Multiple Regression Design for a Full Factorial Base Model Associated with a Commutative Jordan Algebra

If for each treatment of a base model we consider a multiple linear regression on the same variables (dependent and independent) a multiple regression design (MRD) is obtained. If the number of observations per regression is equal, the MRD is balanced, otherwise it is unbalanced. The purpose of this work is to show that is possible to extend the study of the full factorial design of fixed effects and the MRD associated to these designs to the unbalanced cases, combining the linear model associated with a commutative Jordan algebra (CJA) and the L-Model theory. The structure of the factorial design used in this work is based on linear spaces on Galois fields as well as on the relationship between a linear model and a CJA.