The coefficients of the above Eq. (6) were calculated, and the linearity and quadratic effect of the treatment variables, their interactions and coefficients on the response variables were obtained by analysis of variance (ANOVA) (Table 2). The results suggested a good fit with the Eq. (6) because the model was acceptable at P = 0.0001 and adequate with satisfactory coefficient of determination (R2) of 96.2%. The predicted model seemed to reasonably represent the observed values. Thus, the response was sufficiently explained by the model. The factor F-test value (53.968) and p-value (P < 0.001) correspond to temperature (x1), and F-test value and p-value corresponding to ethanol concentration (x4) were 63.176 and 0.0001 (P < 0.001), while the F-test values for x2 and x3 were smaller (0.6748 and 4.1497, respectively). These results suggested that the temperature and ethanol concentration were directly related to the flavonoids yield. Furthermore, the model F-value of 10.903 also showed that the model was significant (Table 2). In addition, the value of R2 (0.991) implied that the sample variations of 99.1% for the yield of flavonoids was attributable to the independent variables, and the adjusted R2 n (AdjR2) of the equation was 0.962 (Table 2), suggesting an excellent correlation between the independent variables. The values of R2 and P (P < 0.005 when very significant) were 0.991 and 0.0001,