# A Correction Method of Mixed Pesticide Content Prediction in Apple by Using Raman Spectra
## 3 Results and Discussion
### Establishment of Regression Models  
The mixture pesticides be detected included the deltamethrin and acetaminophen mixtures with same content and the ones with different concentration. As most pesticide mixture applied in farmland was in low content, detailed analyze of correction coefficient change rule was focused in low concentration. Deltamethrin, acetaminophen with concentration of 100, 10, 1, 10\({}^{-1}\), 10\({}^{-2}\) and 10\({}^{-3}\) mg\(\cdot\)kg\({}^{-1}\) were mixed as mixture in pairs. And there were 36 mixed mode. At least 15 sample points would be detected to get the average as representative concentration in each mixed mode to make sure the representative. The characteristic peak intensity of the pesticide detected directly cannot be directly used to predict the concentration of the mixed pesticide. By analyzing the reduction ratio of mixed pesticides characteristic peak intensity compared with the intensity of single pesticides, a model of mixed pesticides peak intensity correction coefficient was established. Firstly, the concentration of the mixed pesticide was estimated by a single pesticide quantitative analysis model to get the estimated pesticide concentration. And then the estimated pesticide concentration was applied in correction coefficient model to acquire the correction coefficient. The characteristic peak intensity of the pesticide was multiply by the correction coefficient to get the corrected peak intensity. Finally the corrected pesticide concentration was obtained by applying corrected peak intensity to quantitative analysis model of the pesticide. It was clear that correction coefficient change rule was the key to get accurate pesticide concentration. The correction coefficient was obtained by dividing the characteristic peak intensity value of a single pesticide by the characteristic peak intensity value of the pesticide mixture with same concentration. As quadratic function relations existed between pesticide concentration and the correction coefficients, two quadratic equations were needed to describe the change rule between content of pesticide mixture and the correction coefficients. And the change rule of one characteristic peak intensity was described by a binary quadratic polynomial. As shown in Figure 4, the fitting effect of mixed pesticides concentrations and the correction coefficients was a smooth and slanted surface. For the characteristic peaks of acetamiprid at 634 cm\({}^{-1}\) and 1114 cm\({}^{-1}\), the correction coefficient reduced with not only the increments of acetamiprid concentration, but also the reduction of deltamethrin concentration. And when the concentration of one pesticide was low, its correction coefficient would be high, which indicated that components with low concentration in mixed pesticides were more likely to be affected by pesticides high concentration. For the change rule fitting model of peak in 634 cm\({}^{-1}\), the sum squared residual (SSE) was 0.0678. Root Mean Square Error (RMSE) and coefficient of correlation were 0.0475 and 0.9328 respectively. And for the change rule fitting model of peak in 1114 cm\({}^{-1}\), the SSE was 0.0328. RMSE and coefficient of correlation were 0.0330 and 0.8883 respectively. A polynomial regression equation (Equation (1)) was acquired from the change rule fitting surface of characteristic peaks at 634 cm\({}^{-1}\). In Equation (1), the concentrations of acetamiprid and deltamethrin were all from 100 mg\(\cdot\)kg\({}^{-1}\) to 10\({}^{-3}\) mg\(\cdot\)kg\({}^{-1}\). \[Z=1.264-0.02345\text{A}+0.01906\text{D}+0.0006864\text{A}^{2}-0.0001839\text{AD }+1.289\times 10^{-5}\text{D}^{2} \tag{1}\]  
where Z is the correction coefficient, A is the estimated concentration value of acetamiprid, D is the concentration value of deltamethrin. The polynomial regression equation (Equation (2)) of characteristic peaks at 1114 cm\({}^{-1}\) was also obtained and shown below.