## 3 Results
### Multivariate Statistical Analysis Based on Optimal Wavelengths  
The selection of the most influential wavelengths was performed by calculating the \(\beta\)-coefficients derived from the PLSR models. Figure 5 shows the regression coefficients of the best PLSR model, an absorbance model. In general, wavelengths with values close to zero do not contribute to the explanation of the chemical variation. High positive values are positively correlated with the dependent variable water; negative values are negatively correlated. The spectral range between 500 and 700 nm did not allow a definite assignment. A maximum was found at 750 nm. This peak is characterized by the O-H stretching second overtone of water and the spectral properties of deoxyhemoglobin. Due to the overlap of the water peak with the hemoglobin peak [51], the wavelength range of hemoglobin absorption (500-800 nm) is not considered for a future model. The influence of lipid absorption in the 930 nm wavelength range is compensated by a minimum of the regression coefficient. To avoid possible influences on the model by image sensor noise, no wavelengths above 980 nm are used. Since the \(\beta\)-regression coefficient method did not show clear minima and maxima, the range of 800-980 nm (37 wavelengths) is selected as an optimized wavelength range. The performance of the wavelength-adapted model for TWC prediction by HSI is represented in Table 4. The best prediction results were obtained with \(\text{R}_{\text{P}}\)\({}^{2}\) values of 0.925 and 0.941, as well as RMSE values of 3.075 and 3.202 for the absorbance data preprocessed with min-max normalization following SNV and reflectance data with area normalization. Figure 4: The Bland–Altman plot for (a) absorbance and (b) reflectance. Figure 5: Regression coefficients of the best PLSR calibration model. The relationship between measured versus predicted TWC values using the optimal PLSR models is shown in Figure 6. The absorbance and the reflectance models showed promising but still slightly worse results than the full spectral models presented above. Figure 7 shows the Bland-Altman plots for evaluating the differences between the measured and the predicted TWC values. There was no average discrepancy between the methods, as well as no \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Normalization**} & \multirow{2}{*}{**Filter**} & \multirow{2}{*}{**LV’s**} & \multicolumn{2}{c}{**Validation Model**} & \multicolumn{2}{c}{**Prediction Model**} \\ \cline{3-6}  & & & **RMSECV** & \(\mathbf{R^{2}_{P}}\) & **RMSEP** \\ \hline \multicolumn{2}{c}{_Absorbance_} & & & & \\ \hline Min-Max & - & 20 & 4.111 & 0.894 & 3.669 \\  & SNV & 7 & **4.486** & **0.925** & **3.075** \\  & MSC & 10 & 7.965 & 0.759 & 5.527 \\  & SG & 14 & 3.868 & 0.904 & 3.481 \\ \hline Area & - & 12 & 5.072 & 0.904 & 3.494 \\  & SNV & 12 & 3.807 & 0.886 & 3.801 \\  & MSC & 4 & 8.610 & 0.824 & 4.725 \\  & SG & 20 & 3.854 & 0.923 & 3.122 \\ \hline Vector & - & 13 & 3.584 & 0.914 & 3.295 \\  & SNV & 12 & 3.789 & 0.887 & 3.779 \\  & MSC & 4 & 7.195 & 0.490 & 8.0441 \\  & SG & 17 & 3.837 & 0.921 & 3.159 \\ \hline \multicolumn{2}{c}{_Reflectance_} & & & & \\ \hline Min-Max & - & 11 & 3.544 & 0.919 & 3.202 \\  & SNV & 13 & 3.698 & 0.911 & 3.352 \\  & MSC & 7 & 7.861 & 0.898 & 3.593 \\  & SG & 13 & 3.752 & 0.929 & 3.001 \\ \hline Area & - & **11** & **3.485** & **0.941** & **3.202** \\  & SNV & 13 & 3.687 & 0.913 & 3.327 \\  & MSC & 1 & 9.641 & 0.201 & 10.065 \\  & SG & 13 & 3.896 & 0.943 & 2.699 \\ \hline Vector & - & 12 & 3.416 & 0.937 & 2.819 \\  & SNV & 13 & 3.687 & 0.913 & 3.327 \\  & MSC & 15 & 8.160 & 0.852 & 4.336 \\  & SG & 10 & 3.828 & 0.920 & 3.180 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of PLSR for prediction TWC based on 37 wavelengths. Figure 6: Measured versus predicted value of TWC for (**a**) absorbance and (**b**) reflectance data. trend of the difference in relation to the mean observed for absorbance and reflectance, respectively.