# Estimable group effects for strongly correlated variables in linear models

## TL;DR

This paper identifies linear combinations of strongly correlated variables in linear models that can be accurately estimated, revealing that the variability weighted average is uniquely estimable and more precise with stronger correlation.

## Contribution

It introduces a method to find estimable linear combinations of parameters for strongly correlated predictors in linear models, highlighting the special role of the variability weighted average.

## Key findings

- The variability weighted average is more accurately estimated with stronger correlation.
- Such linear combinations can be computed easily in all linear models.
- The approach has applications in inference and estimation for correlated variables.

## Abstract

It is well known that parameters for strongly correlated predictor variables in a linear model cannot be accurately estimated. We look for linear combinations of these parameters that can be. Under a uniform model, we find such linear combinations in a neighborhood of a simple variability weighted average of these parameters. Surprisingly, this variability weighted average is more accurately estimated when the variables are more strongly correlated, and it is the only linear combination with this property. It can be easily computed for strongly correlated predictor variables in all linear models and has applications in inference and estimation concerning parameters of such variables.