## 3 Results
### Optimization and Modeling by Response Surface

Table 6: Matrix of experiments with coded, uncoded factors and the response. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **DF** & **Adj SS** & **Adj MS** & **F-Value** & _p-Value_ \\ \hline Model & 9 & 1458.65 & 162.072 & 17.98 & 0.003 \\ Linear & 3 & 1176.94 & 392.312 & 43.52 & 0.001 \\ \(C_{i}\) & 1 & 57.33 & 57.332 & 6.36 & 0.053 \\ \(m\) & 1 & 550.38 & 550.385 & 61.05 & 0.001 \\ pH & 1 & 569.22 & 569.219 & 63.14 & 0.001 \\ Square & 3 & 165.71 & 55.238 & 6.13 & 0.040 \\ C\({}_{i}\)C\({}_{i}\) & 1 & 0.66 & 0.657 & 0.07 & 0.798 \\ m\(\cdot\)m & 1 & 47.55 & 47.550 & 5.27 & 0.070 \\ pH\(\cdot\)pH & 1 & 128.99 & 128.986 & 14.31 & 0.013 \\
2-way Interaction & 3 & 116.00 & 38.667 & 4.29 & 0.075 \\ C\({}_{i}\)\(\cdot\)m & 1 & 25.94 & 25.940 & 2.88 & 0.151 \\ C\({}_{i}\)\(\cdot\)pH & 1 & 3.57 & 3.571 & 0.40 & 0.557 \\ m\(\cdot\)pH & 1 & 86.49 & 86.490 & 9.59 & 0.027 \\ Error & 5 & 45.08 & 9.015 & \\ Lack-of-fit & 3 & 42.37 & 14.124 & 10.44 & 0.089 \\ Pure error & 2 & 2.70 & 1.352 & & \\ Total & 14 & 1503.73 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Analysis of variance (ANOVA) of the model. The quadratic model well describes the adsorption efficiency (Y%) of MC on the adsorbent (SSS). It is significant and adequate as proved by the \(p\)-value (\(p\)-value = 0.003) with only 3% of total unapplied variations for the model (R\({}^{2}\) = 97%) [35; 44]. Figure 7 shows the 3-D response surfaces of the individual and interaction effects of the parameters that influence the MC adsorption process on SSS. The 3-D curves were plotted by varying two parameters in the experimental domain while the third parameter is kept constant (at the center level). It was found that high adsorption efficiency can be attained at low initial concentrations and high pH (Figure 7b). With respect to the effect of amount on adsorption efficiency, it can be seen in Figure 7a,c that high efficiency can be obtained when the adsorbent dosage of SSS is high [35]. This is confirmed by Figure 8 which shows the optimal conditions for maximum MC adsorption efficiency onto SSS. Figure 8: Optimal conditions for maximum MC adsorption efficiency onto SSS: (**a**) C\({}_{i}\) (mg/L) MC initial concentration, (**b**) m (g/L) SSS dosage and (**c**) pH. Figure 7: Response surface plots of Y% or R%: (**a**) interaction Ci\({}^{*}\)m, (**b**) interaction Ci\({}^{*}\)pH, (**c**) interaction m\({}^{*}\)pH. Model terms with a \(p\)-value \(<\)0.05 are significant at a 95% confidence level, while terms with a \(p\)-value \(<\)0.05 do not affect the response [44]. Based on the analysis of the statistical results, it can be concluded that the resulting quadratic model is adequate and appropriate for describing the relationship between experimental parameters and adsorption efficiency [35]. Moreover, the optimization of the operating conditions was conducted using the maximum response function (Y = 98.77%) which could be obtained by taking the following operating conditions: Ci = 20 mg /L, m = 2.4 g/L and pH = 8.9. The predicted optimal adsorption yield was verified by performing three tests under optimal operating conditions (Y = 95.58%). The standard deviation of the achieved experimental results in comparison to the theoretical results is 2.25. Thus, it can be concluded that the model describing the adsorption of MC on SSS is valid.