Revisiting the Conceptualization of Multiple Linear Regression

TL;DR

This paper examines how multicollinearity affects the development and interpretation of multiple linear regression models, highlighting its serious implications through theoretical and visual analysis.

Contribution

It revisits the conceptual understanding of multicollinearity's impact on MLR, emphasizing its effects on model development and statistical inference.

Findings

Multicollinearity can significantly distort regression coefficients.

Traditional equations and diagrams reveal the depth of multicollinearity issues.

Real data examples demonstrate the practical implications of multicollinearity.

Abstract

The problem known as multicolinearity has long been recognized to fundamentally and negatively influence multiple regression. This paper does not intend to either propose a numerical assessment of the degree to which this problem exists within any data set or a solution to the problem itself. Rather, it is our intent to illustrate the potentially serious ramifications multicolinearity has on the traditional development of the multiple linear regression (MLR) model and its associated statistics using established equations, Venn diagrams, and real data.