A method is presented for the simultaneous weighted-least-squares estimation of regression parameters (assumed to be the same within and between units) and of the variance components for the within- and between-unit errors. The algebraic results required for a fully non-orthogonal analysis are derived and the method is illustrated with an example. The data in the example consist of 150 observations (y) on relatives rates of bromide and chloride renal reabsorption in 19 dogs (units) with numbers per dog varying from 4 to 13. Corresponding observations are available on 13 regressors. Regression estimates are obtained from the within-dog information, from between dogs, and by the proposed method, as a weighted combination of both. Estimates of the variance components for within- and between-dog errors are obtained from the algebraic results. These are used mainly to provide weights required in the combined regression. A considerable increase is noted in the regression information provided by the combined analysis. A reference is given to a computer program available for the method.