## Results and Discussions  
### RFTW Description Efficiency from FTWR  
#### 3.1.1 Statistical Analysis  
The matrix for different experimental conditions was presented in Table 3. According to the design matrix, a total of 20 sets of experiments were designed. Table 3 showed the experimental and predicted values corresponding to different experimental conditions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Run Order** & **Temperature (\({}^{\circ}\)C)** & **Retention Time (h)** &
\begin{tabular}{c} **Liquid–Solid Ratio** \\ **(mL/g)** \\ \end{tabular} & \multicolumn{2}{c}{**RFTW Yield (wt\%)**} \\ \cline{3-5}
1 & 50 & 0.5 & 30 & 20.66 & 26.18 \\
2 & 50 & 2 & 20 & 54.97 & 54.16 \\
3 & 50 & 2 & 20 & 49.71 & 54.16 \\
4 & 80 & 0.5 & 20 & 55.59 & 55.25 \\
5 & 25 & 0.5 & 20 & 28.22 & 20.45  
Externally studentized residuals were used to check regression assumptions, which will map all the different normal distributions to a single standard normal distribution and make it more sensitive to find problems with the analysis. Figure 1a was a normal probability plot, which indicated whether the residuals followed a normal distribution. Figure 1b was a plot of the residuals versus the ascending predicted response values. Figure 1c was a plot of the residuals versus the experimental run order. It checked for lurking variables that may have influenced the response during the experiment. Figure 1d was a plot of residuals versus temperature. It checked whether the variance not accounted for by the model is different for different levels of temperature. The graph exhibited a random scatter, which indicates that everything is normal. Figure 1e showed the predicted response values versus the experimental response values. The 45\({}^{\circ}\) line represents the expected value, and the dot represents the experimental value obtained by the actual experiment [32]. The figure showed that the two are close, which means that the obtained model can better represent the real experimental data [33; 34].  
Figure 1: (**a**) Normal plot of residuals, (**b**) residuals vs. predicted, (**c**) residuals vs. run, (**d**) residuals vs. A: temperature (\({}^{\circ}\)C), (**e**) predicted vs. experimental.  
Table 4 showed the analysis of variance of the desorption rate regression model. The model F-value of 71.59 implied that the model is significant. The chance that an F-value this large could occur due to noise is 0.01%. \(p\)-values less than 0.0500 indicated that model terms are significant. In this case, A, B, BC, B\({}^{2}\), and C\({}^{2}\) are significant model terms. Values greater than 0.1000 indicate that the model terms are insignificant. The lack of fit F-value of 2.35 implies the lack of fit is not significant relative to the pure error. The chance that a lack of fit F-value this large could occur due to noise is 18.03%. Non-significant lack of fit is good. Table 5 shows the correlation coefficient of the statistical model. The predicted R\({}^{2}\) of 0.8992 was in reasonable agreement with the adjusted R\({}^{2}\) of 0.9489 (i.e., the difference is less than 0.2). Adeq precision measures the signal to noise ratio. A ratio greater than 4 was desirable. A ratio of 30.650 indicated an adequate signal. This model can be used to navigate the design space [35].  
The polynomial equation between response (yield) and variables (temperature (A), retention time (B), and liquid-solid ratio (C)) is given by Equation (3).  
\[\mathrm{Y}=57.74+17.40\mathrm{A}+13.00\mathrm{B}+4.70\mathrm{BC}\ -\ 6.89\mathrm{B}^{2}\ -\ 5.39\mathrm{C}^{2} \tag{3}\]