## 3 Results and Discussion
### Data Analysis by Response Surface Methodology  
The optimization of the adsorption of MB on the 4 AZW process needs 27 (that is: (3)3) experiences, but it can be reduced to 15 by using a BBD. The experimental design matrix and the predicted values obtained by BBD are compared to experimental data in Table 4, and the analysis of variance (ANOVA) allowed us to check the quality of the model (Table 5). The relationship between the experimental response (Yield (%)) and the uncoded forms of the three variables is:  
\[ \begin{array}{c}Yield(\%)=69.88-2.340X_{1}+1406X_{2}-6.50X_{3}+0.0395X_{1}^{ 2}-2605X_{2}^{2}\\ +0.562X_{3}^{2}-33.64X_{1}.X_{2}-0.1523X_{1}.X_{3}+19.7X_{2}.X_{3}\end{array}  \tag{15}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Run**} & \multicolumn{2}{c}{**Initial Dye Concentration**} & \multicolumn{2}{c}{**Amount of Adsorbent**} & \multirow{2}{*}{\(\mathbf{pH}\)} & \multicolumn{2}{c}{**Yield (\%)**} \\ \cline{3-6}  & (\(X_{1}\)) (mg/L) & & (\(X_{2}\)) (g) & & **Observed** & **Predicted** & **Residual** \\ \hline
1 & 14 & 0.0250 & 4.0 & 42.46 & 43.00 & \(-\)0.54125 \\
2 & 8 & 0.0425 & 4.0 & 79.79 & 78.71 & \(1.07375\) \\
3 & 8 & 0.0600 & 6.5 & 93.76 & 93.69 & \(0.07000\) \\
4 & 8 & 0.0425 & 9.0 & 80.17 & 80.78 & \(-\)0.61125 \\
5 & 20 & 0.0425 & 4.0 & 40.05 & 39.44 & \(0.61125\) \\
6 & 20 & 0.0250 & 6.5 & 20.34 & 20.41 & \(-\)0.07000 \\
7 & 14 & 0.0600 & 4.0 & 69.57 & 70.71 & \(-\)1.14375 \\
8 & 14 & 0.0425 & 6.5 & 53.15 & 52.89 & \(0.52667\) \\
9 & 14 & 0.0250 & 9.0 & 39.92 & 38.77 & \(1.14375\) \\
10 & 20 & 0.0425 & 9.0 & 31.29 & 32.36 & \(-\)1.07375 \\
11 & 14 & 0.0425 & 6.5 & 52.02 & 52.89 & \(-\)0.87333 \\
12 & 14 & 0.0425 & 6.5 & 53.51 & 52.89 & \(0.61667\) \\
13 & 20 & 0.0600 & 6.5 & 43.31 & 42.77 & \(0.53250\) \\
14 & 14 & 0.0600 & 9.0 & 70.47 & 69.93 & \(0.54125\) \\
15 & 8 & 0.0250 & 6.5 & 56.66 & 57.19 & \(-\)0.53250 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The uncoded Box-Behnken design matrix of experiments for MB removal. Figure 8: The Langmuir adsorption isotherms models for MB and MG adsorption on 4 AZW(S/L = 1 g/L, T = 25 \(\pm\) 1 \({}^{\circ}\)C and unadjusted pH), as a nonlinear expression. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**MB**} & \multicolumn{4}{c}{**MG**} \\ \hline
**Langmuir** & **q\({}_{\text{max}}\) (mg/g)** & **K\({}_{\text{L}}\) (L/mg)** & **R\({}^{2}\)** & **SD** & **q\({}_{\text{max}}\) (mg/g)** & **K\({}_{\text{L}}\) (L/mg)** & **R\({}^{2}\)** & **SD** \\ \hline  & \(9.95\pm 0.16\) & \(4.45\pm 0.54\) & \(0.993\) & \(0.241\) & \(45.64\pm 1.17\) & \(4.34\pm 0.20\) & \(0.994\) & \(0.315\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of Langmuir isotherm for removal of MB and MG onto 4 AZW at 25 \({}^{\circ}\)C.  
The model Equation (15) indicates that the initial MB concentration (X\({}_{1}\)) had a significant effect (\(p\)\(<\) 0.001, F = 2390) on the yield, followed by the amount of adsorbent m (X\({}_{2}\)) and the solution pH (X\({}_{3}\)) with a low F = 7.8. The positive coefficients of X\({}_{2}\), (X\({}_{2}\),X\({}_{3}\)) and quadratic terms (X\({}_{12}\), X\({}_{32}\)) indicated a direct effect on the removal yield of MB. In contrast, the negative terms X\({}_{1}\), X\({}_{3}\), (X\({}_{1}\),X\({}_{2}\)), (X\({}_{1}\),X\({}_{3}\)) and the quadratic term (X\({}_{22}\)) had an inverse effect on MB adsorption. In addition, ANOVA results (Table 5) showed that this regression model was very significant with \(p\)\(<\) 0.0001 and F = 395.15. Moreover, regression analysis data indicated that quadratic terms X\({}_{12}\), X\({}_{22}\), and the interactive term X\({}_{2}\).X\({}_{3}\) are not significant at all (\(p\)\(>\) 0.05). From Table 4, the agreement between the yield predicted by Equation (15) and the corresponding experimental data is very strong: The values of the determination coefficient R\({}^{2}\) = 0.9986 and of its adjusted R\({}^{2}\)adj = 0.9961 indicate a good correlation between the observed and predicted values of MB removal efficiency.