The Effect of Multivariate Regression Over Multiple Linear Regression Models Using Non-Normal Data

Abstract

Purpose:
This study evaluated the performance of multivariate linear regression relative to multiple linear regression when applied to non-normal data, with the objective of identifying the model that offers greater accuracy and reliability under conditions of equal mean vectors and known variance–covariance matrices.

Methodology:
Simulated datasets were generated using R software. Prior to estimation, all relevant assumptions for both multivariate and multiple linear regression were tested. Model evaluation involved examining residual symmetry, assessing the influence of independent variables on dependent variables, and testing overall model significance. Multivariate regression performance was assessed using Pillai’s Trace, Wilks’ Lambda, Hotelling–Lawley Trace, and Roy’s Largest Root, while the multiple linear regression model was evaluated using analysis of variance.

Results:
The findings revealed that the multivariate linear regression model outperformed the multiple linear regression model under non-normal conditions. The multivariate approach demonstrated more stable residual behavior and stronger statistical evidence of relationships among variables, indicating superior model fit and robustness.

Novelty and contribution:
This study provides new empirical evidence on the comparative suitability of regression models under non-normal data conditions, highlighting the superior performance of multivariate linear regression in handling multiple dependent and independent variables simultaneously.

Practical and social implications:
The results offer practical guidance for researchers, data analysts, and policymakers in selecting appropriate analytical techniques for non-normal multivariate datasets. Improved model selection enhances the accuracy of empirical findings and supports more reliable decision-making in education, health, and the social sciences.