## 4 Statistical Analysis of Multiple Factors
### Statistical Analysis  
The MNLR models for predicting \(q_{\text{u}}\) of BFUSM and BFCSM with varying factors based on 120 experiment data points are obtained as Equations (6) and (7) showed, respectively. \[q_{\text{u}BFUSM}=0.2191+0.0892B+0.0231D-0.5663B^{2}-0.0005D^{2}+0.0076 BD,\ R_{ 2}^{2}=0.824 \tag{6}\]  
\[q_{\text{u}BFCSM}=0.5295+1.4716B+0.0691D-3.3955B^{2}-0.0011D^{2}+0.0069 BD,\ R_{ 2}^{2}=0.919 \tag{7}\]  
\[q_{\text{u}BFCSM\text{-}R}=0.1968+0.0246D-0.0005D^{2}+0.0009 BD,\ R_{a}^{2}=0. 821 \tag{8}\]  
\[q_{\text{u}BFCSM\text{-}R}=0.5892+0.0693D-0.0011D^{2}+0.0128 BD,\ R_{a}^{2}=0. 907 \tag{9}\]  
The \(R_{a}^{2}\) value of MNLR models for BFUSM and BFCSM is 0.824 in Equation (6) and 0.919 in Equation (7), respectively, implying that fiber contents and curing time are relevant to \(q_{\text{u}BFUSM}\) and \(q_{\text{u}BFCSM}\). However, the P-values of coefficients with \(B\) and \(B^{2}\) are larger than 0.05 as Table 4 showed, manifesting that the variables of \(B\) and \(B^{2}\) have nothing to do with \(q_{\text{u}BFUSM}\) and \(q_{\text{u}BFCSM}\), thus the two variables should be eliminated. Therefore, the developed MNLR models are obtained in Equations (8) and (9), respectively. It is  
Figure 8: Correlation between unconfined compressive strength and splitting tensile strength: (a) BFUSM and (b) BFCSM. obvious that the coefficients of variable \(BD\) in the developed MNLR models are 0.0009 and 0.0128, respectively, showing that the interaction between fiber contents and curing time on the UCS is significant. Simultaneously, the \(p\)-values of the coefficients associated with variables which are both less than 0.05 as Table 4 displayed, indicating the effectiveness of the developed models. Meanwhile, the experimental data and the predicted data have a good relationship, as Figure 9 displayed, implying that the developed MNLR models are more reasonable to predict \(q_{uBFUSM}\) and \(q_{uBFCSM}\). Similarly, the MNLR models for predicting STS of BFUSM and BFCSM with a length of 12 mm based on 120 experimental data points are shown in Equations (10) and (11), respectively. \[q_{uBFUSM}=0.0090+0.0249B+0.0030D-0.0535B^{2}-0.0001D^{2}-0.0004 BD,\ R_{a}^{2}=0. 859 \tag{10}\]  
\[q_{uBFCSM}=0.0470+0.3629B+0.0074D-0.7531B^{2}-0.0001D^{2}-0.0020 BD,\ R_{a}^{2}=0. 967 \tag{11}\]  
\[q_{uBFUSM}=0.0090+0.0102B+0.0030D-0.0001D^{2}-0.0006 BD,\ R_{a}^{2}=0.880 \tag{12}\]  
\[q_{uBFCSM}=0.0621+0.0616B+0.0074D-0.0001D^{2}-0.0020 BD,\ R_{a}^{2}=0.971 \tag{13}\]  
The \(R_{a}^{2}\) value of MNLR models for BFCSM (0.967 for Equation (11)) is higher than that for BFUSM (0.859 for Equation (10)), indicating that the correlation between fiber contents, curing time, and \(q_{uBFCSM}\) is better than that with \(q_{uBFUSM}\). The influence of variables on \(q_{uBFCSM}\) is more evident. However, the \(p\)-value of coefficients associated with \(B^{2}\) is larger than 0.05 in Table 5, showing that the variables of \(B^{2}\) could be eliminated. Therefore, the developed MNLR models are displayed in Equations (12) and (13), respectively. From Equations (12) and (13), the coefficients of variable \(BD\) in the developed models are 0.0006 and 0.0020, respectively, manifesting that the interaction between fiber contents and curing