Statistical parameters of the ten GFA-MLR models.

RMSE (a): root mean square error of the training set; RMSE (b): root mean square error of the test set. F: The F test is a standard statistical test for the equality of the variances of two populations having normal distributions.R2, R2cv and F for Model 1 were 0.934, 0.888 and 45.31, respectively, and these values are the largest found among the ten models. Moreover, RMSE(a) was the smallest among the models, and the difference between R2 and R2cv was the lowest. These results suggest that Model 1 exhibits the best fitting ability and the best internal predictive ability. To examine the stability of Model 1, the Y-randomization test was conducted, and a residual scatter diagram was plotted. After repeating the Y-randomization test more than 500 times, the mean values of R2 and R2cv became 0.043 and 0.005, respectively, much lower than 0.5, indicating that Model 1 is more stable, and there is no “chance correlation” phenomenon occurring for Model 1. As seen in Fig. 3, the points are distributed irregularly and randomly, proving that Model 1 is more stable.Statistical parameters of the ten GFA-MLR models.