## 3 Results and Discussion
### Results of Ultrasound-Assisted Extraction
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \multicolumn{1}{c}{**Extinction Conditions**} & \multicolumn{1}{c}{**Total Premic Contrast (mg-Gallic Acid (ggg)**} & \multicolumn{1}{c}{**Additional Activity (ggg)**} & \multicolumn{1}{c}{**Froned By-Product Extracts**} & \multicolumn{1}{c}{**Chicago By-Product Extracts**} & \multicolumn{1}{c}{**Froned By-Product Extracts**} & \multicolumn{1}{c}{**Froned By-Product Extracts**} \\ \cline{3-14}
**Solid/Water** & T & **t** & **Power**  
Compared to the conventional method, ultrasounds allowed the increase of the TPC of chicory extracts by about 48%, simultaneously reducing the extraction time from 180 to 40 min and the fixed temperature from 60 to 45 \({}^{\circ}\)C. This high efficiency can be attributed to the ability of ultrasounds to increase the diffusion of the solvent into the vegetable matrix and to break the cell walls, facilitating the release and the mass transfer [35]. In the case of fennel, the conventional solvent extraction allowed for the recovery of slightly more phenolic compounds than the UAE (+11.7%) by employing a time more than double (90 min vs. 40 min) and working at a higher temperature (65 \({}^{\circ}\)C vs. 45 \({}^{\circ}\)C). These results are in agreement with the findings of [PERSON] et al. [22]. The antioxidant activity values are reported in Table 2. The AA of chicory extracts were in the range of 0.0120-0.0424 mmol Trolox/g dm, and the extraction conditions that allowed the maximization of this index were the following: solid-water ratio = 5 g/100 mL; T = 55 \({}^{\circ}\)C; t = 40 min; power = 72 W. AA of fennel extracts were in the range of 0.0180-0.0534 mmol Trolox/g dm, and the highest values were obtained in the following conditions: solid-water ratio = 5 g/100 mL; T = 45 \({}^{\circ}\)C; t = 40 min; power = 24 W.  
Compared to the conventional method, ultrasounds allowed the increase in the AA of chicory extracts by about 50%, simultaneously reducing the temperature (from 60 to 55 \({}^{\circ}\)C) and prolonging the treatment (from 30 to 40 min). Ultrasound also allowed the increase (+89%) of AA of fennel extracts, simultaneously reducing the temperature (from 60 to 45 \({}^{\circ}\)C) and increasing the time (from 30 to 40 min). Contrary to what was observed for the conventional extraction, the total phenolic contents of the extracts produced by ultrasounds were not or poorly correlated with their antioxidant activity values, as evidenced by the correlation coefficients (R = 0.2035 for chicory and 0.7173 for fennel). This result can be attributed to the evidence that the various extraction conditions tested (amount and type of thermal energy and the time of treatment) can influence the quantity and type of individual phenolic compounds extracted. Multiple regression analysis aimed to evaluate the ability of the mathematical model to describe the experimental data and evaluate the influence of the four independent variables on the phenolic content and antioxidant activity of the extracts, identifying the variables that exerted the most significant effects and the extent of these effects. In more depth, the ANOVA of the model and the calculation of R\({}^{2}\), F and \(p\) allowed the evaluation of the ability of the model itself to fit the data to a 95% confidence level (\(p<0.05\)). The quadratic model excellently described the results observed on chicory extracts (R\({}^{2}\) = 0.8473, \(p\) = 0.000909 for TPC; R\({}^{2}\) = 0.8638, \(p\) = 0.000000 for AA) and the AA values of the fennel extract (R\({}^{2}\) = 0.9238, \(p\) = 0.000000), while the fitting was significant in the case of fennel TPC (\(p\) = 0.220484) (Table 2). Similarly, through the analysis of variance, the statistical significance of the effects of the independent variables on TPC and AA was measured (Table 2) and the regression coefficients were calculated in order to write the equations describing the relationships between the independent variables and the TPC or AA.