Analyzing the Impact of Uncertainty on Multiple Regression Metrics and Model Performance

Abstract

Regression models based on classical statistics have been extensively applied across various fields. However, these traditional models fail to account for the degree of indeterminacy when dealing with uncertainty. To address these limitations, this manuscript presents multiple regression models within the neutrosophic statistics framework, emphasizing key metrics relevant to the proposed regression approach. The concept of the neutrosophic random variable is introduced, with its essential properties and the formulation of the neutrosophic regression line, along with metrics such as multiple R, the coefficient of determination, and neutrosophic analysis of variance. Extended simulation studies examine how varying degrees of uncertainty influence multiple R, standard error, and F-test values. Analysis of a real-world example shows that uncertainty levels significantly affect both predicted and residual values generated by the regression model. The results indicate that variations in the degree of indeterminacy lead to significant differences in the multiple R, coefficient of determination, and F-test values. The findings further suggest that regression modeling outcomes may diverge from traditional regression analysis under neutrosophic statistics, making the proposed multiple regression method suitable for situations where data uncertainty plays a critical role.