On relationship between coefficients of the different dimensions linear regression models

TL;DR

This paper investigates the relationship between coefficients of linear regression models with different predictor sets, establishing a linear connection and exploring its implications.

Contribution

It proves a linear relationship between coefficients of models with different predictor subsets, providing new theoretical insights.

Findings

Established a linear relationship between model coefficients.

Derived corollaries from the main theorem.

Enhanced understanding of model coefficient behavior.

Abstract

Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is considered.