## 3 Results and Discussion
### Analysis of Variance (ANOVA)  
Table 4 presents the ANOVA results of the model, with the \(p\)-value indicating the significance of the factor. A \(p\)-value less than 0.001 is highly significant, while one that is generally less than 0.05 is considered significant. The results in Table 4 reveal that the \(p\)-value of the regression model is less than 0.0001, signifying the high significance of the response surface model and the regression effect [18,32]. The single-parameter analysis demonstrates that the \(p\)-values of regression terms X\({}_{1}\) and X\({}_{2}\) are less than 0.0001, highlighting the highly significant effects of jet pressure and target distance on the pressure of the jet striking the track tooth. The \(p\)-value of X\({}_{3}\) is 0.0017, indicating that the effects of jet angle on the pressure of the jet striking the track tooth are significant; the two-parameter analysis shows that the \(p\)-values of the combinations X\({}_{1}\)X\({}_{2}\) and X\({}_{1}\)X\({}_{3}\) are 0.0472 and 0.0264, respectively, which are distributed in 0.001 \(<\)\(p\)-value \(<\) 0.05, indicating that the effect of two two-parameter combinations on the jet striking the tracked teeth's pressure is significant. From the F-value, it can be seen that the order of influence on the pressure of the jet striking the track tooth is X\({}_{1}\) > X\({}_{2}\) > X\({}_{3}\). The quality of the regression model was assessed by the linear regression coefficient of determination, coefficient of variation, signal-to-noise ratio, and the sum of squares of forecasts [33]. The coefficient of variation CV = 2.45%, indicating \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Input Parameters** & **Variables Coded** & **Units** & **Level 1** & **Level 2** & **Level 3** \\ \hline Injection pressure & X\({}_{1}\) & MPa & 0.4 & 0.7 & 1 \\ Target distance & X\({}_{2}\) & m & 0.14 & 0.16 & 0.18 \\ Impact angle & X\({}_{3}\) & \({}^{\circ}\) & 60 & 75 & 90 \\ Constant parameters & & & & & \\ Nozzle type & Linear nozzle & & & & \\ Nozzle diameter & 30 mm & & & & \\ Ambient pressure & 50 MPa & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Response surface test factor levels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Run** & **X\({}_{1}\)/MPa** & **X\({}_{2}\)/m** & **X\({}_{3}\)/\({}^{\circ}\)** & **Y/Pa** \\ \hline
1 & 0.7 & 0.18 & 90 & 413,480 \\
2 & 0.7 & 0.14 & 90 & 492,057 \\
3 & 0.4 & 0.14 & 75 & 286  
that only 2.45% of the total variation cannot be explained by this model. The signal-to-noise ratio is 52.8. Refs. [32; 34] indicates that when the model coefficient of variation is less than 10 and the signal-to-noise ratio is greater than 4, the model fits with a high accuracy and good reproducibility. The established response prediction model in this study is proven to be reliable in describing the response law of jet striking tracked teeth. The model phase test results are presented in Table 5, showing a high correlation coefficient of R\({}^{2}\) = 0.9972 and a close-to-1 correction coefficient of R\({}^{2}\)adj =0.9935. These values indicate that the predicted model exhibits a high degree of correspondence with the actual data, demonstrating a strong fit. Figure 5 presents a comparative analysis of the predicted and simulated responses of the jet impacting the tracked teeth. The graphical representation indicates that the predicted and simulated values closely follow the y = x line and neighboring positions, with experimental values predominantly corresponding with the predicted values. This further confirms the accuracy of the prediction model established in this article. Furthermore, distinct colored squares are used to distinguish between the actual values of the experiment and the expected values of the equation.