## 3 Results and Discussion
Diagnostics of the model are shown by plots of the normal distribution of residuals, residuals versus predicted values, and predicted versus actual values, presented in Figure 10. Based on them, it can be said that the residuals are normally distributed and there are no extreme values among them. Figure 11 presents the perturbation and contour plots with a quadratic influence of the factors. The influence of the factors hydro module and duration is the most significant (Figure 11a). Figure 11b shows the effect of the hydro module and duration on the Ache inhibition potential while keeping the temperature and extractant at values of 70 \({}^{\circ}\)C and 80%, respectively. Under these conditions, the maximum AChE (IC20 0.27 mg/mL) could be obtained with a hydro module of 10 for a duration time of 30 min. Proposing optimal conditions for AChE inhibition is important not only because the topic is not well-exploited yet, but also because the treatment of Alzheimer's and Parkinson's diseases is gradually advancing. Any information that can spare resources and time is valuable for future industrial uses. Other authors confirm that RSM can be a useful prediction tool for the plants' AChE inhibition potential [35]. Figure 11c shows the effect of the hydro module and temperature on the AChE while keeping the duration and extractant at values of 40 and 80, respectively. Under these conditions, the maximum Ache could be obtained with a hydro module of 10 and a temperature of 60 \({}^{\circ}\)C. Figure 11d shows the effect of the hydro module and extractant on the AChE while keeping the duration and temperature at values of 20 and 50 \({}^{\circ}\)C, respectively. Under these conditions, the maximum Ache could be obtained with a hydro module of 10 and an extractant of 90%. Figure 11e shows the effect of the temperature and extractant on the AChE while keeping the hydro module and duration at values of 20 and  
keeping the hydro module and extractant at values of 5 and 80, respectively. Under these conditions, the maximum AChE could be obtained with a duration of 30 and a temperature of 60 \({}^{\circ}\)C. Other authors have reported the optimal conditions for UAE in terms of high AChE-inhibitory activity to be the following: methanol concentration of 85.06%, ultrasonic time of 39.1 min, and material-to-liquid ratio of 1.06:10 (g/mL) [36]. In order for the conclusions from the dispersion analyzes to be sufficiently reliable, the following is necessary. Figure 10: Diagnostics of the AChE model: (**a**) normal plot of residuals; (**b**) residuals vs. predicted plot; (**c**) predicted vs. actual plot. Figure 11: AChE inhibition model analysis: (**a**) Perturbation plot; (**b**) contour surface plots of AChE against hydro module (ratio) and duration (min); (**c**) contour surface plots of AChE against hydro module (ratio) and temperature; (**d**) contour surface plots of AChE against hydro module (ratio) and extractant; (**e**) contour surface plots of AChE against temperature and extractant; (**f**) contour surface plots of AChE against duration (min) and temperature. All samples must be drawn from normally distributed populations. To ascertain this, a normality check was performed. The Shapiro-Wilk test is a more appropriate method for small sample sizes (<50 samples), as is the case here. In this test, the null hypothesis states that the data were taken from a normally distributed population. Thus, when the \(p\)-value > 0.05, the null hypothesis is accepted and the data are assumed to be normally distributed. The results are presented in Table 15. The software product SPSS v.26 was used to obtain them. The reason is that the Design Expert v.13 software does not provide specific tools for performing tests for normality, homogeneity, etc., of populations such as those available in SPSS or other statistical software packages. Instead, Design Expert focuses on experimental design and analysis of experimental results.