## 3 Results and Discussion
### Recovery of Lycopene from Tomato Peels
#### 3.1.1 Model Fitting  
The results from fitting the experimental data to the response surface model for the lycopene content in the extracted samples are presented in Table 2. The model showed a coefficient of determination (\(R^{2}\)) value 0.92, suggesting a strong correlation between \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Coefficients** & \
\begin{tabular}{c} **Standard** \\ **Error** \\ \end{tabular} &
\begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **DF** & **Mean Square** & **F-Value** \\ \hline \multicolumn{6}{l}{**Lycopene content (\(\mu\)g/g**} \\
**of tomato peels) 1 ** & & & & \\ \hline Model & 8.83 & 4.38 & 28.0/0.13 & 10 & 2807.01 & 459.01 *** \\ \(X_{1}\) & \(-\)2.38 & 9.05 & 43.50 & 1 & 43.50 & 7.11 * \\ \(X_{1}\)2 & 9.23 & 2.06 & 7.10 & 1 & 7.10 & 1.16  \\ \(X_{2}\) & 15.45 & 2.10 & 1444.02 & 1 & 1444.02 & 236.13 *** \\ \(X_{2}\)2 & 4.70 & 4.36 & 2.08 & 1 & 2.08 & 0.34  \\ \(X_{3}\) & \(-\)0.46 & 0.79 & 59.31 & 1 & 59.31 & 9.70 ** \\ \(X_{3}\)2 & \(-\)0.65 & 0.88 & 3.38 & 1 & 3.38 & 0.55 N \\ \(X_{1}X_{2}\) & 0.25 & 0.82 & 0.58 & 1 & 0.58 & 0.09  \\ \(X_{1}X_{3}\) & \(-\)9.52 & 0.89 & 694.19 & 1 & 694.19 & 113.51 *** \\ \(X_{2}X_{3}\) & \(-\)2.06 & 0.47 & 119.56 & 1 & 119.56 & 19.55 *** \\ Residual & & & & 232.39 & 38 & 6.12 & \\ Total & & & 2690.30 & 47 & & \\ \hline \multicolumn{6}{l}{**EY (\%) b**} \\ \hline Model & 21.72 & 7.88 & 169,789.04 & 10 & 16,978.90 & 856.09 *** \\ \(X_{1}\) & \(-\)5.86 & 16.31 & 263.13 & 1 & 263.13 & 13.27 ** \\ \(X_{1}\)2 & 22.69 & 3.71 & 42.93 & 1 & 42.93 & 2.16  \\ \(X_{2}\) & 37.99 & 3.77 & 8734.52 & 1 & 8734.52 & 440.40 *** \\ \(X_{2}\)2 & 11.55 & 7.85 & 12.57 & 1 & 12.57 & 0.63 N \\ \(X_{3}\) & \(-\)1.13 & 1.42 & 358.74 & 1 & 358.74 & 18.09 *** \\ \(X_{3}\)2 & \(-\)1.61 & 1.58 & 20.46 & 1 & 20.46 & 1.03 N \\ \(X_{1}X_{2}\) & 0.62 & 1.48 & 3.49 & 1 & 3.49 & 0.18 N \\ \(X_{1}X_{3}\) & \(-\)23.41 & 1.61 & 4198.97 & 1 & 4198.97 & 211.71 *** \\ \(X_{2}X_{3}\) & \(-\)5.06 & 0.84 & 723.16 & 1 & 723.16 & 36.46 *** \\ Residual & & & 753.66 & 38 & 19.83 & \\ Total & & & 15,620.94 & 47 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis of variance for the response surface model of the lycopene content (mg/100 g of tomato peels) and \(EY\) (%) of tomato peel extracts. the experimental data and the model's predictions. The F-values and \(p\)-values indicate the significance of each coefficient for the various terms, with higher F-values and lower \(p\)-values reflecting more impactful factors [27]. The response surface model that describes the lycopene content is represented by Equation (5):  
\[ \begin{split}\textit{Lycopene content}=8.83-2.38X_{1}+9.23{X_{1}}^{2}+ 15.45X_{2}+4.70{X_{2}}^{2}-0.46X_{3}-0.65{X_{3}}^{2}+0.25X_{1}X_{2}\\ -9.52X_{1}X_{3}-2.06X_{2}X_{3}.\end{split}  \tag{5}\]  
Among the model terms, the linear effect of microwave power (\(X_{2}\)) was found to be the most influential factor on the lycopene content, as indicated by its F-value of 236.13 (\(p\) < 0.001). This was followed by the interaction between the solid/liquid ratio and ultrasound power (\(X_{1}X_{3}\)). The interaction between microwave power and ultrasound power (\(X_{2}X_{3}\)) and the linear terms of the solid/liquid ratio (\(X_{1}\)) and ultrasound power (\(X_{3}\)) showed smaller but still statistically significant impacts. Non-significant factors included the quadratic terms for the solid/liquid ratio (\(X_{1}\)2), microwave power (\(X_{2}\)2), and ultrasound power (\(X_{3}\)2), as well as the interaction between the solid/liquid ratio and microwave power (\(X_{1}X_{2}\)). In summary, the most critical factors affecting the lycopene content were the linear terms for the solid/liquid ratio, microwave power, and ultrasound power, and the interaction terms of \(X_{1}X_{3}\) and \(X_{2}X_{3}\). Based on these results, a new regression analysis was carried out, excluding the non-significant terms. The revised fitted surface model for predicting lycopene content is expressed as follows:  
\[