3.2.1. Model Fitting and Statistical Analysis

Due to the association between variables, BBD with four factors and three levels was employed to optimize the individual parameters. BBD matrix and response values were listed in Table 1. Subsequently, statistical regression analysis of experimental data was carried out, and a second-order polynomial equation yielded was represented as below:

$$\begin{array}{l} \text{Y} = & 4.59 - 0.068X\_1 + 0.27X\_2 + 0.27X\_3 + 0.015X\_4 \\ & - 0.23X\_1X\_2 - 0.29X\_1X\_3 + 0.098X\_1X\_4 + 0.14X\_2X\_3 \\ & - 0.19X\_2X\_4 - 0.098X\_3X\_4 - 0.54X\_1^2 - 0.38X\_2^2 \\ & - 0.55X\_3^2 - 0.33X\_4^2 \end{array} \tag{4}$$

where *X*1, *X*2, *X*3, and *X*<sup>4</sup> are the ethanol concentration, extraction time, extraction temperature, and liquid/solid ratio, respectively. *Y* is the predicted value of TFY.


**Table 1.** Box–Behnken design matrix and experimental values for the TFY.

**Table 1.** *Cont*.


The fitness and adequacy of the regression model were evaluated using a variance analysis (ANOVA), and results were given in Table 2. *F*-value (41.92) and *p*-value (<0.0001) of the regression model indicated that the established model was very significant. Whereas, *F*-value (3.28) and *p*-value (0.1317) of the lack of fit indicated that the lack of fit was not significant as compared with the pure error. In addition, the determination coefficient (*R*2) obtained for this model was 0.9767, implying that the model could satisfactorily fit the variability of the TFY. The predicted *R*<sup>2</sup> of 0.8764 was in reasonable agreement with the adjusted *R*<sup>2</sup> of 0.9534, implying that the predicted values were highly consistent with the experimental values. In this study, the linear coefficients (*X*1, *X*2, and *X*3), quadratic term coefficients (*X*12, *X*22, *X*32, and *X*42), and the cross product coefficients (*X*1*X*2, *X*1*X*3, *X*2*X*3, and *X*2*X*4) had statistically significant effects on the TFY (*p* < 0.05).

**Table 2.** The analysis of variance for the second-order polynomial model.

