3.2.2. Response Surface Analysis

The three-dimensional (3D) response surface images illustrate the mutual influence of any two independent variables on the dependent variable while keeping other variables at the 0 level, and the shape of the 3D response surface plots provides information on the influence degree. To be specific, elliptical or saddle shapes of the 3D surfaces usually represent the interaction between two independent variables on the dependent variable, which is relatively significant, whereas a gently sloping surface indicates that the interaction between two factors on the dependent variable is relatively mild [34,35].

Figure 2a–f offered a visual interpretation of the interactions between two variables (*X*1*X*2, *X*1*X*3, *X*1*X*4, *X*2*X*3, *X*2*X*4, and *X*3*X*4) on the response variable (*Y*). Figure 2a–c showed the influences of ethanol concentration (*X*1) with extraction time (*X*2) and extraction temperature (*X*3) on the extraction yields of TF, respectively. The initial increase of *X*<sup>1</sup> (50% to about 57%) led to an increase in TFY and followed by a decline thereafter (about 57% to 70%). Similarly, as could be seen from Figure 2a,d,e, a rapid rise in TFY was obtained when *X*<sup>2</sup> varied from 30 to about 46 min, then the extraction yield of TF was decreased slowly with increasing extraction time. Figure 2b,d,f indicated that with an increase of *X*<sup>3</sup> from 60 to about 74 ◦C, the TFY increased quickly, followed by a slight decline with further

increase in *X*3. According to Figure 2c,e,f, it could be found that a maximum level of TFY was obtained at a *X*<sup>4</sup> of 34 mL/g. The graphs also indicated that the influence of *X*<sup>4</sup> on the TFY is insignificant (*p* > 0.05). In addition, as evident from Figure 2c, the interaction effect of *X*<sup>1</sup> and *X*<sup>4</sup> had a insignificant influence on the TFY from *P. cretica* (*p* > 0.05).

**Figure 2.** Response surface plots showing interaction between different variables (*X*1: Ethanol concentration; *X*2: Extraction time; *X*3: Extraction temperature; and *X*4: Liquid/solid ratio) on the TFY.
