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The predictive estimator of the gradient in simple regression is assumed to be the product of the gradient given by least-squares fitting and a constant (ρ). The results of numerical simulations show that when generalized cross-validation is used to obtain the optimal ρ, the resultant predictive estimator is not of great use. However, when the parametric bootstrap method is applied for this purpose, the resulting predictive estimator is often superior to the maximum likelihood estimator in terms of prediction accuracy. Therefore, statistics reflecting the characteristics of data should be used to determine which estimator should be adopted.