## 3 Results and Discussion
### Optimisation of Extraction Performance
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Term** & **Standard Error** & **t Ratio** & \(\boldsymbol{p}\)**-Value** & **Sum of Squares** & \(\boldsymbol{F}\) **Ratio** \\ \hline _No pretreatment_ & & & & \\ \(\text{C}_{\text{DES}}\) & \(0.778011\) & \(5.09\) & \(0.0038\) * & 125.215 & 25.858 \\ \(\text{R}_{\text{L/S}}\) & \(0.778011\) & \(0.72\) & \(0.5057\) & 2.48645 & 0.5135 \\ \(\text{S}_{\text{S}}\) & \(0.778011\) & \(6.95\) & \(0.0009\) * & 233.820 & 48.286 \\ \(\text{C}_{\text{DES}}\) & \(1.100274\) & \(-3.54\) & \(0.0166\) * & 60.6841 & 12.531 \\ \(\text{C}_{\text{DES}}\) & \(1.100274\) & \(-1.33\) & \(0.2398\) & 8.61423 & 1.7789 \\ \(\text{R}_{\text{L/S}}\) & \(1.100274\) & \(0.40\) & \(0.7089\) & 0.75690 & 0.1563 \\ \(\text{C}_{\text{DES}}\)\(\text{C}_{\text{DES}}\) & \(1.145201\) & \(-2.27\) & \(0.0726\) & 24.9200 & 5.1462 \\ \(\text{R}_{\text{L/S}}\)\(\text{R}_{\text{L/S}}\) & \(1.145201\) & \(0.17\) & \(0.8685\) & 0.14708 & 0.0304 \\ \(\text{S}_{\text{S}}\)\(\text{S}_{\text{S}}\) & \(1.145201\) & \(-0.39\) & \(0.7118\) & 0.74079 & 0.1530 \\ \hline \hline Lack-of-fit & & & \(0.1133\) & 22.3468 & 7.9870 \\ \hline _Ultrasonication_ & & & & \\ _pretreatment_ & & & & \\ \(\text{C}_{\text{DES}}\) & \(1.074859\) & \(63.28\) & \(<\)\(0.0001\) * & 28.38811 & 8.1905 \\ \(\text{R}_{\text{L/S}}\) & \(0.658214\) & \(-2.86\) & \(0.0353\) * & 199.7001 & 57.617 \\ \(\text{S}_{\text{S}}\) & \(0.658214\) & \(7.59\) & \(0.0006\) * & 21.38580 & 6.1702 \\ \(\text{C}_{\text{DES}}\)\(\text{R}_{\text{L/S}}\) & \(0.658214\) & \(-2.48\) & \(0.0556\) & 18.19023 & 5.2482 \\ \(\text{C}_{\text{DES}}\)\(\text{S}_{\text{S}}\) & \(0.930855\) & \(2.29\) & \(0.0706\) & 18.14760 & 5.2359 \\ \(\text{R}_{\text{L/S}}\)\(\text{S}_{\text{S}}\) & \(0.930855\) & \(-2.29\) & \(0.0708\) & 22.46760 & 6.4824 \\ \(\text{C}_{\text{DES}}\)\(\text{C}_{\text{DES}}\) & \(0.930855\) & \(-2.55\) & \(0.0515\) & 43.53467 & 12.560 \\ \(\text{R}_{\text{L/S}}\)\(\text{R}_{\text{L/S}}\) & \(0.968865\) & \(-3.54\) & \(0.0165\) * & 24.50608 & 7.0705 \\ \(\text{S}_{\text{S}}\)\(\text{S}_{\text{S}}\) & \(0.968865\) & \(2.66\) & \(0.0449\) * & 30.17521 & 8.7061 \\ \hline Lack-of-fit & & & \(0.4891\) & 11.0748 & 1.1804 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical data obtained after implementing response surface methodology. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Polynomial Equations** & \(\mathbf{R^{2}}\) & \(\boldsymbol{p}\) \\ \hline No pretreatment & \(72.98+3.96\text{X}_{1}+5.41\text{X}_{3}-3.90\text{X}_{1}\text{X}_{2}\)
Ultrasonication of samples prior to stirred-tank extraction had a very pronounced effect on the extraction models, as can be concluded by the equations derived (Table 3). Thus, while \(C_{\text{DES}}\) (X\({}_{1}\)) had a positive contribution in maximizing Y\({}_{\text{TP}}\) in the extraction without ultrasonication pretreatment, it negatively affected the ultrasound-pretreated extraction. On the contrary, increased S\({}_{\text{S}}\) (X\({}_{3}\)) was significant for maximizing Y\({}_{\text{TP}}\) in samples received no pretreatment, whereas ultrasound-pretreated samples required the lowest S\({}_{\text{S}}\) used to give maximum Y\({}_{\text{TP}}\). Figure 3: Desirability graphs displaying optimal settings and maximum theoretical extraction yields for total polyphenols (mg GAE g\({}^{-1}\) dm). \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Case**} & **Maximum Predicted Response** & \multicolumn{3}{c}{**Optimal Conditions**} \\  & **(Y\({}_{\text{TP}}\), mg GAE g\({}^{-1}\) dm)** & \(C_{\text{DES}}\) **(_uv/v, \%_)** & **R\({}_{\text{L/S}}\) (mL g\({}^{-1}\))** & **S\({}_{\text{S}}\) (rpm)** \\ \hline No pretreatment & 80.93 \(\pm\) 6.68 & 85 & 20 & 800 \\ Ultrasonication & 82.87 \(\pm\) 4.28 & 75 & 100 & 200 \\ pretreatment & & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Optimal predicted conditions and maximum predicted values (\(\pm\)sd) for the extraction of _M. oleifera_ with and without ultrasonication pretreatment.