## 3 Results and Discussion
### Quantification Analysis
While the predicted values should have been zero or close to zero because the samples did not contain DNT, the average predicted concentrations were 8.8% (BA), 3.1% (IBP), -8.0% (PETN), 2.3% (RDX), and 25.8% (TNT) (see Table 4). The objective was to measure the model's capability of discriminating against these interferences. To improve the model with respect to the recognition of interferences, an optimization procedure was applied. This procedure involved implementing the optimization of the most significant regions of the spectra after using various preprocessing steps. During optimization, the spectral region was divided into equal spectral sub-regions. Then, the optimum combination of sub-regions was determined by starting with 10 sub-regions and successively excluding one sub-region. This procedure continued until the values of the cross-validation errors did not improve further. The RMSECV values were calculated for each combination of the preprocessing steps, and the models with the lowest values of errors were selected. Twenty spectra of each interference were introduced together with the validation spectra set off with 0% of DNT true value. Then, optimization was performed by minimizing the RMSECV value. This was labeled as an optimization of the validation set (OPT-Val). In OPT-Val, all interferences were stabilized with the correct rejections. The parameters for the NAT-S OPT-Val model were approximately similar to those of the NAT-S model except for the LV. In particular, nine LV were added to the NAT-S OPT-Val model to stabilize the interferences (Table 5). In the optimization process, the entire region was selected, and the best pretreatment was found to be VN. Therefore, the only difference between the two models was that the optimized model had more LVs. This procedure was optimum for the elimination of the interferences; however, it assumed that the interferences do not interact with the analyte or the matrix. As part of our future work, samples of DNT in soil with interferences interacting with DNT can be added to the model to remove these potential errors. \begin{table}
\begin{tabular}{c c c} \hline  & **NAT-S** & **NAT-S OPT-Val** \\ \hline
**BA** & 8.8 & 0.02 \\
**IBP** & 3.8 & \(-\)0.02 \\
**PENT** & \(-\)8.0 & 0.00 \\
**RDX** & 2.3 & 0.02 \\
**TNT** & 25.8 & 0.11 \\ \hline \end{tabular}
\end{table} 
Table 4: Prediction of %DNT from the NAT-S models. \begin{table}
\begin{tabular}{c c c} \hline  & **NAT-S** & **NAT-S OPT-Val** \\ \hline
**R\({}^{2}\) cal** & 99.87 & 99.65 \\
**R\({}^{2}\) val** & 99.61 & 98.92 \\
**R\({}^{2}\) test** & 99.63 & 98.07 \\
**RMSE** & 0.245\% & 0.425\% \\
**RMSECV** & 0.39\% & 0.72\% \\
**RMSEP** & 0.39\% & 0.88\% \\
**Bias** & 0.001 & \(-\)0.0016 \\ LV & 10 & 19 \\
**ho** & 0.06 & 0.021 \\
**LOD** & 0.80\% & 1.4\% \\
**RPD** & 16.1 & 9.61 \\ \hline \end{tabular}
\end{table} 
Table 5: Performance indicators parameters for the NAT-S models. For the NAT-S OPT-Val model, 19 LV were required to obtain a good RMSECV value. Figure 5 shows the dependence of the RMSECV values for the prediction of each interference as a function of the LV. The NAT-S OPT-Val and NAT-S models were generated to determine how the RMSECV values decrease with the LV and compare the two models. The NAT-S model showed the minimum RMSECV at L = 10. Adding more LV resulted in worse RMSECV values. For the NAT-S OPT-Val model, the minimum RMSECV was achieved with 19 LV. Nevertheless, at 10 LV, the RMSECV values for other interferences were also sufficiently close to the RMSECV value for the model. For that reason, TNT and IBP interferences did not allow the RMSECV value of the NAT-S OPT-Val model to approach the RMSECV value of the NAT-S model.