## 3 Results and Discussion
### Recovery of Lycopene from Tomato Peels
#### 3.1.1 Model Fitting
\begin{split}\textit{Lycopene content}=4.61+7.40X_{1}+8.47X_{2 }+14.14X_{3}-9.52X_{1}X_{3}-2.06X_{2}X_{3}.\end{split}  \tag{6}\]  
The updated model, with an F-value of 809.02 and a \(p\)-value of 0.00, demonstrated a highly significant ability to predict the lycopene content. The coefficient of determination (\(R^{2}\)) was 0.91, indicating that the model explained the majority of the variation in the data, which suggested a very strong fit. Figure 1 presents a plot of the predicted versus observed values for the lycopene content, showing a strong correlation between them. This close agreement further validates the model's accuracy and its ability to predict the lycopene content based on the specified extraction parameters. Figure 1: Plots of predicted versus actual values for the lycopene content (mg/100 g of tomato peels) of tomato peel extracts using UAE-MAE. The red line represents the line of perfect prediction (predicted = actual), and the blue circles indicate the individual experimental data points. Extraction Yield (EY)  
The response surface model for \(EY\) also resulted in a high \(R^{2}\) value of 0.95 (Table 2). The corresponding mathematical model for \(EY\) is given by Equation (7):  
\[ \begin{array}{c}EY=21.72-5.86X_{1}+22.69{X_{1}}^{2}+37.99X_{2}+11.55{X_{2}}^{2 }-1.13X_{3}-1.61{X_{3}}^{2}\\ +0.62X_{1}X_{2}-23.41X_{1}X_{3}-5.06X_{2}X_{3}.\end{array}  \tag{7}\]  
The linear term for microwave power (\(X_{2}\)) was the most significant factor (F-value = 440.40, \(p\)-value \(<\) 0.001) affecting \(EY\), followed by the interaction between the solid/liquid ratio and ultrasound power (\(X_{1}X_{3}\)). The interaction between microwave power and ultrasound power (\(X_{2}X_{3}\)), along with the linear effects of the solid/liquid ratio (\(X_{1}\)) and ultrasound power (\(X_{3}\)) were also found to be significant. In contrast, the quadratic terms for the solid/liquid ratio (\({X_{1}}^{2}\)), microwave power (\({X_{2}}^{2}\)), and ultrasound power (\({X_{3}}^{2}\)) and the interaction between the solid/liquid ratio and microwave power (\(X_{1}X_{2}\)) were not significant in influencing \(EY\). The results indicate that the linear terms for the solid/liquid ratio, microwave power, and ultrasound power, and the interaction terms of \(X_{1}X_{3}\) and \(X_{2}X_{3}\) are critical factors influencing \(EY\), similar to the findings for the lycopene content. To refine the model, a new regression analysis was performed by excluding the non-significant variables, resulting in the following updated surface model:  
\[EY=11.33+18.20X_{1}+20.84X_{2}+34.77X_{3}-23.41X_{1}X_{3}-5.06X_{2}X_{3}. \tag{8}\]  
The F-value of 1454.97 and \(p\)-value below 0.00 indicate that the model is highly significant in predicting the \(EY\). The R\({}^{2}\) value of 0.95 confirms that the model accounts for most of the variability in the data. As shown in Figure 2, the data points are tightly clustered around the diagonal, which suggests minimal discrepancy between the predicted and observed \(EY\) values. This indicates that the model consistently predicts the \(EY\) with only small errors across the entire range of values tested, demonstrating its accuracy and reliability. Research on lycopene extraction from tomato peels using combined UAE-MAE method remains limited. A study by [PERSON] et al. (2008) applied the UAE-MAE technique for ly  
Figure 2: Plots of predicted versus actual values for the \(EY\) (%) of tomato peel extracts using UAE-MAE. The red line represents the line of perfect prediction (predicted = actual), and the blue circles indicate the individual experimental data points. copene recovery from tomatoes, revealing that microwave power and the solid/liquid ratio were key factors influencing lycopene yield. Their findings demonstrated that increasing the microwave power and decreasing the solid/liquid ratio led to a maximized lycopene yield [28].