## 3 Results and Discussion
### Multivariate Data Analysis
#### 3.3.3 Regression Models  
It is important to monitor the \({}^{\circ}\)Brix and sucrose contents in maple syrup to ensure product quality and stability [26]. Partial least square regression (PLSR) prediction models were developed with FT-IR and Raman spectra and reference values of \({}^{\circ}\)Brix and sucrose  
Figure 4: Soft independent modeling of class analogy (SIMCA) projection plots of classification of traditional and BBL maple syrups with (**a**) FT-IR and (**c**) Raman; prediction of external validation sets, including authentic traditional and BBL samples and suspicious samples by (**b**) FT-IR and (**d**) Raman.  
contents (Figure 14). Performance statistics of the PLSR models developed using training (\(n=26\)) and external validation (\(n=11\)) data sets are listed in Table 2. The number of samples and the range in training models are not all the same due to outlier exclusion. Four and five factors were selected to generate FT-IR and Raman training models, respectively, according to the standard error of cross-validation (SECV) (leave-out-out) result from carrying out the best quality of the models as well as to avoid possible overfitting.  
Our PLSR models showed strong correlations (Rcal > 0.98 and Rval > 0.95) in predicting \({}^{\circ}\)Brix and sucrose contents in traditional map syrups, BBL maple syrups, and table syrup samples. The standard error of prediction (SEP) values were 0.88% and 1.66% for FT-IR validation models for \({}^{\circ}\)Brix and sucrose, respectively, and were 1.23% and 1.67% for Raman validation models for \({}^{\circ}\)Brix and sucrose, respectively. Similar SECV and SEP were obtained, indicating the robustness of the models. Standard errors of laboratory (SEL) for reference methods of \({}^{\circ}\)Brix and sucrose were 0.21% and 0.62%, respectively. The SEL values were compared with the prediction performances of the models (SEP), and we found that the SEP values (Table 2) were always higher than those of SEL because the SEP includes not only the sampling and analysis errors but also the spectroscopy and model errors [45]. The SEP obtained for the FT-IR and Raman models were 2.7 times those of the SEL for sucrose, representing good precision of the models [46]. Conversely, the models predicting \({}^{\circ}\)Brix had a SEP/SEL ratio of 4.2 (FT-IR) and 5.9 (Raman), which were higher than the SEP/SEL threshold of 2 [46] for acceptable precision compared to the referenced method. However, our models show superior performance compared to reported \({}^{\circ}\)Brix predictions for honey using FTIR (R2 val = 0.86, SEP = 1.84%) and Raman (R2 val = 0.87, SEP = 1.32%) [47; 48]. [PERSON] et al. quantified the total sugar contents in Manuka nectar using FT-IR, reporting Rval = 0.95 and SEP = 1.17% values [15].  
The regression vector plots, shown in Figure 15, help to identify the functional groups whose variance is the highest for correlating between reference values and spectral data. The key FT-IR region for the \({}^{\circ}\)Brix and sucrose predictions was in the 1750-700 cm\({}^{-1}\) range, with distinguished bands centered at 1635 (OH bending vibration characteristic of absorbed water) and the 1125 to 900 cm\({}^{-1}\) related to C-O stretching and ring vibrational modes of sugars [8; 34]. The regression vector plots for Raman data indicated that the bands at 835, 990, 1100 cm\({}^{-1}\) explained most of the variance for the Brix model, and the bands at 424, 600, and 890 cm\({}^{-1}\) explained for the Sucrose model. The scattering bands in the vicinity of 424 and 600 cm\({}^{-1}\) are associated with the deformation of C-C-O and C-C-C [38]. The bands near 990 and 1100 cm\({}^{-1}\) are related to the deformation modes of saccharides functional groups [28; 38].