This work represents a survey of some results of the theory of random interpolation which enable us to set and to solve in some cases a problem of the robust design regression experiment (with respect to a systematic error). In case of a regression function being a linear combination of Haar functions it succeeds in solving the comparison problem of procedures interpolation by the method of least squares entirely. Obtained yields allow to construct randomized robust designs for the regression experiment of LSM estimators and to compare their goodness.