Reliability of a Variance Estimate Obtained from a Sample Augmented by Multivariate Regression

A sample of size n1 of a normal random variable y is augmented by n2 regression estimates obtained from p other random variables which, along with y, follow a (p + 1) dimensional normal probability law. The sampling variance of sy2, the estimate of the variance of y obtained from the augmented sample, is derived. The relative reliability of sy2 and sy2 (n1), the variance estimate based on the original n1 observations, is found to depend on n1, n2, p, and R, the multiple correlation between y and the remaining p variables.