# The b1A + b2B + b3C +

The experimental results obtained for Eosin B sonoocatalyticdegradation according to the CCD experiments are illustrated in Table 1. Basedon the experimental design, a quadratic response surface model was found todescribe the experimental relationships between the independent variables andthe response according to the following equation:% Degradation Eosin B = b0 + b1A + b2B + b3C + b4D +b12AB + b13AC + b14AD + b23x2x3+ b24BD + b34CD + b11AA + b22BB + b33CB+ b44DBAs can be seen Table 1, there was a considerablevariation in the degradation efficiency at different values of the chosenvariables. The analysis of variance (ANOVA) was performed to specify thesignificance of the statistical method, as given in Table 4. F-value of modelshould be greater than the tabulated value of the F-distribution for a certainnumber of degrees of freedom at a level of significance, ?=5%.

F-values of the degradationpercentage of Eosin B dye were reported as 36.43 which are significant.P-values of model for Eosin B degradation were significant. The insignificantlack of fit, P-value of 0.3504 (more than 0.05) for the degradation percentageof Eosin B, showed that the quadratic model was valid for the present study.The minimum value of standard error design (0.

479) around the centroid indicatesthat the model can be used to behavior the design space (Fig. 2).Thesignificance of each coefficient for the degradation percentage of Eosin wasdetermined by F-values and P-values as listed in Table 5. Based on theseresults, a relationship between the degradation percentage of Eosin B andselected variables was explained by the second-order polynomial equation. Theregression equation obtained after the ANOVA showed that the coefficient ofdetermination (R2) was 0.9855 for Eosin B dye degradation, meaningthat more than 99.

91 % of the data deviation can be expressed by the model. Itcorrects the R2 value for the sample size and the number of terms in the modelby using the degrees of freedom on its calculation. If there are many terms ina model and not a very large sample size, adjusted R2 may be smaller than R2 30.Therefore the high value of adjusted R2 (0.9982) indicates a highdegree of correlation between the experimental and predicted values andconsequently a good predictability of the model.

It was observed that thepredicted R2 was 0.9324. Thus, predicted R2 is inagreement with the adjusted R2. Hence, the quadratic model can beused to navigate the design space. The low values of coefficient of variationCV (1.13%) and standard deviation SD (1.

01) showed high reliability. In thiscase, low CV and SD values indicate the capability with which the experimentwas conducted. The low predicted residual sum of squares (PRESS) (70.87) is ameasure of how well the model fits each point in the model 32. The smallerthe PRESS statistic, the better the model fits the data points.

Thus, the highR2 value, significant F-value, insignificant lack-of-fit P-value,high adequate precision and low PRESS indicate high suitability and reliabilityof models in predicting the Eosin B dye degradation. Therefore, these modelswere used for further analysis.