## 3 Results
### Statistical Analysis of the Model  
Twelve mixture formulations were run according to the experimental design, and the respective coefficients of the regression model and ANOVA of the mathematical models were adjusted to the response function (Tables 3 and 4). Based on Tables 3 and 4, the model _F_-value of ABTS radical activity was 45.41, while the phenolic content was 87.90, which implies that the models are significant. There is only a 0.03% and <0.0001% chance that a model _F_-value this large could occur due to noise. Moreover, according to [PERSON] et al. [13], it can be concluded that since the _p_-values were 0.0003 and <0.0001, which are less than <0.05, the main effect of regression was statistically significant. Therefore, in this case, it shows that the model is significant. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & **Sum of Square** & **Degrees of Freedom (df)** & \multirow{2}{*}{**Mean Square**} & **_F_-Value** & **_p_-Value** & \\ \hline Model & 3.93 & 6 & 0.66 & 45.41 & 0.0003 & significant \\ Linear & 0.40 & 2 & 0.20 & 13.78 & 0.0092 & \\ mixture & 0.39 & 1 & 0.39 & 27.28 & 0.0034 & \\ \(x_{1}x_{3}\) & 2.38 & 1 & 2.38 & 164.86 & \textless{}0.0001 & \\ \(x_{2}x_{3}\) & 1.67 & 1 & 1.67 & 115.74 & 0.0001 & \\ \(x_{1}x_{2}x_{3}\) & 1.29 & 1 & 1.29 & 89.61 & 0.0002 & \\ Residual & 0.07 & 5 & 0.014 & & & \\ Lack of fit & 0.069 & 3 & 0.023 & 16.12 & 0.059 & not significant \\ Pure error & 0.00028 & 2 & 0.00014 & 45.41 & 0.0003 & \\ Cor total & 4.01 & 11 & 0.66 & 13.78 & 0.0092 & \\ R\({}^{2}\) & 0.9820 & & & & & \\ Adj. R\({}^{2}\) & 0.9604 & & & & & \\ CV & 0.13 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of variance (ANOVA) for the ABTS radical antioxidant activity. Meanwhile, the entire model terms in the ABTS radical activity response (\(x_{1}\), \(x_{2}\), and \(x_{3}\)), where the values of probability \(>\) F are less than 0.05, indicate that the model terms are also significant. In this study, the linear mixture components \(x_{1}x_{2}\), \(x_{1}x_{3}\), \(x_{2}x_{3}\), and \(x_{1}x_{2}x_{3}\) are significant model terms. According to the model terms in Table 3, the ABTS antioxidant activity was highly significant (\(p\)-value \(<\) 0.0001) for binary (\(x_{1}x_{3}\)) _M. malabathricum_ and _M. decemfidum_, followed by (\(x_{2}x_{3}\)) _M. hitra_ and _M. decemfidum_ and tertiary (\(x_{1}x_{2}x_{3}\)) _M. malabathricum_, _M. decemfidum_, and _M. hitra_. The mathematical model of ABTS antioxidant activity is presented in Equation (3), as follows:  
\[\text{ABTS}=+92.917_{x1}+92.988_{x2}+93.154_{x3}+3.052_{x1x2}+7.502_{x1x3}+6.28 6_{x2x3}-30.088_{x1x2x3} \tag{3}\]  
Meanwhile, the model terms for the phenolic content response (\(x_{1}\), \(x_{2}\), and \(x_{3}\)), where the values of probability \(>\) F are less than 0.05, indicate that the model terms are significant. In this study, the linear mixture components \(x_{1}x_{3}\), \(x_{2}x_{3}\), and \(x_{1}x_{2}x_{3}\) are significant model terms, except for the interaction between \(x_{1}x_{2}\) with a larger \(p\)-value (0.2585), indicating that the combination of the mixtures produced the least response of interest. According to the model terms in Table 4, the phenolic content activity was highly significant (\(p\)-value \(<\) 0.0001) for tertiary (\(x_{1}x_{2}x_{3}\)) _M. malabathricum_, _M. decemfidum_, and _M. hitra_, followed by binary (\(x_{1}x_{3}\)) _M. malabathricum_ and _M. decemfidum_ and binary (\(x_{2}x_{3}\)) _M. hitra_ and _M. decemfidum_. The mathematical model of phenolic content activity is presented as follows in Equation (4):  
\[ \begin{array}{c}\text{Phenolic content}=+22.094_{x1}+25.385_{x2}+29.498_{x3 }+3.958_{x1x2}-36.814_{x1x3}+9.767_{x2x3}+\\ 207.468_{x1x2x3}\end{array}  \tag{4}\]  
This study shows that the models of the coefficients of determination were 98.20% for ABTS radical activity and 99.06% for phenolic content, which present the maximum degree of correlation between the observed and predicted values.