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Interval systems of linear algebraic equations (ISLAE) are considered in thecontext of constructing of linear models according to data with intervaluncertainty. Sufficient conditions for boundedness and convexity of anadmissible domain (AD) of ISLAE and its belonging to only one orthant of an$n$-dimensional space are proposed, which can be verified in polynomial time bythe methods of computational linear algebra. In this case, AD ISLAE turns outto be a convex bounded polyhedron, entirely lying in the corresponding ortant.These properties of AD ISLAE allow, firstly, to find solutions to thecorresponding ISLAE in polynomial time by linear programming methods (whilefinding a solution to ISLAE of a general form is an NP-hard problem). Secondly,the coefficients of the linear model obtained by solving the correspondingISLAE have an analogue of the significance property of the coefficient of thelinear model, since the coefficients of the linear model do not change theirsign within the limits of the AD. The formulation and proof of thecorresponding theorem are presented. The error estimation and convergence of anarbitrary solution of ISLAE to the normal solution of a hypothetical exactsystem of linear algebraic equations are also investigated. An illustrativenumerical example is given.

Sufficient Conditions for the Joined Set of Solutions of the  Overdetermined Interval System of Linear Algebraic Equations Membership to  Only One Orthant