As can be seen Table 1, there was a considerable

variation in the degradation efficiency at different values of the selected

variables. The analysis of variance (ANOVA) was implemented to specify the

significance and adequacy of the statistical method, as given in Table 4. F-value

of model should be greater than the tabulated value of the F-distribution for a

certain number of degrees of freedom at a level of significance, ?=5%. F-values

of the degradation percentage of Eosin B dye by ZnO nanoparticles were reported

as 36.43 which are significant. P-values of model for Eosin B degradation were

significant. The insignificant lack of fit, P-value of 0.3504 (more than 0.05) for

the degradation percentage of Eosin B dye for ZnO nanoparticles, indicated that

the quadratic model was valid for the present study. The minimum value of

standard error design (0.479) around the centroid indicates that the present

model can be used to conduct the design space (Fig. 2).The significance of each

coefficient for the degradation percentage of Eosin B dye by ZnO nanoparticles

was determined by F-values and P-values as listed in Table 5. Values were used

to understand the pattern of the interactions between the test variables. Based

on these results, a relationship between the degradation percentage of Eosin B

dye and selected variables was expressed by the second-order polynomial

equation. The regression equation obtained after the ANOVA showed that the coefficient

of determination (R2) was 0.9855 for Eosin B dye degradation, meaning

that more than 99.91 % of the data deviation can be explained by the model. It

corrects the R2 value for the sample size and the number of terms in

the model by using the degrees of freedom on its computations. So, if there are

many terms in a model and not a very large sample size, adjusted R2

may be visibly smaller than R2 30. Hence, the high value of adjusted

R2 (0.9982) indicates a high degree of correlation between the

experimental and predicted values and consequently a good predictability of the

model. 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 of

coefficient of variation CV (1.13%) and standard deviation SD (1.01) showed

high reliability. In this case, low CV and SD values indicate the capability with

which 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 model

32. The smaller the PRESS statistic, the better the model fits the data

points. Thus, the high R2 value, significant F-value, insignificant

lack-of-fit P-value, high adequate precision and low PRESS indicate high

adequacy and validity of models in predicting the Eosin B dye degradation.

Therefore, these models were used for further analysis.

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