## 2 Materials and Methods
### Methods
#### 2.2.6 Individual Determination of Carotenoids
Model Adjustment and Statistical Analysis  
To assess and refine the outcomes, various factors (solvent/liquid ratio, temperature, time) were submitted to statistical analysis in relation to the outcome parameters (lycopene content, DPPH, TPC, and TFC). A total of 81 experiments were conducted using random combinations of these factors, as dictated by the Box-Behnken design. The results obtained from these experiments are detailed in Tables 3-5. A second-order polynomial equation was derived from the observed data using multiple regression analysis. The Box-Behnken design results present linear, quadratic, and interaction effects of the parameters used for the extraction of bioactive compounds. It can be observed that the major part of the model for predicting the parameters is significant, as follows: in the case of acetone as a solvent, the lycopene and TPC models are significant (\(p<0.01\)); in the case of ethanol as a solvent, the lycopene, DPPH, and TPC models are significant (\(p<0.01\)); and in the case of ethyl acetate as a solvent, the lycopene, TPC, and TFC models are significant (\(p<0.01\)). The results from the fitting method were subjected to analysis of variance (ANOVA). Following this, a Tukey test was conducted to identify significant differences in the carotenoid content as determined by HPLC. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multirow{2}{*}{**DF**} & \multicolumn{2}{c}{**Lycopene mg/100 g**} & \multicolumn{2}{c}{**DPPH (\%)**} & \multicolumn{2}{c}{**TPC (mgGAE/L)**} & \multicolumn{2}{c}{**TFC (mgQE/L)**} \\ \cline{3-11}  & & **F-Value** & _p-Value_ & **F-Value** & _p-Value_ & **F-Value** & _p-Value_ & **F-Value** & _p-Value_ \\ \hline Model & 9 & 140.26 & \textless{}0.0001 & 48.43 & \textless{}0.0001 & 51.02 & \textless{}0.0001 & 2.55 & 0.1151 \\ X\({}_{1}\) & 1 & 1052.17 & \textless{}0.0001 & 278.41 & \textless{}0.0001 & 391.46 & \textless{}0.0001 & 0.33 & 0.5824 \\ X\({}_{2}\) & 1 & 24.58 & 0.0016 & 12.50 & 0.0095 & 12.52 & 0.0095 & 0.25 & 0.6294 \\ X\({}_{3}\) & 1 & 2.08 & 0.1927 & 17.91 & 0.0039 & 7.04 & 0.0328 & 1.39 & 0.2775 \\ X\({}_{12}\) & 1 & 1.51 & 0.2582 & 9.54 & 0.0176 & 0.73 & 0.4204 & 0.61 & 0.4601 \\ X\({}_{13}\) & 1 & 6.08 & 0.0431 & 19.68 & 0.0030 & 5.62 & 0.0496 & 1.58 & 0.2490 \\ X\({}_{23}\) & 1 & 0.25 & 0.6264 & 3.12 & 0.1208 & 8.78 & 0.0210 & 3.12 & 0.1206 \\ X\({}_{1}^{2}\) & 1 & 168.42 & \textless{}0.0001 & 78.70 & \textless{}0.0001 & 21.09 & 0.0025 & 1.09 & 0.3303 \\ X\({}_{2}^{2}\) & 1 & 0.71 & 0.4244 & 8.88 & 0.0205 & 1.65 & 0.2402 & 8.37 & 0.0232 \\ X\({}_{2}^{2}\) & 1 & 8.86 & 0.0206 & 1.84 & 0.2171 & 9.65 & 0.0172 & 4.82 & 0.0641 \\ R\({}^{2}\) & & 0.99 & & 0.98 & & 0.98 & & 0.76 \\ Adj-R\({}^{2}\) & & 0.98 & & 0.96 & & 0.96 & & 0.46 \\ CV\(\%\) & & 5.64 & & 1.57 & & 8.24 & & 19.16 \\ Adeq.Pre & & 36.36 & & 21.16 & & 25.98 & & 5.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of variance (ANOVA) of the model response for lycopene, DPPH, TPC, and TFC content extracted with ethanol. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multirow{2}{*}{**DF**} & \multicolumn{2}{c}{**Lycopene mg/100 g**} & \multicolumn{2}{c}{**DPPH (\%)**} & \multicolumn{2}{c}{**TPC (mgGAE/L)**} & \multicolumn{2}{c}{**TFC (mgQE/L)**} \\ \cline{3-11}  & & **F-Value** & _p-Value_ & **F-Value** & _p-Value_ & **F-Value** & _p-Value_ & **F-Value** & _p-Value_ \\ \hline Model & 9 & 36.42 & \textless{}0.0001 & 1.38 & 0.3438 & 12.55 & 0.0015 & 2.49 & 0.1209 \\ X\({}_{1}\) & 1 & 275.36 & \textless{}0.00  
Tables 2-4 provide the results of the statistical analysis of the experimental data models using ANOVA. Each model was chosen based on its suitability to the experimental data, with all models being second-order polynomial response surface models. The adequacy of each selected model was confirmed through the values of R\({}^{2}\), adjusted R\({}^{2}\), coefficient of variance, F-value, and \(p\)-value.