## 3 Results and Discussion
### Optimization-Effect of Process Variables  
The optimization procedure was designed to evaluate the influence exerted by three critical extraction variables, pH, R\({}_{\text{L/S}}\) and S\({}_{\text{S}}\), on the response (Y\({}_{\text{TP}}\)), and to reveal possible synergistic effects between them. The assessment of the fitted model and the suitability of response surface were accomplished by performing ANOVA and a lack-of-fit test (Figure 2), on the basis of the proximity of measured and predicted values (Table 2). Taking into consideration only the significant terms (Parameter Estimates, Figure 2), the second-degree mathematical model derived was as follows:  
\[\text{Y}_{\text{TP}}\;\text{(mg CGAE g}^{-1}\;\text{dm)}=11.35+2.62\text{X}_{2 }+0.32\text{X}_{3}+1.30\text{X}_{1}{}^{2}+1.36\text{X}_{3}{}^{2} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Design Point** & \multicolumn{2}{c}{**Independent Variables**} & \multicolumn{3}{c}{**Response (Y\({}_{\text{TP}}\), mg CGAE g\({}^{-1}\) dw)**} \\ \hline  & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & **Measured** & **Predicted** \\ \hline
1 & –1 & –1 & 0 & 10.00 & 9.83 \\
2 & –1 & 1 & 0 & 14.66 & 14.54 \\
3 & 1 & –1 & 0 & 9.57 & 9.69 \\
4 & 1 & 1 & 0 & 15.27 & 15.44 \\
5 & 0 & –1 & –1 & 9.58 & 9.44 \\
6 & 0 & –1 & 1 & 10.00 & 10.20 \\
7 & 0 & 1 & –1 & 14.99 & 14.79 \\
8 & 0 & 1 & 1 & 15.16 & 15.30 \\
9 & –1 & 0 & –1 & 13.4 & 13.72 \\
10 & 1 & 0 & –1 & 13.64 & 13.66 \\
11 & –1 & 0 & 1 & 13.94 & 13.92 \\
12 & 1 & 0 & 1 & 15.05 & 14.73 \\
13 & 0 & 0 & 0 & 11.41 & 11.35 \\
14 & 0 & 0 & 0 & 11.16 & 11.35 \\
15 & 0 & 0 & 0 & 11.49 & 11.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analytical display of individual design points and measured and predicted values of the response. Figure 2: Desirability function (**A**), actual-by-predicted plot (**B**) and statistical information (lack-of-fit and parameter estimates inset tables) generated by performing response surface methodology, concerning the effect of process variables on the response. Asterisks (*) on the “Parameter Estimates” inset table denote statistically significant terms (\(p\) < 0.05). The square correlation coefficient (R\({}^{2}\)) provides an indication of the total variability around the mean, as determined by the model [13]. Given that R\({}^{2}\) was 0.99 (\(p<0.0001\)) and the lack-of-fit was significant at least at a 95% significance level, it could be supported that the mathematical equation (Equation (2)) describing the model showed excellent adjustment to the experimental data. The 3D diagrams representing the model (Figure 3) visualize the effect of the process variables on the response (Y\({}_{\rm TP}\)). Using the desirability function (Figure 2), the maximum Y\({}_{\rm TP}\) was estimated to be 17.27 \(\pm\) 0.93 mg CGAE g\({}^{-1}\) dm, at the following optimal settings: pH = 5.0, R\({}_{\rm LJS}\) = 80 mL g\({}^{-1}\) and S\({}_{\rm S}\) = 800 rpm. To confirm  
Figure 3: Three-dimensional diagrams portraying the effect of process variables on the response. the validity of this prediction, the optimal settings were employed to carry out three individual extractions and the Y\({}_{\text{TP}}\) found was 16.86 \(\pm\) 1.75 mg CGAE g\({}^{-1}\) dm. This finding demonstrated the reliability of the predictive model. The Y\({}_{\text{TP}}\) level determined in this study was of a similar magnitude to 20 mg GAE g\({}^{-1}\) dm attained by employing subcritical water extraction of PP [14], but exceeded significantly 7.67 mg GAE g\({}^{-1}\) dm achieved with 80% methanol and ultrasound-assisted extraction [15], 9.11 mg CAE g\({}^{-1}\) dm achieved with 59% (_v/v_) ethanol and ultrasound-assisted extraction [16], and 11.0 mg GAE g\({}^{-1}\) dm achieved with 60% ethanol and microwave-assisted extraction [17]. Lower yields of 6.4 mg g\({}^{-1}\) dm obtained with 55% ethanol and ultrasound-assisted extraction [18], and 4.39 mg GAE g\({}^{-1}\) dm obtained with pressurized water/ethanol mixtures [19] have also been reported.