Multivariate Linear Calibration with Univariate Controlled Variable

This paper gives some new results on the multivariate linear calibration problem in the case when the controlled variable is univariate. Firstly, a condition under which one can obtain a finite closed confidence interval of $x_0$(unknown controlled variable) is suggested. Secondly, this article considers a criterion to find out whether the multivariate calibration significantly shortens the confidence interval of $x_0$ and supports this criterion by examples. Finally, a multivariate extension of the results in Lwin Maritz (1982) is given.