  Interval systems of linear algebraic equations (ISLAE) are considered in the
context of constructing of linear models according to data with interval
uncertainty. Sufficient conditions for boundedness and convexity of an
admissible 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 by
the methods of computational linear algebra. In this case, AD ISLAE turns out
to be a convex bounded polyhedron, entirely lying in the corresponding ortant.
These properties of AD ISLAE allow, firstly, to find solutions to the
corresponding ISLAE in polynomial time by linear programming methods (while
finding a solution to ISLAE of a general form is an NP-hard problem). Secondly,
the coefficients of the linear model obtained by solving the corresponding
ISLAE have an analogue of the significance property of the coefficient of the
linear model, since the coefficients of the linear model do not change their
sign within the limits of the AD. The formulation and proof of the
corresponding theorem are presented. The error estimation and convergence of an
arbitrary solution of ISLAE to the normal solution of a hypothetical exact
system of linear algebraic equations are also investigated. An illustrative
numerical example is given.
