## 3 Results and Discussions
### Chemical Composition of Whole Fruit and Pulp of S. melongena
#### 3.5.5 Optimization of the Analysis of the Response Surface Methodology  
The optimal values obtained by optimizing the extraction using the ultrasound technique are divided into specific response values: \(Y_{1}\) (solvent = 64%; ratio = 5 g/L; and time = 0.5 min), \(Y_{2}\) = (solvent = 58%; ratio = 5 g/L; and time = 0.5 min), and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Extraction**} \\ \cline{3-5}  & & \(Y_{1}\) & \(Y_{2}\) & \(Y_{3}\) \\ \hline
**Model** & & \(<\)0.0001 & 0.00 & \(<\)0.0001 \\ \hline
**Intercept** & \(\mathbf{b_{0}}\) & 1.83 (***) & 6.61 (***) & 27.34 (***) \\
**Linear** & \(\mathbf{b_{1}}\) & 0.1398 (NS) & 0.4445 (NS) & 0.1962 (NS) \\  & \(\mathbf{b_{2}}\) & 0.1163 (NS) & \(-\)0.7166 (*) & \(-\)0.6195 (NS) \\  & \(\mathbf{b_{3}}\) & \(-\)1.34 (***) & \(-\)1.86 (***) & \(-\)5.1 (***) \\ \hline
**Interaction** & \(\mathbf{b_{12}}\) & \(-\)0.0113 (NS) & \(-\)0.2858 (NS) & 1.66 (NS) \\  & \(\mathbf{b_{13}}\) & \(-\)0.1738 (NS) & \(-\)0.4649 (*) & \(-\)0.5325 (NS) \\  & \(\mathbf{b_{23}}\) & \(-\)0.1163 (NS) & \(-\)0.4955 (*) & 0.4913 (NS) \\ \hline
**Quadratic** & \(\mathbf{b_{11}}\) & 0.0387 (NS) & \(-\)0.0827 (NS) & 0.028 (NS) \\  & \(\mathbf{b_{22}}\) & \(-\)0.290 (**) & \(-\)0.3197(NS) & \(-\)4.62 (***) \\  & \(\mathbf{b_{33}}\) & 0.2261 (*) & \(-\)1.05 (***) & 6.61 (***) \\ \hline \multicolumn{5}{c}{**Adaptation analysis statistical information**} \\ \hline
**Observations** & 20 & 20 & 20 \\
**R\({}^{2}\)** & 0.96 & 0.94 & 0.94 \\
**R\({}^{2}\)adj** & 0.93 & 0.98 & 0.88 \\ \hline \multicolumn{5}{c}{**Factorial optimization response**} \\ \hline
**Optimal value** & 5.64 & 12.15 & 43.04 \\ \(X_{1}\) & 0.54 & 0.52 & 0.55 \\ \(X_{2}\) & 64.2398 & 58.4479 & 54.1773 \\ \(X_{3}\) & 4.65966 & 4.65966 & 4.66865 \\ \hline \multicolumn{5}{c}{**General optimization**} \\ \hline
**Optimal response (Y)** & \(\max\) & \(\max\) & \(\max\) \\
**Desirability** & 1 & 40.96 \\
**Optimal factorial value** & \(X_{1}\) = 0.5 & \(X_{2}\) = 68.2 & \(X_{3}\) = 5 \\ \hline \hline \end{tabular}  
Significance values within parenthesis: * \(p\) 0.05, ** \(p<\) 0.01; *** \(p<\) 0.001, NS: Not significant. R\({}^{2}\): coefficients of determination; R\({}^{2}\)adj: adjusted coefficients of determination, coefficients b1: time, b2: temp, and b3: solv. The responses are summarized as \(Y_{1}\): total anthocyanins (mg/g dry matter), \(Y_{2}\): total anthocyanins (mg/g extract), \(Y_{3}\): yield (%). Fixed variables are summarized as \(X_{1}\) = time (min); \(X_{2}\) = concentration of ethanol (%); and \(X_{3}\) = solid/liquid ratio (g/L).  
\end{table}
Table 9: Statistical analysis (ANOVA) of the central composite design (CCD), including response terms for building the predictive models and optimal response values for the parametric response criteria.  
(solvent = 54%; ratio = 5 g/L; and time = 0.5 min); and in general optimization values for the three responses involved: with an optimal disability value of 0.99, 68.2% ethanol concentration (v/v), 5 g of _S. melongena_ per liter of solvent, and 0.5 min extraction time.