Assume that p random variables, Y(sub n) where n=1,...,p, are distributed according to some multivariate normal distribution (called the p variate normal). Methods of predicting the value of one, Y(sub p) given the values of the other p-1 variables are discussed. A study is made of the problems encountered whenever one tries to reduce the number of variables used to predict Y(sub p) and at the same time minimize loss in prediction accuracy. Modifications of the step-wise procedure of adding predictor variables one at a time are considered, and methods of using an automatic high speed electronic computer to perform the numerous calculations involved are described. A high speed computer program was written to generate samples from any specified p variate normal.