# Optimization and Preparation of Tallow with a Strong Aroma by Mild Oxidation
## 2 Results and Discussion
### Response Surface Optimization  
Based on the single-factor test, three factors, including reaction temperature, reaction time, and airflow rate, were selected to design the response surface test. The factor-level table is shown in Table 6 and the response surface analysis scheme and results are shown in Table 7. The results were analyzed by Design-Expert data software and the response surface diagrams for the obtained data were shown in Figures 6-8  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & _p-Value Prob \textgreater{} F** & **Significance** \\ \hline Model & 6.54 & 9 & 0.73 & 27.61 & 0.0001 & significance \\ A: Temperature & 0.0032 & 1 & 0.0032 & 0.12 & 0.7375 & \\ B: Time & 0.63 & 1 & 0.63 & 23.85 & 0.0018 & \\ C: Air velocity & 2.2 & 1 & 2.2 & 83.83 & \textless{}0.0001 & \\ AB & 0 & 1 & 0 & 0 & 1 & \\ AC & 0 & 1 & 0 & 0 & 1 & \\ BC & 0 & 1 & 0 & 0 & 1 & \\ A\({}^{2}\) & 0.29 & 1 & 0.29 & 10.99 & 0.0129 & \\ B\({}^{2}\) & 0.75 & 1 & 0.75 & 28.51 & 0.0011 & \\ C\({}^{2}\) & 2.35 & 1 & 2.35 & 89.33 & \textless{}0.0001 & \\ Residual & 0.18 & 7 & 0.026 & & & \\ Lack of fit & 0 & 3 & 0 & 0 & 1 & no significance \\ Pure error & 0.18 & 4 & 0.046 & & & \\ Cor total & 6.72 & 16 & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\ \end{tabular}
\end{table}
Table 7: Variance analysis of the response surface quadratic model.  
Figure 6: The effect of the interaction between reaction temperature and reaction time on sensory evaluation (**1**) and a contour map of the reaction temperature and reaction time (**2**).  
The significance test and analysis of variance for the regression equation are shown in Table 5. The significance for regression analysis of variance indicates that the regression is extremely significant, \(p\) = 0.0001, and non-significant, \(p\) = 1.0000, for the missing term, with R\({}^{2}\) = 0.9726 and R\({}^{2}\)Adj = 0.9374. The model indicates that the equation fits the experiment well. When describing the relationship between each factor and response value, the linear relationship between the dependent variable and the independent variable is significant for the regression equation.  
In the process of studying the influence of related variables on the processing results, in order to further study the interaction between variables, the quadratic regression model was analyzed by software and the response surface stereogram was drawn. The response surface isochronal diagram could intuitively reflect the effects of various factors on the  
Figure 7: The effect of the interaction between reaction temperature and air velocity on sensory evaluation (**1**) and the contour map of reaction temperature and air velocity (**2**).  
After regression fitting of each factor, the regression equation was obtained as follows: R1 = 9.03 - 0.020A - 0.28B - 0.53C + 0.000 AB + 0.000 AC + 0.000 BC + 3.81 BD - 0.26A2 - 0.42B2 - 0.75C2. The RSM analysis system showed that the optimal conditions for oxidative melting of tallow were a reaction temperature of 149.61 \({}^{\circ}\)C, a reaction time of 31.68 min, and an airflow rate of 97.44 L/h.