Abstract This paper provides an evaluation of the effects of a particular regression-estimation technique used to augment measurements when concurrent and additional measurements are available for two other variates. The investigation demonstrates that this use of regression does not always produce better estimates of population parameters, and indeed, that it may produce poorer estimates than could be obtained from the original data alone. Tables of a parameter I, the relative information, are provided so that the utility of making regression estimates to decrease the variance of the mean or variance may be easily evaluated. And finally, the use of these results in the specification of an optimal sampling program is briefly indicated.