## 3 Results and Discussion
### Sulfur Analysis
#### 3.1.2 Partial Least Square Regression (PLSR)  
Figure 4a represents the PLSR of original data. The coefficients of determination, \(R^{2}\), for calibration and cross-validation were 0.9265 and 0.8981, respectively. They are larger than or very close to 0.90, which shows a good agreement between calibration and cross-validation. The RMSEC and RMSECV were calculated as 0.0746 and 0.0893, respectively. As shown in Figure 4b, the \(R^{2}\) for calibration, the \(R^{2}\) for cross-validation, the RMSEC, and the RMSECV were improved slightly when the third-order polynomial with five points was used in the SG smoothing method. The \(R^{2}\) of calibration, the \(R^{2}\) of cross-validation, the RMSEC, and the RMSECV were 0.9357, 0.9085, 0.0698, and 0.0847, respectively. The most widely used third-order polynomial with seven points mode is shown in Figure 4c. More precise values can be seen and compared in Figure 4a,b. The \(R^{2}\)s for calibration and cross-validation were 0.9408 and 0.9146, respectively. The RMSEC and RMSECV decreased to 0.0670 and 0.0818, respectively. This means that there is close correlation between the reference data and the estimated data. In Figure 4d, both the \(R^{2}\) for calibration and cross-validation decrease slightly. The \(R^{2}\) of calibration, the \(R^{2}\) of cross-validation, the RMSEC, and the RMSECV were 0.9384, 0.9107, 0.0683, and 0.0837, respectively. This shows that smoothing with many points does not always produce more accurate results. The third-order polynomial with seven points removes only noise but at more points, the information related to the PLSR as well as the noise is lost due to excessive smoothing. Therefore, the estimated \(Y\) variance dropped below 95% in the nine points mode. The \(Y\) variance value means how well the variables fitted in the PLSR model and how well they predict new data. Therefore, with regard to the prediction of sulfur content, the SG smoothing mode with third-order polynomial and seven points provided the best result among the above-mentioned four cases. The cases for the fifth-order polynomial are represented in Figure 5a-d. The \(R^{2}\) of calibration, the \(R^{2}\) of cross-validation, the RMSEC, and the RMSECV for the fifth-order polynomial with seven points were 0.9357, 0.9091, 0.0698, and 0.0844, respectively. In Figure 5b, the \(R^{2}\) of calibration, the \(R^{2}\) of cross-validation, the RMSEC, and the RMSECV for the fifth-order polynomial with nine points were 0.9352, 0.9072, 0.0701, and 0.0853, respectively. In case of the fifth-order polynomial with eleven points, the \(R^{2}\) of calibration, the \(R^{2}\) of cross-validation, the RMSEC, and the RMSECV were 0.9408, 0.9146, 0.067, and 0.0818, respectively. Figure 5d depicts slightly lower values than the data presented in Figure 5c. The \(R^{2}\) of calibration, the \(R^{2}\) of cross-validation, the RMSEC, and the RMSECV for the fifth-order polynomial with thirteen points were 0.9392, 0.9121, 0.0679, and 0.0830, respectively. From the fifth-order mode, the results were improved successively up to the eleven points mode and deteriorated after the thirteen points mode, which caused the \(R^{2}\) value to decrease and the RMSE values to increase. The explained \(Y\) variance fell below 95% from the thirteen points mode. Since the third-order polynomial with seven points and the fifth-order polynomial with eleven points yielded similar results, the third-order polynomial with seven points was selected as an appropriate data processing mode. Figure 4: _Cont._Compared with the PLSR results obtained from the original data, PLSR from processed data by the SG smoothing method produced better results in terms of the \(R^{2}\) and the RMSE values. The \(R^{2}\) value of ideal target line is one. This means that the correlation between the predicted value and spectral data is robust as the \(R^{2}\) is close to unity. The RMSE is reduced by approaching the ideal target line. As the RMSE is smaller, the correlation is closer to the ideal target line.