## 3 Results and Discussion
### Optimization of Extraction Conditions Using Response Surface Methodology
#### 3.3.3 Verification of Optimal Values through Experimental Validation  
Based on the established optimization models, the optimal values of the extraction conditions for extraction were determined as 178 min, 45 \({}^{\circ}\)C and 68 mL/g for TPC; 60 min, 57 \({}^{\circ}\)C and 80 mL/g for TSC; and 180 min, 40 \({}^{\circ}\)C and 80 mL/g for the DPPH antioxidant activity. These optimal values were validated through practical experiments and the obtained experimental results are presented in Table 4.  
The validation data indicate that, after extraction under the optimal conditions for saponins (60 min, 57 \({}^{\circ}\)C with a ratio of 80 mL/g), the actual recovery yield of TSC was 11.33 mg AE/g DW. Under practical extraction conditions of 178 min and 45 \({}^{\circ}\)C with a ratio of 80 mL/g, the TPC yield was 23.58 mg GAE/g DW (the predicted value was 24.32 mg GAE/g DW), and the experimentally obtained antioxidant activity was 133.45 uM TE/g DW compared to the predicted value of 138.52 uM TE/g DW. Although there are variations between the actual experimental values and the corresponding predicted values, these differences are not statistically significant (Table 4). The consistency of the actual values and the predicted values suggests that the optimization models used to assess the impact and determine the optimal extraction conditions for the recovery of active compounds and the antioxidant activity are suitable for the prediction of the recovery yields of TPC, TSC and DPPH antioxidant activity from COG rhizomes.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Output Responses** & **Optimal Conditions** & **Predicted Values** & **Actual Values** \\ \hline TPC & 178 min & & \\ (mg GAE/g DW) & 45 \({}^{\circ}\)C & 24.32 \(\pm\) 2.15 \({}^{\text{b}}\) & 23.58 \(\pm\) 2.24 \({}^{\text{b}}\) \\  & 68 mL/g & & \\ \hline TSC & 60 min & & \\ (mg AE/g DW) & 57 \({}^{\circ}\)C & 10.95 \(\pm\) 1.72 \({}^{\text{a}}\) & 11.33 \(\pm\) 1.20 \({}^{\text{a}}\) \\  & 80 mL/g & & \\ \hline \multirow{2}{*}{Antioxidant activity (\(\mu\)M TE/g DW)} & 180 min & & \\ \cline{1-1}  & 40 \({}^{\circ}\)C & 138.52 \(\pm\) 29.49 \({}^{\text{c}}\) & 133.45 \(\pm\) 19.95 \({}^{\text{c}}\) \\ \cline{1-1}  & 80 mL/g & & \\ \hline \hline \end{tabular} Different letters show statistically significant differences between actual values and predicted values (\(p<0.05\)).  
\end{table}
Table 4: Results of the validation experiments using the predicted optimal extraction conditions.  
Figure 6: Interactive effects of input variables on the extraction yields of TPC (**A\({}_{\text{1}}\)**–**A\({}_{\text{3}}\)**), TSC (**B\({}_{\text{1}}\)**–**B\({}_{\text{3}}\)**) and DPPH antioxidant activity (**C\({}_{\text{1}}\)**–**C\({}_{\text{3}}\)**) from COG rhizomes. X\({}_{\text{1}}\): time (minutes), X\({}_{\text{2}}\): temperature (\({}^{\text{c}}\)C), X\({}_{\text{3}}\): solvent-to-material ratio (mL/g).  
The total saponin content and total phenolic content in the initial material were 22.85 mg AE/g DW and 36.59 mg GAE/g DW, respectively. Thus, the recovery efficiency for TSC was determined to be 49.5%, and that for TPC was 64.4%. A study by [PERSON] et al. (2018) [37] reported the TPC extraction efficiency using alcohol from orange peel to be 35%, while another study by [PERSON] et al. (2015) [38] using alcohol achieved efficiency of 87%. Regarding saponin extraction, a study by [PERSON] et al. (2022) [39] reported TSC recovery efficiency of 14.5% from _Polyscias fruticosa_ leaves. The optimal extraction time for TPC from COG rhizomes in this study is longer than the optimal extraction duration of TPC from limau purut peel (126 min) [21] and for TPC from mashua tubers (60 min) [24]. However, the optimal time for the recovery of TSC in this study is shorter than the time for TSC extraction from _Polyscias fruticosa_ roots [29]. The variations in both the optimal conditions and the extraction yields may depend on the properties of the different raw materials used in the studies.