In order to optimize the chosen adsorption factors, a CCD was applied. The design of experimental (DOE) software (version 8) was employed to investigate how pH, the amount of adsorbent, initial concentration, and the time of RR2 dye affect the responses. F-test was done in order to examine the statistical model and to find out the mathematical relationship between responses and process parameters including contact time (X1), pH (X2), adsorbent dosage (X3), and the initial concentration of RR2 (X4). The regression model was also examined for its significance and performance and it was done with the analysis of variance ANOVA for the adsorption of RR2 dye using AC. The ANOVA results for the adsorption of RR2 dye are shown in Table 4. The F-value of the model (156.90) indicates that the model has a significant level. Only 0.01% of the ‘F-value of model’ is likely to be due to noise. P-value is used to determine the significance of each parameter. The amounts of Prob > F when they are lower than 0.05 reveal that the model terms are acceptable for the adsorption of RR2 dye and that the parameters or their interactions are statistically significant. When they are more than 0.5 and are not significant, they reveal that the quadratic model is proper for this research. As shown in Table 4, the P-values of X1, X2, X3, X4, X1 × 3, and X3 × 4 are less than 0.05, indicating a significant effect of these variables on RR2 removal. Adsorbent dose and contact time have the greatest effect on RR2 adsorption. Pred R2 and Adj R2 for RR2 dye removal are 0.95 and 0.96, respectively, which confirms that there is a good match between predicted data and experimental data. The R2 (Adj) and R2 (pred) should be within approximately 0.2 of each other to be in reasonable agreement (Mousavi et al. 2017).
The results from the ANOVA for the quadratic equation
| Source | Sum of squares | df | Mean square | F-value | P-value |
|---|---|---|---|---|---|
| Model | 65,602.65 | 14 | 4,685.90 | 156.90 | <0.0001 |
| X1 | 10,783.36 | 1 | 10,783.36 | 361.06 | <0.0001 |
| X2 | 382.50 | 1 | 382.50 | 12.81 | 0.0007 |
| X3 | 22,408.69 | 1 | 22,408.69 | 750.32 | <0.0001 |
| X4 | 7,477.79 | 1 | 7,477.79 | 250.38 | <0.0001 |
| X1 X2 | 27.45 | 1 | 27.45 | 0.92 | 0.3414 |
| X1 X3 | 7,161.41 | 1 | 7,161.41 | 239.79 | <0.0001 |
| X1 X4 | 113.78 | 1 | 113.78 | 3.81 | 0.0554 |
| X2X3 | 16.69 | 1 | 16.69 | 0.56 | 0.4576 |
| X2 X4 | 2.57 | 1 | 2.57 | 0.086 | 0.7704 |
| X3 X4 | 458.19 | 1 | 458.19 | 15.34 | 0.0002 |
 | 361.09 | 1 | 361.09 | 12.09 | 0.0009 |
 | 361.09 | 1 | 149.34 | 5.00 | 0.0289 |
 | 382.89 | 1 | 382.89 | 12.82 | 0.0007 |
 | 854.06 | 1 | 854.06 | 28.60 | <0.0001 |
| Residual | 1,881.53 | 63 | 29.87 | ||
| Lack of fit | 416.33 | 10 | 41.63 | 1.51 | 0.1633 |
| Pure error | 1,465.21 | 53 | 27.65 | ||
| Cor. total | 67,484.18 | 77 | |||
| Std. dev. | 5.46 | ||||
| Mean | 42.29 | ||||
| C.V.% | 12.92 | ||||
| Adeq Precision | 42.651 |
| Source | Sum of squares | df | Mean square | F-value | P-value |
|---|---|---|---|---|---|
| Model | 65,602.65 | 14 | 4,685.90 | 156.90 | <0.0001 |
| X1 | 10,783.36 | 1 | 10,783.36 | 361.06 | <0.0001 |
| X2 | 382.50 | 1 | 382.50 | 12.81 | 0.0007 |
| X3 | 22,408.69 | 1 | 22,408.69 | 750.32 | <0.0001 |
| X4 | 7,477.79 | 1 | 7,477.79 | 250.38 | <0.0001 |
| X1 X2 | 27.45 | 1 | 27.45 | 0.92 | 0.3414 |
| X1 X3 | 7,161.41 | 1 | 7,161.41 | 239.79 | <0.0001 |
| X1 X4 | 113.78 | 1 | 113.78 | 3.81 | 0.0554 |
| X2X3 | 16.69 | 1 | 16.69 | 0.56 | 0.4576 |
| X2 X4 | 2.57 | 1 | 2.57 | 0.086 | 0.7704 |
| X3 X4 | 458.19 | 1 | 458.19 | 15.34 | 0.0002 |
| | 361.09 | 1 | 361.09 | 12.09 | 0.0009 |
| | 361.09 | 1 | 149.34 | 5.00 | 0.0289 |
| | 382.89 | 1 | 382.89 | 12.82 | 0.0007 |
| | 854.06 | 1 | 854.06 | 28.60 | <0.0001 |
| Residual | 1,881.53 | 63 | 29.87 | ||
| Lack of fit | 416.33 | 10 | 41.63 | 1.51 | 0.1633 |
| Pure error | 1,465.21 | 53 | 27.65 | ||
| Cor. total | 67,484.18 | 77 | |||
| Std. dev. | 5.46 | ||||
| Mean | 42.29 | ||||
| C.V.% | 12.92 | ||||
| Adeq Precision | 42.651 |