## 3 Results and Discussion
### Model Fitting
Other than the linear source, quadratic terms indicated statistically significant effects on the extraction of the studied specific phenolic compounds. Quadratic term of temperature (\(X_{1}\)\({}^{2}\)) indicated statistically significant effects on the models of apigenin and luteolin (\(p<0.05\)). Ratio of solvent to dry parsley (\(X_{3}\)\({}^{2}\)) indicated statistically significant effects on the model of caffeic acid (\(p<0.05\)), and quadratic term of ethanol concentration (\(X_{4}\)\({}^{2}\)) indicated statistically significant effects on the models of apigenin and caffeic acid (\(p<0.05\)). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Independent Factors**} \\ \cline{2-9}
**Run** & \(X_{1}\) & \(X_{2}\) & \(X_{3}\) & \(X_{4}\) & \(X_{4}\) & **Luteolin** & **Caffeic Acid** & **Apigenin/(ug/g)** \\  & **Temperature** (\({}^{\circ}\)C) & **Time (min)** & **Ethanol (\% \%/v)** & \({}^{1}\) LS Ratio** & **(ug/g)** & **Lifeic Acid** & **Apigenin/(ug/g)** \\  & & & & **mL/g Parsley** & & & \\ \hline
60 & 47.5 (0) & 10 (\(-\)1) & 40 (\(+\)1) & 60 & 19.4 & 2.2 & 10.1 \\
61 & 70 (\(+\)1) & 10 (\(-\)1) & 20 (0) & 60 & 21.0 & 2.4 & 10.0 \\
62 & 70 (\(+\)1) & 25 (0) & 0 (\(-\)1) & 60 & 11.4 & 13.6 & 4.3 \\
63 & 47.5 (0) & 25 (0) & 20 (0) & 60 & 20.4 & 3.3 & 10.3 \\
64 & 47.5 (0) & 10 (\(-\)1) & 20 (0) & 100 & 15.3 & 2.1 & 10.0 \\
65 & 25 (\(-\)1) & 25 (0) & 0 (\(-\)1) & 60 & 18.9 & 10.9 & 21.0 \\
66 & 47.5 (0) & 40 (\(+\)1) & 40 (\(+\)1) & 60 & 19.3 & 2.0 & 9.7 \\
67 & 47.5 (0) & 40 (\(+\)1) & 40 (\(+\)1) & 60 & 19.0 & 1.7 & 9.9 \\
68 & 47.5 (0) & 25 (0) & 20 (0) & 60 & 19.8 & 1.2 & 8.3 \\
69 & 70 (\(+\)1) & 25 (0) & 40 (\(+\)1) & 60 & 21.0 & 1.4 & 9.1 \\
70 & 47.5 (0) & 40 (\(+\)1) & 20 (0) & 100 & 19.9 & 2.5 & 9.6 \\
71 & 25 (\(-\)1) & 25 (0) & 20 (0) & 20 & 15.3 & 1.2 & 7.5 \\
72 & 47.5 (0) & 25 (0) & 20 (0) & 60 & 17.6 & 2.6 & 8.5 \\
73 & 70 (\(+\)1) & 40 (\(+\)1) & 20 (0) & 60 & 21.3 & 2.4 & 10.3 \\
74 & 25 (\(-\)1) & 25 (0) & 0 (\(-\)1) & 60 & 19.1 & 10.3 & 20.1 \\
75 & 25 (\(-\)1) & 25 (0) & 40 (\(+\)1) & 60 & 18.9 & 1.1 & 9.7 \\
76 & 47.5 (0) & 40 (\(+\)1) & 0 (\(-\)1) & 60 & 20.6 & 16.0 & 13.1 \\
77 & 47.5 (0) & 40 (\(+\)1) & 40 (\(+\)1) & 60 & 19.0 & 1.9 & 9.7 \\
78 & 47.5 (0) & 25 (0) & 40 (\(+\)1) & 100 & 22.6 & 2.3 & 13.5 \\
79 & 25 (\(-\)1) & 25 (0) & 20 (0) & 100 & 20.5 & 2.4 & 11.2 \\
80 & 47.5 (0) & 10 (\(-\)1) & 0 (\(-\)1) & 60 & 19.2 & 11.2 & 11.8 \\
81 & 47.5 (0) & 25 (0) & 40 (\(+\)1) & 20 & 14.9 & 1.2 & 7.3 \\ \hline \hline \end{tabular} \({}^{1}\) LS ratio: Liquid of solvent to Solid of dried parsley sample ratio; \({}^{2}\): ug of lutein of caffeic acid or apigenin per g of dried parsley.  
\end{table} 
Table 2: _Cont._Moreover, concerning the interaction coefficient that exert statistically significant effects on the models, the interaction of temperature and ethanol concentration (X\({}_{1}\)X\({}_{4}\)) showed a statistically significant effect on the model of apigenin and luteolin, the interaction of ratio of solvent to dry parsley with ethanol concentration showed a statistically significant effect on the model of apigenin (\(p<0.05\)) while the interaction of temperature with ratio of solvent to dry parsley (X\({}_{1}\)X\({}_{3}\)) and that of time with ethanol concentration (X\({}_{2}\)X\({}_{4}\)) showed a statistically significant effect on the model of caffeic acid (\(p<0.05\)). The viscosity of the mixture of solvents and studied sample during extraction is affected by the solvent to sample ratio (LSr), which alters the effectiveness of ultrasound assisted extraction. This mixture has a high viscosity when LSr is low, which could prevent the cavitation effect because the negative pressure in the region of rarefaction needs to be greater than the strong cohesiveness between particles. In contrast, when the LSr is high, the medium's decreased viscosity might boost cavitation, resulting in improved extraction up to a point at which a more significant cavitation may cause the extracted molecules to disintegrate [26, 27].