## 3 Results and Discussion
### Model Fitting
Depending on the substance and the molecules extracted, variations in ethanol may alter solution polarity, which could be extremely important for extraction as it impacts phenolic solubility. On the other hand, high ethanol concentrations can result in pectin dehydration and protein denaturation, which prevent phenolics from diffusing through the matrix of plant material into the solution. Additionally, the right amount of water in the solution may cause the dry matter of plants to swell, expanding the contact surface between the solvent and the solute, thereby having a positive effect on the extraction [28]. To increase the mass transfer rate and cavitation effect, and to increase the solubility of phenolic compounds, solvent extraction is often carried out at relatively high temperatures, but high temperatures may also cause phenolic deterioration [26, 27]. Increased temperature improves the extraction efficiency of phenolics because it increases their solubility and diffusivity, which in turn improves the mass transfer. However, heat may be able to lessen the severity of collapsing in cavitation bubbles by reducing the variations in vapor pressure between the interior and exterior of the bubbles. When the temperature of the extracted material is raised, the surface tension decreases, reducing the shear force of the popping bubbles [29]. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**1 Apigenin**} & \multicolumn{3}{c}{**1 Caffe Acid**} & \multicolumn{3}{c}{**1 Luteolin**} \\ \hline
**Source** & **2 DF** & **F-Value** & \(p\)**-Value** & **DF** & **F-Value** & \(p\)**-Value** & **DF** & **F-Value** & \(p\)**-Value** \\ \hline Model & 7 & 14.56 & 0.000 & 8 & 105.45 & 0.000 & 5 & 15.77 & 0.000 \\ Linear & 3 & 15.40 & 0.000 & 4 & 132.21 & 0.000 & 3 & 21.54 & 0.000 \\ T (C) (X\({}_{1}\)) & 1 & 4.95 & 0.029 & 1 & 37.98 & 0.000 & 1 & 8.54 & 0.005 \\ Time (min) (X\({}_{2}\)) & - & - & - & 1 & 0.16 & 0.688 & - & - & - \\ LS ratio (mL/g) (X\({}_{3}\)) & 1 & 40.36 & 0.000 & 1 & 2.13 & 0.148 & 1 & 53.01 & 0.000 \\ Ethanol (5) (X\({}_{4}\)) & 1 & 0.90 & 0.345 & 1 & 488.56 & 0.000 & 1 & 3.06 & 0.084 \\ Square & 2 & 6.01 & 0.004 & 2 & 130.70 & 0.000 & 1 & 6.82 & 0.011 \\ T (C)+T (C) (X\({}_{1}\)2) & 1 & 4.41 & 0.039 & - & - & - & 1 & 6.82 & 0.011 \\ LSr (mL/g)+LSr (mL/g) (X\({}_{3}\)2) & - & - & - & 1 & 12.29 & 0.001 & - & - & - \\ Ethanol (C)+Ethanol (C) (X\({}_{4}\)2) & 1 & 9.76 & 0.003 & 1 & 261.31 & 0.000 & - & - & - \\ 2-Way Interaction & 2 & 21.83 & 0.000 & 2 & 26.70 & 0.000 & 1 & 7.44 & 0.008 \\ T (C)+Ethanol (C) (X\({}_{1}\)X\({}_{4}\)) & 1 & 36.56 & 0.000 & - & - & - & 1 & 7.44 & 0.008 \\ LSr (mL/g)+Ethanol (C) (X\({}_{2}\)X\({}_{4}\)) & 1 & 7.11 & 0.009 & - & - & - & - & - & - \\ T (C)+T (C)+Sr (mL/g) (X\({}_{1}\)X\({}_{3}\)) & - & - & - & 1 & 49.01 & 0.000 & - & - & - \\ Time (min)+Ethanol (C) (X\({}_{2}\)X\({}_{4}\)) & - & - & - & 1 & 4.39 & 0.040 & - & - & - \\ Error & 73 & & & 72 & & & 75 & & \\ Lack-of-Fit & 67 & 1.03 & 0.550 & 66 & 0.74 & 0.756 & 69 & 0.45 & 0.947 \\ Pure Error & 6 & & & & & & 6 & & \\ Total & 80 & & & 80 & & & 80 & & \\ \hline \end{tabular}  
* \({}^{1}\): Box-Cox data transformation was performed using optimal \(\lambda=0.38\) for apigenin, \(\lambda=0.43\) for caffeic acid, and \(\lambda=2.89\) for luteolin. Reduction of the models was performed backward \(p>0.05\) for eliminating terms, while the term in the final step was added to produce a hierarchical model. \({}^{2}\): DF stands for Degree of freedom.  
\end{table} 
Table 3: Results of the analysis of the variance (ANOVA) for transformed data concerning the fitting of reduced response surface model for USE extraction of apigenin, caffeic acid, and luteolin. Extracting at the lowest possible cost is largely dependent on how quickly the procedure can be completed [26]. Typically, better extraction efficiency may be seen during the first time periods owing to the steep gradient solvent slope, which gradually diminishes with time.