# A Laser Irradiation Method for Controlling _Pieris rapae_ Larvae
## 3 Results
### Establishment of Regression Model  
To simplify the regression equation, the nonsignificant terms based on the original equation were removed, the model was manually optimized, and the second-order polynomial equation is provided below [(40; 41)]. The three-dimensional (3D) contour plot of an equation is the best method for expressing the linear, interaction and quadratic effects of working parameters on the responses, and the third and fourth variables were maintained at the zero level to obtain the 3D response surfaces [(42)]. The plots of the significant interaction terms for \(Y_{1}\), \(Y_{2}\) and \(K\) are illustrated in Figure 3.  
1. 24 h antifeedant percentage (%) \(Y_{1}\): \[Y_{1}\ =\ 79.14+7.28A+6.28B+7.09C+5.85D-4.36 AC-1.92 BC-3.86 BD-4.11A^{2}+4.54B^{2}-5.42 C^{2}-2.76D^{2}\] (3) where \(A\), \(B\), \(C\) and \(D\) represent the laser power, irradiation area, laser opening time and irradiation position, respectively. In this case, \(A\), \(B\), \(C\), \(D\), \(AC\), \(BD\), \(A^{2}\), \(B^{2}\), \(C^{2}\) and \(D^{2}\) were found to be significant model terms (\(p<0.05\)). The effect of laser power (\(A\)) on the antifeedant percentage was the most significant (\(F=96.41\), df = 1, 13, \(p<0.0001\)). The interactions \(AC\) (laser power and laser opening time; \(F=11.53\), df = 1, 13, \(p=0.0034\); Figure 3a) and \(BD\) (irradiation area and irradiation position; \(F=9.03\), df = 1, 13, \(p=0.0080\); Figure 3b) had a more significant positive impact on the 24 h antifeedant percentage than the other interactions. The \(R^{2}\) value was found to be 0.9616, which indicated a realistic fit of the model to the experimental data [40]. The predicted \(R^{2}\) (0.9061) and the adjusted \(R^{2}\) (0.9367) values were within 0.2 of each other, whereas adequate precision values were greater than 4, which indicated a satisfactory model fit [39]. 2. 24 h mortality rate (%) \(Y_{2}\):  
\[Y_{2}\ =\ 70.00+15.83A+11.11B+16.11C+11.39D+2.50 AB+4.17 AD-3.47A^{2}+4.44B^{2}-8.06 C^{2}-3.47D^{2} \tag{4}\]  
where \(A\), \(B\), \(C\) and \(D\) represent the laser power, irradiation area, laser opening time and irradiation position, respectively. In this case, \(A\), \(B\), \(C\), \(D\), \(AD\), \(A^{2}\), \(B^{2}\), \(C^{2}\) and \(D^{2}\) were found to be significant model terms (\(p<0.001\)). The laser opening time (C) had the most significant effect on the mortality rate (\(F=245.15\), df = 1, 14, \(p<0.0001\)). The interaction \(AD\) (laser power and irradiation position; \(F=5.47\), df = 1, 14, \(p=0.0311\); Figure 3c) had a more significant positive impact on the 24 h mortality rate than the other interactions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Experiment Number 1**} & \multicolumn{3}{c}{**Working Parameters 2**} & \multicolumn{3}{c}{**Mean (\%) 24 h**} & \multicolumn{2}{c}{**Mean (\%) 24 h**} & \multirow{2}{*}{**Comprehensive Score 3**} \\ \cline{2-3} \cline{5-8}  & \(A\) & \(B\) & \(C\) & \(D\) & & & & \\ \hline  
(-1\) & \(-1\) & 0 & \(64.81\pm 3.91\) & \(40.00\pm 5.77\) & 0.2830 \\ \hline \end{tabular}
\end{table} 
Table 3: Antifeedant percentages and mortality rates (Mean \(\pm\) SE) of 4 th-instr _Pieris rapque_ larvae after 24 h of irradiation in 29 groups of different working parameter combination tests. The \(R^{2}\) value was found to equal 0.9777, which indicated a realistic fit of the model to the experimental data [40]. The predicted \(R^{2}\) (0.9467) and the adjusted \(R^{2}\) (0.9653) values were within 0.2 of each other, whereas adequate precision values were greater than 4, which indicated a satisfactory model fit [39]. 3. Comprehensive score \(K\): \[K\ =\ 0.66+0.19A+0.16B+0.19C+0.15D-0.08 AC-0.037 BC-0.067 BD-0.086A^{2}+0.098B^{2}-0. 13C^{2}-0.062D^{2}\] (5) where \(A\), \(B\), \(C\) and \(D\) represent the laser power, irradiation area, laser opening time and irradiation position, respectively.