## 3 Results
### Model Fitting  
Response surface methodology (RSM) can be used to investigate and optimize multi-variable applications by identifying the correlation between the responses of antioxidant compounds, as well as DPPH scavenging activity, and the independent variables of MAE factors. A face-centered central composite design (FCCD) was employed to investigate and optimize the effects of MAE factors, including the MAE time, microwave power, and solid-to-liquid ratio, to yield a polyphenol-rich crude extract from cinnamon leaves (PCL) with maximum yield, TPC, TPC, and DPPH activity. Twenty experimental designs for RSM were constructed using an FCCD with six center points. The experiment values obtained ranged from 14.26 \(\pm\) 0.37 to 20.22 \(\pm\) 0.52% for antioxidant yield, 16.43 \(\pm\) 0.21 to 23.75 \(\pm\) 0.56 mg GAE/g for TPC, 9.37 \(\pm\) 0.46 to 14.68 \(\pm\) 0.72 mg QE/g for TPC, and 80.02 \(\pm\) 3.90 to 120.12 \(\pm\) 7.25 ug/mL for IC\({}_{50}\) of DPPH scavenging activity (Table 2). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Run** & **X\({}_{1}\)** & **X\({}_{2}\)** & **X\({}_{3}\)** & **Y\({}_{1}\)** & **Y\({}_{2}\)** & **Y\({}_{3}\)** & **Y\({}_{4}\)** \\  & & & **(\%)** & **(mg GAE/g)** & **(mg QE/g)** & **(ug/mL)** \\ \hline
**6** & 1 (25) & \(-\)1 (70) & 1 (1:300) & 19.96 \(\pm\) 0.69 & 18.00 \(\pm\) 0.02 & 10.43 \(\pm\) 0.18 & 105.47 \(\pm\) 0.45 \\ \hline
**17** & 0 (15) & 0 (210) & 0 (1:180) & 17.06 \(\pm\) 0.86 & 22.42 \(\pm\) 0.94 & 13.65 \(\pm\) 0.35 & 95.65 \(\pm\) 12.16 \\ \hline
**14** & 0 (15) & 0 (210) & 1 (1:300) & 20.22 \(\pm\) 0.52 & 20.25 \(\pm\) 0.28 & 12.01 \(\pm\) 0.88 & 95.75 \(\pm\) 11.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The FCCD of the MAE experiment and response data. Based on ANOVA (Table 3), the data for antioxidant yield, TPC, TFC, and DPPH in all four models were remarkably significant (\(p\) < 0.05). The respective values of R\({}^{2}\) and Adj-R\({}^{2}\) for antioxidant yield (0.9497 and 0.9044, respectively), TPC (0.9494 and 0.9038, respectively), TFC (0.9199 and 0.8479, respectively), and IC\({}_{50}\) of DPPH (0.9570 and 0.9183, respectively) were all close to 1, indicating that the models were substantial and reasonable. In terms of pure error, the lack-of-fit analysis was not significant (\(p\) > 0.05), indicating that the quadratic model was not statistically significant for the antioxidant yield, TPC, TFC, and DPPH assay. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Run**} & \multirow{2}{*}{**X\({}_{1}\)**} & \multirow{2}{*}{**X\({}_{2}\)**} & \multirow{2}{*}{**X\({}_{3}\)**} & \multirow{2}{*}{**Y\({}_{1}\)**} & \multirow{2}{*}{**Y\({}_{2}\)**} & \multirow{2}{*}{**Y\({}_{3}\)**} & \multirow{2}{*}{**Y\({}_{4}\)**} \\  & & & & & & & & \\ \hline  
\hline \end{tabular}
\end{table} 
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multicolumn{2}{c}{**Y\({}_{1}\)–Yield**} & \multicolumn{2}{c}{**Y\({}_{2}\)—TPC**} & \multicolumn{2}{c}{**Y\({}_{3}\)—TFC**} & \multicolumn{2}{c}{**Y\({}_{4}\)—IC\({}_{50}\)**} \\ \cline{2-9}  & \(\mathbf{F}\)**-Value** & \(\mathbf{p}\)**-Value** & \(\mathbf{F}\)**-Value** & \(\mathbf{p}\)**-Value** & \(\mathbf{F}\)**-Value** & \(\mathbf{p}\)**-Value** & \(\mathbf{F}\)**-Value** & \(\mathbf{p}\)**-Value** \\ \hline Model & 20.97 & 0.000 \({}^{\text{a}}\) & 20.83 & 0.000 \({}^{\text{a}}\) & 12.77 & 0.000 \({}^{\text{a}}\) &Yield: The MAE time (X\({}_{1}\)), microwave power (X\({}_{2}\)), and solid-liquid ratio (X\({}_{3}\)) were significant (\(p<0.05\)). The quadratic effect (X\({}_{2}\)\({}^{2}\)) was also significant (\(p<0.05\)). The second-order polynomial equation for yield is shown as Equation (4). \[\mathrm{Y_{1}=17.760+0.859X_{1}+0.493X_{2}+2.100X_{3}-0.922X_{2}{}^{2}-1.040X_{ 1}X_{2}} \tag{4}\]  
Figure 3a-c show the 3D response surface plots that illustrate the impact of the MAE independent factors and their interactions on antioxidant yield.