego_theseparation,
author = {Francisco Samaniego and Mitchell R. Watnik},
title = {The Separation Principle in Linear Regression},
year = {}
}
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Abstract
In linear regression problems in which an independent variable is a total of two or more characteristics of interest, it may be possible to improve the fit of a regression equation substantially by regressing against one of two separate components of this sum rather than the sum itself. As motivation for this "separation principle," we provide necessary and sufficient conditions for an increased coefficient of determination. In teaching regression analysis, one might use an example such as the one contained herein, in which the number of wins of Major League Baseball teams is regressed against team payrolls, for the purpose of demonstrating that an investigator can often exploit intuition and/or subject-matter expertise to identify an efficacious separation. 1. Introduction We will both motivate and illustrate the Separation Principle through the following real example. Suppose we wish to relate the number of wins, Y , achieved by a Major League Baseball team in a given season to th...
Keyphrases
separation principle linear regression major league baseball team efficacious separation sufficient condition subject-matter expertise regression analysis independent variable team payroll separate component following real example regression equation increased coefficient linear regression problem
