AbstractThis paper is concerned with the generalized model E(φ(Y)!X) =φ(X) involving the transformations on both the predictor vectorXand the response variableY.For this purpose, Taylor expansions and canonical analysis are applied. For optimizing the expansions, it is shown by a simulation study that not only prediction error, the combination of model error and noise error, is an important index, but the distribution of the residuals and thet‐values of the coefficients also must be considered. Furthermore, the results of penicillin titrition show that the practical situations often need to be considered in selecting an appropriate model for a real‐life pr