# Analysis of Fluid Velocity inside an Agricultural Sprayer Using Generalized Linear Mixed Models
## 3 Results and Discussion
### Comparison of IBM SPSS and SAS Model Results  
The estimate of the residual variance and the estimated variance of [PERSON]'s residues, predicted by the model computed through SAS, offered better values than the one computed through SPSS (Table 7). Additionally, SAS showed the ratio of the generalized chi-square with its degrees of freedom, which is a measure of the variability of the observation on the mean model. The distribution of Pearson's residues on the predicted values did not fit a normal distribution in either case. However, the probability of the result of the model computed with SAS showed a lower significance (K-S = 0.029; \(p=2.79\times 10^{-15}\)) than the one computed with SPSS (K-S = 0.034; \(p=4.61\times 10^{-21}\)). As shown in Table 8, with the exception of the number of active nozzles in the SPSS model, all three FE had a significant effect on the internal fluid velocity. Both software showed that the level of liquid in the tank (TL) had the greatest influence on the fluid velocity, followed by the agitation system pressure (P), and finally, the number of open nozzles (NN). Considering the SPSS model, the most different FE was the number of open nozzles, as it seemed to have the least influence, with respect to the other two (<F). Considering the SAS model, the agitation system pressure and the number of open nozzles had a significant effect, and which was more similar to each other and much less than that of the liquid level in the tank. Results obtained with both software agreed that fluid velocity was significantly lower as the liquid level inside the tank increased. While no differences were observed at 8 or 10 bar, the fluid velocity increased significantly when the pressure reached 12 bar. However, the results differed in the effect of the number of active nozzles. While the SPSS model did not observe differences between the presence of 2 and 4 open nozzles, the SAS model observed and separated them, highlighting that the velocity was significantly lower with four open nozzles, potentially due to their geometric location in the tank as they were facing each other (Figure 1). Thus, when the four nozzles operated, the liquid flowed facing 2 to 2 and produced a braking effect. In this case, the four nozzles were arranged on the same work plane and aligned with two sets of nozzles facing each other, with each pair located at the ends of the tank. In contrast, when two nozzles were used, they were located in the same plane but misaligned with each other, and thus did not directly face the fluid flows. There was, however, a gap in the flow lines of approximately 700 mm. This is consistent with the significance of the \(\sigma_{3}\) covariance, between the first and last section, observed in the Toeplitz variance-covariance matrix (Equation (6)). Generally, the least square means obtained with SAS were slightly higher than those obtained with SPSS, with the exception of the cases of 2000 L and 3000 L of liquid in the tank. The predictions on the fluid velocity of the best model revealed significant differences between all the levels of FE (Figure 4). It is noteworthy that these were slightly lower than those observed during the test (Table 8), with the differences between what was predicted by the SPSS and SAS models, and the differences in the analysis of the observations made by both software being in a certain proportion. Without the pretension of establishing a correct linear regression, as several of its premises are not fulfilled, if this method was used to find the output that adjusts its predictions with the measurements in the laboratory better, it was observed that the best model, computed with SAS, revealed a better adjustment in the coefficient of determination (R\({}^{2}\); almost 8%), a higher correlation and, the residues, having less skewness and kurtosis, than that computed using SPSS (Table 9). Therefore, the best model was the one computed with SAS, considering the parameters that have been discussed throughout the study.