## 3 Results and Discussion
### Optimization of Extraction Conditions Using Response Surface Methodology
Based on the statistical analysis in Table 3, most of the individual effects and combined effects of the input variables on the TPC recovery yield (\(\text{Y}_{1}\)) were statistically significant (\(p<0.05\)), with the exception of the individual effect of temperature (\(\text{X}_{2}\)) and the two combined effects of \(\text{X}_{1}\text{X}_{2}\) and \(\text{X}_{2}\text{X}_{3}\). Among the investigated factors, the effect of the extraction time on the polyphenol extraction efficiency was the greatest (\(p=0.0027\)), followed by the effect of the solvent/material ratio (\(p=0.0398\)) and, finally, the temperature (\(p=0.8302\)). Regarding the statistical analysis of the estimated coefficients in the model predicting the TSC yield (\(\text{Y}_{2}\)), the solvent-to-material ratio had the greatest impact on the TSC yield, followed by the extraction temperature and, finally, the extraction time. Only the solvent  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Regression**} & \multicolumn{2}{c}{\(\text{Y}_{1}\)} & \multicolumn{2}{c}{\(\text{Y}_{2}\)} & \multicolumn{2}{c}{\(\text{Y}_{3}\)} \\ \cline{2-7}  & **Estimated Value** & **Prob \textgreater-to-material ratio (X\({}_{3}\)) showed a statistically significant impact on the TSC yield, and all interactive and quadratic effects of the factors on the TSC yield were not statistically significant (\(p>0.05\)). In addition, the positive coefficients of the extraction temperature and solvent-to-material ratio suggest that the TSC yield tended to be increased when a higher extraction temperature and solvent-to-material ratio were applied. Similar to the effects on the TPC and TSC yields, the solvent-to-material ratio (X\({}_{3}\)) also contributed the highest impact on the DPPH antioxidant activity (Y\({}_{3}\)) of the obtained extracts from the COG rhizomes (\(p=0.0082\)). The extraction temperature (X\({}_{2}\)) also showed a statistically significant effect (\(p=0.0259\)) on the DPPH antioxidant activity but that of the extraction time was not significant (\(p=0.1576\)). The negative coefficient of X\({}_{2}\) indicates that the obtained antioxidant activity decreases as the extraction temperature increases within the range of 40-60 \({}^{\circ}\)C. Conversely, the antioxidant activity increases along with a larger used amount of the ethanol solvent. The interactive influences of the input factors on the desired responses are also visualized in the response surface plots in Figure 6. The plots in Figure 6A\({}_{1}\),A\({}_{2}\) show that the TPC extraction efficiency increases with a longer extraction time and higher solvent-to-material ratio but the TPC shows a downward trend with the rise in the temperature. The changing trends in the TPC yield in the response surface plots are consistent with the values of the influence coefficients and the corresponding combined effects of the technological factors analyzed in Table 3.  
Figure 6B\({}_{1}\) shows that the TSC yield reached the highest level (over 9.5 mg AE/g DW) in the temperature range of 50-58 \({}^{\circ}\)C combined with an extraction time of 60-110 min. However, further extending the extraction time caused a decrease in the recovery of TSC. The clearly increasing trend of the TSC yield with the increase in the solvent-to-material ratio observed in Figure 6B\({}_{2}\) confirms the significant impact of this parameter, as analyzed in Table 3.  
Similar to the plots for the TSC, it can be observed that the obtained antioxidant activity was higher as the solvent-to-material ratio increased and the temperature decreased. The upward curves, along with the increase in time and the solvent-to-material ratio, clearly demonstrate the positive relationship between the antioxidant activity and these factors, while the inverse relationship between the temperature and DPPH antioxidant activity is illustrated by the downward curves.