Behavioral consistency criterion for an interval linear regression model

The problem of formalizing the criterion for the consistency of calculated and specified values of the output variable in a linear regression model built using data with interval uncertainty is considered. Three variants of the interval criterion for the consistency of behavior are proposed, one of which is based on the rules of interval arithmetic. Algorithms for identifying the model parameters are presented; they are reduced to solving linear Boolean programming problems. The conditions for the applicability of each of the three methods for specifying the criterion for the consistency of behavior are formulated, and their correctness is proven. The effectiveness of the proposed criteria is demonstrated, and a comparison has been made with the classical regression approach.