## 3 Results and Discussion
### Extraction Process Optimization
Values from the experiments carried out at the predicted conditions were close to the predicted values in the case of GL-Lys and GL-Arg, and the difference between the two values (experimental and predicted) did not have a practical significance on the good fit of the two models. This small difference could be due to an uncontrolled source of variation during the extraction process (temperature, stirring, etc.) or minor experimental errors, whereas the measured value for GL-Pro was in the range of the predicted values. Considering the entire statistical parameters for model verification, it can be concluded that these results indicated valid and suitable mathematical prediction models for the optimization of polyphenol extraction conditions. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**DES** & **Second Order Polynomial Equations** & **r\({}^{2}\)** & **_p_** \\ \hline GL–Lys & \(Y_{TP}\) = 133.49 + 10.22 \(X_{1}\) + 21.86 \(X_{2}\) + 24.78 \(X_{3}\) + 10.04 \(X_{3}^{2}\) & 0.99 & 0.0002 \\ GL–Pro & \(Y_{TP}\) = 74.63 + 4.91 \(X_{1}\) + 3.80 \(X_{2}\) + 8.76 \(X_{3}\) & 0.98 & 0.0006 \\ GL–Arg & \(Y_{TP}\) = 0.83 + 2.64 \(\times\) 10 \({}^{-4}\)\(X_{1}\) + 1.55 \(\times\) 10 \({}^{-4}\)\(X_{2}\) + 9.06 \(\times\) 10 \({}^{-4}\)\(X_{3}\) + 1.98 \(\times\) 10 \({}^{-4}\)\(X_{2}^{2}\) + 4.36 \(\times\) 10 \({}^{-4}\)\(X_{3}^{2}\) & 0.99 & 0.0002 \\ \hline \hline \end{tabular}  
* \(X_{1},X_{2},X_{3}\): main effects; \(X_{2}^{2},\ X_{3}^{2}\): quadratic effects.  
\end{table} 
Table 4: Polynomial equations and statistical parameters calculated after implementation of the design. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**DES** & **Interval Predicted** & **Observed Value \({}^{*}\)** & **Optimal Conditions** \\  & **Values (mg g\({}^{-1}\))** & **(mg g\({}^{-1}\))** & **\(\mathbf{C_{DES}}\) (\%, _w/v_)** & **\(\mathbf{T}\) (\({}^{\circ}\mathbf{C}\))** \\ \hline GL–Lys & \([189.58,\ 216.27]\) & 188.39 \(\pm\) 0.37 & 150 & 90 & 80 \\ GL–Pro & \([86.31,\ 97.00]\) & 95.97 \(\pm\) 0.74 & 150 & 90 & 80 \\ GL–Arg & \([0.83053,\ 0.8313]\) a & 0.83002 \(\pm\) 0.47 a & 150 & 90 & 80 \\ GL–Arg & \([112.48,\ 129.68]\) b & 100.01 \(\pm\) 1.98 b & 150 & 90 & 80 \\ \hline \hline \end{tabular}  
* * Mean \(\pm\) standard deviation of triplicate determinations from predicted optimum experiments a: Box–Cox transformed data; b: untransformed data.  
\end{table} 
Table 5: Optimal predicted conditions and comparison of experimental and predicted values on the \(Y_{TP}\) in all DESs tested. Extractions were performed under stirring (900 rpm) for 150 min. Furthermore, the experimental design enabled the detection of a statistical significance in the quadratic coefficient \(X_{3}^{2}\) (\(T\)) in two models including GL-Lys and GL-Arg and no cross effect among the variables. Additionally, the obtained results supported that all the variables (\(X_{1}\), \(X_{2}\), \(X_{3}\)) have a significant effect (\(p<0.05\)) on the extraction process, as also reported in the literature. This outcome can be visualized through the prediction profilers, which examine the dynamic relationships among all the inputs and outputs simultaneously (Figure 1). The prediction profilers present a general curvature trend of the model profile lines, which illustrates the non-linear responses of the model's effects. An observed increase in every single variable led to an increased response in all three DESs tested. Desirable \(Y_{TP}\) was achieved under \(R_{L/S}\) 150 mL g\({}^{-1}\), \(C_{\text{DES}}\) 90%, _w/v_, and \(T\) 80 \({}^{\circ}\)C in all three DESs by the desirability function, which produced the maximum overall desirability of 0.992, 0.995, and 0.958 for of GL-Lys, GL-Pro and GL-Arg, respectively. The findings herein indicated that \(R_{L/S}\), \(C_{\text{DES}}\), and \(T\) strongly affect the extraction yield of polyphenols from OLL.