## 3 Results
### Optimization and Validation of Extraction Conditions  
The experimental results presented in Section 3.1 for the conventional extraction of bioactive compounds from the comelian cherry revealed that the extraction of the TPC, the TFC, and the TAA could be fitted to a second-order polynomial, according to the R\({}^{2}\) values presented in Table 2.  
The optimization section is obtained from the statistical program that provides the optimal conditions and the predicted values for the variables. As the fitting for the UAE experiments is poor, no optimal conditions will be calculated as there is no statistically significant effect of any of the experimental variables on the responses studied.  
The final model for conventional extraction of comelian cherry fruits in terms of three factors, coded with X\({}_{1}\)--temperature (\({}^{\circ}\)C); X\({}_{2}\)--time (min); and X\({}_{3}\)--ethanol concentration (%) was as follows:  
\[\text{TPC}=169.67-1.374\text{X}_{2}-1.1097\text{X}_{3}+0.04019\text{X}_{1}{}^{2 }+0.017\text{X}_{2}{}^{2} \tag{7}\]  
\[\text{TFC}=1.02+0.08\text{X}_{3}-0.00074\text{X}_{3}{}^{2} \tag{8}\]  
\[\text{TAA}=142-1.03\text{X}_{2}-0.522\text{X}_{3}+0.043\text{X}_{1}{}^{2}-0.01 125\text{X}_{1}\text{X}_{2}+0.018\text{X}_{2}{}^{2} \tag{9}\]  
Finally, using the optimization tool provided by the Statgraphics 18.0 statistical software it was possible to determine the experimental conditions that maximized the three responses simultaneously. This procedure tries to find the levels of the experimental factors that maximize a combined desirability function, which is a function that expresses the desirability of a solution involving the three responses studied (TPC, TFC and TAA). The results are presented in Table 5. In order to verify the optimal parameters proposed by the polynomial equation and the statistical software, the experiments were conducted with the following parameters: 40 \({}^{\circ}\)C, 15 min, 60% ethanol (_v/v_), which are the optimal extraction conditions predicted by the statistical software. For validation, the values of the experimental answers were compared with the values predicted by the quadratic (polynomial) model expressed by the Equations (4)-(6).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Response** & **Predicted** & **Lower 95\%** & **Upper 95\%** & **Desirability** & **Experimental** & **CV** & **Error** \\  & **Value** & **Limit** & **Limit** & **Values** & **(\%)** & **(\%)** & **(\%)** \\ \hline TPC (mg GAE/g dw) & 34.7 & 30.8 & 38.6 & & 33.1 \(\pm\) 1.9 & 5.81 & 4.60 \\ TFC (mg QE/g dw) & 1.70 & 1.33 & 2.1 & 0.9789 & 1.65 \(\pm\) 0.07 & 4.20 & 2.11 \\ TAA (mg Trolox/g dw) & 34.0 & 30.6 & 37.4 & & 33.2 \(\pm\) 0.5 & 1.60 & 2.04 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Validation of the polynomial (quadratic) Box-Behnken model for conventional extraction by combelian cherry fruits.  
The percentage error between the experimental values and the predicted values was determined by applying the Equation (7):  
\[\text{Err}\;(\%)=1\,\text{X}_{\text{exp}}-\text{X}_{\text{pred}}/\,\text{X}_{ \text{pred}}\mid\,\times 100 \tag{10}\]  
where Xexp--experimental (actual) value and Xpred--predicted value.  
In Table 5, the experimental results are compared with the results predicted by the polynomial models. The proximity of the experimental and predicted values demonstrated the high validity and adequacy of the fitted model.