2.3.2. RSM Design

Based on the results of single-factor experiments, the UAE of TF from *P. cretica* was further optimized by RSM. In this work, the BBD with four variables (ethanol concentration *X*1, extraction time *X*2, extraction temperature *X*3, and liquid/solid ratio *X*4) at three levels (−1, 0, 1) was carried out to evaluate the effect between every two variables on the response value (TFY *Y*). The BBD procedure of RSM resulted in a total of 29 randomized experiments, and a quadratic model used to analyze experimental data was shown as follows:

$$Y = \alpha\_0 + \sum\_{i=1}^{4} \alpha\_i X\_{\text{i}} + \sum\_{i=1}^{4} \alpha\_{\text{i}i} X\_{\text{i}}^2 + \sum\_{i=1}^{3} \sum\_{j=i+1}^{4} \alpha\_{\text{i}j} X\_{\text{i}} X\_{\text{j}} \tag{1}$$

where *Y* is the response value; α<sup>0</sup> refers to the intercept; αi, αii, and αij refer to the linear, quadratic, and interactive coefficients, respectively; *X*<sup>i</sup> and *X*<sup>j</sup> represent the independent variables (i j).
