Some uses of the square root method as a tool in multiple prediction

It is shown how the square root method can be used in the derivation of formulas in multiple prediction and in the computations necessary for their application. A formula derived by Horst indicates the validity a test must possess in order to contribute a specified amount to the multiple correlation of a battery. Then a formula is derived which relates the length of one test in a battery to the multiple correlation of the battery as a whole. The formulas hold for population parameters; in this paper, sampling theory is not discussed. A numerical example is presented; it is shown that one square root analysis provides all the data needed for the formulas.