The weighted least squares (WLS) procedure has been widely used in the analysis of generation means in biometrical genetics. Two methods to carry out the analysis have been presented in the literature (Mather & Jinks, 1971; Rowe & Alexander, 1980). Neither method identified the factors that need to be taken into account when deciding which procedure to use. This paper examines the fitting of the additive-dominance model using the general principles of least squares analysis and presents the statistical basis of each procedure. Mather & Jink's method, which is more realistic according to genetic theory, is based on the assumption that the populations have nonhomogeneous variances. Rowe & Alexander's method is based on the assumption that the populations have homogeneous variances. In the latter case, there is actually no need to do a WLS analysis. The ordinary least square analysis using the original observations rather than the means, will produce the regression parameter estimates.