## 3 Results and Discussion
### Models Fitting and Statistical Verification  
The response values in Table 2 were fitted to the second-order polynomial Equation (1) using the Design-Expert software, but just the significant parameters (assessed at a 95% confidence level) were used in the development of the theoretical models. The results of ANOVA and regression analyses are presented in Supplementary Materials Table S2. The developed polynomial models, expressed in coded values, are presented in Equations (2)-(7):  
\[Y_{1}=50.4+1.1t+2.7P-3.1S+1.8P^{2}-2.5S^{2} \tag{2}\]  
\[Y_{2}\ =0.308-0.014t+0.002P+0.002S+0.034t^{2}+0.046P^{2}+0.107S^{2} \tag{3}\]  
\[Y_{3}=1.04+0.04t-0.11S-0.07 tS-0.26t^{2}-0.22S^{2} \tag{4}\]  
\[Y_{4}=0.155-0.019P+0.002S+0.021 PS-0.015P^{2}-0.016S^{2} \tag{5}\]  
\[Y_{5}=0.1464+0.0011t+0.001S-0.0046S^{2} \tag{6}\]  
\[Y_{6}=1.66+0.03t-0.05P-0.09S-0.06 tS+0.06 PS-0.22t^{2}-0.13S^{2} \tag{7}\]  
In the mathematical models developed for each response variable, the coefficients of the terms \(t\), \(P\), and \(S\) illustrate the effect of the independent variables time, ultrasonic power, and ethanol concentration, respectively, and their interactions. Since the expected effects on the response are denoted by the parametric values, the higher the parametric value, the more significant the weight of the respective variable will be, regardless of its sign. For interactions, synergistic effects are denoted by a positive sign, while an antagonistic interaction between variables is translated by a negative sign [23]. In each model Equations (2)-(7), the intercept corresponds to the overall average response of the 20 experimental runs of the CCRD design in Table 2. Based on the intercept values, epicatechin stands out as the main phenolic compound (corresponding to almost 63% of the total content) identified in the kiwi peel by-product, followed by B-type (epi)catechin dimer (18.6%), and the two quercetin glycosides (18.2%) (Supplementary Materials Table S2). All Equations (2)-(7) presented a non-significant lack-of-fit (\(p>0.05\)) and an adequate precision greater than 22.4, which indicates that the theoretical models adequately describe the effects of the independent variables on the target responses [24]. The coefficients R\({}^{2}\) and R\({}^{2}_{\text{adj}}\) were higher than 0.888 and 0.864 in all cases, respectively (Supplementary Material Table S2), indicating that the variability of each response can be explained by  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Runs** & \multicolumn{3}{c}{**Experimental Domain**} & \multicolumn{3}{c}{**Experimental Responses \({}^{*}\)**} \\ \hline  & **f (min)** & **P**(W) & **EOHH (\%)** & **Y\({}_{1}\) (\%,w/w)** & **Y\({}_{2}\) (mg/g dw)** & **Y\({}_{3}\) (mg/g dw)** & **Y\({}_{4}\) (mg/g dw)** & **Y\({}_{5}\) (mg/g dw)** \\ \hline
1 &  
the independent variables involved in the extraction. In addition, values \(\geq\) 22.49 were obtained for adequate precision, which is a measure of signal-to-noise ratio that compares the range of the predicted values at the design points to the average prediction error. High accuracy was also demonstrated by the low values of the coefficient of variance. Thus, the developed theoretical models were statistically validated and used in the following steps to predict the optimal UAE conditions for recovery of polyphenols from kiwi peel. Certain peculiarities regarding the overall effects of the independent variables on the UAE of flavonoids from kiwi peel can be inferred from the complexity of the model equations. Based on Equation (2) and Supplementary Material Table S2, it can be settled that the extraction yield was significantly affected by the three independent variables involved in the extraction. The ethanol concentration was the most relevant process variable, effecting the extraction through negative linear and quadratic effects. The ultrasonic power ranked second and caused positive linear and quadratic effects, while the extraction time only induced a linear effect.