Average group effect of strongly correlated predictor variables is estimable

TL;DR

This paper demonstrates that while individual coefficients of strongly correlated predictors are hard to estimate, their average can be estimated with high accuracy, offering new insights into multicollinearity issues in linear models.

Contribution

It introduces the concept that the average effect of strongly correlated predictors is estimable, providing a novel perspective on handling multicollinearity in regression analysis.

Findings

The average group effect of correlated predictors is estimable with high precision.

Individual parameters remain unidentifiable due to multicollinearity.

The results have implications for interpreting regression models with correlated variables.

Abstract

It is well known that individual parameters of strongly correlated predictor variables in a linear model cannot be accurately estimated by the least squares regression due to multicollinearity generated by such variables. Surprisingly, an average of these parameters can be extremely accurately estimated. We find this average and briefly discuss its applications in the least squares regression.