## 3 Results and Discussion
### Data Analysis by Response Surface Methodology  
The optimization of the DR-81 textile dye adsorption process by cockleshells was carried out be performing 15 experiments in a Box-Behnken design. The experimental matrix and prediction values are shown in Table 6, and the model fit and significance were analyzed by ANOVA (Table 7). The model is considered significant when the \(p\)-values \(<5\%\):  
\[ \begin{split}\text{Y (R}\%)=58.39-14.7888\text{X}_{1}+16.7988\text{X}_{2} -27.3025\text{X}_{3}+1.42625\text{X}_{1}{}^{2}+1.01125\text{X}_{2}{}^{2}-13.99 12\text{X}_{3}{}^{2}+4.92750\text{X}_{1}\text{X}_{2}\\ +6.065\text{X}_{1}\text{X}_{3}-2.41\text{X}_{2}\text{X}_{3}\end{split}  \tag{18}\]  
Table 6 shows that the individual effects of concentration (X1), mass (X2), and pH (X3) are significant, since the \(p\)-values \(<0\). The regression \(p\)-value of less than 0.001 indicates that the model is favorable for studying the biosorption process of DR-81. The surface trace was used to develop the potential relationship between the three variables (C, m, and pH). The surface trace in Figure 13a shows that good removal of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Real Values**} & \multicolumn{3}{c}{**Coded Values**} & \multicolumn{3}{c}{**Y (R \%)**} \\ \hline
**Experiences** & **X1** & **X2** & **X3** & **C (mg/L)** & **m (g)** & **pH** & **Observed** & **Predicted** \\ \hline
1 & \(-1\) & \(-1\) & 0 & 10 & 0.3 & 7 & 61.77 & 63.75 \\
2 & \(+1\) & \(-1\) & 0 & 100 & 0.3 & 7 & 21.61 & 24.31 \\
3 & \(-1\) & \(+1\) & 0 & 10 & 1.5 & 7 & 90.19 & 87.49 \\
4 & \(+1\) & \(+1\) & 0 & 100 & 1.5 & 7 & 69.74 & 67.77 \\
5 & \(-1\) & 0 & \(-1\) & 10 & 0.9 & 2 & 93.17 & 94.00 \\
6 & \(+1\) & 0 & \(-1\) & 100 & 0.9 & 2 & 52.15 & 52.25 \\
7 & \(-1\) & 0 & \(+1\) & 10 & 0.9 & 12 & 27.33 & 27.23 \\
8 & \(+1\) & 0 & \(+1\) & 100 & 0.9 & 12 & 10.65 & 9.82 \\
9 & 0 & \(-1\) & \(-1\) & 55 & 0.3 & 2 & 56.31 & 53.50 \\
10 & 0 & \(+1\) & \(-1\) & 55 & 1.5 & 2 & 90.05 & 91.92 \\
11 & 0 & \(-1\) & \(+1\) & 55 & 0.3 & 12 & 5.59 & 3.72 \\
12 & 0 & \(+1\) & \(+1\) & 55 & 1.5 & 12 & 29.62 & 32.50 \\
13 & 0 & 0 & 0 & 55 & 0.9 & 7 & 58.39 & 58.39 \\
14 & 0 & 0 & 0 & 55 & 0.9 & 7 & 58.39 & 58.39 \\
15 & 0 & 0 & 0 & 55 & 0.9 & 7 & 58.39 & 58.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The uncoded Box–Behnken design matrix of experiments for DR-81 removal. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factor** & **DF** & **Sum of Squares** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Regression & 9 & 10,998.8 & 1222.09 & 131.22 & 0.000 \\ Linear & 3 & 9970.7 & 3323.55 & 356.87 & 0.000 \\ C (mg/L) & 1 & 1749.7 & 1749.66 & 187.87 & 0.000 \\ m (g) & 1 & 2257.6 & 2257.58 & 242.41 & 0.000 \\ pH & 1 & 5963.4 & 5963.41 & 640.33 & 0.000 \\ Square & 3 & 759.7 & 253.22 & 27.19 & 0.002 \\ C (mg/L) \(*\) C (mg/L) & 1 & 20.7 & 7.51 & 0.81 & 0.410 \\ m (g) \(*\) m (g) & 1 & 16.2 & 3.78 & 0.41 & 0.552 \\ pH \(*\) pH & 1 & 722.8 & 722.79 & 77.61 & 0.000 \\ Interaction & 3 & 268.5 & 89.49 & 9.61 & 0.016 \\ C (mg/L) \(*\) m (g) & 1 & 97.1 & 97.12 & 10.43 & 0.023 \\ C (mg/L) \(*\) pH & 1 & 148.1 & 148.11 & 15.90 & 0.010 \\ m (g) \(*\) pH & 1 & 23.2 & 23.23 & 2.49 & 0.175 \\ \hline Residual & 5 & 46.6 & 9.31 & & & \\ Lack of fit & 3 & 46.6 & 15.52 & 3.77 & 0.217 \\ Pure error & 2 & 0.0 & 0. 0 & & \\ Total & 14 & 11,045.3 & & & & \\ \hline \hline \end{tabular} \(S=3.05172;\) R\({}^{2}=99.58\%;\) R\({}^{2}\) (adj) = 98.82\%; R\({}^{2}\) (pred) = 93.25\%.  
\end{table} 
Table 7: ANOVA for the fit of the experimental results to the response surface model. DR-81 by CS was achieved at a concentration of 10 mg/L and at a biosorbent dose of 1.5 g. Figure 13b shows that there is maximum dye removal for a concentration of 10 mg/L and a pH of 2. Figure 13c shows that a pH of 2 and a bio-adsorbent dose of 1.5 g give a good DR-81 dye removal efficiency.