## 3 Results and Discussion
### Model Fitting  
The optimization of the extraction procedure by ultrasound assisted extraction (UAE) of luteolin, caffeic acid, and apigenin from parsley was carried out by response surface methodology. More specifically, a Box-Behnken design was used to find out the combined effect between the factors of extraction temperature (25, 47.5, and 70 \({}^{\circ}\)C) (X\({}_{1}\)), extraction time (10, 25, and 40 min) (X\({}_{2}\)), ethanol concentration (0, 20, and 40% \(v/v\)) (X\({}_{3}\)) and solvent to dry parsley ratio (20, 60, 100 mL/g) (X\({}_{4}\)) on the extractability of luteolin, caffeic acid and apigenin as quantified with the use of a HPLC PDA methodology. The experimental design matrix produced was based on BBD consisted of 27 combinations, including three center points, and was carried out in triplicate, resulting in a total of 81 runs that were conducted in a randomizing run order to reduce impact of variation on response values owing to the external factors. Results obtained from the USE of parsley are shown in Table 2. The experimental values varied from 7.8 to 24.8 \(\mu\) luteolin/g dry parsley, 0.42 to 16.1 \(\mu\)g caffeic acid/g dry parsley, and 4.3 to 21.0 \(\mu\)g apigenin/g dry parsley (Table 2). The fitting of the full quadratic approximation of the BBD response surface model was estimated by the analysis of variance (ANOVA). The F-values and relevant \(p\)-values were used to examine the significance of each source of terms, that is, linear, two-factor interaction, and quadratic, and the regression coefficients of the fitted models. Terms with \(p\)-value lower than 0.05 at the 95% confidence interval were identified as statistically significant. A multiple regression analysis was employed to fit the response value and the experiment data. Model reduction was carried out to further refine the full quadratic response surface model by clicking off the insignificant terms with a significance level greater than 5% (\(p>\) 0.05). To further refine the full quadratic response surface model, because of the  
Figure 3: Mass spectrum of parsley extract samples at negative ionization were the precursor ion of apigenin—\(m/z\) 269 (a), caffeic acid—\(m/z\) 185 (b), and luteolin—\(m/z\) 285 (c) are obtained. existence of non-significance effect of factors, transformation of the data and backward elimination of terms was performed. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Independent Factors**} \\ \cline{2-8}
**Run** & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{X_{4}}\) & **Luteolin** & **Caffeic Acid** & **Apigenin/(ug/g)** \\  & **Temperature (\({}^{\circ}\)C)** & **Time (min)** & **Ethanol (\% \%/\(v\))** & **1 LS Ratio** & **(ug/g) 2** & **2.2** & 7.1 \\
2 & 25 (\(-  
Results of the analysis of variance (ANOVA), after data transformation and model reduction, were used to determine the degree to which the quadratic approximation of the BBD response surface reduced models fitted the data are presented in Table 3.  
The ANOVA results (Table 3) suggested that the refined second-order models were statistically significant for apigenin, caffeic acid, and luteolin, since the F-values of 14.56, 105.45, and 15.77 have a zero percent chance to occur due to noise. Table 3 also indicates the linear, quadratic, and interaction terms that are significant for the models concerning the studied phenolic molecules. The linear terms temperature (\(X_{1}\)) showed significant effects in all three models for apigenin, caffeic acid and luteolin. Time (\(X_{2}\)) did not show significant effect in any model (\(p>0.05\)). Ratio of solvent to dry parsley (\(X_{3}\)) showed significant effect only in the models of apigenin and luteolin (\(p<0.05\)). Finally, the linear term of ethanol showed significant effect only in the model of caffeic acid (\(p<0.05\)). Temperature, time, ratio of solvent to sample, and ethanol as solvent have been previously shown to be factors of interest when optimization of phenolic compound green extraction is studied [25; 26].