## 3 Results
### PLS-DA and PLSR Model Validation
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Model**} & \multirow{2}{*}{**N \({}^{a}\)**} & \multirow{2}{*}{**LV \({}^{b}\)**} & \multirow{2}{*}{**Training \({}^{c}\)**} & \multirow{2}{*}{**Test \({}^{c}\)**} & \multicolumn{6}{c}{**Test on Selected Origins \({}^{c}\)**} \\ \cline{5-10}  & & & & & & & & **Australia** & **Greece** & **Portugal** & **Italy** & **Spain** \\ \hline \multirow{5}{*}{PLS-DA} & Global & 240 & 18 & 99.95 & 98.12 & N/A & N/A & N/A & N/A & N/A \\  & European & 216 & 15 & 99.77 & 98.60 & 87.92 & N/A & N/A & N/A & N/A \\  & Spanish & 96 & 10 & 99.61 & 97.37 & 62.50 & 62.50 & 67.50 & 85.97 & N/A \\  & Italian & 72 & 7 & 99.48 & 97.14 & 59.58 & 62.50 & 64.17 & N/A & 82.47 \\  & Global & 160 & 24 & 0.62 & 1.77 & N/A & N/A & N/A & N/A & N/A \\  & European & 144 & 19 & 0.84 & 2.03 & 31.39 & N/A & N/A & N/A & N/A \\  & Spanish & 64 & 13 & 0.50 & 1.44 & 76.86 & 6.81 & 13.40 & 24.59 & N/A \\  & Italian & 48 & 12 & 0.32 & 0.64 & 67.39 & 17.77 & 10.08 & N/A & 14.28 \\ \hline \hline \end{tabular}  
* \({}^{a}\): Number of samples in the dataset. \({}^{b}\): Latent variables used to build the PLS-DA model. \({}^{c}\): Results are shown as percent prediction accuracy for PLS-DA (rows 1–4), and root mean squared error (RMSE) for PLSR (rows 5–8). N/A, not available.  
\end{table} 
Table 1: EVOO adulteration prediction by UV-Vis spectra according to geographical origins. Figure 5: Local partial least-squares regression (PLSR) model predictions. (**A**) European. (**B**) Spanish. (**C**) Italian. The black line starts from the origin with a slope of 1, representing the ideal regression result. All predictions from the training, internal, and external test sets are plotted in colored markers in each subfigure for better comparison. The results of our attempt to establish EVOO adulteration detection models based on different EVOO origins indicated that it may be difficult to establish a universal model for EVOO adulteration detection using UV-Vis spectroscopy. Since multiple EVOO origins, adulteration types, and the interaction between factors are the sources of differences in the original data matrix, all influencing factors must be considered when trying to establish a general model. Otherwise, it is likely that adulteration in the external test set cannot be predicted. The previous studies did not include such variety of samples and the involvement of different influencing factors. On the other hand, although the PLS-DA and PLSR models established by using all data have achieved adequate prediction results with prediction accuracy more than 99% and RSME less than 2%, there may still be issues remaining in the generalization ability of the model. Specifically, with external test sets composed of other EVOO origins or adulterants that are outside the training set, the prediction remains problematic. Additionally, a model with too many latent variables may be prone to overfit, as the model is becoming too complicated. Therefore, it is recommended to build a chemometric model with controlled samples included in the training set for a more accurate prediction.