Examples of the application of matrix factors of a design matrix

When the elements of a design matrix are rational numbers and the variances of the observations are rational multiples of a common real constant, the covariances being zero, the design matrix may be factorised into a product of matrices which have usefil statistical interpretations. The main factor matrices have integer elements, while the other factor matrices are diagonal with rational elements. Weights which are rational numbers, and missing observations, are readily accommodated. A computer is usually needed to find the factors. This paper shows how, once the factors have been found, they may be employed for any suitable set of observations without further need for such assistance.