## 3 Results and Discussion
### Optimization of the Enzymatic Hydrolysis Process
The F-value of 24.37 suggests that the model is statistically significant, with a mere 0.01% probability that such a high F-value could be attributed to random noise. \(p\)-values below 0.0500 further confirm the significance of the model terms, with factors A, B, C, and B\({}^{2}\) being particularly noteworthy. \begin{table}
\begin{tabular}{c c c} \hline
**Dependent Variables** & **Symbols** & **Model** \\ \hline DPPH & Y\({}_{1}\) & Y\({}_{1}=61.58+3.64\)X\({}_{1}+5.30\)X\({}_{2}+1.19\)X\({}_{3}-2.85\)X\({}_{2}^{2}\) \\ ABTS & Y\({}_{2}\) & Y\({}_{2}=51.61+4.88\)X\({}_{1}+10.52\)X\({}_{2}-4.64\)X\({}_{1}\)X\({}_{2}-\) \\  & & \(8.46\)X\({}_{1}\)X\({}_{3}+1.21\)X\({}_{1}^{2}+1.09\)X\({}_{3}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Dependent variable models used in the RSM framework. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{2}{c}{**Factor 1**} & \multicolumn{2}{c}{**Factor 2**} & \multicolumn{2}{c}{**Factor 3**} & \multicolumn{2}{c}{**Y\({}_{1}\)**} & \multicolumn{2}{c}{**Y\({}_{2}\)**} \\ \hline \multicolumn{2}{c}{**A: Bromelain Concentration**} & \multicolumn{2}{c}{**B: Temperature**} & \multicolumn{2}{c}{**C: Hydrolysis Time**} & \multicolumn{2}{c}{**DPPH**} & \multicolumn{1}{c}{**ABTS**} \\ \hline \(-1\) & 1\% & \(-1\) & 20 \({}^{\circ}\)C & 0 & 2 h & 51.48 & 33.81 \\ \(0\) & 2\% & 0 & 30 \({}^{\circ}\)C & 0 & 2 h & 60.50 & 49.60 \\ \(0\) &  
The accuracy assessments of the model, presented in Table 6, show that the high R\({}^{2}\) and adjusted R\({}^{2}\) values effectively capture the variability in DPPH activity. Additionally, the Adeq Precision value, which measures the signal-to-noise ratio, is 19.46--well above the threshold of four--indicating a strong and reliable signal. This adequacy suggests that the model is well-suited for navigating the design space, allowing for reliable predictions and optimizations within the defined parameters. The robustness of this model facilitates a deeper understanding of the factors influencing DPPH activity and provides a solid foundation for future studies seeking to optimize antioxidant activity through enzymatic hydrolysis. The model's high predictive accuracy and signal strength make it a valuable tool for guiding experimental design and process optimization in related research. Three types of diagnostics were used to evaluate the model: 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 depicted in Figure 1. The normal probability plot (Figure 1a) was used to assess whether the residuals follow a normal distribution. The plot reveals that the residuals generally align with a straight line, with only minor deviations, indicating that the residuals are normally distributed. The plot of residuals versus predicted values (Figure 1b) shows that the residuals are randomly dispersed around the line where residual = 0, suggesting that the model is adequate and free from significant biases. Additionally, the absence of any residuals that deviate markedly from the random pattern indicates that no outliers are influencing the model. Lastly, the plot of actual versus predicted values (Figure 1c) illustrates that while the points do not perfectly align with the diagonal line, they remain within reasonable bounds, which is expected given an R\({}^{2}\) value of 0.9132. This suggests that the model has a strong predictive capability, albeit with some inherent variability. \begin{table}
\begin{tabular}{c c c c} \hline Std. Dev. & 1.33 & R\({}^{2}\) & 0.9522 \\ Mean & 60.64 & Adjusted R\({}^{2}\) & 0.9132 \\ C.V. \% & 2.20 & Predicted R\({}^{2}\) & 0.7457 \\  & & Adeq Precision & 19.4608 \\ \hline \end{tabular}
\end{table} 
Table 6: Model accuracy metrics for DPPH (output 1).