## 3 Results
### Response Surface Analysis and Optimization  
According to [PERSON] et al. [17], in the statistical methods, the response surface design is used to discover the effects of process variables on the specific responses of a system. In our study, the response surface for ABTS antioxidant activity with respect to the different proportions of the three _Melastoma_ leaf extracts, _M. malabathricum_ (\(x_{1}\)), _M. hirta_ (\(x_{2}\)), and _M. decemfidum_ (\(x_{3}\)), are shown in Figure 4. The mixture contour plots in Figure 4A,B show that the percentage inhibition of ABTS radical scavenging activity significantly increased with the addition of the \(x_{3}\) component to both interactions of \(x_{1}\) and \(x_{2}\) components. This interaction can also be supported through the greater \(F\)-values of these coefficients, \(x_{1}x_{3}\), \(x_{2}x_{3}\), and \(x_{1}x_{2}x_{3}\), which yielded 164.86, 115.74, and 89.61, respectively in Table 3.  
Figure 3: Actual phenolic content versus predicted phenolic content.  
Figure 2: Actual ABTS (2, 2\({}^{\prime}\)-azino-bis (ethylbenzthiazol-6-sulfonic acid)) radical activity versus predicted ABTS radical activity.  
Simultaneously, the response surface for the phenolic content activity of the _Melastoma_ leaf mixture extract is shown in Figure 5. The mixture contour plots in Figure 5a,b show that the phenolic content activity also increased with the addition of the \(x_{3}\) component to both interactions of mixtures \(x_{1}\) and \(x_{2}\) components. From this result, the highest interaction between the mixtures can be seen from the coefficients of \(x_{1}x_{3}\) and \(x_{1}x_{2}x_{3}\) where the greater \(F\)-values of both coefficients yielded 140.51 and 150.81, respectively, in Table 4. This result can be justified using the study of antimicrobial efficacy of essential oils by [PERSON] et al. [24] where different compounds can interact to either reduce or increase the response outcomes. On the other hand, in terms of ABTS radical activity, the component \(x_{1}\) had a slight effect on the interaction of both \(x_{2}\) and \(x_{3}\) components, where the synergistic effect was found between the mixtures of \(x_{1}\) and \(x_{3}\), while antagonistic effects were found in the mixture of \(x_{1}\) and \(x_{2}\). Meanwhile, for the phenolic content activity of the mixture of _Melastoma_ extracts, the component \(x_{3}\) showed a significant synergistic effect on either \(x_{1}\) or \(x_{2}\) coefficients. Therefore, it can be seen that the interaction between the three _Melastoma_ leaf extracts resulted in a significant effect on the scavenging activity of radical species and on the phenolic content activity.  
Figure 4: (**A**) Contour charts. (**B**) 3-Dimensional response surface of ABTS radical activity.  
Figure 5: (**a**) Contour plot. (**b**) 3-Dimensional optimal points of phenolic content.  
The optimization technique was further evaluated after considering the simultaneous response surface and contour plot from the interaction between the independent variables and the response. This technique has been applied by [PERSON] et al. [25] where a visual inspection of the contour charts was evaluated and studied in order to determine good operational conditions. In this study, a desirability function was generated to predict (1.00) the optimal points for each _Melastoma_ leaf extract. By performing real experiments on each optimal point mixture based on the prediction, the best optimum antioxidant activity for the simultaneous three _Melastoma_ leaf extracts was 30% _M. malabathriculum_, 40% _M. hitra_, and 30% _M. decemfidum_, yielding 93.0% antioxidant activity against radical species for the ABTS assay and 30.96 mg/g GAE for phenolic content. Table 5 shows the optimal points for optimum antioxidant activity in the mixture of _Melastoma_ leaf extracts for both the ABTS radical assay and phenolic content.