Response transformations are a popular approach to adapt data to a linear regression model. The regression coefficients, as well as the parameter defining the transformation, are often estimated by maximum likelihood assuming homoscedastic normal errors. Unfortunately, consistency to the true parameters holds only if the assumptions of normality and homoscedasticity are satisfied. In addition, these estimates are nonrobust in the presence of outliers. New estimates are proposed, which are robust and consistent even if the assumptions of normality and homoscedasticity do not hold. These estimates are based on the minimization of a robust measure of residual autocorrelation. [Authors]