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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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