## 3 Results and Discussions
### Validation of the Calibration Model  
A portion of the sample set with viscosity reference values (15 motor oil samples) was left outside the calibration set and used for initial verification of the calibration equations.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**PLS**} & \multicolumn{3}{c}{**PCR**} \\ \cline{2-7}
**Spectral Range** & **PCs** & **R** & \
\begin{tabular}{c} **RMSEC** \\ **(mm\({}^{2}\)s\({}^{-1}\))** \\ \end{tabular} & **PCs** & **R** &
\begin{tabular}{c} **RMSEC** \\ **(mm\({}^{2}\)s\({}^{-1}\))** \\ \end{tabular} \\ \hline not adjusted & 7 & 0.89 & 0.197 & 10 & 0.88 & 0.204 \\
1 st derivation & 5 & 0.88 & 0.197 & 10 & 0.85 & 0.186 \\
2 nd derivation & 10 & 0.95 & 0.148 & 10 & 0.47 & 0.372 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of FTIR-PLS/PCR regression models for kinematic viscosity prediction at 100 \({}^{\circ}\)C.  
Figure 2: Regression dependence between kinematic viscosity values at 100 \({}^{\circ}\)C predicted by FTIR-PLS model and determined by the standardized method; the regression line equation is y = 0.8774x + 1.7230, R = 0.95  
Validation of the calibration models was selected based on the RMSEP (Root Mean Square Error of Prediction) value [45; 51]. Equation (3) was used for the calculation.  
\[RMSEP=\sqrt{\frac{\sum\limits_{i=1}^{m}(c_{iev}-c_{irv})^{2}}{m_{v}}} \tag{3}\]  
where: \(c_{iev.}\) is a predicted value of an \(i\)-th validation sample, \(c_{irv}\) stands for a value of a parameter of the \(i\)-th validation sample defined based on a standardized method, \(m_{v}\) is a total number of validation samples.  
The RMSEP of reliable calibration is usually not much larger than RMSEC [12]. In the case of validation of the FTIR-PLS model without spectrum adjustment, the value of RMSEP = 0.179 mm\({}^{2}\)s\({}^{-1}\); in the case of the model with spectrum adjustment by the 1 st derivative, the value of RMSEP = 0.182 mm\({}^{2}\)s\({}^{-1}\); and in the case of the best calibration model with spectrum adjustment by the second derivative, the value of RMSEP = 0.190 mm\({}^{2}\)s\({}^{-1}\). For all predictive models for determining viscosity at 100 \({}^{\circ}\)C, the RMSEC differed only minimally from the RMSEP error expected in future predictions.  
Table 2 presents the results of testing the predictive ability to determine KV\({}_{100\ ^{\circ}\mathrm{C}}\) by the best FTIR-PLS model (using the adjustment of the spectra of the second derivatives) on fifteen external samples of motor oils. This model provided a relative standard error of prediction 2.3%.  
The viscosity values predicted by the best FTIR-PLS model, constructed from the data points of the spectra adjusted by the second derivative (for the wavenumber range 1750-650 cm\({}^{-1}\)), were further statistically compared with the results obtained by the standardized method. Based on the paired \(t\)-test (\(\alpha\) = 0.05), it was shown that the differences between the reference and predicted values are not statistically significant. The F-test confirmed that both methods have similar accuracy.  
Due to the fact that the quality of the engine oil is affected by the operating conditions and the technical condition of the vehicle, there may be significant changes in its physical and chemical properties. For this reason, the predictive ability of the proposed calibration model should be continuously verified by real samples of operated oils, for which the kinematic viscosity was determined by the standardized method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Validation**} & **Measured** & **Predicted** & **Standard** \\  & **KV\({}_{100\ ^{\circ}\mathrm{C}}\)** & **KV\({}_{100\ ^{\circ}\mathrm{C}}\)** & **Deviation** \\  & **(mm\({}^{2}\)s\({}^{-1}\))** & **(mm\({}^{2}\)s\({}^{-1}\))** & **(mm\({}^{2}\)s\({}^{-1}\))** \\ \hline
1 & 14.275 & 14.107 & 0.119 \\
2 & 14.219 & 14.111 & 0.076 \\
3 & 14.534 &