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Effects of Selection and Errors of Prediction on Relationships between Progeny Tests of Sires and Sons^1,2,

Department of Dairy Science, Virginia Polytechnic Institute and State University, Blacksburg 24061

ABSTRACT

Expected regressions and correlations for progeny test evaluations of sires and sons were examined to consider effects of selection and errors of sampling in evaluations of sires.

The failure of evaluations for sires to be measured without error violates the condition for regression analysis of zero correlation between independent variables and deviations from regression. However, when progeny test evaluations are by selection index and in the absence of selection, son-sire regressions and correlations are consistent estimators of their respective parameters.

Selection of sires has no effect on the limit, with infinite sample size, of the son-sire regression but causes under-estimation of the son-sire correlation.

¹ Published with the approval of the Director of the Agricultural Experiment Station.

² Partially supported by a grant from the National Association of Animal Breeders.