Abstract: In this paper, compression LS estimate B(k) of the regression coefficient B isconsidered when the design matrix present ill-condition in multivariate linear model.The MSE (mean square error)of the estimate β(k)=Vec(B(k))is less than theMSE of LS estimate β^* of the regression coefficient β= Vec(B) by choosing the pa-rameter k. Admissibility , numerical stability and relative efficiency of β(k)are proved. The method of determining k value for practical use is also suggested.

Key words: compressible hyper-elastic material, cavitated bifurcation, catastrophe and concentration of stress, energy comparison, multivariate linear model, least square estimate, compression LS estimate, mean square error