## 3 Results and Discussion
### Quantitative Analysis of the Sediment Using the PLSR Model
The \(R^{2}\) values for calibration and cross-validation, the RMSEC, and the RMSECV with the SG derivative were 0.9836, 0.7120, 0.9430, and 4.1029, respectively. In the case of Cr, the \(R^{2}\) values for cross-validation and the RMSECV without preprocessing were better. For the cases of Cd and Pb, the \(R^{2}\) values for cross-validation and the RMSECV were improved when the SG derivative preprocessing method was applied. To quantitatively compare the RMSEC and RMSECV for metals, the averages of the RMSEC and RMSECV were employed as follows [21]:  
\[\text{RMSEC}(\text{V})_{\text{avg}}(\%)=\frac{\text{RMSEC}(\text{V})}{ \text{Average of Property}}\times 100 \tag{4}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Metal**} & \multirow{2}{*}{**Process**} & \multicolumn{2}{c}{**Original**} & \multicolumn{2}{c}{**SG Derivative**} \\ \cline{3-6}  & & \(\mathbf{R^{2}}\) & RMSE & \(\mathbf{R^{2}}\) & RMSE \\ \hline \multirow{2}{*}{Cd} & Calibration & 0.9963 & 0.0063 & 0.9989 & 0.0035 \\  & Validation & 0.9406 & 0.0264 & 0.9670 & 0.0197 \\ \hline \multirow{2}{*}{Cr} & Calibration & 0.9690 & 7.9131 & 0.9736 & 7.3066 \\  & Validation & 0.8574 & 17.6165 & 0.8136 & 20.1409 \\ \hline \multirow{2}{*}{Pb} & Calibration & 0.9718 & 1.2379 & 0.9836 & 0.9430 \\  & Validation & 0.6815 & 4.3146 & 0.7120 & 4.1029 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The calibration and validation performance of the PLSR model. The averages of the RMSECV were calculated by dividing the RMSECV by the average of the properties to quantitatively compare the RMSECV for each metal. This value allows for comparisons between the properties of samples with unequal sizes [25]. The authors of [26] used the averages of the RMSECV to find the lowest errors of different spectral features in the standard volume of forests. The authors of [27] used the averages of the RMSECV to determine the optimal model between multilinear regression and an artificial neural network for biomass. Table 3 lists the averaged RMSECV values that were calculated. The results of the Cd analysis with the SG derivative show the lowest averaged RMSECV of 8.35. Although the Cd content was low in the sediment, the Cd analysis showed a somewhat higher error value. The results of the analysis of Cd showed the lowest error among the metals because Cd was in a similar concentration range. In the case of Cr, the RMSECV values were high. This can be attributed to the large deviations among the amounts of Cr contained in the samples. In terms of the averaged RMSECV, except for the Cr analysis, the application of the preprocessing with the SG derivative to the original data was conducive to the reduction of errors in the results. The accuracy of quantitative analyses that use PLSR models can be improved by utilizing data-preprocessing techniques, such as the SG derivative. From LIBS measurements, a good amount of data can be obtained. The RSD can be too high to find a reliable correlation. Therefore, this approach will be effective in improving the ability to detect heavy metals in sediments for in situ monitoring of rivers. Furthermore, the combination of the LIBS technique with a data-processing method is expected to contribute to the provision of better interpretations and visualizations of data. From the results of this research, it was determined that the LIBS system together with multivariate chemometric analysis is useful for providing practical guidelines for the management of freshwater sediments and water quality by understanding and evaluating many potential pollutants in the sediments.