## 3 Results and Discussion  
After the exclusion of non-informative alvaDesc descriptors, a pool of 3006 MDs was merged with the 11 quantum descriptors. Then, V-WSP variable reduction was applied at a threshold value of 0.95 (thr = 0.95). Thus, 1237 descriptors were submitted to supervised selection through GA-VSS coupled with the OLS method to develop the QSPR model. For splitting the 102 VOCs and SVOCs, the BSM was used to define the training set (71 molecules) and the test set (31 molecules). Refer to Table S1 for the training set and test set assignments. Subsequently, the 71 training molecules were used for GA-VSS coupled with the OLS method in order to search for the optimal pool of MDs. During the supervised selection, the root-mean-square error (RMSE) in the Venetian blinds cross-validation was optimized (minimized) to avoid overfitting the models. The coefficient of determination (\(R^{2}\)) was also considered as a parameter of the model. Thus, a three-variable model was retained as the QSPR model for further analysis:  
\[I=327.63+5.24\ MW+375.44\ MDEN-23\ -385.26\ Mor13v \tag{1}\]  
The statistical parameters for the training set (\(R^{2}\) = 0.920 and \(RMSEC\) = 71.78) and the test set (\(R^{2}\) = 0.897 and \(RMSEP\) = 81.50) reflected negligible differences and indicated the absence of potential overfitting in the model. Consequently, an appropriate QSPR model for predicting the \(I\) property was achieved. In addition, the model derived by Equation (1) was subjected to several cross-validation approaches: leave-one-out (\(R^{2}\) = 0.869 and \(RMSECV\) = 91.74); Venetian blinds (\(R^{2}\) = 0.872 and \(RMSECV\) = 90.62); Monte Carlo, leaving 20% out with 1000 iterations (\(R^{2}\) = 0.870 and \(RMSECV\) = 90.74); and the Bootstrap method with 1000 iterations (\(R^{2}\) = 0.867 and \(RMSECV\) = 92.97). Details of the \(I\) predicted by Equation (1) are available in Table S1, while the numerical values for the three MDs are available in Table S2. Figure 0(a) shows the relationship between the experimental and predicted retention indices obtained by Equation (1). This figure suggests that this property has a linear relationship around the perfect fit line. Complementarily, Figure 0(b) shows the dispersion of the residuals vs. the predicted \(I\), which suggests the random distribution of residuals around the zero line. In this model, no training molecules lie outside the limit of \(\pm\) 2 times the RMSEC. The mechanism of action of the retention index phenomenon presented in Equation (1) was constituted by two conformation-independent molecular descriptors: molecular weight (_MW_) and the molecular distance edge between all secondary and tertiary nitrogen atoms (_MDEN-23_). In addition, signal 13/weighted by van der Waals volume (_Mor13v_) conformation-dependent descriptor complements the topological information of the retention phenomenon. The maximum correlation (\(R^{2}\) = 0.189) between _MW_ and _Mor13v_ suggests a low internal correlation in the QSPR model. Consequently, each molecular descriptor contributed to particular aspects of the retention mechanism in the DVB/CAR/PDMS fiber in the HS-SPME-GC-TOFMS system. The standardized regression coefficients of the model indicate the degree of contribution of each descriptor in predicting the \(I\) property: _MW_ (0.75) > _Mor13v_ (0.25) > _MDEN-23_ (0.21). Figure 1: (**a**) Experimental versus predicted retention indices for the volatile and semi-volatile organic compounds of coffee detected in the DVB/CAR/PDMS fiber in the HS-SPME-GC-TOFMS technique. (**b**) Standardized residuals versus the predicted retention indices for the VOCs and SVOCs identified in coffee samples. Training set molecules are labeled in black, and test set compounds are labeled in blue. The molecular weight is a zero-order constitutional index calculated as the sum of the atomic weights of all of the atoms present in a molecule; that is, it describes the molecular size of both volatile and semi-volatile organic compounds [18].