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Title: Dimension Reduction of the Explanatory Variables in Multiple Linear Regression
Authors: Filzmoser, P.
Croux, C.
Keywords: Multiple Linear Regression
Principal Component Regression
Dimension Reduction
Robust Regression
Issue Date: 2003
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Pliska Studia Mathematica Bulgarica, Vol. 14, No 1, (2003), 59p-70p
Abstract: In classical multiple linear regression analysis problems will occur if the regressors are either multicollinear or if the number of regressors is larger than the number of observations. In this note a new method is introduced which constructs orthogonal predictor variables in a way to have a maximal correlation with the dependent variable. The predictor variables are linear combinations of the original regressors. This method allows a major reduction of the number of predictors in the model, compared to other standard methods like principal component regression. Its computation is simple and quite fast. Moreover, it can easily be robustified using a robust regression technique and a robust measure of correlation.
Description: 2002 Mathematics Subject Classification: 62J05, 62G35.
ISSN: 0204-9805
Appears in Collections:2003 Volume 14

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