*3.4. Modelling and Accuracy Assessment*

After determining the optimal spectral wavelengths and indices, two regression approaches—i.e., MLR and SVM—were applied to model the relationships between spectral data and heavy metal concentrations. Table 3 illustrates the best-developed models and validation results using the SVM algorithm. Based on this table, the RBF function was selected as the optimal central function in 60% of the developed models, followed by the linear function (30%). These two functions were therefore considered as the optimal functions for relevant modelling in the studied grapevine leaves.


**Table 3.** Modelling and validation results of the best support vector machine (SVM) models based on optimal wavelengths and spectral indices for estimating heavy metal concentrations in grapevine leaves in training and testing sets. RBF: radial basis function.

\* mg/kg: dry weight.

Table 4 shows the modelling results using the MLR method. In cases where the Durbin–Watson coefficient ranged from 1.5 to 2.5, there was a lack of self-correlation between error terms in the regression model that included 60% of the presented models [40]. However, in relation to the presented models for Pb–Cd (based on wavelengths) and Cr–Cd (based on spectral indices), the Durbin–Watson coefficient was less than 1.5 and lacked one of the most important conditions for using regression modelling. VIF was also considered for the multicollinearity checking between the predictor variables in the regression models. According to Table 4, there was serious multicollinearity (some predictor VIFs exceeded the critical threshold of 10) in the Pb-based-wavelength and Zn-based-spectral index models. Therefore, these models violate the key assumption of multiple linear regression, making these models invalid.

**Table 4.** The results of modelling and validation of the best multiple linear regression (MLR) models based on optimal wavelengths and spectral indices for estimating heavy metals concentrations in grapevine leaves in training and testing sets.


\* mg/kg: dry weight, Rn: reflections at a certain wavelength, Cn: concentration of a certain heavy metal.
