The grouping problem in distribution-free general linear regression

An exact distribution-free method is proposed for solving general linear regression problems, which have identically distributed errors and one of the slope parameters of interest. The method reduces the model to simple linear regression form through grouping of observations, and then uses an exact distribution-free method for slope in simple linear regression to test or estimate the parameter of interest. Of course reducing the model involves a loss of efficiency. The choice of an optimal grouping to minimize efficiency loss is discussed.