## 3 Results and Discussion
### Analysis and Discussion
#### 3.2.2 Slump Analysis (SP)  
The results of SP (R\({}_{1}\)) analysis of variance are shown in the first row of Table 7. R-squared and Adj. R-squared are both close to 1, which means that the fitted model is significant. In addition, Adeq. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Respenses** & **Standard Deviation** & **R-Squared** & **Adj. R-Squared** & **Adeq. Precision** & **F-Value** & **\(p\)-Value** & **Significant** \\ \hline
**R\({}_{1}\)** & SP & 2.32 & 0.9832 & 0.9617 & 23.737 & 45.62 & \textless{0.0001} & Yes \\
**R\({}_{2}\)** & CS & 1.32 & 0.9563 & 0.9000 & 17.159 & 17.01 & 0.0006 & Yes \\
**R\({}_{3}\)** & FS & 0.10 & 0.9461 & 0.9180 & 17.397 & 20.90 & 0.0003 & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model analysis of variance results. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Respenses** & **Factors** & \begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & \
\begin{tabular}{c} **Degree of** \\ **Freedom** \\ \end{tabular} &
\begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & **F-Value** & **\(p\)-Value** & **Significant** \\ \hline SP & WBR & 171.30 & 1 & 171.30 & 31.80 & 0.0008 & Yes \\  & BFC & 516.10 & 1 & 516.10 & 95.82 & \textless{0.0001} & Yes \\  & RC & 654.44 & 1 & 654.44 & 121.51 & \textless{0.0001} & Yes \\  & WBR \(\times\) & 42.25 & 1 & 42.25 & 7.84 & 0.0265 & Yes \\  & WBR \(\times\) RC & 0.25 & 1 & 0.25 & 0.046 & 0.8356 & No \\  & BFC \(\times\) RC & 20.25 & 1 & 20.25 & 3.75 & 0.0937 & No \\  & (WBR)\({}^{2}\) & 142.86 & 1 & 142.86 & 26.52 & 0.0013 & Yes \\  & (BFC)\({}^{2}\) & 22.76 & 1 & 22.76 & 4.22 & 0.0789 & No \\  & (RC)\({}^{2}\) & 7.39 & 1 & 7.39 & 1.37 & 0.2797 & No \\ CS & WBR & 38.84 & 1 & 38.84 & 20.92 & 0.0026 & Yes \\  & BFC & 37.05 & 1 & 37.05 & 19.96 & 0.0029 & Yes \\  & RC & 131.31 & 1 & 131.31 & 70.73 & \textless{0.0001} & Yes \\  & WBR \(\times\) & 0.09 & 1 & 0.09 & 0.050 & 0.8293 & No \\  & WBR \(\times\) RC & 0.37 & 1 & 0.37 & 0.20 & 0.6654 & No \\  & BFC \(\times\) RC & 0.36 & 1 & 0.36 & 0.19 & 0.6730 & No \\  & (WBR)\({}^{2}\) & 3.79 & 1 & 3.79 & 2.04 & 0.1960 & No \\  & (BFC)\({}^{2}\) & 40.03 & 1 & 40.03 & 21.56 & 0.0024 & Yes \\  & (RC)\({}^{2}\) & 3.70 & 1 & 3.70 & 1.99 & 0.2004 & No \\ FS & WBR & 0.0098 & 1 & 0.0098 & 1.32 & 0.2877 & No \\  & BFC & 0.071 & 1 & 0.071 & 9.58 & 0.0174 & Yes \\  & RC & 0.41 & 1 & 0.41 & 55.90 & 0.0001 & Yes \\  & WBR \(\times\) & 0.02 & 1 & 0.02 & 3.02 & 0.1253 & No \\  & BFC \(\times\) & 0.02 & 1 & 0.02 & 3.02 & 0.1253 & No \\  & BFC \(\times\) & 0.12 & 1 & 0.12 & 16.49 & 0.0048 & Yes \\  & CRC & (WBR)\({}^{2}\) & 0.073 & 1 & 0.073 & 9.95 & 0.0161 & Yes \\  & (BFC)\({}^{2}\) & 0.46 & 1 & 0.46 & 62.66 & \textless{0.0001} & Yes \\  & (RC)\({}^{2}\) & 0.004 & 1 & 0.004 & 0.59 & 0.4644 & No \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Response variable analysis of variance results. Precision represents the signal-to-noise ratio. When it is greater than 4, it indicates that the model is desirable. It can be seen from Table 7 that the Adeq. Precision of SP is 23.737, indicating that the model is desirable. According to the ANOVA results in Table 8, X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), X\({}_{1}\) X\({}_{2}\) and (X\({}_{1}\))\({}^{2}\) are the significant factors of the SP quadratic model. After excluding insignificant factors, the least squares method is used to fit the SP second-order polynomial equation:  
\[\text{SP}=50.91+7.65X_{1}-8.73X_{2}-9.75X_{3}+4.23X_{1}X_{2}+10.19{(X_{1})}^{2} \tag{2}\]  
The diagnostic results of the statistical model in Figure 1 showed that the data points are approximately a linear set, indicating that the model has high significance. Figure 2 is a three-dimensional response surface diagram of SP, revealing the relationship between WBR, BFC, RC and SP, and the interaction between WBR, BFC, and RC. As shown in Figure 2, the SP of RBFC increased significantly with the increase of WBR. Because with the increase of WBR, the free water in the mixture increased, which would inevitably lead to the increase of SP [34].