## 3 Results and Discussion
### Analysis of Variance  
The purpose of ANOVA is to determine whether the resulting polynomial model can explain the experimental data within a 95% confidence interval. The quadratic model variance regression analysis of actual power is shown in Table 4. As can be seen from Table 4, the \"Prob > F\" value of the regression model is less than 0.0001, indicating that the model is significant. In this analysis, only \(xz\), \(yz\), and \(z^{2}\) have high \(p\) values, and all other terms are extremely significant model terms, which also indicates the correctness of the quadratic polynomial equation of actual power.  
In the response surface analysis method, \"Adequate Precision\" is used to measure the signal-to-noise ratio. Its value is 42.177, which is greater than 4, indicating the reliability of the model. Meanwhile, the coefficient of determination R\({}^{2}\) is 0.9819, which further proves the accuracy of the fitting effect. The values of R\({}^{2}_{\text{adj}}\) (0.9494) and R\({}^{2}_{\text{pred}}\) (0.9159)  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Source** & **Degrees of Freedom** & **F Value** & \(p\)**Value Prob > F** \\ \hline Model & 9 & 98.53 & \textless{}0.0001 \\ x & 1 & 242.97 & \textless{}0.0001 \\ y & 1 & 33.25 & 0.0007 \\ z & 1 & 19.4 & 0.003 \\ xy & 1 & 4.51 & 0.031 \\ xz & 1 & 15 & 0.0047 \\ yz & 1 & 42 & \textless{}0.0001 \\ x\({}^{2}\) & 1 & 25.26 & 0.001 \\ y\({}^{2}\) & 1 & 18.9 & 0.0043 \\ z\({}^{2}\) & 1 & 9.15 & 0.034 \\ R\({}^{2}\) = 0.9819, R\({}^{2}_{\text{adj}}\) = 0.9494, R\({}^{2}_{\text{pred}}\) = 0.9159, Adequate Precision = 94.03 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Analysis of variance of the regression model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & **Velocity** & **Displacement (t)** & **Appendage** \\  & **(m/s) (x)** & **(y)** & **(z)** \\ \hline \(-1\) & 0.44 & 0.36 & 0 \\
0 & 1.25 & 0.385 & 0.5 \\
1 & 2.06 & 0.41 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coded levels and range of independent variables.  
also have a good agreement. The values of these parameters show that the actual ship power has a good correspondence with the ship speed, displacement, and appendages in the ship resistance test experiment, which conforms to the quadratic polynomial variation law. Figure 5a shows the relationship between normal percentage probability and the studentized residual. The linear correlation shows that there is no obvious problem with normality. In order to further analyze the corresponding relationship between the measured values and the predicted values of the fitting model, a comparison graph is drawn between them. It can be clearly seen from Figure 5b that there is a high degree of coincidence between the tested value and the predicted value. The difference between the tested value and the predicted value is very small, indicating the correctness of the model under this experimental condition. All of the above results show that the response surface analysis method can be effectively used to analyze the relationship between actual ship power and ship speed, displacement, and appendages, and the obtained results have high reliability.