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The genetic change from multiple-trait selection experiments can be equated to the regression of genotype on phenotype. This gives rise to a method of obtaining estimates of additive genetic variances and covariances. The method requires the use of selection weights, derived by means of the index-in-retrospect, to provide invariant solutions. Solution variance estimates obtained from Monte Carlo simulation do not agree with variance estimates from ordinary least squares methods. This indicates that the errors are distributed with some structure V. A form of V is proposed which utilizes knowledge of the errors. Monte Carlo variance estimates from generalized least squares (GLS) methods agree closely with the average variance estimates from GLS when the proposed V is used. Use of an estimated V, derived after the initial estimation procedure, is shown to provide adequate information on the variance of the estimates.