Correspondence between a Linear Restriction and a Generalized Inverse in Linear Model Analysis

In experimental statistics the usual method of estimating treatment effects is to introduce arbitrary linear restrictions among the treatment effects in order to obtain solutions of the normal equations.A comparatively recent approach is to dispense with the linear restriction and use a generalized inverse solution to the normal equations.The present note is an attempt to bring these two methods closer together and show their correspondence; namely, for each given linear restriction, there exists a corresponding generalized inverse that yields the same solution for the treatment effects as the linear restriction does.