Multivariate regression estimates for finite populations

The theory on regression estimate based on one auxiliary variable has been extended to that for more than one auxiliary variable. It has been found that the multivariate regression estimate (MRE) is not unbiased in general. The form of the approximate standard error of MRE is the same as that of simple regression estimate based on one auxiliary variable with the exception that the multiple correlation coefficient replaces the total correlation coefficient in the expression. It has also been found that the precision of MRE is non-decreasing, rather usually increasing as the number of auxiliary variables correlated with the dependent variable increases, assuming sample size to be large compared to the number of auxiliary variables.