## 3 Results
### Model Fitting
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Tomato**} & \multicolumn{2}{c}{**Pumpkin**} \\ \hline
**Source** & **DF** & **F-Value** & _p-Value_ & **F-Value** & _p-Value_ \\ \hline \({}^{1}\) Model & 5 & 92.71 & 0.000 & 32.61 & 0.000 \\ Linear & 2 & 151.38 & 0.000 & 45.62 & 0.000 \\ Ethanol & 1 & 251.73 & 0.000 & 34.14 & 0.001 \\ time & 1 & 25.61 & 0.001 & 67.90 & 0.000 \\ Square & 2 & 185.50 & 0.000 & 24.44 & 0.001 \\ Ethanol \(\times\) Ethanol & 1 & 187.21 & 0.000 & 10.78 & 0.013 \\ time \(\times\) time & 1 & 53.62 & 0.000 & 48.41 & 0.000 \\
2-Way Interaction & 1 & 30.98 & 0.001 & 24.56 & 0.002 \\ Ethanol \(\times\) time & 1 & 30.98 & 0.001 & 24.56 & 0.002 \\ Error & 7 & & & & \\ Lack-of-Fit & 3 & 5.48 & 0.067 & 1.16 & 0.429 \\ Pure Error & 4 & & & & \\ Total & 12 & & & & \\ \hline \hline \end{tabular} \({}^{1}\) Box-Cox data transformation was conducted using optimal \(\lambda=-0.495565\) for tomato, and \(\lambda=1.30359\) for pumpkin.  
\end{table} 
Table 5: Outcomes of the ANOVA for the fitting of transformed data from total phenolics (TPC). Concerning model adequacy, while some deviation from a perfect fit is noted, as evidenced by an F-value of 5.48 and a \(p\)-value of 0.067, these results do not reach the threshold of statistical significance at the conventional level of 0.05. Thus, it can be concluded that the model demonstrates an acceptable fit to the data. Additionally, the \(p\)-value of 0.429 for the variable \"pumpkin\" further supports the notion that the model provides a satisfactory fit to the observed data (Table 5). In conclusion, the analysis of variance (ANOVA) for both extracts demonstrates that the model is highly significant. This significance extends to both the linear and quadratic effects of the factors involved. Furthermore, the interaction between these factors also shows statistical significance. The lack-of-fit test, which is not statistically significant, indicates that the model provides an adequate fit to the data. This is corroborated by the lack-of-fit test results, reinforcing the model's reliability and the robustness of its conclusions (Table 5). Polynomial predictive equations that are utilized to represent response surfaces of total phenolics (TPC) in tomato and pumpkin are presented in Table 6.  
Ultrasound-assisted extraction (UAE) is a method that employs acoustic cavitation to improve the efficiency of the extraction process. This technique involves the application of ultrasound waves to a solvent, inducing alternating cycles of high and low pressure within the medium. During the low-pressure cycles, cavitation bubbles form because of the solvent's rapid expansion. Subsequently, these bubbles collapse abruptly under the high-pressure cycles, producing localized hot spots and high-speed liquid jets. These phenomena significantly enhance the mass transfer and extraction rates. Cavitation-induced microjets and shock waves are pivotal in ultrasonic-assisted extraction (UAE), exerting significant mechanical forces on plant tissues. This action facilitates the physical breakdown of cell walls, thereby augmenting the liberation of phenolic compounds into the extraction solvent. Additionally, the turbulent flow resulting from cavitation enhances mass transfer, thereby accelerating the kinetics of extraction and improving the overall efficiency of the process. Ethanol and water are effective solvents for ultrasound-assisted extraction, primarily because of their proficient transmission of ultrasound waves. These solvents possess relatively low acoustic impedances, facilitating the penetration and propagation of ultrasound energy through the solvent with minimal attenuation. Consequently, this allows for effective coupling of ultrasound energy with the solvent, optimizing cavitation effects and thus enhancing the extraction process. Ethanol and water are highly effective solvents, also due to their capacity to dissolve a diverse array of compounds.