## 3 Results and Discussion
### Optimization of the Enzymatic Hydrolysis Process
The Model F-value of 16.95 implies the model is significant. There is only a 0.01% chance that an F-value this large could occur due to noise. This model includes the A, B, C, and BC terms, which are significant. The fit statistics for the obtained model are presented in Table 8. The values of R\({}^{2}\) and adjusted R\({}^{2}\) indicate a good explanation of the variability by the selected model for ABTS. The Adeq Precision value of 15.8639 indicates an adequate signal. Therefore, this model can be used to navigate the design space. The diagnosis of the model is shown in Figure 3. The normal probability plot (Figure 3a) shows that the residuals have a normal distribution because they follow a straight line with small deviations. The plot of the residuals against the predicted (Figure 3b) shows that the residuals are randomly located around the line residual = 0. This suggests that the resulting relationship pattern is reasonable. Also, no residues \"stand out\" from the random residue pattern. This assumes there are no outliers. Finally, the actual versus predicted plot (Figure 3c) shows that the points are close to the diagonal line. In Figure 4, a series of model graphs is presented. The perturbation plot (Figure 4a) shows that all three factors have approximately the same influence on the response ABTS, as they have almost the same slope. Figure 4b reveals that the maximum value of ABTS can be achieved by keeping the temperature and papain concentration at 40 \({}^{\circ}\)C and 1.0%, respectively, while the hydrolysis time is chosen to be a minimum of 60 min. Figure 4c shows that the maximum value of ABTS can be achieved with a maximum hydrolysis time (180 min), papain concentration in the range of 1-1.5%, and minimum temperature. From Figure 4d, it can be seen that the maximum ABTS value is obtained in the following conditions: the minimum temperature value (20 \({}^{\circ}\)C), maximum hydrolysis time (180 min), and 1.0% papain concentration, or at the maximum temperature value (40 \({}^{\circ}\)C), minimum hydrolysis time (60 min), and 1.0% papain concentration. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & **\(p\)-Value** & \\ \hline Model & 174.76 & 6 & 29.13 & 16.95 & \textless{}0.0001 & significant \\ A-Papain & 45.27 & 1 & 45.27 & 26.35 & 0.0002 & \\ concentration & 31.22 & 1 & 31.22 & 18.18 & 0.0008 & \\ C-hydrolysis time & 53.40 & 1 & 53406 & 31.08 & \textless{}0.0001 & \\ AB & 0.0001 & 1 & 0.0001 & 0.0001 & 0.9942 & \\ AC & 6.77 & 1 & 6.77 & 3.94 & 0.0671 & \\ BC & 38.10 & 1 & 38.10 & 22.18 & 0.0003 & \\ \hline \end{tabular}
\end{table} 
Table 7: ANOVA for 2 FI model for Response 2: ABTS. \begin{table}
\begin{tabular}{c c c c} \hline
**Std. Dev.** & **1.31** & **R\({}^{2}\)** & **0.8790** \\ \hline Mean & 37.05 & Adjusted R\({}^{2}\) & 0.8272 \\ C.V.\% & 3.54 & Predicted R\({}^{2}\) & 0.6643 \\  & & Adeq Precision & 15.8639 \\ \hline \end{tabular}
\end{table} 
Table 8: Fit statistics for Response 2: ABTS. Figure 4: _Cont._  
Figure 3: Model diagnostics plots: ABTS. (**a**) normality; (**b**) residuals vs. predicted; (**c**) predicted vs. actual. A numerical optimization, which finds a point that maximizes the desirability function, was made to find the optimal process conditions. Table 9 presents the specific optimum conditions for obtaining the highest level of bioactive compounds. The Design Expert software returns a table of 100 possible solutions. For brevity, only the first ten of them are presented here.