A Note on Collinearity and Centering in Linear Regression

• Activity Number: 142
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Santiago Velilla*
• Companies: Universidad Carlos III de Madrid
• Keywords: collinearity ; diagnostics ; regression

Abstract

The usual approach for diagnosing collinearity in practice proceeds by centering and scaling the regressors. The sample correlation matrix of the predictors is the basic tool for detecting linear combinations that may distort the conclusions of a standard least squares analysis. However, as indicated by Belsley (1984), centering may fail. In spite of this author's earlier claim, there does not seem to be in the literature a fully clear description of the reasons of this potentially bad behavior of the traditional strategy for analyzing collinearity. This communication studies this issue in some detail. Two well known real data sets are analyzed.