## 3 Results and Discussion
### Optimization of Extraction Conditions Using Response Surface Methodology
\begin{table}
\begin{tabular}{c c c c c c c} \hline \(\mathbf{N_{o}}\) & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{Y_{1}}\) & \(\mathbf{Y_{2}}\) & \(\mathbf{Y_{3}}\) \\  & & & & **(mg GAE/g DW)** & **(mg AE/g DW)** & **(\(\mu\)M TE/g DW)** \\ \hline
4 & \(-1\) & \(+1\) & 0 & 19.07 & 9.46 & 68.40 \\
5 & 0 & \(-1\) & \(-1\) & 16.98 & 7.20 & 95.48 \\
6 & 0 & \(-1\) & \(+1\) & 20.81 & 8.40 & 109.26 \\
7 & 0 & 0 & 0 & 22.35 & 8.66 & 67.28 \\
8 & 0 & 0 & 0 & 22.48 & 9.63 & 66.31 \\
9 & 0 & 0 & 0 & 24.07 & 9.95 & 75.29 \\
10 & 0 & \(+1\) & \(-1\) & 17.08 & 6.85 & 76.10 \\
11 & 0 & \(+1\) & \(+1\) & 17.84 & 10.14 & 106.12 \\
12 & \(+1\) & \(-1\) & 0 & 22.80 & 8.18 & 104.15 \\
13 & \(+1\) & 0 & \(-1\) & 16.29 & 7.30 & 73.13 \\
14 & \(+1\) & 0 & \(+1\) & 22.24 & 10.70 & 124.69 \\
15 & \(+1\) & \(+1\) & 0 & 23.39 & 9.18 & 62.42 \\ \hline \end{tabular} \(X_{1}\): time (minutes), \(X_{2}\): temperature (\({}^{\circ}\)C), \(X_{3}\): solvent-to-material ratio (mL/g). \(Y_{1}\): total phenolic extraction yield (TPC), \(Y_{2}\): total saponin extraction yield (TSC), \(Y_{3}\): DPPH antioxidant capacity.  
\end{table} 
Table 2: _Cont._  
Figure 5: Correlations between predicted and actual values: (**A**) TPC (mg GAE/g DW), (**B**) TSC (mg AE/g DW) and (**C**) DPPH antioxidant activity (\(\mu\)M TE/g DW). \(X_{1}\): time (minutes), \(X_{2}\): temperature (\({}^{\circ}\)C), \(X_{3}\): solvent-to-material ratio (mL/g). \(Y_{1}\): total phenolic extraction yield (TPC), \(Y_{2}\): total saponin extraction yield (TSC), \(Y_{3}\): DPPH antioxidant capacity. \[ \begin{split}\text{Y}_{1}&=-57.29625+0.1353\times\text{X}_{1 }+1.1562\times\text{X}_{2}+1.2885\times\text{X}_{3}-0.001042\times\text{X}_{1} \text{X}_{2}+0.001373\times\text{X}_{1}\text{X}_{3}-0.0038375\times\text{X}_{2} \text{X}_{3}\\ -0.000518\times\text{X}_{1}{}^{2}-0.007908\times\text{X}_{2}{}^{2}-0.00999 6\times\text{X}_{3}{}^{2}\end{split} \]  
\[ \begin{split}\text{Y}_{2}&=-14.505+0.0093\times\text{X}_{ 1}+0.6742\times\text{X}_{2}+0.1042\times\text{X}_{3}-0.000171\times\text{X}_{1} \text{X}_{2}-0.000089\times\text{X}_{1}\text{X}_{3}+0.002612\times\text{X}_{2} \text{X}_{3}+\\ 0.000018\times\text{X}_{1}{}^{2}-0.007629\times\text{X}_{2}{}^{2}-0.00 1257\times\text{X}_{3}{}^{2}\end{split} \]  
\[ \begin{split}\text{Y}_{3}&=528.8575-0.0171\times\text{X}_{ 1}-10.7325\times\text{X}_{2}-6.3518\times\text{X}_{3}-0.008329\times\text{X}_{1 }\text{X}_{2}+0.006352\times\text{X}_{1}\text{X}_{3}+0.020352\times\text{X}_{2} \text{X}_{3}+\\ 0.000614\times\text{X}_{1}{}^{2}+0.094392\times\text{X}_{2}{}^{2}+0.0 44185\times\text{X}_{3}{}^{2}\end{split} \]  
Here, \(\text{Y}_{1}\) is the extraction yield of the total phenolic content (TPC), \(\text{Y}_{2}\) is the extraction yield of the total saponin content (TSC) and \(\text{Y}_{3}\) is the DPPH antioxidant capacity of the obtained extracts; \(\text{X}_{1}\) is the extraction time (minute), \(\text{X}_{2}\) is the extraction temperature (\({}^{\circ}\)C) and \(\text{X}_{3}\) is the solvent-to-material ratio (mL/g). 3.2 Statistical Analysis of Individual and Interacting Impacts of Technological Factors on Output Responses  
Table 3 shows the individual effects of the input factors and their combined impacts on the yields of the TPC, TSC and DPPH antioxidant activity based on the statistical analysis of the estimated coefficients in the second-order regression equations. The effects of a single factor or the interaction between any two input factors on the output responses are considered as proportional influences if the corresponding coefficients are positive; conversely, a negative coefficient indicates an adverse effect of the technological factors on the desired outputs. In addition, the smaller the \(p\)-value, the greater the impact of the input factor, which is considered significant when the \(p\)-value is less than 0.05.