## 4 Conclusions  
Multivariate analyses for the carbon, hydrogen, oxygen, and sulfur components of mixed coals measured by LIBS were quantitatively analyzed. The data treated by SG smoothing and the SG derivative were adopted in the PLSR models. The coefficient of determination (\(R^{2}\)), the root mean square error, the relative error, and the RMSE average were adopted as parameters. The most reliable PLSR model was selected by introducing the RPD parameter. The concentration of each element was predicted by the selected PLSR model, and the calorific value was obtained by using the estimated concentration of elements and substituting them into [PERSON]'s equation. The data pre-processed with the SG derivative showed better results regarding the calorific value of the mixed coals. Figure 16: Relative errors between measured and predicted values for the PLSR model of the original data and the PLSR model pre-processed by SG derivative. **Author Contributions:** Conceptualization, J.H.P. and S.J.M. ; methodology, J.H.P. ; software, K.H.P. and C.M.R. ; validation, K.H.P. ; formal analysis, J.H.P. ; investigation, C.M.R. and K.H.P. ; data curation, C.M.R. ; resources, J.H.C. ; funding--acquisition, S.J.M. and J.H.C. ; writing--original draft preparation, J.H.P. ; writing--review and editing, J.H.C., S.J.M. and K.H.P. ; visualization, C.M.R. ; supervision, S.J.M. ; All authors have read and agreed to the published version of the manuscript. **Funding:** This work was partially supported by the Technology Innovation Program (or Industrial Strategic Technology Development Program--Development of technical support platform for welding material and process) (20017251, Development of laser-welding automation systems for electric coil-joining system to manufacture electrical vehicle motors) funded by the Ministry of Trade, Industry, and Energy (MOTIE, Republic of Korea). This work was partially supported by the National Research Foundation of Korea (NRF) entitled \"Development of Coal Analyzing System Using Laser-induced Breakdown Spectroscopy/LIBS. Korean J. Soil Sci. Fertil. **2009**, 42, 399-407. [PERSON]; [PERSON]; [PERSON]; [PERSON] Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy. _Anal. Chim. Acta_**2001**, 429, 269-278. [CrossRef]  
[PERSON]; [PERSON]; [PERSON]; [PERSON] Calibration-free quantitative analysis of thin-film oxide layers in semiconductors using laser induced breakdown spectroscopy (LIBS). _J. Anal. At. Spectrom._**2017**, 32, 1378-1387. [CrossRef]  
[PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Extracting coal ash content from laser-induced breakdown spectroscopy (LIBS) spectra by multivariate analysis. _Appl. Spectrosc._**2011**, _65_, 1197-1201. [CrossRef] [PubMed]  
[PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Coal property analysis using laser-induced breakdown spectroscopy. _J. Anal. At. Spectrom._**2013**, _28_, 1045-1058. [CrossRef]  
[PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Application of LIBS for direct determination of volatile matter content in coal. _J. Anal. At. Spectrom._**2011**, _26_, 2183-2188. [CrossRef]  
[PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Analysis of Pluverized Coal by Laser-Induced Breakdown Spectroscopy. _Plasma Sci. Technol._**2005**, \(7\), 3041-3044. [CrossRef]  
[PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Major elements analysis in bituminous coals under different ambient gases by laser-induced breakdown spectroscopy with PLS modeling. _Front. Phys._**2012**, \(7\), 708-713. [CrossRef]  
[PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Time-of-flight secondary ion mass spectrometry of a range of coal samples: A chemometrics (PCA, cluster, and PLS) analysis. _Energy Fuels_**2008**, _22_, 1059-1072. [CrossRef]  
[PERSON]; [PERSON] Reflection and transmission mid-infrared spectroscopy for rapid determination of coal properties by multivariate analysis. _Tilatta_**2008**, _74_, 998-1007.