We apply the local-influence method of Lawrance to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox regression model. We show that this method is the same as the local-influence method proposed by Cook. Furthermore, the difference in local-influence diagnostics between the case-weights perturbation and the constant-variances perturbation is examined and the relationship between the localinfluence diagnostic and the deletion diagnostic is studied. An example is presented to illustrate local-influence diagnostics.