## 3 Results
### RSM for Optimization of A. tegmentosum
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & \
\begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **DF** &
\begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Value** & \(p\)**-Value** \\ \hline P & 17544.67 & 9 & 1949.41 & 23.79 & \textless{}0.0001 \\ X\({}_{1}\) & 1195.25 & 1 & 1195.25 & 14.58 & 0.0034 \\ X\({}_{2}\) & 718.95 & 1 & 718.95 & 8.77 & 0.0142 \\ X\({}_{3}\) & 11653.01 & 1 & 11653.01 & 142.18 & \textless{}0.0001 \\ X\({}_{1}\times X_{2}\) & 91.64 & 1 & 91.64 & 1.12 & 0.3152 \\ X\({}_{1}\times X_{3}\) & 990.69 & 1 & 990.69 & 12.09 & 0.006 \\ X\({}_{2}\times X_{3}\) & 163.74 & 1 & 163.74 & 2 & 0.1879 \\ X\({}_{1}\)\({}^{2}\) & 2454.68 & 1 & 2454.68 & 29.95 & 0.0003 \\ X\({}_{2}\)\({}^{2}\) & 448.25 & 1 & 448.25 & 5.47 & 0.0414 \\ X\({}_{3}\)\({}^{2}\) & 90.49 & 1 & 90.49 & 1.1 & 0.3181 \\ Residual error & 819.58 & 10 & 81.96 & & \\ Lack of fit & 518.92 & 5 & 103.78 & 1.73 & 0.2819 \\ Pure error & 300.66 & 5 & 60.13 & & \\ Correlation & 18364.24 & 19 & & & \\ total & & & & & \\ \hline \hline \end{tabular} \({}^{2}\): 0.9554; adjusted R\({}^{2}\): 0.9152; predicted R\({}^{2}\): 0.7548; X\({}_{1}\), extraction temperature; X\({}_{2}\), extraction time; X\({}_{3}\), solvent-to-solid ratio.  
\end{table} 
Table 5: Analysis of variance and coefficient estimation for a second-order model using the extract of _Acer legumtosum_. Figure 3: _Cont_. Figure 3: Response surface and contour plots exhibit the effect of hydrothermal extraction temperature, time, and solvent-to-solid ratio on the total phenolic contents (TPC) from _Acer legmentosum_. **(A/B)** Effect of extraction temperature and extraction time on the TPC as **(A)** a 3D response surface graph and **(B)** a contour plot. **(C/D)** Effect of extraction temperature and solvent-to-solid ratio on the TPC as **(C)** a 3D response surface graph and **(D)** a contour plot. **(E/F)** Effect of extraction time and solvent-to-solid ratio on the TPC as **(E)** a 3D response surface graph and **(F)** a contour plot. The maximal point of the TPC was not determined in the CCD range since the highest point existed under 90 \({}^{\circ}\)C. However, the highest point of the TPC was observed under the tested conditions (under 7.36 h; Figure 3A/B). The peaks of the solvent-to-solid ratio and the extraction time were not within the testable range; however, as the extraction time and the solvent-to-solid ratio increased, the probability of TPC also increased. The expected maximal point was 228.52 mg GAE/g, with a solvent-to-solid ratio of 150 at 90 \({}^{\circ}\)C. As the extraction time and the solvent-to-solid ratio increased, the TPC also increased; therefore, it was not possible to find the maximum point within the CCD measurement range. The highest TPC is expected under the following conditions: 239.42 mg GAE/g, a solvent-to-solid ratio of 150, and an extraction time of 6 h.  
The DPPH activity is given in the following equation:  
\[\begin{split}\text{\text{\text{\text{\text{\text{\text{\text{ \text{\text{\text{\text{\text{\text{\  
Figure 4: _Cont._  
Figure 5: _Cont._  
Among the extraction conditions of _A. tegmentosum_, the extraction temperature (X\({}_{1}\), \(p\) < 0.001; X\({}_{1}\)\({}^{2}\), \(p\) < 0.001) and the solvent-to-solid ratio (X\({}_{3}\), \(p\) < 0.001; X\({}_{1}\)\({}^{2}\), \(p\) = 0.072) significantly affected DPPH activity (Table 6). Therefore, both the extraction temperature and the solvent-to-solid ratio were included in our experimental conditions. Extraction temperature and solvent-to-solid ratio had significant effects on the DPPH activity of _A. tegmentosum_ (X\({}_{1}\)\(\times\) X\({}_{3}\), \(p\) = 0.002; Table 6). Despite the optimal extract temperature for DPPH activity being between 80-90 \({}^{\circ}\)C, an increased solvent-to-solid ratio and increased extraction time led to the best DPPH activity under the CCD conditions (24.99%).