## 3 Results and Discussion
### Process Parameter Optimization Using Response Surface Methodology  
Table 3 presents the experimental matrix for the three-variable, three-level Box-Behnken design, which assesses how temperature (\({}^{\circ}\)C), time (min), and the liquid/solid ratio (\(v/w\)) influence TPC and AA in \(L\). _japonica_ flower extracts. The experimental matrix showed notable differences in TPC, ranging from 58.38 to 75.94 mg/g and antioxidant activity (AA) from 204.90 to 451.00 umol of Trolox/g across the tested parameters. The highest TPC (75.94 mg/g) and AA (451.00 umol/g) were obtained under specific conditions: TPC reached its maximum at 80 \({}^{\circ}\)C for 30 min with a 15 \(v/w\) ratio (Exp. 8), while AA peaked at 60 \({}^{\circ}\)C for 10 min with the same ratio (Exp. 11), emphasizing the critical importance of solvent accessibility during extended heating. The Pareto charts (Figure 7) highlight the standardized effects of individual factors and their interactions on the TPC and antioxidant activity. The alignment between the experimental model and the observed total phenolic content (TPC) and antioxidant activity was assessed for the linear-quadratic model (Tables S1-S4, Figure S1) using the coefficient of determination, known as R\({}^{2}\). In this context, R\({}^{2}\) values of 0.9981 and 0.9985 were obtained, respectively. After adjustment, the R\({}^{2}\)Adj values dropped to 0.9870 and 0.9900; nevertheless, these figures still indicated a strong fit of the model with the collected data. For total \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Exp. No.**} & \multirow{2}{*}{**Temperature (\({}^{\circ}\)C)**} & \multirow{2}{*}{**Time (min)**} & \multirow{2}{*}{**Liquid/Solid Ratio** (\(v/w\))**} & \multirow{2}{*}{**TPC \({}^{\ast}\)**} & \multirow{2}{*}{**TPC (\({}^{\ast}\)**)**} & \multirow{2}{*}{**AA**} & \multirow{2}{*}{**AA (Approximated)**} \\  & & & & & & & \\ \hline
1 & 40 & 10 & 10 & \(64.57\pm 6.22\) & 64.57 & 278.49 \(\pm\) 21.95 & 278.49 \\
2 & 80 & 10 & 10 & \(59.51\pm 5.66\) & 59.51 & 280.60 \(\pm\) 11.55 & 280.60 \\
3 & 40 & 50 & 10 & \(64.97\pm 6.34\) & 64.97 & 284.93 \(\pm\) 8.72 & 284.93 \\
4 & 80 & 50 & 10 & \(68.04\pm 5.37\) & 68.04 & 326.43 \(\pm\) 28.55 & 326.43 \\
5 & 40 & 30 & 5 & \(62.42\pm 4.41\) & 62.42 & 204.90 \(\pm\) 23.93 & 204.90 \\
6 & 80 & 30 & 5 & \(66.03\pm 1.43\) & 66.03 & 248.81 \(\pm\) 2.30 & 248.81 \\
7 & 40 & 30 & 15 & \(68.43\pm 3.96\) & 68.43 & 348.62 \(\pm\) 20.79 & 348.62 \\
8 & 80 & 30 & 15 & \(75.94\pm 2.94\) & 75.94 & 418.29 \(\pm\) 29.32 & 418.29 \\
9 & 60 & 10 & 5 & \(58.38\pm 2.17\) & 58.38 & 240.76 \(\pm\) 4.55 & 240.76 \\
10 & 60 & 50 & 5 & \(69.31\pm 5.70\) & 69.31 & 248.37 \(\pm\) 2.51 & 248.37 \\
11 & 60 & 10 & 15 & \(74.75\pm 2.66\) & 74.75 & 451.00 \(\pm\) 9.46 & 451.00 \\
12 & 60 & 50 & 15 & \(72.95\pm 6.66\) & 72.95 & 345.27 \(\pm\) 19.99 & 345.27 \\
13 & 60 & 30 & 10 & \(69.46\pm 4.82\) & 69.96 & 328.53 \(\pm\) 8.59 & 336.09 \\
14 & 60 & 30 & 10 & \(69.81\pm 7.18\) & 69.96 & 338.20 \(\pm\) 13.93 & 336.09 \\
15 & 60 & 30 & 10 & \(70.60\pm 2.29\) & 69.96 & 341.54 \(\pm\) 30.97 & 336.09 \\ \hline \hline \end{tabular} \({}^{\ast}\) TPC—total phenolic content (mg of chlorogenic acid/g d.m.), AA—antioxidant activity (umol of Trolox/g d.m.).  
\end{table} 
Table 3: Experimental matrix for the three-variable Box–Behnken design with the total phenolic content (mg of chlorogenic acid/g d.m.) and antioxidant activity (μmol of Trolox/g d.m.) in \(L\). _japonica_ flower extracts. -phenolic content, the liquid/solid ratio (linear term, 19.850) was identified as the key factor, having a significant positive influence on TPC. Following this, the quadratic effect of temperature (10.446) and the linear effect of incubation time (10.338) were observed. Importantly, interactions among these factors also had significant impacts. The antagonistic interaction between the linear effects of incubation time (2 L) and the liquid/solid ratio (3 L) (2 L vs. 3 L: \(-\)10.888) suggested that increasing both parameters simultaneously may lower TPC.