This paper presents a technique using quantities termed "elements" which are derived from a limited number of regression equations, and assist in the computations leading to tests of a regression model. It will be seen that special attention is given to "secondary elements" in choosing variables either for predicting the result arising from certain specified circumstances or for explaining the operation in terms of recognizably useful parameters. The meaning of these elements is argued geometrically, and their advantages in computation can easily be demonstrated; they have already helped to clarify complex industrial data.