## 3 Results and Discussion
### Optimization of Multiple Parameters  
For each parameter assessed, a regression analysis was performed to determine the model that best explained the responses. In this study, it was possible to predict significant effects on several parameters, such as coalescence stability, flocculation stability, particle size, HCT, emulsifying activity, and zeta potential. The quadratic and special cubic models allowed the evaluation of the influence of the variables on the responses. In addition, the analysis of variance (ANOVA) confirmed the significance of the influence of the model on these responses (Table 3). To select the parameters for the optimization of the emulsion, a correlation analysis was performed between the analyses carried out to determine which variables are related to \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Evaluated Parameters** & **Pea (\%)** & \begin{tabular}{c} **Lentil** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Fava Bean** \\ **(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Experimental** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Adjusted** \\ **R\({}^{2}\)** \\ \end{tabular} \\ \hline Zeta potential (mV) & 33.33 & 33.33 & 33.33 & \(-\)30.43 & 0.99 \\ Coalescence & 34.87 & 27.76 & 37.37 & 2.99 & 0.98 \\ Flocculation Index & 36.73 & 21.85 & 41.41 & 1.0 & 0.99 \\ Centrifugal stability (\%) & 41.41 & 30.60 & 27.99 & 0.5 & 0.98 \\ HCT (min) & 56.73 & 43.26 & 0 & 27.00 & 0.99 \\ EAI (m\({}^{2}\)/g) & 19.19 & 80.81 & 0 & 32.85 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental optimization of the response variable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Response Variable** & **Model** & **F-Test** & **R\({}^{2}\)** & _p-Value_ \\ \hline Zeta potential (mV) & Linear & 5.04 & 76.81 & 0.022 \\ Coalescence (\%) & Linear & 1008.87 & 99.88 & \(<\)0.001 \\ Flocculation Index (\%) & Quadratic & 139.34 & 98.00 & \(<\)0.001 \\ Centrifugal stability (\%) & Special cubic & 140.81 & 99.96 & \(<\)0.001 \\ HCT (min) & Quadratic & 8.62 & 74.36 & 0.010 \\ EAI (m\({}^{2}\)/g) & Quadratic & 7.75 & 73.76 & 0.002 \\ Centrifugal stability & Special & 79.63 & 99.58 & \(<\)0.001 \\ constant—KE (\%) & Quadratic & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model fit for each response variable and the statistical data obtained when applying ANOVA of the selected models. each other and, thus, select the relevant variables. Table 5 shows the significant correlation values between the variables. In order to optimize the formulation of the ideal protein concentration and address multiple variables with optimal solutions, it is important to select the key parameters for analysis. The fewer variables considered during the optimization, the more accurate the results will be. We use correlation analysis to determine which response variables are related to one another. Through the correlation analysis, it was possible to cross the data from emulsifying activity with the results of the centrifugation stability and the polydispersity index. The zeta potential was correlated with the emulsion stability. Coalescence stability was correlated with flocculation stability, which in turn correlated with particle size. Based on these correlations, the following parameters were selected for optimization of the mixture: EAI, HCT, zeta potential, particle size, and coalescence stability. For each analysis, the parameters of interest were defined. The variables EAI and HCT were maximized, while the zeta potential, coalescence stability, and IPD variables were minimized (Table 6). The lower and upper limits for each dependent variable were set to values that guarantee the integrity and intrinsic properties of the product based on the maximum or minimum values obtained for each response (Table 3). The optimization results provide information about the influence of the mixture on the stability of the emulsion.