## 3 Results and Discussion
### Regression Models and Response Surfaces
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Source** & **SS** & **MS** & **F-Value** & _p-Value_ \\ \hline  & & Daidzin & & \\ \hline Model & 0.21320 & 0.03045 & 83.34809 & 0.00000 \\ Total error & 0.00438 & 0.00036 & & \\ Lack of fit & 0.00180 & 0.00090 & 3.50217 & 0.07034 \\ Pure error & 0.00257 & 0.00025 & & \\ Cor total & 0.21758 & 0.01145 & & \\ Model fit R\({}^{2}\) = 0.9681 Accuracy: Adj. R\({}^{2}\) = 0.9798 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model fit and analysis of variance explained by the model form and lack of fit for five isoflavues using a mixture design with three solvents: ethanol, H\({}_{2}\)O, and propanediol. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Solvents Linear Factors** & **Coefficient** & **Standard Error** & _p-Value_ \\ \hline  & & Daidzin & \\ \hline (A) EtOH & 0.005976 & 0.012274 & 0.635129 \\ (B) H\({}_{2}\)O & 0.046436 & 0.013484 & 0.004860 \\ (C) Propanediol & 0.104128 & 0.012274 & 0.000002 \\ AB & 0.743744 & 0.065217 & 0.000000 \\ BC & 0.626670 & 0.065217 & 0.000001 \\ ABC & 3.578962 & 0.396505 & 0.000001 \\ AC (A–C) & 1.013699 & 0.219349 & 0.000589 \\ BC (B–C) & \(-0.390842\) & 0.218512 & 0.098924 \\ \hline  & & Genistin & \\ \hline (A) EtOH & 0.010618 & 0.017566 & 0.555965 \\ (B) H\({}_{2}\)O & 0.048974 & 0.019273 & 0.024604 \\ (C) Propanediol & 0.105408 & 0.016896 & 0.000030 \\ AB & 1.095919 & 0.093359 & 0.000000 \\ BC & 0.782245 & 0.093849 & 0.000001 \\ ABC & 3.070757 & 0.570956 & 0.000126 \\ AB (A–B) & 1.015913 & 0.272909 & 0.002558 \\ \hline  & & Malonyldiaidzin & & \\ \hline (A) EtOH & 0.005035 & 0.013116 & 0.707798 \\ (B) H\({}_{2}\)O & 0.395916 & 0.014408 & 0.000000 \\ (C) Propanediol & 0.182057 & 0.013116 & 0.000000 \\ AB & 1.411829 & 0.069688 & 0.000000 \\ BC & 1.133447 & 0.069688 & 0.000000 \\ ABC & 6.566528 & 0.423685 & 0.000000 \\ AB (A–B) & 1.159180 & 0.233490 & 0.000328 \\ AC (A–C) & 1.252320 & 0.234385 & 0.000176 \\ \hline  & & Malonylglycitin & & \\ \hline (A) EtOH & 0.002846 & 0.009474 & 0.768255 \\ (B) H\({}_{2}\)O & 0.063592 & 0.010561 & 0.000031 \\ (C) Propanediol & 0.036284 & 0.009474 & 0.001839 \\ AB & 0.272083 & 0.052391 & 0.000136 \\ BC & 0.196498 & 0.052391 & 0.002151 \\ ABC & 1.662748 & 0.320204 & 0.000136 \\ \hline  & & Malonylgenistin & & \\ \hline (A) EtOH & 0.017682 & 0.027268 & 0.527991 \\ (B) H\({}_{2}\)O & 0.447711 & 0.029917 & 0.000000 \\ (C) Propanediol & 0.238918 & 0.026227 & 0.000001 \\ AB & 2.183971 & 0.144919 & 0.000000 \\ BC & 1.629657 & 0.145679 & 0.000000 \\ ABC & 5.432483 & 0.886282 & 0.000036 \\ AB (A–B) & 2.537765 & 0.423631 & 0.000045 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: An evaluation of the influence and regression coefficients of models for five isoflavues, using a mixture design with three solvents: (A) ethanol, (B) H\({}_{2}\)O, and (C) propanediol. To show the effect of the solvents' proportion on the extraction efficiency, the response surface plots were generated (Figure 3). Additionally, profiles of approximated values and desirability of the composition of three solvents for the extraction efficiency of daidzin, genistin, malonyldaidzin, malonylglycitin, and malonylgenistin are presented in Figure 4. It can be seen that response patterns were very similar for all compounds. Parabolic shapes of the trace plots prove that the extraction rate increases up to ca. 30% of each solvent and then decreases rapidly. A very high overall desirability of 0.9682 was obtained. The use of experimental planning techniques, such as the design of experiments (DOE) and response surface methodology (RSM), has proven to be an effective approach for optimizing extraction processes [28]. For instance, [PERSON] et al. [24] applied the DOE method to optimize the extraction of phenolic compounds from white mulberry, revealing the importance of two factors--ethanol concentration and temperature--on extraction efficiency.