## 4 Discussion
If models (17) and (19) are compared in the same manner, the \(p\)-value equals 0.1091 which leads us to the same conclusion for the density as a predictor variable. On the other hand, the regression tree model (Table 4) has a larger adjusted \(R^{2}\) than every linear model. The models based on regression trees give significantly better results according to \(R^{2}\) and adjusted \(R^{2}\). Except for bagging, they give slightly worse results due to the value of \(RMSECV\). The size of the \(R^{2}\) models in this paper was compared with those in other papers [30; 31; 43]. One obstacle to the comparison is that the same success coefficients were not used, so the comparison can only be made using the size \(R^{2}\) that all models had. This is most evident when comparing the \(R^{2}\) model which was created using artificial neural networks which have a black box in their structure and therefore cannot explain their outputs, and it has undesirable negative properties such as complexity in its multilayer structure, possibility of overlearning [31]. Taking this into consideration, it can only be argued that the models developed in this paper have lower \(R^{2}\) than the neural network models [43]. It is noticeable that the most successful model Bagging in this paper has a very similar value \(R^{2}\) (0.8934) to the model created earlier, whose coefficient of determination is 0.908 [31], and it was created using the Least Square Support Vector Machine method \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **RMSECV** & \(R^{2}\) & **Adjusted \(R^{2}\)** \\ \hline Regression tree (Figure 8) & 10.2387 & 0.7624 & 0.7285 \\ Pruned tree (Figure 9) & 10.0712 & 0.7424 & 0.7157 \\ Bagging (m = 6) & 9.8033 & 0.8934 & 0.8687 \\ Random Forest (m = 2) & 10.1133 & 0.8736 & 0.8652 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measures of accuracy of the three models. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Linear Model** & **RMSECV Rank (Value)** & **Adjusted \(R^{2}\) Rank (Value)** \\ \hline (17) & 1. (10.0025) & 4. (0.5129) \\ (18) & 2. (10.0313) & 7. (0.4890) \\ (19) & 3. (10.0798) & 8. (0.4837) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMSECV, adjusted \(R^{2}\) values and their ranking numbers for multiple linear regression models. (LS-SVM). This is an advanced version that is superior to the artificial neural networks method in terms of predictive performance, generality, and robustness. This is consistent with the research of [29] who investigated the advantages and disadvantages of fuzzy inference systems, artificial neural networks and LS -SVM methods and found that the performance of the LS -SVM model was the best among the other methods. However, the small difference in \(R^{2}\) between the models in this paper and [31] shows the similarity of the success of both models and does not imply that the Bagging model is less useful or less accurate. More so, if the emphasis is on simplicity and great attention is paid to avoiding overfitting, then it is quite justified to use the models of the authors of this paper, as they have used other very rigorous measures (RMSECV and adjusted \(R^{2}\)) to evaluate model performance. Of course, it is important to point out that the results of this study do not replace laboratory tests on the elastic properties of rocks, which still need to be carried out. The analysis in this paper shows that for a simpler prediction of elastic rock properties using pruned tree, it is sufficient to know the data of three parameters (P-wave velocity, uniaxial compressive strength and the point load strength index). To reliably predict the elastic rock properties, the remaining four parameters are also used for modelling. Therefore, the application of this method in engineering practice depends on the amount of available data. Actual application of this method in engineering practice is possible in the preliminary stages of work to improve property estimation when direct determination of elastic modulus would be uneconomical.