# Using Geospatial Information to Map Yield Gain from the Use of _Azospirillum brasilense_ in Furrow
## 3 Results  
Figure 3 presents the frequency diagram and descriptive statistics values from the yield data of the samples presented in Figure 2.  
According to Figure 3, Br2 presented a higher yield and lower coefficient of variation (9249.64 Kg; 10.11%) than Br1 (8802.05 Kg; 11.10%). For both trials, from the samples used for Kriging and image models, a higher yield was observed in the sites where treatment was applied. From the samples used for Kriging, the productivities of the TS plots presented normality, with no normality in the STD data.  
Figure 4 and Table 1 present data from the adjusted Kriging models and descriptive data of the semivariograms, such as the nugget effect, range, and path.  
For the STD areas, the semivariograms fit to theoretical Gaussian and spherical models for the TS areas all obtained a lower error in the 110\({}^{\circ}\) direction. The semivariograms of the STD areas showed higher values than the TS areas for the nugget effect, range, and path, where the highest values were for STD Br1 (0.25, 4.68, and 0.80, respectively).  
Figure 5 shows the performance graphs of the prediction models (RMSE%, MAPE%, and R2) by Kriging (Kriging Method) and by MLP from images obtained by remote sensing (RS). The yields obtained in the field and the abscissa axis are presented in the ordinate axis, the yield estimated by the models.  
When analyzing the Kriging performances, the models generated from samples from STD sites had a minimum RMSE% and MAPE% of 6.75 and 5.42, respectively, for Br2, compared to 7.32 and 6.04, respectively, for models generated from samples from TS sites. The prediction performances by MLP/RS indicated that the models generated from samples from STD sites had a minimum RMSE% and MAPE% of 9.30 and 7.71, respectively, for Br2. For the models generated from samples of the TS sites, the minimum RMSE% and MAPE% were 9.34 and 7.79, respectively, for Br1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Br1 (STD/TS)** & **Br2 (STD/TS)** \\ \hline Nugget effect & 0.25/0.01 & 0.22/0.01 \\ Reach & 4.68/0.87 & 0.55/0.77 \\ Plateau & 0.80/0.65 & 0.50/0.70 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Descriptive data of semivariograms adjusted for BR1 and BR2 for STD and TS.  
Figure 5: Performance graphs of the prediction models for areas Br1 and Br2 by Kriging and MLP/RS methods from the sampled yield data.  
The correlation coefficients between estimated and measured yield for the models of estimation by Kriging varied from 0.70 to 0.88, respectively, whereas for the TS and STD sites in the Br2 area, maximum values were 0.88 and 0.82, respectively. For the models generated by neural networks, in Br2, the TS and STD treatments obtained the highest correlation coefficients (0.8 and 0.72, respectively).  
Figure 6 shows the maps of corn yield gain by applying _A. brasilense_ generated by the Kriging method and MLP/RS, and the comparison between the surfaces.  
Analyses of the data of yield gain surfaces in Figure 6 indicated a more significant yield gain of surface generated by the MLP/RS method when _A. brasilense_ was applied. In a general context, Kriging data revealed the distribution of areas that showed a gain mostly over the places where the treatments were applied. In contrast, the MLP technique indicated the yield gain throughout the entire area. The difference reflects the lower densification of points used for surface generation from the spectral model. There is an overestimation of the real value of yield gain due to the different amounts of samples used  
Figure 6: Yield gain surfaces from Kriging and MLP/RS methods and comparison between surfaces for areas Br1 and Br2. Correlation between surfaces for Br1 = 53.04% and Br2 = 56.08%.  
by different models in the generation of surfaces, culminating in similarities of 53.04% (Br1) and 56.08% (Br2) in the correlation between the methods.