## 3 Results and Discussion
The Perturbation plot (Figure 1a) represents the factors with the most significant influence. The hydro module's and the duration's graphs have the steepest slope. Since the extraction of bioactive molecules is evaluated as the first and most important step in functional ingredients to foods, pharmaceuticals, and cosmetology, among others, researchers have pointed out that an increase in the hydro module improves the diffusion rate in a solid-liquid extraction [27]. Figure 1b presents the actual versus predicted values. The response surface plots (Figure 1c-e) visualize the variation in the values of two independent variables within the experimental domain while holding the other two constant. Figure 1c reveals that the maximum TPC value can be achieved by keeping the temperature and the extractant at 70 \({}^{\circ}\)C and 80%, respectively. Considering the effect of hydro module and temperature on the TPC (max. 105.596 mg GAE/100 g fw), Figure 1d predicts an optimal duration of 20 min and an 80% extractant (110.37 mg GAE/100 g fw). Two-factor interaction terms have been added to further describe the dependence of TFC on the input variables. The results within the framework of the model appeared not statistically significant and were not visualized. An attempt was also made to define the model as linear. The results are presented in Table 5.  
It turned out that this model was also not suitable because the model's F-value of 1.60 meant that the model was not robust to noise. There was a 20.74% chance that such a large F-value was due to noise. Finally, the 2 FI model was chosen, and the results are presented in Table 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & \(\mathbf{p}\)-Value** \\ \hline Model & 2114.34 & 4 & 528.58 & 10.08 & \textless{}0.0001 & significant \\ A-hydromodule (ratio) & 1095.66 & \(1\) & 1095.66 & 20.89 & 0.0001 & \\ B-Duration & 291.47 & \(1\) & 291.47 & 5.56 & 0.0269 & \\ C-Temperature & 579.36 & \(1\) & 579.36 & 11.05 & 0.0028 & \\ D-Extractant & 147.96 & \(1\) & 147.96 & 2.82 & 0.1060 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ANOVA for Linear model Response 1: TPC. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & \(\mathbf{p}\)**-Value** \\ \hline Model & 2739.79 & 14 & 195.70 & 4.33 & 0.0049 & significant \\ A-hydromodule (ratio) & 1141.70 & 1 & 1141.70 & 25.24 & 0.0002 & \\ B-Duration & 340.86 & \(1\) & 340.86 & 7.54 & 0.0158 & \\ C-Temperature & 443.07 & 1 & 443.07 & 9.80 & 0.0074 & \\ D-Extractant & 196.55 & 1 & 196.55 & 4.35 & 0.0559 & \\ AB & 49.35 & 1 & 49.35 & 1.09 & 0.3139 & \\ AC & 20.11 & 1 & 20.11 & 0.4446 & 0.5158 & \\ AD & 58.34 & 1 & 58.34 & 1.29 & 0.2751 & \\ BC & 19.05 & 1 & 19.05 & 0.4211 & 0.5269 & \\ BD & 5.30 & 1 & 5.30 & 0.1171 & 0.7373 & \\ CD & 74.47 & 1 & 74.47 & 1.65 & 0.2203 & \\ A\({}^{2}\) & 18.72 & 1 & 18.72 & 0.4138 & 0.5304 & \\ B\({}^{2}\) & 143.38 & 1 & 143.38 & 3.17 & 0.0967 & \\ C\({}^{2}\) & 48.84 & 1 & 48.84 & 1.08 & 0.3164 & \\ D\({}^{2}\) & 131.04 & 1 & 131.04 & 2.90 & 0.1108 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: ANOVA for Quadratic model for Response 1: TPC. Figure 1: TPC model analysis: (**a**) Perturbation plot; (**b**) predicted vs. actual plot; (**c**) contour surface plots of TPC against hydro module (ratio) and duration (min); (**d**) contour surface plots of TPC against hydro module (ratio) and temperature; (**e**) contour surface plots of TPC against duration (min) and temperature. It shows that the F-value is 11.68, which means that the model is significant. There is only a 0.01% chance that the F-value is due to noise. The coefficient of determination is \(\mathbb{R}^{2}\) = 0.82 with a standard error of 2.63. This confirms the fact that the higher the R-squared value, the smaller the error (compared to a TPC regression model). Thus, when estimating the TFC value, an average error of less than 2.63 mg GAE/100 g fw can be expected.