## 3 Results and Discussion
### FRAP Assay  
Figure 3 shows the influence of the input variables on the value of the FRAP assay for extraction vessels with diameters of 35 and 25 mm. The shape of the curve shown in Figure 3a 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 FRAP value. For the vessel with a diameter of 25 mm, a linear decrease in the FRAP value was observed with increasing solvent concentration. For the vessel with a diameter of 35 mm, a linear increase in the FRAP value with increasing time and a non-linear increase with increasing ultrasound amplitude were observed. For the vessel with a diameter of 25 mm, increases in the ultrasound time and amplitude result in a linear increase in the value of the FRAP assay (Figure 3b). In order to confirm the significance of the influence of the examined input variables on the value of the FRAP assay, a statistical analysis was performed. The findings of this analysis are displayed in Tables 6 and 7. It can be observed that in the case of both analysed models, the linear effects of all variables had a significant impact on the value of the FRAP assay. In the case of extraction in the vessel with a diameter of 35 mm, the square coefficients of solvent concentration and ultrasound amplitude are also statistically significant. In the case of extraction in the vessel with a diameter of 35 mm, the ultrasound amplitude had the greatest impact on the value of the FRAP assay, and time had the least impact. In the case of extraction in the vessel with a diameter of 25 mm, the solvent concentration had the greatest impact on the FRAP value, and time had the least effect. The influence of individual variables on the FRAP values for both models is the same as in the case of the DPPH values. \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 & 8936.26 & 3 & 2978.75 & 13.16 & 0.0006 & significant \\ X1 & 1226.55 & 1 & 1226.55 & 5.42 & 0.0400 & \\ X2 & 2774.67 & 1 & 2774.67 & 12.26 & 0.0050 & \\ X3 & 4935.04 & 1 & 4935.04 & 21.80 & 0.0007 & \\ \hline Residual & 2490.42 & 11 & 226.40 & & \\ \hline Lack of Fit & 2440.31 & 9 & 271.15 & 10.82 & 0.0874 & not significant \\ \hline Pure Error & 50.11 & 2 & 25.06 & & \\ \hline Total & 11,426.68 & 14 & & & \\ \hline \(R^{2}\) = 0.7821, adj \(R^{2}\) = 0.7226, CV = 15.05, Adeq Precision 11.19 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Effect of the independent variables on the dependent variables and statistical significance for \(FRAP_{2}\) of extracts obtained in vessels with a diameter of 25 mm. Figure 3: Dependence of FRAP on time, ultrasound amplitude, and solvent concentration for extracts obtained in vessels with diameters of (**a**) 35 mm, (**b**) 25 mm. The \(p\)-values of models are statistically significant (\(p<0.0001\); \(p=0.0006\)), and the lack of fit of the models are statistically insignificant (\(p=0.1252\) and \(p=0.0874\)), which indicates the correct validation of the equations. In the case of the first model (\(FRAP_{1}\)), the determination coefficient (0.9613) and the adjusted coefficient (0.9323) are high which shows the existence of a high correlation between the input variables and the FRAP value. In the case of second equation (\(FRAP_{2}\)), the determination and adjusted coefficients are lower (0.7821 and 0.7226) which signifies that the scatter of the data around the regression lines is higher. Furthermore, the coefficient of variation for the first model (5.20%) is much lower than for the second (15.05%), which means that the deviations between the experimental and predicted values are lower.