ower than 0.05 in this column were considered significant.[@bib0155] The corresponding variables would be more significant if the *F*-value becomes greater and the *p*-value becomes smaller.[@bib0160] The *F*-test suggested that the model had a high *F*-value (*F* = 61.57) and a low *p*-value (*p \<* 0.001), indicating that this model was highly significant. In this case, the linear, quadratic, and interaction terms had high model *F*-values of 95.83, 56.75, and 32.12, respectively, and all *p*-values (*p \<* 0.001) were low, indicating that this model was highly significant.

3.4. Optimization of GA extraction conditions by RSM {#sec0060}
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The application of RSM offers, based on parameter estimates, an empirical relationship between the response variable (extraction yield of GA) and the test variables under consideration. By applying multiple regression analysis on the experimental data, the response variable and the test variables are related by the following second-order polynomial equation:where Y is the yield of GA (%) and X~1~, X~2,~ and X~3~ are the coded variables for extraction temperature, extraction time, and methanol concentration, respectively.

[Table 5](#tbl0025){ref-type="table"} shows the regression coefficients for each term in the model and the Student's *t*-test statistics and probability values for the significance of the terms. The *p*-value is used as a tool to check the significance of each coefficient and the interaction strength between each independent variable.[@bib0165] The corresponding variables will be more significant if the absolute *t*-value becomes larger and the *p*-value becomes smaller.[@bib0170] Thus, the smaller the values of *p* were, the more significant the corresponding coefficients were. It can be seen from this table that the linear coefficients (X~1~, X~2~, X~3~) were significant at the level of *p \<* 0.01 or *p \<* 0.001. The quadratic terms for all factors X~1~X~1~, X~2~X~2~, X~3~X~3~ and the interact