## 3 Experimental Outcomes
### Process Optimization  
The quadratic model in the fraction factorial experimental design (FEED) is used to statistically optimize the adsorption capacity under response surface methodology (RSM) [40; 41]. The general equation of model can be explained:  
\[Y=\beta_{0}+\sum\beta_{i}X_{i}+\sum\beta_{ii}X^{2}+\sum\beta_{ij}X_{i}X_{j}\]  
where \(Y\) is the response variable, \(\beta_{0}\) is the coefficient of regression, \(\beta_{i}\) is the linear influence, \(\beta_{ii}\) is the quadratic influence and \(\beta_{ij}\) is the variable \(X\) interaction influence. The Design expert (7.0.0), statistical software was used for the RSM study, and the graphical representation of 3D and contour plots can be achieved for the response obtained for independent variables with an effect. The quadratic regression equation derived from the analysis of variance (ANOVA) shows the possible individual and combined effect of the factors for the CV-NIFGS system (Table 4). The \(p\)-value < 0.05% was considered significant with a 95% confidence interval. The regression equation obtained for CV-NIFGS system is shown below:  
\[\text{CV-NIFGS}=36.14+28.10^{\bullet}\text{A}-3.52^{\bullet}\text{B}+19.15^{ \bullet}\text{C}-21.21^{\bullet}\text{D62.29}^{\bullet}\text{E}+11.92^{\bullet} \text{AC}+\]  
\[2.91^{\bullet}\text{BC}~{}20.29^{\bullet}\text{A}2+12.54^{\bullet}\text{B}2- 35.16^{\bullet}\text{C}2+10.77^{\bullet}\text{D}2+20.80^{\bullet}\text{E}2\]  
The values of the regression coefficient direct the parametric influence on the adsorption capacity. Surface and contour graphs illustrate the combined influence on adsorption by two factors. Graphical representation of the obtained results is in Figure 4. The fit of the second-order polynomial equation suggests A, C, D, AC and CE have maximum effects with the regression coefficient value of 0.978, which revealed the interaction of parameters studied and predicted adsorption capacity of 184 mg g\({}^{-1}\) with the following optimum values based on a multiple regression analysis and the FFED model: pH 2, NIFGS dosage of 0.03 g L\({}^{-1}\), 204 mg L\({}^{-1}\) as initial dye concentration and 165 min as adsorption time. Based on these optimal values, the estimated adsorption capacity is 184 mg/g. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Summation of**} & \multirow{2}{*}{**DoF**} & \multirow{2}{*}{**Square Mean**} & \multirow{2}{*}{**\(F\)-Value**} & \multirow{2}{*}{**\(p\)-Value**} \\  & & & & & \\ \hline Model & 13,547.2 & 1 & 13,547.2 & 103.2 & \textless{}0.0001 \\ \hline A & 113.6 & 1 & 113.6 & 0.9 & 0.3566 \\ \hline B & 717.6 & 1 & 717.6 & 5.5 & 0.0233 \\ \hline C & 1826.0 & 1 & 1826.0 & 13.9 & 0.0005 \\ \hline D & 10,862.6 & 1 & 10,862.6 & 82.7 & \textless{}0.0001 \\ \hline E & 878.9 & 1 & 878.9 & 6.7 & 0.0126 \\ \hline AC & 20.1 & 1 & 20.1 & 0.2 & 0.6972 \\ \hline BC & 1323.5 & 1 & 1323.5 & 10.1 & 0.0025 \\ \hline A\({}^{2}\) & 736.5 & 1 & 736.5 & 4.8 & 0.0322 \\ \hline B\({}^{2}\) & 100.7 & 1 & 100.7 & 0.7 & 0.4218 \\ \hline C\({}^{2}\) & 223.0 & 1 & 223.0 & 1.4 & 0.2333 \\ \hline D\({}^{2}\) & 2437.6 & 1 & 2437.6 & 15.8 & 0.0002 \\ \hline E\({}^{2}\) & 494.3 & 1 & 494.3 & 3.2 & 0.0777 \\ \hline
**Residual** & 6695.6 & 51 & 131.3 & & \\ \hline Lack of fit & 5782.9 & 49 & 118.0 & 0.3 & 0.9724 \\ \hline Total & 54,053.8 & 63 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: CV-NIFGS ANOVA table. Figure 4: A 3D-surface plot and 2D-contour plot representing adsorption capacity variation relative to: (**a**) duration vs. temperature, (**b**) duration vs. concentration, (**c**) duration vs. adsorbent quantity and (**d**) duration vs. pH. The effect of the interaction between two parameters and all other values are fixed and can be analysed by 3D response surface plots [42; 43; 44; 45; 46; 47]. For example, the capacity increase in adsorption is noted at reduced pH grades and smaller NIFGS dosage. Significant effect on the dye adsorption was observed related to initial CV dye concentration.