## 3 Results and Discussion
### ABTS Assay  
Figure 4 shows the influence of input variables on the ABTS assay value for extraction vessels with diameters of 35 and 25 mm. Based on the analysis of the graph, it can be concluded that in the case of the vessel with a diameter of 35 mm, the ABTS value decreases linearly with increasing solvent concentration (Figure 4a). The shape of the curve shown in Figure 4b indicates that the solvent concentration variable has reached an inflection point, which means that further increases in the value of this variable will result in a decrease in the ABTS value. Increases in the ultrasound time and amplitude resulted in a linear increase in the ABTS value for both extraction vessels. In order to confirm the significance of the impact of the tested input variables on the value of the ABTS assay, a statistical analysis was performed. The findings of this analysis are presented in Tables 8 and 9. It can be observed that in the case of both models, the linear effects of all variables had a significant impact on the value of the ABTS assay. In the case of extraction in the vessel with a diameter of 25 mm, the square effect of solvent concentration was also significant. For both models, time had the least impact on the ABTS values. In the case of extraction in the vessel with a diameter of 25 mm, the concentration of the solvent had the greatest influence on the ABTS value, and in the case of the vessel with a diameter of 35 mm, the ultrasound amplitude had the greatest impact. The \(p\)-values of the models are statistically significant (\(p<0.0015\); \(p<0.0001\)), and the lack of fit of the models are statistically insignificant (\(p=0.0577\) and \(p=0.2097\)), which indicates the correct validation of the equations. In the case of the second model \(ABTS_{2}\), the determination coefficient (0.9579) and the adjusted coefficient (0.9410) are high, which shows the existence of a high correlation between the input variables and the ABTS value. In the case of the first equation \(ABTS_{1}\), the determination and adjusted coefficients are lower (0.7395 and 0.6685), which means a greater scattering of data around the regression line. The model developed for extraction in the vessel with a diameter of 25 mm (\(ABTS_{2}\)) is characterised by a much higher correlation between variables. \begin{table}
\begin{tabular}{l l l l l l l} \hline
**Source** & **Sum of Squares** & **DF** & **Mean Square** & **\(F\)-Value** & **\(p\)-Value** & \\ \hline Model & 8514.31 & 3 & 2838.10 & 10.41 & 0.0015 & significant \\ \(X_{1}\) & 1427.29 & 1 & 1427.29 & 5.24 & 0.0429 & \\ \(X_{2}\) & 5631.75 & 1 & 5631.75 & 20.66 & 0.0008 & \\ \(X_{3}\) & 1455.27 & 1 & 1455.27 & 5.34 & 0.0413 & \\ \hline Residual & 2998.84 & 11 & 272.62 & & & \\ \hline Lack of Fit & 2959.49 & 9 & 328.83 & 16.72 & 0.0577 & not significant \\ \hline Pure Error & 39.34 & 2 & 19.67 & & & \\ \hline Total & 11,513.15 & 14 & & & \\ \hline \multicolumn{6}{l}{\(R^{2}=0.7395\), adj \(R^{2}=0.6685\), CV = 17.46, Adeq Precision 9.39} \\ \end{tabular}
\end{table} 
Table 8: Effect of the independent variables on the dependent variables and statistical significance for \(ABTS_{1}\) of extracts obtained in vessels with a diameter of 35 mm. Figure 4: Dependence of ABTS on time, ultrasound amplitude, and solvent concentration for extracts obtained in vessels with diameters of **(a)** 35 mm, **(b)** 25 mm. A regression analysis was employed to develop two models (Equations (7) and (8)) that describe the effect of input variables on the ABTS value:  
\[ABTS_{1}=41.776+2.671X_{1}+2.211X_{2}-0.450X_{3} \tag{7}\]  
\[ABTS_{2}=-39.218+2.843X_{1}+1.834X_{2}+2.810X_{3}-0.031X_{3}^{2} \tag{8}\]  
The ABTS values range from 18.89 to 134.06 umol TE/g for the 35 mm diameter vessel and from 32.56 to 126.13 umol TE/g for the 25 mm diameter vessel depending on other experimental conditions. The obtained results coincide with the values given by [PERSON] et al. [27] (91.6 umol TE/g d.w.). [PERSON] et al. [31] showed that the ABTS value for _S. aucuparia_ L. fruits is \(5.94\pm 0.06\) m TE/g f.w.