The Model *F *value of 108.24 shows that there is a 6.78% probability that a "Model *F *value" this large could be a result of interference, impurity or noise. If the probability value is greater than the fishers test "Prob > F", that is, less than 0.0500 level, this indicates that the terms of the model are significant. It was noted that statistically when the value of the terms or factors appearing in the model is greater than 0.1000, it signifies the model terms are not significant. While optimizing the model, there were some model terms that appear insignificant, and so they were removed in order to improve our model.

SD | 0.20 | *R*^{2}
| 0.9954 |

Mean | 96.45 | Adj *R*^{2} | 0.9862 |

C.V. % | 0.21 | Pred *R*^{2} | 0.9264 |

Press | 0.64 | Adeq precision | 22.748 |

The plot in Fig. 1 gives a clear picture of the effect of interactions of the factors on the response; the plot shows that percentage removal of lead decreases at constant pH of 1, when the concentration of the solution containing the metal ions increases. The plot reflects the response behaviour to improve at high concentration, when the pH is alkaline. The validation plot of the model is shown in Fig. 2, the plot supports the ANOVA statistics that gives a close correlation between the response predicted by the model and the actual values of the experimental response.

### Percentage removal of lead (Pb) using groundnut shell (GS) as adsorbent ANOVA for selected factorial model

$${\text{Removal}} \left( {{\text{Pb}}} \right) GS = 93.497 + 0.053 \left( {{\text{Conc}}} \right) - 0.029 \left( {{\text{Time}}} \right)$$

The "Model *F *value" of 26.07 implies the model is not significant relative to the noise. There is a 13.72% probability that a "Model *F *value" this large could be a result of interference, impurity or noise. If the probability value is greater than the fishers test "Prob > F", that is, less than 0.0500 level, this indicates that the terms of the model are significant (Figs. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12).

The "Pred *R*^{2}" of 0.6989 is not as close to the "Adj *R*^{2}" of 0.9435 as one might normally expect. This may indicate a large block effect or a possible problem with your model and/or data. Things to consider are model reduction, response transformation, outliers, etc. “Adeq Precision" measures the signal-to-noise ratio. A ratio greater than 4 is desirable. Your ratio of 10.497 indicates an adequate signal. This model can be used to navigate the design space.

### Percentage removal of chromium (Cr) using tea bag residues as adsorbent *ANOVA for selected factorial model*

$${\text{Removal}} \left( {{\text{Cr}}} \right)TB = 97.154 - 0.274\left( {{\text{pH}}} \right) + 0.052\left( {{\text{Time}}} \right)$$

The Model *F *value of 156.12 implies there is a 5.65% chance that a "Model *F *value" this large could occur due to noise.

The "Pred *R*^{2}" of 0.9489 is in reasonable agreement with the "Adj *R*^{2}" of 0.9904. "Adeq Precision" measures the signal-to-noise ratio. A ratio greater than 4 is desirable. Your ratio of 28.703 indicates an adequate signal. This model can be used to navigate the design space.

SD | 0.14 | *R*^{2}
| 0.9968 |

Mean | 98.26 | Adj *R*^{2} | 0.9904 |

C.V. % | 0.14 | Pred *R*^{2} | 0.9489 |

PRESS | 0.31 | Adeq precision | 28.703 |

### Percentage removal of chromium (Cr) using groundnut shell (GS) ANOVA for selected factorial model

$${\text{Removal}} \left( E \right) {\text{GS}} = 94.407 + 0.013\left( {{\text{Conc}}} \right) + 0.066\left( {{\text{Time}}} \right)$$

The "Model *F* value" of 2.00 implies the model is not significant relative to the noise. There is a 44.75% chance that a "Model *F *value" this large could occur due to noise.

SD | 1.03 | *R*^{2}
| 0.7997 |

Mean | 98.32 | Adj *R*^{2} | 0.3991 |

C.V. % | 1.05 | Pred *R*^{2} | 2.2046 |

Press | 17.14 | Adeq precision | 2.912 |

A negative "Pred *R*^{2}" implies that the overall mean is a better predictor of your response than the current model. "Adeq Precision" measures the signal-to-noise ratio. A ratio of 2.91 indicates an inadequate signal, and we should not use this model to navigate the design space.

### Percentage removal of nickel (Ni) using tea bag residues as adsorbent ANOVA for selected factorial model

$${\text{Removal }}\left( {{\text{Ni}}} \right){\text{ TB}} = 83.315 + 0.141\left( {{\text{Conc}}} \right) - 0.0686\left( {{\text{Time}}} \right)$$

The "Model *F *value" of 17.35 implies the model is not significant relative to the noise. There is a 16.74% chance that a "Model *F *value" this large could occur due to noise.

SD | 1.25 | *R*^{2}
| 0.9720 |

Mean | 90.83 | Adj *R*^{2} | 0.9160 |

C.V.% | 1.38 | Pred *R*^{2} | 0.5519 |

Press | 25.00 | Adeq precision | 8.434 |

The "Pred *R*^{2}" of 0.5519 is not as close to the "Adj *R*^{2}" of 0.9160 as one might normally expect. This may indicate a large block effect or a possible problem with your model and/or data. Things to consider are model reduction, response transformation, outliers, etc. "Adeq Precision" measures the signal-to-noise ratio. A ratio greater than 4 is desirable. Your ratio of 8.434 indicates an adequate signal. This model can be used to navigate the design space.

### Percentage removal of nickel (Ni) using groundnut shell (GS) ANOVA for selected factorial model

$${\text{Removal }}\left( {{\text{Ni}}} \right){\text{ GS}} = 99.570 - 0.189{ }\left( {{\text{Time}}} \right)$$

The Model *F *value of 11.82 implies there is a 7.52% chance that a "Model *F *value" this large could occur due to noise.

SD | 1.65 | *R*^{2}
| 0.8553 |

Mean | 91.06 | Adj *R*^{2} | 0.7830 |

C.V.% | 1.81 | Pred *R*^{2} | 0.4212 |

PRESS | 21.76 | Adeq precision | 4.863 |

The "Pred *R*^{2}" of 0.4212 is not as close to the "Adj *R*^{2}" of 0.7830 as one might normally expect. This may indicate a large block effect or a possible problem with your model and/or data. Things to consider are model reduction, response transformation, outliers, etc. "Adeq Precision" measures the signal-to-noise ratio. A ratio greater than 4 is desirable. Your ratio of 4.863 indicates an adequate signal. This model can be used to navigate the design space.