## 3 Results
### Dpph
During ultrasound-assisted extraction, the optimal particle size may change due to the fact that ultrasonic exposure alone leads to a reduction in the size of particles. Research conducted by [PERSON] [51] showed that ultrasound caused a decline in particle size, narrowed their distribution, and expanded the specific free surface in all whey protein samples. In addition, ultrasonic treatment cause erosion of plant structures which enhanced the accessibility of solvent to the solute contained in plant material [52] and produce a sonocapillary effect which increases solvent penetration of liquid into capillaries and pores of plant material [53]. All of these phenomena suggest that optimal ultrasonic extraction yields and, thus, the antioxidant activity can be obtained with slightly larger particle sizes than in the case of conventional extractions. Based on the regression analysis, the model was fitted to the experimental data, as shown in the Equation (4):  
\[DPPH=-44.05+83.48X_{1}+8.52X_{2}+12.07X_{3}-0.47X_{2}X_{3}-67.07X_{1}^{2}-0.23X_ {2}^{2}-0.46X_{3}^{2} \tag{4}\]  
The Equation (4) was verified with analysis of variance (ANOVA), as can be seen in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & **\(p\)-Value** & **Coefficient** \\ \hline Model & 3149.25 & 7 & 449.89 & 61.39 & \textless{}0.0001 & & significant \\ \(X_{1}\) & 586.22 & 1 & 586.22 & 79.99 & \textless{}0.0001 & \textless{}83.48110 & \\ \(X_{2}\) & 408.74 & 1 & 408.74 & 55.77 & 0.0001 & \textless{}8.52065 & \\ \(X_{3}\) & 705.70 & 1 & 705.70 & 96.29 & \textless{}0.0001 & \textless{}12.07336 & \\ \(X_{2}X_{3}\) & 274.34 & 1 & 274.34 & 37.43 & 0.0005 & \textless{}0.473237 & \\ \(X_{1}^{2}\) & 1038.02 & 1 & 1038.02 & 141.64 & \textless{}0.0001 & \textless{}67.06768 & \\ \(X_{2}^{2}\) & 126.23 & 1 & 126.23 & 17.22 & 0.0043 & \textless{}0.233878 & \\ \(X_{3}^{2}\) & 115.53 & 1 & 115.53 & 15.76 & 0.0054 & \textless{}0.456619 & \\ \hline Residual & 51.30 & 7 & 7.33 & & & & \\ \hline Lack of Fit & 45.43 & 5 & 9.09 & 3.10 & 0.2620 & not significant \\ \hline Pure Error & 5.87 & 2 & 2.94 & & & \\ \hline Cor Total & 3200.55 & 14 & & & & \\ \hline \hline \end{tabular} \(\textless{}^{2}=0.9840\). adj-\(\textless{}^{2}=0.9679\). CV = 5.09. Adeq Precision 20.3907.  
\end{table} 
Table 2: ANOVA results for response: the DPPH test. The \(p\)-value of the model is less than 0.05 which indicates that the coefficients in the model have a significant impact on the DPPH response. The \(p\)-value of the lack of fit is statistically insignificant (\(p>0.2620\)), which was desirable for correct model verification. The determination coefficient and adjusted coefficient are close to 1, which is desirable. A low value of the coefficient of variation (5.08%) means that the derivation between the predicted and experimental values arise low. The value of the adequate precision was found to be 20.3907 and is much greater than 4, which confirms that the model can be useful for the prediction of the value of the DPPH test. The model was also validated by residual analysis as presented in Figure A2 (Appendix A). The result shows a good correlation between the experimental and the predicted values of the response and that the residuals are symmetric about the origin and they have a high density close to the origin and a low density away from the origin. This indicates that the developed model is appropriate and can be applied for the optimization of the DPPH assay.