Abstract
Abstract The inflation in variance of the ratio of regression parameters, due to estimation of the transformation, in a power transformation model with two independent variables is considered. It is shown that the cost of estimating the transformation parameter is generally small and frequently zero. This is in contrast to the results of Bickel and Doksum (1981), who show that the inflation in variance of a single regression parameter can be extremely large. A small study of the effect of the design and parameter values on the inflation in variance of the ratio of parameters, shows that the design of the independent variables is an important determinant of the variance inflation. If the design contains no outlying or influential observations the cost of estimating the transformation parameter is very small; however for designs with outliers the cost can be significant, although nowhere near as large as those found by Bickel and Doksum.
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