## 3 Results and Discussion  
The regression model analysis of variance is shown in Table 3. The regression parameters of the response surface were analyzed through Analysis of Variance. The F-test was conducted to evaluate the significance of the influence of variables in the regression equation on the response value. Typically, a smaller probability \(P\) (\(P\)-Value) is associated with a higher significance of the corresponding variable. In the proposed model, \(P=0.0406<0.05\), and the response surface regression model reached a significant level; while the lack of fit was \(P=0.0873>0.05\), which was not significant, suggesting that all experimental points were expressed using the model, high degree of fitting was achieved, and the regression equation model was successfully established. These findings demonstrate that, the _Salix_ carbon-based solid acid catalyst can well catalyze the preparation of biodiesel. Among the linear terms, the solid-liquid ratio C had the greatest influence \(P=0.0486<0.05\), ranking a significant level. Among the quadratic terms, reaction temperature A\({}^{2}\) (\(P=0.0032<0.01\)) reached an extremely significant level and the interaction terms \(P_{AC}=0.0394\) (significant level of model in reaction temperature and solid-liquid ratio factors) and \(P_{CD}=0.0469\) (significant level of model in solid-liquid ratio and standing time factors) exerted significant influence on the catalyst performance (\(P<0.05\)). Within the range of each factor selected in the present study, the solid-liquid ratio had the greatest influence on the catalytic performance of the _Salix_ carboniferous solid acid catalyst. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **A: Reaction** & **B: Reaction** & **C:** & **D: Standing** & **Conversion** \\  & **Temperature\({}^{\text{\text{\text@underline{c}}}}\)C** & **Time/min** & **Ratio** & **Time/min** & **Level/\%** \\ \hline
1 & 135 & 120 & 1:5 & 30 & 83.19 \\
2 & 135 & 90 & 1:6 & 30 & 89.98 \\
3 & 135 & 90 &  
A 3D diagram can represent not only the characters of the response surface function, but also intuitively illustrate the effect of interaction between factors on the response value. As can be observed from Figure 1, the interactions between reaction temperature and the solid-liquid ratio, as well as the between standing time and solid-liquid ratio, are extremely significant. They are manifested by a relatively steep curve, verifying that the interactive items of reaction temperature, standing time, and solid-liquid ratio exert significant influence on the catalytic activity of the catalyst. According to Figure 2a, when the reaction temperature remains unchanged, the conversion level shows an increasing trend with an extension in reaction time, and the catalyst activity is enhanced. When the reaction time remains unchanged, the conversion level also displays an increasing trend with the increase in reaction temperature. In linear terms, reaction time and reaction temperature  
Figure 1: (**a**) Response surface diagram of the effect of solid–liquid ratio and standing time interaction on conversion level; (**b**) response surface diagram of the effects of reaction temperature and solid–liquid ratio interaction on conversion level.