ON THE USE OF CORRELATION TO AUGMENT DATA

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 1, 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. GENERAL THIS problem came to the author's attention in connection with an investigation of stream gaging practice conducted under the auspices of The United States Geological Survey. Desirous of operating an efficient streamgaging network, the Survey is establishing base or permanent stations to be supplemented by short-term gaging at additional sites. The flow records are combined if they jointly produce better and cheaper estimates of the mean and variance of annual flow at the temporary site than could be obtained from the temporary gaging station alone. The results have been generalized here to include a broader range of application. It is a common practice in applied statistics to attempt to improve estimates of population parameters by means of correlation analysis with data which are obtained from additional measurements of other variables. Formulae are derived here which define the utility of making least square regression estimates to improve parameter estimation in a three-variable model. To clarify the problem, it would be well to consider a simplified example involving two variables, X and Y. The following assumption, made for this example, is applicable throughout with but a few additions: