 of glycyrrhizic acid for licorice in various solvents.Table 3SolventContent of glycyrrhizic acid (%)MeanSDPost-hoc[a](#tblfn0005){ref-type="table-fn"}Methanol0.8450.030AEthanol0.1690.004BDistilled waterND[b](#tblfn0010){ref-type="table-fn"}--C[^1][^2]

3.3. Statistical analysis and model fitting {#sec0055}
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A total of 20 runs were needed for optimizing the three individual parameters in the current CCD. [Table 2](#tbl0010){ref-type="table"} shows the experimental conditions and the GA extraction yield results according to the factorial design. The ANOVA results ([Table 4](#tbl0020){ref-type="table"}) shows that it is possible to plot the response surface for this experimental design. The correlation measure for testing the goodness-of-fit of the regression equation is the adjusted determination coefficient (R^2^~adj~).[@bib0150] The value of R^2^~adj~ is 0.902, which is reasonably close to 1 and indicates a high degree of correlation between the observed and predicted values.[@bib0075] The lack-of-fit (*p*-value) was calculated as 0.126. The fitness of the model was evaluated through the lack of fit test (*p \>* 0.05), which indicated the adequacy of models to accurately predict the variation.[@bib0125]Table 4Analysis of variance for the fitted quadratic polynomial model of extraction of glycyrrhizic acid.Table 4SourceDF[a](#tblfn0015){ref-type="table-fn"}Sum of squares*F*-value*p*-valueRegression930.133561.570.000Linear315.634295.830.000X~1~110.8811200.090.000X~2~10.737313.560.001X~3~14.015873.840.000Square39.258256.750.000X~1~X~1~11.577548.010.000X~2~X~2~13.595780.130.000X~3~X~3~14.085075.120.000Interaction35.241132.120.000X~1~X~2~10.00360.070.797X~1~X~3~10.07081.300.259X~2~X~3~15.166795.010.000Residual error502.7191----Lack of fit50.45971.830.126Pure error452.2594----Total5932.8526----[^3]

The significance of the *F*-value depends on the number of degrees of freedom (DF) in the model and is shown in the *p*-value column (95% confidence level). Thus, the effects l