## 3 Results and Discussion
### Experimental Design and Optimization
#### 3.1.2 The Influence of Experimental Factors on TFC and ABTS  
The coefficient graph shown in Figure 2 can be used to identify the most relevant impact of individual and interaction factors on the assayed dependent parameters (TFC and ABTS). For this analysis, a confidence level of 0.90 has been chosen. Regarding TFC, the following factors have been statistically significant (\(p<0.05\)): amplitude, extraction time, the quadratic interaction of EtOH concentration (sol \(\times\) sol), and the interaction factor between EtOH concentration and time (sol \(\times\) time). Regarding the antioxidant activity using the ABTS radical, the following factors have been statistically significant (\(p<0.05\)): EtOH concentration, amplitude, and the quadratic interaction of EtOH concentration (sol \(\times\) sol). There were no significant interaction factors identified, which suggests that in this case there was no synergic effect on the yield of antioxidant species.  
Both the extraction of flavonoids and the antioxidant activity from corn silk were influenced by various factors. Ethanol concentration plays a crucial role in the extraction mix, as was previously suggested by various studies. Specifically, the utilization of water and ethanol mixtures induces a synergistic effect; therefore, an optimal concentration is necessary to assure the efficient recovery of flavonoids [37; 38]. Different concentrations of ethanol can influence the solubility of various compounds, including antioxidants [39]; this fact was also noticed for ABTS as a dependent variable, where raising the concentration of ethanol in the extraction medium negatively influenced the in vitro antioxidant activity. To sum up, optimal ethanol concentrations may enhance the extraction of antioxidant and flavonoid species from corn silk, contributing to higher antioxidant activity in the final extract. Higher ultrasonic amplitude facilitates vigorous mixing and cavitation, improving the mass transfer of flavonoids [40], and this parameter showed a positive influence on both factors, TFC and ABTS. Extended extraction times enhance the thorough recovery of bioactive compounds; however, it may lead to the extraction of unwanted compounds or even to flavonoid degradation [41]. The extractive time was statistically significant only in the case of TFC. The response surface plot (RSP) in Figure 3 highlights the fact that ethanol  
Figure 2: Coefficient plots representing the influence of individual and interaction factors on the outcome (quantified through TFC and ABTS methods) of the extraction process. Note: * represents the interaction between two factors.  
concentration shows a quadratic interaction in both cases, manifesting a negative influence; moreover, it induces non-linear effects, suggesting optimal ethanol concentrations can enhance solubility and extraction efficiency. The interaction factor between ethanol concentration and time considers their joint influence, necessitating a balanced approach for optimal extraction efficiency, and it presented a statistically significant negative influence only in the case of TFC. This result suggests an analogous theory as to the influence of ethanol concentration, indicating that the combination of higher concentration and time leads to a final decrease in flavonoid yield. Thus, it is highlighted once again that the identification of the optimal mix of parameters is crucial and dependent on the specific phytochemical class of interest. The extraction parameters that we have analyzed collectively impact physical and chemical processes, including solubility, mass transfer [42], and cell structure breakdown [43].