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As can be seen Table 1, there was a considerablevariation in the degradation efficiency at different values of the selectedvariables. The analysis of variance (ANOVA) was implemented to specify thesignificance and adequacy of the statistical method, as given in Table 4. F-valueof model should be greater than the tabulated value of the F-distribution for acertain number of degrees of freedom at a level of significance, ?=5%. F-valuesof the degradation percentage of Eosin B dye by ZnO nanoparticles were reportedas 36.43 which are significant. P-values of model for Eosin B degradation weresignificant.

The insignificant lack of fit, P-value of 0.3504 (more than 0.05) forthe degradation percentage of Eosin B dye for ZnO nanoparticles, indicated thatthe quadratic model was valid for the present study. The minimum value ofstandard error design (0.479) around the centroid indicates that the presentmodel can be used to conduct the design space (Fig. 2).The significance of eachcoefficient for the degradation percentage of Eosin B dye by ZnO nanoparticleswas determined by F-values and P-values as listed in Table 5.

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Values were usedto understand the pattern of the interactions between the test variables. Basedon these results, a relationship between the degradation percentage of Eosin Bdye and selected variables was expressed by the second-order polynomialequation. The regression equation obtained after the ANOVA showed that the coefficientof determination (R2) was 0.9855 for Eosin B dye degradation, meaningthat more than 99.91 % of the data deviation can be explained by the model. Itcorrects the R2 value for the sample size and the number of terms inthe model by using the degrees of freedom on its computations.

So, if there aremany terms in a model and not a very large sample size, adjusted R2may be visibly smaller than R2 30. Hence, the high value of adjustedR2 (0.9982) indicates a high degree of correlation between theexperimental and predicted values and consequently a good predictability of themodel. It was observed that the predicted R2 was 0.9324. Thus,predicted R2 is in agreement with the adjusted R2. Hence,the quadratic model can be used to navigate the design space. The low values ofcoefficient of variation CV (1.

13%) and standard deviation SD (1.01) showedhigh reliability. In this case, low CV and SD values indicate the capability withwhich the experiment was conducted. The low predicted residual sum of squares(PRESS) (70.87) is a measure of how well the model fits each point in the model32. The smaller the PRESS statistic, the better the model fits the datapoints. Thus, the high R2 value, significant F-value, insignificantlack-of-fit P-value, high adequate precision and low PRESS indicate highadequacy and validity of models in predicting the Eosin B dye degradation.Therefore, these models were used for further analysis.

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