## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source Model** & \begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & \begin{tabular}{c} **Degrees** \\ **Freedom** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Value** & \
\begin{tabular}{c} **P-Value >** \\ **F-Value** \\ \end{tabular} &
\begin{tabular}{c} **Significant** \\ **Level** \\ \end{tabular} \\ \hline model & 603.943 & 14 & 43.139 & 2.6279 & 0.041 & significant \\ A & 16.4034 & 1 & 16.403 & 0.9993 & 0.335 & \\ B & 2.9403 & 1 & 2.940 & 0.1791 & 0.679 & \\ C & 76.6085 & 1 & 76.609 & 4.6669 & 0.049 & significant \\ D & 12.1807 & 1 & 12.181 & 0.7420 & 0.404 & \\ AB & 36.5420 & 1 & 36.542 & 2.2261 & 0.158 & \\ AC & 84.7320 & 1 & 84.732 & 5.1617 & 0.039 & significant \\ AD & 24.4530 & 1 & 24.453 & 1.4896 & 0.242 & \\ BC & 20.8392 & 1 & 20.839 & 1.2695 & 0.279 & \\ BD & 20.6116 & 1 & 20.612 & 1.2556 & 0.281 & \\ CD & 77.9689 & 1 & 77.969 & 4.7497 & 0.047 & significant \\ A\({}^{2}\) & 206.912 & 1 & 206.91 & 12.605 & 0.003 & significant \\ B\({}^{2}\) & 55.2748 & 1 & 55.275 & 3.3672 & 0.088 & \\ C\({}^{2}\) & 18.2349 & 1 & 18.235 & 1.1108 & 0.310 & \\ D\({}^{2}\) & 14.0723 & 1 & 14.072 & 0.8573 & 0.370 & \\ Residual & 229.816 & 14 & 16.415 & & & \\ Lack of Fit & 210.121 & 10 & 21.012 & 4.2675 & 0.087 & \\ Pure Error & 19.6952 & 4 & 4.924 & & & significant \\ Cor Total & & 28 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of variance analysis of regression models. make basically the same influence on the catalyst. Figure 2b shows that with the reaction temperature remaining unchanged, the conversion level presents a decreasing trend with an increase in standing time, and the catalyst activity is weakened; when the standing time remains unchanged, the conversion level is first increased and then decreased with the increase in reaction temperature. As can be observed from Figure 3a, with a constant reaction time, the conversion level shows an increasing trend with the increase of concentrated sulfuric acid in solid-liquid ratio, and the catalyst activity is also enhanced. When the solid-liquid ratio remains unchanged, the conversion level is relatively gentle with the increase in reaction time. Among the linear terms, solid-liquid ratio has more significant influence than reaction temperature on the catalyst. As presented in Figure 3b, under the condition that the standing time remains unchanged, the conversion level shows an increasing trend with the extension in reaction time, and the catalyst activity is promoted. When the reaction time is unchanged, the conversion level also displays an increasing trend with the increase in standing time. The maximum response value maximum was determined using the numerical function of Design-Expert software, and the optimal reaction conditions are obtained as follows: reaction  
Figure 3: (**a**) Response surface diagram of the effect of solid–liquid ratio and reaction time interaction on conversion level; (**b**) response surface diagram of the effect of standing time and reaction time interaction on conversion level. Figure 2: (**a**) Response surface diagram of the effect of reaction temperature, reaction time interaction on conversion level; (**b**) response surface diagram of the effect of reaction temperature, standing time interaction on conversion level. temperature of 125 \({}^{\circ}\)C, reaction time of 102 min, solid-liquid ratio of 17 g/100 mL, standing time of 30 min, and highest conversion level of 95%. After optimization with the above-mentioned software, the above conditions were employed to verify the experiment. The conversion level of esterification reaction for the preparation of biodiesel catalyzed by the _Salix_ carbon-based solid acid catalyst was 94.15%. The relative deviation between the software predicted value and the experimental value was 0.89%. Therefore, it is feasible to employ this model to analyze and predict the catalytic performance of the _Salix_ carboniferous solid acid catalyst.