## 3 Results and Discussion
### Analysis of Response Output Index Results
#### 3.1.1 Density
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Types** & **Continuous P Value** & **Out-of-Fit P Value** & **Correct R\({}^{2}\)** & **Predict R\({}^{2}\)** & **Result** \\ \hline Linear & 0.3169 & \textless{}0.0001 & 0.0528 & \textless{}0.1622 & — \\
2 FI & 0.9247 & \textless{}0.0001 & \textless{}0.1768 & \textless{}0.9142 & — \\ Quadratic & \textless{}0.0001 & \textless{}0.0001 & 0.9416 & 0.5912 & Recommended \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comprehensive analysis of fitting degree. 2 FI, two-factor model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source of Variance** & **Sum of Squares** & **Degrees of Freedom** & **Mean Square** & **F Value** & **Probability \textgreater{} F** & **Result** \\ \hline Mean vs. Total & 96.3291 & 1 & 96.3291 & — & — & — \\ Linear vs. Mean & 0.0046 & 3 & 0.0015 & 1.2978 & 0.3169 & — \\
2 FI vs. Linear & 0.0006 & 3 & 0.0002 & 0.1540 & 0.9247 & — \\ Quadratic vs. 2 FI & 0.0143 & 3 & 0.0047 & 64.8540 & \textless{}0.0001 & Recommended \\ Residual & \(2.59\times 10^{-12}\) & 4 & \(6.48\times 10^{-13}\) & — & — \\ Total & 96.349 & 17 & 5.6676 & — & — & — \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Variance analysis of multiple models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Types** & **Sample Standard Deviation** & **Fit** & **Corrected Fit** & **Prediction Fit** & **Result** \\ \hline Linear & 0.0345 & 0.2304 & 0.0528 & -0.1622 & — \\
2 FI & 0.0385 & 0.2644 & \(-\)0.1768 & \(-\)0.9142 & — \\ Quadratic & 0.0085 & 0.9744 & 0.9416 & 0.5912 & Recommended \\ Cubic & \(8.0538\times 10^{-7}\) & 1 & 0.9999 & — & Poor \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Model summary statistics. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Project** & **Sum of Squares** & **Degrees of Freedom** & **Mean Square Error** & **F Value** & **P Value** & **Significant** \\ \hline Model & 0.02 & 9 & \(2.18\times 10^{-3}\) & 29.67 & \(<\)0.0001 & \(\surd\) \\ A: Fiber Content & \(1.08\times 10^{-3}\) & 1 & \(1.08\times 10^{-3}\) & 14.6 & 0.0065 & \(\surd\) \\ B: Nano-Material Content & \(3.13\times 10^{-3}\) & 1 & \(3.13\times 10^{-3}\) & 42.5 & 0.0003 & \(\surd\) \\ C: Asphal-Aggregate Ratio & \(4.46\times 10^{-4}\) & 1 & \(4.46\times 10^{-4}\) & 6.06 & 0.0434 & \(\surd\) \\ AB & \(3.96\times 10^{-6}\) & 1 & \(3.96\times 10^{-6}\) & 0.054 & 0.8233 & \(\times\) \\ AC & \(6.72\times 10^{-4}\) & 1 & \(6.72\times 10^{-4}\) & 9.14 & 0.0193 & \(\surd\) \\ BC & \(9.27\times 10^{-6}\) & 1 & \(9.27\times 10^{-6}\) & 0.13 & 0.7331 & \(\times\) \\ A’2 & \(2.11\times 10^{-5}\) & 1 & \(2.11\times 10^{-3}\) & 28.64 & 0.0011 & \(\surd\) \\ B’2 & \(2.86\times 10^{-3}\) & 1 & \(2.86\times 10^{-3}\) & 38.88 & 0.0004 & \(\surd\) \\ C’2 & \(8.01\times 10^{-3}\) & 1 & \(8.01\times 10^{-3}\) & 108.77 & \(<\)0.0001 & \(\surd\) \\ Residual & \(5.15\times 10^{-4}\) & 7 & \(7.36\times 10^{-5}\) & — & — & — \\ Mismatch & \(5.15\times 10^{-4}\) & 3 & \(1.72\times 10^{-4}\) & — & — & — \\ Pure Error & 0 & 4 & 0 & — & — & — \\ Total Deviation & 0.02 & 16 & — & — & — & — \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Density variance test. According to the results of analysis of variance, the fitting equation of the response index can be obtained:  
Density = 1.78911 + 5.94747 \(\times\) 10\({}^{-4}\times\) A + 0.020 \(\times\) B + 0.205 \(\times\) C - 8.289 \(\times\) 10\({}^{-5}\times\) A \(\times\) B + 0.0029 \(\times\) A \(\times\) C + 2.53744 \(\times\) 10\({}^{-4}\times\) B \(\times\) C - 0.0024862 \(\times\) A\({}^{2}\) - 1.62926 \(\times\) 10\({}^{-3}\times\) B\({}^{2}\) - 0.019378 \(\times\) C\({}^{2}\)  
In the Equation, A is the amount of BF; B is the amount of NTC; C is the asphalt-aggregate ratio. The distribution of predicted and measured values is shown in Figure 3.  
Figure 3 shows the relationship between the response index predicted by the final equation and the measured values.