On relationship between regression models and interpretation of multiple regression coefficients

TL;DR

This paper explores the interpretability challenges of regression coefficients with correlated predictors and proposes a transformation method to isolate the unique contribution of each predictor.

Contribution

It introduces a linear transformation approach that simplifies multiple regression to a single predictor model while preserving interpretability of the coefficient of interest.

Findings

Linear regression coefficients lack natural interpretation with correlated predictors.

Proposed transformations isolate the unique effect of each predictor.

Method retains interpretability while reducing multicollinearity issues.

Abstract

In this paper, we consider the problem of treating linear regression equation coefficients in the case of correlated predictors. It is shown that in general there are no natural ways of interpreting these coefficients similar to the case of single predictor. Nevertheless we suggest linear transformations of predictors, reducing multiple regression to a simple one and retaining the coefficient at variable of interest. The new variable can be treated as the part of the old variable that has no linear statistical dependence on other presented variables.