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

A sample of size n 1 of a normal random variable y is augmented by n 2 regression estimates obtained from p other random variables which, along with y , follow a ( p + 1) dimensional normal probability law. The sampling variance of s y 2 , the estimate of the variance of y obtained from the augmented sample, is derived. The relative reliability of s y 2 and s y 2 ( n 1 ), the variance estimate based on the original n 1 observations, is found to depend on n 1 , n 2 , p , and R , the multiple correlation between y and the remaining p variables.