## 3 Results and Discussion
### Optimization of the Enzymatic Hydrolysis Process
Additionally, the Adeq Precision value, which measures the signal-to-noise ratio, is 50.7486, far exceeding the minimum threshold of four. This indicates a strong and reliable signal, confirming that the model is well-suited for navigating the design space and making accurate predictions. The robustness and precision of this model make it a valuable tool for optimizing ABTS radical scavenging activity in future studies, providing reliable guidance for process adjustments and enhancements. Model diagnostics were conducted using three key plots: the normal probability plot, the plot of residuals versus ascending predicted response values, and the plot of predicted response values versus actual response values, as shown in Figure 3. The normal probability plot (Figure 3a) was used to determine whether the residuals followed a normal distribution. In this instance, the residuals align closely with a straight line, with only minor deviations, indicating that they are normally distributed. The residuals versus predicted values plot (Figure 3b) reveals that the residuals are randomly dispersed around the line where residual = 0. This random scatter suggests that the model is well-fitted and free from significant bias. Moreover, the absence of any residuals that significantly deviate from the overall pattern indicates that no outliers are affecting the model's accuracy. The actual versus predicted values plot (Figure 3c) shows that while the points do not align perfectly with the diagonal line, they remain within acceptable limits. This slight deviation is reasonable given the high R2 value of 0.9926, which indicates that the model has an excellent fit and strong predictive power. These diagnostic plots collectively confirm the adequacy and reliability of the model, ensuring its robustness in predicting the response variable accurately across the design space. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & _p-Value_ \\ \hline Model & 1465.21 & 9 & 162.80 & 164.76 & \textless{}0.0001 & significant \\ A—Bromelain concentration & 190.69 & 1 & 190.69 & 192.98 & \textless{}0.0001 & \\ B—Temperature & 884.94 & 1 & 884.94 & 895.60 & \textless{}0.0001 & \\ C—Hydrolysis time & 0.9748 & 1 & 0.9748 & 0.9865 & 0.3419 & \\ AB & 86.05 & 1 & 86.05 & 87.08 & \textless{}0.0001 & \\ AC & 286.12 & 1 & 286.12 & 289.56 & \textless{}0.0001 & \\ BC & 0.7854 & 1 & 0.7854 & 0.7949 & 0.3917 & \\ A2 & 6.76 & 1 & 6.76 & 6.84 & 0.0240 & \\ B2 & 0.0003 & 1 & 0.0003 & 0.0003 & 0.9865 & \\ C2 & 5.54 & 1 & 5.54 & 5.61 & 0.0373 & \\ Residual & 10.87 & 11 & 0.9881 & & & \\ Lack of Fit & 4.71 & 3 & 1.57 & 2.04 & 0.1871 & not significant \\ Pure Error & 6.16 & 8 & 0.7700 & & & \\ Cor Total & 1476.08 & 20 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Analysis of variance for the quadratic model of ABTS (output 2). \begin{table}
\begin{tabular}{c c c c} \hline \hline Std. Dev. & 0.9940 & R2 & 0.9926 \\ Mean & 52.49 & Adjusted R2 & 0.9866 \\ C.V. \% & 1.89 & Predicted R2 & 0.9437 \\  & & Adeq Precision & 50.7486 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Model accuracy metrics for ABTS (output 2). Figure 4 presents a series of model plots that illustrate the effects of the input factors on the output. Plot 4a highlights the influence of the input factors on ABTS radical scavenging activity, with factor B (temperature) exerting the most significant impact, followed by factor A (bromelain concentration). The line representing factor C (hydrolysis time) is nearly parallel to the \(x\)-axis, indicating that it has little to no significant influence on the ABTS activity. The response surface plots (Figure 4b-d) provide a visual representation of how two independent variables interact within the experimental range while the third variable is held constant.