## 3 Materials and Methods
### Filed Test Regression Analysis  
The \(p\)-value of the lack of fitness \(P_{l}\) is 0.5256, as shown in Table 4, suggesting that the experimental index's regression equation fits well. We regarded it as the significance level when taking \(\alpha\) = 0.05. The primary term \(x_{2}\) and square term \({x_{2}}^{2}\) have highly significant impacts, the primary term \(x_{1}\) has significant effects, and the other components have no significant effects. The final equation in terms of coded factors is derived after deleting the insignificant terms:  
\[\hat{y}_{1}=93.88+0.7154x_{1}-1.49x_{2}-1.6x_{2}^{2} \tag{19}\]  
It can be shown from Equation (19) that the crank rotation speed has more influence on QRNDSM than transplanting depth. After sorting, the true QRNDSM regression equation was found by Table 2:  
\[y_{1}=62.5424+0.0866z_{1}+1.2819z_{2}-0.015z_{2}^{2} \tag{20}\]  
The \(p\)-value of the lack of fitness \(P_{l}\) is 0.2537, as shown in Table 5, suggesting that the experimental index's regression equation fits well. We regarded it as the significance level when taking \(\alpha\) = 0.05. The primary term \(x_{2}\) and square term \({x_{2}}^{2}\) have highly significant impacts, the primary term \(x_{1}\) has significant effects, and the other components have no significant effects. The final equation in terms of coded factors after deleting the insignificant terms is as follows:  
\[\hat{y}_{2}=94.14-0.6933x_{1}-1.84x_{2}-1.18x_{2}^{2} \tag{21}\]  
It can be shown from Equation (21) that the crank rotation speed has more influence on QRSRD than transplanting depth. After sorting, the true QRSRD regression equation was determined by Table 2:  
\[y_{2}=81.9245-0.0839z_{1}+0.8684z_{2}-0.011z_{2}^{2} \tag{22}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source** & **Squared Sum** & **Freedom Level** & **Mean Square** & **F Value** & **\(p\)-Value** \\ \hline Model & 31.72 & 4 & 7.93 & 46.07 & \textless{}0.0001 ** \\ \(x_{1}\) & 3.65 & 1 & 3.65 & 21.22 & 0.0025 ** \\ \(x_{2}\) & 13.04 & 1 & 13.04 & 75.74 & \textless{}0.0001 ** \\ \({x_{1}}^{2}\) & 1.87 & 1 & 1.87 & 10.84 & 0.0133 ** \\ \({x_{2}}^{2}\) & 13.17 & 1 & 13.17 & 76.50 & \textless{}0.0001 ** \\ Residuals & 1.20 & 7 & 0.1721 & / & / \\ The Lack of & 1.18 & 4 & 0.2943 & 31.87 & 0.0086 \\ Fitness & 0.0277 & 3 & 0.0092 & / & / \\ Core Total & 32.92 & 11 & / & / & / \\ \hline \hline \end{tabular} Note: ** expresses highly significant (\(p\leq 0.01\)); * expresses significant (\(0.01\leq p\leq 0.05\)).  
\end{table} 
Table 6: QRSLS variance analysis. Figure 11: Transplanting renderings. (**a**) Boat-bottom-shaped transplanting, (**b**) plant spacing measurement. The \(p\)-value of the lack of fitness \(P_{l}\) is 0.0086, as shown in Table 6, suggesting that the experimental index's regression equation fits well. We regarded it as the significance level when taking \(\alpha\) = 0.05. The principal terms \(x_{1}\) and \(x_{2}\) as well as the square term \({x_{2}}^{2}\) have highly significant effects, and the square term \({x_{1}}^{2}\) has significant effects, whereas the other components have no effect. The final equation in terms of coded factors is derived after deleting the insignificant terms:  
\[\hat{y}_{3}=94.46+0.726x_{1}-1.37x_{2}-0.6596x_{1}^{2}-1.75x_{2}^{2} \tag{23}\]  
Transplanting depth has more influence on QRSL than crank rotation speed, as shown by Equation (23). After sorting, the true QRSLS regression equation was derived by Table 2:  
\[y_{3}=35.1835+1.0536x_{1}+1.4272x_{2}-0.0097x_{1}^{2}-0.0164x_{2}^{2} \tag{24}\]  
Table 7 describes the analysis of regression. The \(R\) values of QRNDSM \(y_{1}\), QRSRD \(y_{2}\), and QRSLS \(y_{3}\) are equal to 0.9728, 0.9672, and 0.9850, respectively, suggesting that the regression model's experimental variables and test indicators have an intense linear relationship. For QRNDSM \(y_{1}\), QRSRD \(y_{2}\), and QRSLS \(y_{3}\), the coefficients of determination \(R_{2}\) are 0.9464, 0.9356, and 0.9703, respectively, indicating a high degree of fit for the regression model.