## 3 Results and Discussion
### Optimization of the Enzymatic Hydrolysis Process
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & _p-Value_ & \\ \hline Model & 388.74 & 9 & 43.19 & 24.37 & \textless{}0.0001 & significant \\ A—Bromelain concentration & 106.17 & 1 & 106.17 & 59.90 & \textless{}0.0001 & \\ B—Temperature & 224.40 & 1 & 224.40 & 126.61 & \textless{}0.0001 & \\ C—hydrolysis time & 11.31 & 1 & 11.31 & 6.38 & 0.0282 & \\ AB & 5.30 & 1 & 5.30 & 2.99 & 0.1118 & \\ AC & 1.68 & 1 & 1.68 & 0.9487 & 0.3510 & \\ BC & 0.7055 & 1 & 0.7055 & 0.3981 & 0.5410 & \\ A\({}^{2}\) & 0.9200 & 1 & 0.9200 & 0.5191 & 0.4863 & \\ B\({}^{2}\) & 37.82 & 1 & 37.82 & 21.34 & 0.0007 & \\ C\({}^{2}\) & 0.0162 & 1 & 0.0162 & 0.0092 & 0.9255 & \\ Residual & 19.50 & 11 & 1.77 & & & \\ Lack of Fit & 5.37 & 3 & 1.79 & 1.01 & 0.4356 & not significant \\ Pure Error & 14.12 & 8 & 1.77 & & & \\ Cor Total & 408.23 & 20 & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Analysis of variance for the quadratic model of DPPH (output 1). The series of model plots presented in Figure 2 illustrates the effects of the input factors on the output variable. In Plot 2a, the influence of the input factors on DPPH radical scavenging activity is highlighted, with factor B (temperature) exerting the most significant impact, followed by factor A (bromelain concentration). The line for factor C (hydrolysis time) is nearly parallel to the \(x\)-axis, indicating that it has little to no significant effect on DPPH activity. The response surface plots (Figure 2b-d) provide a visual representation of how two independent variables interact within the experimental range, while the third variable remains constant. Figure 2b shows that the maximum DPPH value can be achieved when both the temperature and bromelain concentration are maintained above 30 \({}^{\circ}\)C and 3.0%, respectively, with hydrolysis time set at a maximum of 180 min. In Figure 2c, it is evident that the highest DPPH value is attainable with a hydrolysis time exceeding 120 min, a bromelain concentration above 2.5%, and the maximum temperature. Figure 2d demonstrates that the optimal DPPH radical scavenging activity is achieved at maximum  
Figure 1: DPPH Radical scavenging activity model diagnostics: (**a**) normality plot; (**b**) residuals vs. predicted; (**c**) predicted vs. actual. levels of both bromelain concentration and temperature, while hydrolysis time does not play a significant role in this scenario. These plots provide valuable insights into the conditions necessary to maximize DPPH activity, emphasizing the critical role of temperature and bromelain concentration in the process while suggesting that hydrolysis time is less influential under the conditions tested. Design-Expert software identified the relationship between ABTS radical scavenging activity and the input variables as quadratic, as shown in Table 7. Although some added terms have statistically insignificant coefficients, the model as a whole remains robust. The model's F-value of 164.76 indicates a high level of statistical significance, with only a 0.01% likelihood that such a large F-value is due to random noise. \(p\)-values below 0.0500 confirm the significance of specific model terms, particularly A (bromelain concentration), B (temperature), AB (interaction between bromelain concentration and temperature), AC (interaction between bromelain concentration and hydrolysis time), A\({}^{2}\), and C\({}^{2}\). Figure 2: DPPH perturbation and response surface plots: (**a**) perturbation plot; (**b**) contour surface plot: bromelain concentration vs. temperature; (**c**) contour surface plot: bromelain concentration vs. hydrolysis time; (**d**) contour surface plot: temperature vs. hydrolysis time. The accuracy of the model is further supported by the assessments presented in Table 8. The high R2 and adjusted R2 values demonstrate that the model effectively captures the variability in ABTS radical scavenging activity.