## 3 Results and Discussion
### Optimization of UEAATPE  
As shown in Table 3, the test resulted in 29 uncontrolled runs. The correlation between the response and the independent variable can be visualized with a 3D surface plot. Figure 2 indicates the influence of the ethanol concentration %, (X1), ammonium sulfate concentration %, (X2), liquid-solid ratio mL/g, (X3), and ultrasound time min, (X4), on the yield of total flavonoids and their interaction. Furthermore, it is possible to predict the optimal value of the response and the corresponding experimental conditions through the F value (>7.84) and \(p\) value (<0.01), as shown in Table 4. This result shows that the model can describe the total flavonoid yield of UEAATPE well. The equation of the response variables and independent variables is as follows:  
\[ \begin{split} Y=59.60-0.03\text{X}_{1}+0.48\text{X}_{2}& -4.66\text{X}_{3}-1.63\text{X}_{4}+1.18\text{X}_{1}\text{X}_{2}+2.95 \text{X}_{1}\text{X}_{3}+3.24\text{X}_{1}\text{X}_{4}+2.00\text{X}_{2}\text{ X}_{3}-0.59\text{X}_{2}\text{X}_{4}-\\ &\text{4.48}\text{X}_{3}\text{X}_{4}-5.19\text{X}_{1}{}^{2}-3. 37\text{X}_{2}{}^{2}-9.60\text{X}_{3}{}^{2}-8.41\text{X}_{4}{}^{2}\end{split}  \tag{2}\]  
where \(Y\) represents yields of total flavonoids (mg/g); X1, X2, X3, and X4, respectively, represent the ethanol concentration (%), ammonium sulfate concentration (%), liquid-solid ratio (mL/g), and ultrasonic time (min). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Runs**} & \multicolumn{5}{c}{**Independent Variables**} \\ \cline{2-6}  & **Ethanol** & **Ammonium Sulfate** & **Liquid–Solid** & **Ultrasonic Time** & **Yield of Total Flavonoids** \\  & **Concentration** & **Concentration** & **Ratio** & **(X\({}_{4}\), min)** & **(mg/g)** \\  & **(X\({}_{1}\), \%)** & **(X\({}_{2}\), \%)** & **(X\({}_{3}\), mL/g)** & **(X\({}_{4}\), min)** & **(mg/g)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 3: Experimental data and total flavonoid extraction analyzed by the Box–Behnken approach. According to appropriate extraction conditions (independent variables) and actual operation analysis by Design Expert software, all these conditions were modified as follows: 38% (\(w/w\)) ethanol/18% (\(w/w\)) ammonium sulfate; liquid-solid ratio of 20:1 mL/g, and ultrasonic time of 30 min. Under these conditions, it was possible to obtain 60.22 mg/g flavonoids by UEAATPE. According to the RSM prediction model, the above experimental value matches the fitted value (RSD < 1.72%). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **Mean Square** & **F-Value** & _p-Value_ & **Significance** \\ \hline Model & \(1.40\times 10^{3}\) & 100.32 & 28.36 & \textless{}0.0001 & significant \\ X\({}_{1}\) & \(1.05\times 10^{-2}\) & \(1.05\times 10^{-2}\) & \(2.97\times 10^{-3}\) & 0.9573 & not significant \\ X\({}_{2}\) & 2.81 & 2.81 & 0.79 & 0.3882 & not significant \\ X\({}_{3}\) & 260.89 & 260.89 & 73.76 & \textless{}0.0001 & significant \\ X\({}_{4}\) & 31.69 & 31.69 & 8.96 & 0.0097 & not significant \\ X\({}_{1}\) X\({}_{2}\) & 5.57 & 5.57 & 1.58 & 0.2301 & not significant \\ X\({}_{1}\) X\({}_{3}\) & 34.76 & 34.76 & 9.83 & 0.0073 & not significant \\ X\({}_{1}\) X\({}_{4}\) & 42.11 & 42.11 & 11.91 & 0.0039 & not significant \\ X\({}_{2}\) X\({}_{3}\) & 16.00 & 16.00 & 4.52 & 0.0517 & not significant \\ X\({}_{2}\) X\({}_{4}\) & 1.44 & 1.44 & 0.41 & 0.5342 & not significant \\ X\({}_{3}\) X\({}_{4}\) & 80.28 & 80.28 & 22.70 & 0.0003 & not significant \\ X\({}_{1}\)\({}^{2}\) & 175.31 & \(1.75\times 10^{2}\) & 49.57 & \textless{}0.0001 & significant \\ X\({}_{2}\)\({}^{2}\) & 73.68 & 73.68 & 20.83 & 0.0004 & not significant \\ X\({}_{3}\)\({}^{2}\) & 598.54 & \(5.99\times 10^{2}\) & \(1.70\times 10^{2}\) & \textless{}0.0001 & significant \\ X\({}_{4}\)\({}^{2}\) & 459.01 & \(4.60\times 10^{2}\) & \(1.30\times 10^{2}\) & \textless{}0.0001 & significant \\ Lack of Fit & 44.82 & 4.48 & 3.82 & 0.1042 & not significant \\ R\({}^{2}\) & & & 0.9659 & & \\ \hline \hline \end{tabular}
\end{table}