Neutrosophic Correlation and Regression with Applications

Abstract

Classical statistical techniques assume that observations are precise and unambiguous. However, real-world data are often affected by uncertainty, vagueness, and incomplete information. Neutrosophic statistics, based on neutrosophic numbers comprising deterministic and indeterminate components, provides a realistic mathematical framework for addressing such situations. In this paper, we develop rigorous formalisms for neutrosophic correlation and regression using theorem–proof structures. Explicit expressions for neutrosophic mean, variance, covariance, correlation coefficient, and regression models are derived. A comprehensive numerical case study of the relationship between working time and income is presented, with all intermediate computations and final results reported in detail. The proposed approach demonstrates clear advantages over classical regression by naturally incorporating uncertainty in both explanatory and response variables.