Analysis of variance (ANOVA) can be used to further examine the model's feasibility and validity (Tables 4 & 5). F-value (Fisher variation ratio), lack of fit, p-value (probability value), adequate precision (AP), R2d (coefficient of determination), R2Adj (adjusted coefficient of determination), R2Pred, were some of the evidences. AP corresponds to signal to noise ratio, which predicts contrasts, the range of expected values at nodes to the prediction error. Model selectivity is adequate when the ratios are higher than four (Zhou et al. 2011; Mishra et al. 2021; Sawood et al. 2021b).
ANOVA for response surface quadratic model
| Source . | Sum of squares . | df . | Mean square . | F-value . | p-value . | . |
|---|---|---|---|---|---|---|
| Model | 8.153E + 005 | 9 | 90,587.12 | 270.24 | <0.0001 | significant |
| A-Influent As(V) concentration | 15,612.35 | 1 | 15,612.35 | 46.58 | <0.0001 | |
| B-Inlet flow rate | 8,273.95 | 1 | 8,273.95 | 24.68 | 0.0006 | |
| C-Bed height | 7.484E+005 | 1 | 7.484E+005 | 2,232.51 | <0.0001 | |
| A2 | 27.66 | 1 | 27.66 | 0.083 | 0.7798 | |
| B2 | 983.96 | 1 | 983.96 | 2.94 | 0.1174 | |
| C2 | 18,866.96 | 1 | 18,866.96 | 56.28 | <0.0001 | |
| AB | 13.78 | 1 | 13.78 | 0.041 | 0.8434 | |
| AC | 4,816.71 | 1 | 4,816.71 | 14.37 | 0.0035 | |
| BC | 117.81 | 1 | 117.81 | 0.35 | 0.5665 | |
| Residual | 3,352.06 | 10 | 335.21 | |||
| Lack of fit | 3,352.06 | 4 | 838.01 | |||
| Pure error | 0.000 | 6 | 0.000 | |||
| Cor total | 8.186E + 005 | 19 |
| Source . | Sum of squares . | df . | Mean square . | F-value . | p-value . | . |
|---|---|---|---|---|---|---|
| Model | 8.153E + 005 | 9 | 90,587.12 | 270.24 | <0.0001 | significant |
| A-Influent As(V) concentration | 15,612.35 | 1 | 15,612.35 | 46.58 | <0.0001 | |
| B-Inlet flow rate | 8,273.95 | 1 | 8,273.95 | 24.68 | 0.0006 | |
| C-Bed height | 7.484E+005 | 1 | 7.484E+005 | 2,232.51 | <0.0001 | |
| A2 | 27.66 | 1 | 27.66 | 0.083 | 0.7798 | |
| B2 | 983.96 | 1 | 983.96 | 2.94 | 0.1174 | |
| C2 | 18,866.96 | 1 | 18,866.96 | 56.28 | <0.0001 | |
| AB | 13.78 | 1 | 13.78 | 0.041 | 0.8434 | |
| AC | 4,816.71 | 1 | 4,816.71 | 14.37 | 0.0035 | |
| BC | 117.81 | 1 | 117.81 | 0.35 | 0.5665 | |
| Residual | 3,352.06 | 10 | 335.21 | |||
| Lack of fit | 3,352.06 | 4 | 838.01 | |||
| Pure error | 0.000 | 6 | 0.000 | |||
| Cor total | 8.186E + 005 | 19 |