## 3 Results and Discussion
### DPPH Assay  
Figure 2 shows the dependence of the DPPH assay value on time, ultrasound amplitude, and solvent concentration for extracts obtained in extraction vessels with diameters of 35 and 25 mm. Figure 2: Dependence of DPPH on time, ultrasound amplitude, and solvent concentration for extracts obtained in vessels with diameters of **(a)** 35 mm, **(b)** 25 mm. The shapes of the curves shown in Figure 2a,b indicate that the solvent concentration has reached an inflection point, which means that further increases in this variable will result in a decrease in the DPPH value. For both vessels, the value of DPPH increases with time. For the vessel with a diameter of 35 mm, increasing the ultrasound amplitude translates into an increase in the DPPH value up to a certain point, and then a decrease in the value (Figure 2a). In the case of the vessel with a diameter of 25 mm, a non-linear increase in the value of the DPPH assay occurs with increasing ultrasound amplitude. Increasing the time translates into a linear increase in the DPPH value for both extraction vessels. In order to confirm the significance of the effect of the examined input variables on the value of the DPPH assay, a statistical analysis was performed. The findings of this analysis are displayed in Tables 4 and 5. The results of the analysis of variance showed that for both models, the linear effects of all variables and the quadratic amplitudes of ultrasound and solvent concentration turned out to be statistically significant. In the case of extraction in the vessel with a diameter of 35 mm, the greatest influence on the value of the DPPH assay was the ultrasound amplitude, and the smallest influence was the time. In the case of the vessel with a diameter of 25 mm, the concentration of the solvent had the greatest influence, and the time had the least. Both equations showed statistical significance (\(p<0.0001\)). Additionally, the lack of fit of the models is statistically insignificant (\(p=0.4170\) and \(p=0.1717\)), which indicates the correct validation of the model. The high values of the determination coefficient (0.9383 and 0.9708) and the adjusted coefficient (0.8921 and 0.9546) indicate a strong correlation between  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Source** & **Sum of Squares** & **DF** & **Mean Square** & **F-Value** & **\(p\)-Value** \\ \hline Model & 2738.10 & 6 & 456.35 & 20.28 & 0.0002 & significant \\ \(X_{1}\) & 306.46 & 1 & 306.46 & 13.62 & 0.0061 & \\ \(X_{2}\) & 1109.99 & 1 & 1109.99 & 49  
the input variables and the value of the DPPH assay. Moreover, the low CV values (7.97% and 6.58%) signify that the deviations between the experimental and predicted values are minimal, reflecting the high precision and reliability of the conducted experiment. A regression analysis was employed to develop two models (Equations (3) and (4)) that describe the effect of the input variables on the DPPH values:  
\[DPPH_{1}=-2.583+1.238X_{1}+2.684X_{2}+0.802X_{3}+0.017X_{2}X_{3}-0.056X_{2}^{2 }-0.012X_{3}^{2} \tag{3}\]  
\[DPPH_{2}=36.081+0.820X_{1}-1.224X_{2}+1.076X_{3}+0.041X_{2}^{2}-0.013X_{3}^{2} \tag{4}\]  
The DPPH values range from 23.63 to 73.28 \(\upmu\)mol TE/g for the 35 mm diameter vessel and from 24.48 to 74.92 \(\upmu\)mol TE/g for the 25 mm diameter vessel depending on other experimental conditions. The obtained results are slightly lower than those reported in the literature. [PERSON] et al. [27] showed that in the fruits of _S. aucuparia_ the value of the DPPH assay is 105.5 \(\upmu\)mol TE/g d.w. [PERSON] et al. [29] obtained a DPPH value of 103 \(\upmu\)mol TE/g of extract for ethanol extracts (_S. aucuparia_ L.), and 309 \(\upmu\)mol TE/g of extract for aqueous extracts. The performed ANOVA and Tukey's test (\(p>0.05\)) showed that the mean value of the DPPH assay obtained for both models differed significantly during the extraction using an ultrasound amplitude of 24 \(\upmu\)m for 10 min and an ultrasound amplitude of 36 \(\upmu\)m at a solvent concentration of 90%.