The effect of response scaling on the detection of linear dependencies among multiresponse data

Summary Box and Draper (1965) introduced a criterion for the estimation of parameters from a multiresponse model. This criterion can lead to misleading results in the presence of linear relationships among the responses. Box et al. (1973) proposed a procedure for detecting the existence of such relationships when the multiresponse data are subject to round-off errors. The procedure is applicable only when the round-off errors are identically distributed as uniform random variates. In many situations, however, the round-off errors can vary considerably. For example, the responses may have distinct physical meanings, and hence distinct scales of measurement with possibly widely different orders of magnitude. This article extends Box et al.’s procedure to cover these situations. Two examples are given to illustrate the implementation of the proposed methodology.