What is it about?
When regression models incorporate predictors that are correlated there is no unique way of defining the contribution of each predictor to the overall prediction. This fact is demonstrated using a generalization of Pythagoras's theorem.
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Why is it important?
Users of linear regression models are often not aware that with correlated predictors there is no unique way to define the contribution of each predictor to the overall prediction. This report clarifies the issues. I use a geometric explanation which, I believe, is easier to understand than the usual algebraic approach.
Perspectives
This report describes a generalization of Pythagoras's theorem due to Pappus that is not well known. It also uses a geometric approach.
Dr James E Carlson
Educational Testing Service
Read the Original
This page is a summary of: A Generalization of Pythagoras's Theorem and Application to Explanations of Variance Contributions in Linear Models, ETS Research Report Series, August 2014, Wiley,
DOI: 10.1002/ets2.12018.
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