## 3 Results and Discussion
After that, prior to the carrying out of calibrations, as mentioned in the Material and Methods section, different mathematical pre-treatments were applied, for the three parameters, to the raw and ground samples, both for the full range and the reduced range. Partial-least-square regression is used to establish the correlation between the spectra and the assayed parameters. Table 4 summarizes the NIRS models' calibration statistics to quantify the NDF. As can be seen in Table 4, the R\({}^{2}\) values are higher and the SEC values are lower in the chemometric models developed with the reduced wavelength range than in those developed using the full one. In relation to the variability in the results depending on the mathematical pretreatment, it is important to note that the SNV plus the second Savitzky-Golay derivative reached the best calibration statistics for the raw and ground samples. Previous authors [22], after evaluating different commercial portable NIRS instruments to analyze ground forages, obtained R\({}^{2}\) values for the NDF ranging between 0.95 and 0.71, depending on the instrumentation employed. Regarding the SEC values, their results were between 2.85 and 1.21. It is not possible to obtain SEC values lower than 1, because the standard error of the laboratory (SEL) for this parameter is higher than 1.3 [22]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**Raw alfalfa**} \\ \hline Wavelength range: & \multicolumn{2}{c}{901–1600 nm} & \multicolumn{2}{c}{901–1700 nm} \\ Mathematical pretreatment & \(R^{2}\) & \(SEC\) & \(R^{2}\) & \(SEC\) \\ \hline
1 4 4 SG & 0.898 & 1.554 & 0.883 & 1.670 \\
2 4 4 SG & 0.784 & 2.184 & 0.786 & 2.289 \\ SNV 1 4 4 SG & 0.911 & 1.392 & 0.791 & 2.187 \\
1 4 4 SG SNV & 0.840 & 1.910 & 0.145 & 1.398 \\ SNV 2 4 4 SG & 0.955 & 1.066 & 0.514 & 3.155 \\
2 4 4 SG SNV & 0.726 & 2.558 & 0.540 & 3.238 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calibration statistics of NIR multivariate models for neutral detergent fiber quantification. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**901–1700 nm**} & \multicolumn{3}{c}{**901–1600 nm**} \\ \hline Sample & Raw & Ground & Raw & Ground \\ \hline
1 & 60,529 & 27,209 & 43,283 & 14,560 \\
2 & 58,378 & 23,853 & 33,386 & 10,886 \\
3 & 54,190 & 20,057 & 34,085 & 7029 \\
4 & 54,854 & 30,655 & 36,262 & 17,678 \\
5 & 48,472 & 33,325 & 34,239 & 21,939 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The root-mean-square error (RMS) values for the paired subsamples of the same scanned sample. Table 5 summarizes the calibration statistics for the CP. Most mathematical treatments reach R\({}^{2}\) values lower than 0.5 for raw alfalfa samples. This could be related to the heterogeneity in alfalfa forage, with two clearly different parts, the leaf and the stem. The leaf is the part of the plant that contains a protein fraction. However, it is important to remark that using the reduced range, the spectrum mathematical pretreatment of the SNV for the scatter correction, and the second Savitzky-Golay derivative (the same mathematical pretreatment as for the NDF), R\({}^{2}\) values of 0.885, with an SEC of 0.377, were achieved. A typical SEL for reference CP analysis is around 0.210 [22]. Feeding animals with minerals is a common practice; however, if there is an abnormal mineral content, there is a high probability of contamination with soil, which is not desirable in animal feeding systems. To quantify the MC in alfalfa forages, 24 different calibration models have been developed, assaying different mathematical pretreatments of spectrum data. The statistics of the proposed PLS models are shown in Table 6. As stated before, the reduced range gave better calibration statistics than the full one. Comparing mathematical pretreatments, the scatter correction applied after the derivatization procedure increased the R\({}^{2}\) values, and reduced the SEC. The highest R\({}^{2}\) and the lowest SEC values were 0.861/0.219 and 0.867/0.318 for the raw and ground samples, respectively.