By using the information provided by the first κ, 2 ≤ κ< N, members of a random sample of sizeNfrom a univariate normal distribution, Hickman [3] obtains prediction intervals for the sample mean, and the sample variance of the complete sample of sizeN.He gives similar results for a univariate normal regression model. Here we present straightforward generalizations of Hickman's results to the multivariate case.