The first term in Eq

In addition, to ensure more validity for the presented ANN models, three validation methods were respectively developed by Shi et al. (Q2F1), Schüürmann et al. (Q2F2) and Consonni et al. (Q2F3) and they are calculated respectively by following equationsequation(44)QF12=1−∑i=1nEXTyiexp−yical2∑i=1nEXTyiexp−y¯TR2equation(45)QF22=1−∑i=1nEXTyiexp−yical2∑i=1nEXTyiexp−y¯EXT2equation(46)QF32=1−∑i=1nEXTyiexp−yical2/nEXT∑i=1nTRyiexp−y¯TR2/nTRwhere yiexp, yical, y¯TR, y¯EXT, nTR and nEXT are respectively defined as the experimental data, the calculated value, the average of training set, the average of external prediction set (test set), the number of compounds in the training set and the number of compounds in the external prediction set. However, Eq.  (44) is widely used in the validation technique by different authors and it ANQ 11125 was also implemented in the software used for QSAR modeling (MOBY DIGS) of Todeschini et al. [53]. After the Q2F1 formulation, Schüürmann et al. proposed an alternative criterion (Q2F2), which differs from Q2F1 because the average value at the denominator is calculated using the prediction data set instead of the training set and at last, as can be seen from Eq.  (45), the suggested validation technique by Consonni et al. differs from both Q2F1 and Q2F2 as the denominator is calculated on the training set, and both the numerator and denominator are divided by the number of the corresponding elements. The calculated results of Q2F1, Q2F2, Q2F3 for proposed ANN models were listed in Table 3. Schüürmann et al. notify a concern about these parameters: QF22 ≤ QF12. The obtained results of these methods reveal gymnosperms the abovementioned concern was satisfied (for example to predict the Z1: QF22 = 0.985 ≤ QF12 = 0.999).