## 3 Results and Discussion  
### Experimental Design and Optimization  
#### 3.1.1 Experimental Design  
The D-optimal DoE that has been generated for the current optimization process comprises three quantitative factors, namely EtOH concentration (0, 50, and 80%; in this case, 0% corresponds to pure water), ultrasound amplitude (30, 40, and 50%), and extraction time (20, 30, and 40 min). Considering the relevant composition of flavone and other flavonoid classes in CS, we have chosen TFC (determined through the AlCl\({}_{3}\) method) as the dependent variable. Furthermore, in order to assess and maximize the potential antioxidant effect of the final extract, we have included an additional dependent variable, namely the TEAC values determined through the ABTS radical assay (Table 1). This dual-dependent variable approach aimed to not only evaluate the flavonoid content but also maximize the potential antioxidant effect of the final extract. By utilizing this comprehensive experimental design, we sought to optimize the extraction process for CS, ensuring both a robust flavonoid profile and potent antioxidant properties in the resulting extract. Figure 1 contains a graphical representation of the statistical parameters for the experimental model that was developed.  
The assessment of model fitting involved the examination of conventional and highly dependable statistical metrics. These metrics encompassed R\({}^{2}\), signifying the goodness of fit by elucidating the proportion of response variation accounted for by the model. Additionally, Q\({}^{2}\), a metric assessing the model's predictive capabilities, was considered to ascertain its performance in making accurate predictions. The evaluation further included the utilization of an ANOVA test and the determination of model reproducibility, a measure derived exclusively from the replicates explicitly defined in the design matrix. As can be seen from Figure 1, these parameters are all notably elevated, indicating a robust and reliable model fit. The substantial R\({}^{2}\) value signifies that a significant portion of the response variation is well-explained by the model, underlining its goodness of fit. Additionally, the elevated Q\({}^{2}\) value reflects the model's proficiency in making accurate predictions. The ANOVA test results further validate the model's statistical significance, while the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Exp. No.** & **EtOH (\%)** & **Amplitude** & **Time** & **TFC** & **ABTS** \\  & & **(\%)** & **(min)** & **(mg QE/g dw)** & **(mg TE/g dw)** \\ \hline
1. & 0 & 30 & 20 & 1.90 & 10.22 \\
2. & 50 & 30 & 20 & 3.82 & 16.00 \\
3. & 0 & 50 & 20 & 2.17 & 10.84 \\
4. & 80 & 50 & 20 & 2.58 & 10.13 \\
5. & 50 & 50 & 20 & 4.15 & 17.77 \\
6. & 80 & 40 & 20 & 2.33 & 8.75 \\
7. & 0 & 30 & 40 & 2.52 & 10.72 \\
8. & 0 & 50 & 40 & 3.25 & 10.79 \\
9. & 80 & 50 & 40 & 2.66 & 10.01 \\
10. & 50 & 40 & 40 & 4.04 & 16.96 \\
11. & 50 & 30 & 30 & 3.69 & 15.69 \\
12. & 80 & 50 & 30 & 2.57 & 9.44 \\
13. & 0 & 40 & 30 & 2.27 & 11.95 \\
14. & 50 & 40 & 30 & 4.28 & 16.74 \\
15. & 50 & 40 & 30 & 3.87 & 16.12 \\
16. & 50 & 40 & 30 & 4.01 & 17.67 \\ \hline \hline \end{tabular} Notes: EtOH represents the concentration of hydroethanolic mix (the value of 0 corresponds to water, \(v/v\)).  
\end{table}
Table 1: Experimental values for responses (TFC and ABTS) obtained during DoE for each of the chosen independent factors (EtOH concentration, amplitude, and time).  
Figure 1: Graphical representation of parameters used for the statistical analysis of the DoE. All parameters are expressed for the two responses (TFC and ABTS).  
demonstrated model reproducibility underscores the reliability of the outcomes derived meticulously from the specified replicates in the design matrix. In summary, the depicted parameters in Figure 1 showcase the model's commendable performance and its capability to effectively capture and predict the observed phenomena.