## 3 Results and Discussion
### VIP-PLSR Analysis to Predict Toluene-Adulterated Grignard Reagent  
For the selection of an optimum number of variables from the PLSR-based results, a model-based variable selection method, namely VIP, was employed. The VIP-based algorithm was developed using MATLAB for the analysis and then further applied to the PLSR based results. The main reason for using  
Figure 4: Multiplicative scatter correction (MSC) preprocessed beta coefficients plot of PLSR model (**a**), and mean plot for the pure Grignard reagent and pure toluene (**b**).  
a variable selection approach was that models that are generated by employing the variable selection approach are easier to interpret; besides, they have good performance for classification or prediction. The best cut-off value determined using the VIP method was 1.5, which acquired the highest accuracy for both the calibration and the prediction when the number of variables was 95. A new PLSR model was then developed based on the VIP threshold value; subsequently, it was further compared with the originally developed MSC preprocessed PLSR model with the highest prediction accuracy using a full wavenumber range of 2046 variables. Table 2 shows the improvement in the prediction results using the selected variables with the threshold value of 1.5 compared with the predicted results obtained using whole variables. The VIP-based PLSR model obtained better prediction results (\(R_{p}^{2}\) = 0.97 and SEP = 0.71%), with bias and ratio of standard error of performance to standard deviation (RPD) values of \(-\)2.21% and 7.15, than the PLS model developed using whole variables (\(R_{p}^{2}\) = 0.95 and SEP = 0.79%), having bias and RPD values of \(-\)0.61% and 5.24. Previous studies showed that the model with RPD values obtained between 2.5 and 3.0 and above 3.0 is considered well-developed and has greater prediction power [24]. Thus, the calculated RPD of 7.15 for the VIP-PLSR model suggested that the established model produces a very accurate prediction of toluene concentration in the Grignard reagent. Furthermore, the obtained VIP score plot (Figure 5) shows a strong peak at 1008 cm\({}^{-1}\), which indicates the presence of a mono-substituted benzene ring C\({}_{6}\)H\({}_{5}\)CH\({}_{3}\); this confirmed the presence of toluene in this region. Some high-intensity peaks were obtained around 787 cm\({}^{-1}\) and 1029 cm\({}^{-1}\), which is related to the symmetric ring breathing vibration from benzene and in-plane CH bending vibrations [25]. The other peaks obtained in the VIP score plot are not considered useful, as they are below the threshold line.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Methods** & \(R_{C}^{2}\) & **SEC (\%)** & \(R_{CV}^{2}\) & **SECV (\%)** & \(R_{p}^{2}\) & **SEP (\%)** & **LVs** & **Bias (\%)** & **RPD** \\ \hline Whole spectra & 0.94 & 0.65 & 0.94 & 0.68 & 0.95 & 0.79 & 4 & \(-\)0.61 & 5.24 \\ \hline VIP-PLSR & 0.98 & 0.60 & 0.96 & 0.66 & 0.97 & 0.71 & 4 & \(-\)2.21 & 7.15 \\ \hline \hline \end{tabular}  
* \(R_{c}^{2}\), \(R_{c}^{2}\), and \(R_{p}^{2}\) are the \(R^{2}\) values for calibration, validation, and prediction, respectively. _SEC, SECV_, and _SEP_ are the standard errors of calibration, cross-validation, and prediction, respectively.  
\end{table}
Table 2: Prediction results for the pure and toluene-adulterated Grignard reagent obtained from the partial least squares regression (PLSR) and VIP variable selection method.  
Figure 5: Plot of variable importance in projection (VIP) scores and selected wavenumbers.