## 3 Results and Discussion
### Experimental Performance of NF
#### 3.1.1 Statistical Analysis and Modelling by RSM  
The NF membrane process responses were studied for the permeate flux and metal rejections (Zn, Cu, and Ni). The findings of the experimental studies were analyzed statistically through analysis of variance (ANOVA). Table 2 shows the ANOVA models.  
For the above models, [PERSON]'s test statistic (\(F\)-Value) clarifies the scattering of actual data around the fitted models, while the \(p\)-value indicates the significance of the model terms. The F value of responses suggested that the respective models were significant regarding the residual error. The \(p\)-value of a model lower than 0.05 indicates a significant model, and higher than 0.10 means an insignificant model. The \(p\)-value of all responses were lower than 0.0001, suggesting that the models are highly significant. The coefficient of regression (\(R^{2}\)) described the system behaviour and the adequacy of the model in the range of independent variables. The high \(R^{2}\) and adjusted \(R^{2}\) in Table 2 also reveal that the models are highly significant.  
The quadratic regression model equations for NF membrane permeate flux (Y\({}_{1}\)), Zn removal (Y\({}_{2}\)), Ni removal (Y\({}_{3}\)), and Cu removal (Y\({}_{4}\)) in terms of coded factors are presented below as Equations (2)-(5), respectively.  
\[\begin{array}{l}\text{Y}_{1}=+26.75+1.84\text{X}_{1}\ +\ 12.96\text{X}_{2}\ +\ 0.51\text{X}_{3}\ +\ 7.08\text{X}_{4}\ -\ 1.06\text{X}_{1}^{2}+0.51\text{X}_{2}^{2}+1.36\text{X}_{3}^{2}+3.04\text{X}_{4 }^{2}\\ \ +\ 1.06\text{X}_{1}\text{X}_{2}-0.53\text{X}_{1}\text{X}_{3}\ +\ 0.82\text{X}_{1}\text{X}_{4}\ +\ 0.33\text{X}_{2}\text{X}_{3}\ +\ 2.5\text{X}_{2}\text{X}_{4}\ +\ 0.77\text{X}_{3}\text{X}_{4 }\end{array} \tag{2}\]  
\[\begin{array}{l}\text{Y}_{2}=+89.32\ +\ 24.78\text{X}_{1}\ -\ 1.62\text{X}_{2}-4.67 \text{X}_{3}\ -\ 2.82\text{X}_{4}\ -\ 6.26\text{X}_{1}^{2}-4.22\text{X}_{2}^{2}\ -\ 4.71\text{X}_{3}^{2}\ -\ 3.91\text{X}_{4 }^{2}\\ \ +\ 0.52\text{X}_{1}\text{X}_{2}\ +\ 1.96\text{X}_{1}\text{X}_{3}+0.67\text{X}_{1} \text{X}_{4}\ -\ 0.34\text{X}_{2}\text{X}_{3}\ -\ 1.25\text{X}_{2}\text{X}_{4}\ +\ 0.23\text{X}_{3}\text{X}_{4 }\end{array} \tag{3}\]  
\[\begin{array}{l}\text{Y}_{3}=+84.38\ +\ 19.27\text{X}_{1}\ -\ 2.23\text{X}_{2}\ -\ 3.82\text{X}_{3}\ -\ 2.17\text{X}_{4}\ -\ 0.43\text{X}_{1}^{2}-3.58\text{X}_{2}^{2}-3.46\text{X}_{3}^{2}-3.75\text{X}_{4 }^{2}\\ \ +\ 0.61\text{X}_{1}\text{X}_{2}\ +\ 0.59\text{X}_{1}\text{X}_{3}+0.31\text{X}_{1} \text{X}_{4}\ -\ 0.52\text{X}_{2}\text{X}_{3}\ +\ 0.07\text{X}_{2}\text{X}_{4}\ +\ 0.26\text{X}_{3}\text{X}_{4 }\end{array} \tag{4}\]  
\[\begin{array}{l}\text{Y}_{4}=+92.65\ +\ 8.88\text{X}_{1}\ -\ 0.85\text{X}_{2}\ -\ 2.02\text{X}_{3}\ -\ 1.04\text{X}_{4}\ -\ 3.76\text{X}_{1}^{2}+0.66\text{X}_{2}^{2}+0.47\text{X}_{2}^{2}-0.46\text{X}_{4 }^{2}\\ \ +\ 0.44\text{X}_{1}\text{X}_{2}\ +\ 1.50\text{X}_{1}\text{X}_{3}\ +\ 0.31\text{X}_{1} \text{X}_{4}\ -\ 0.33\text{X}_{2}\text{X}_{3}\ +\ 0.07\text{X}_{2}\text{X}_{4}\ +\ 0.27\text{X}_{3}\text{X}_{4 }\end{array} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **Degree of Freedom** & **Mean Square** & \(F\)**-Value** & \(p\)**-Value** & \(R^{2}\) & \(R^{2}\)**\({}_{\text{all}}\)** & **Resposes** \\ \hline Model & 5816.87 & 14 & 415.49 & 70.29 & \textless{}0.0001 & 0.985 & 0.971 & Flux \\ \hline Model & 17,449.52 & 14 & 1246.39 & 12.41 & \textless{}0.0001 & 0.9205 & 0.8464 & Zn Removal\% \\ \hline Model & 10,360.61 & 14 & 740.04 & 5.07 & 0.0017 & 0.8255 & 0.6626 & Ni Removal\% \\ \hline Model & 2541.01 & 14 & 181.50 & 19.12 & \textless{}0.0001 & 0.9469 & 0.8974 & Cu Removal\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: ANOVA analysis for the NF membrane.