## 4 Results and Discussion
### Miscellaneous Discussion  
The previous sections demonstrate the effectiveness of developing regression methods for estimating the enological parameters considered, namely sugar content, pH, and anthocyanin concentration, expanding the existing approaches on the same subject. The best results obtained for each enological parameter are highlighted in Table A3 (Appendix A) for an easier interpretation and comparison of the finding. The columns contain information's such as the ranking of the three best methods, the mean and standard deviation of the RMSEs obtained for the external data set, the rather important spectral regions identified by the regression coefficients of the best model, and the relevant peaks that might be related to the enological parameter in the study and identified by the highest regression coefficients of the best model. Analyzing the overall results, it is possible to verify that sometimes one method was more adequate for one parameter, and another method was more explanatory for another. The reason for this can be justified by the fact that each method has its strengths and weaknesses in terms of modelling the entire spectra vs. the narrow region, linear vs. non-linear relationships, and sparse vs. correlated features. This means that the best method depends on the underlying relationship between the hyperspectral image and a particular  
Figure 13: Anthocyanin concentration regression coefficients obtained during the model training: (**a**) ridge regression and (**b**) elastic net. enological parameter, and in practice, the best method is never known a priori. This fact supports conducting such extensive studies as the one that we have done here, in order to identify the most suitable regression methods per the observed enological parameters. Interestingly, our study found that the combination of the Savitzky\(-\)Golay preprocessing and ridge regression methods led to the best or near best performance across all enological parameters, and was more robust in comparison to other linear approaches, as well as more complex non-linear methods. Therefore, researchers are incentivized to also consider this particular combination when modeling such enological parameters. On the other hand, the present results do not extend to enological parameters that were not considered in this study. Instead, the application of the complete L&NL-PAC is suggested as a robust framework to identify superior methods for modeling additional enological properties of interest. Another interesting feature of this work concerns the identification of important spectral regions by screening the regression coefficients. In this regard, the complete spectra of the samples (ranging from 380 to 1028 nm; Figure 2) were used to establish and validate (with samples not employed during the training) the models, and the identification of the best method allowed us to understand which spectral regions may be more relevant to further design more specific equipment, reducing the dimensionality of data and providing a faster and more cost-effective methodology (e.g., a smaller number of bands leads to cheaper equipment). Notably, the most important spectral regions seemed to range between 700 and 960 nm for the three enological parameters, with some other important peaks appearing between 400 and 520 nm for the anthocyanin parameter. The spectral regions between 400 and 500 nm also had some important predictors for sugar content and pH, but they tended to be noisier. It is important to denote that, due to differences in terroric, the grape berries were at various ripening stages (even within the same bunch and day), so it was already expected that for the 30 runs of Monte Carlo double cross-validation the highest regression coefficients would present some scenarios of variation (as it is possible to observe in Figures 7, 10 and 13). Furthermore, the measurements were done for samples composed of a small number of berries, which increased the sample variability when compared with a large number of berries per sample.