## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **R** & **R Square** & **Adjusted R Square** & **Std. Error of the Estimate** \\ \hline
1 & 0.621 1  & 0.385 & 0.373 & 0.314 \\ \hline
2 & 0.936  & 0.875 & 0.873 & 0.561 \\ \hline
3 & 0.938  & 0.880 & 0.878 & 0.256 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Model summaries. Figure 3: Box plots and pairwise comparisons of the absorption acoustic class and absorption class performance. (**a**) thickness, (**c**) sound absorption coefficient and (**e**) frequency among different class materials, (**b**,**d**,**f**) the pairwise comparisons. (**g**) Thickness across ACP. (**h**) Sound absorption across ACP. (**i**) Frequencies. For Model 1, with _acoustic comfort_ as the dependent variable (from most important to least important according to the values of the standardized beta coefficient), there were the sound absorption coefficient, frequency and material type. Practically, with an increase of 1 unit of sound absorption coefficient, the acoustic comfort increases by 0.792; with an increase of 1 unit of frequency, the acoustic comfort decreases by \(-4.116\times 10^{-5}\); and with an increase of 1 unit of thickness, from basic to composite material, the acoustic comfort increases by 0.083. For Model 2, with the absorption acoustic class as the dependent variable, the only best predictor was the sound absorption coefficient; when the sound absorption coefficient increased by 1 unit, the absorption acoustic class decreased by 4.580 from the E class or other classes to the A class. For Model 3, with absorption class performance as the dependent variable, as in the previous model, the only best predictor was the sound absorption coefficient; when the absorption class decreased by 2.142 from the E class or other classes to the A class, the value increased with 1 unit of the sound absorption coefficient. The ANOVA test results for all models indicate statistical significance (\(p<0.001\)), confirming the reliability of the model;  
The impact of the absorption coefficient on acoustic performance is consistent and significant across all models, highlighting the importance of this factor in the design, evaluation and selection of materials for passive noise control in vehicles;  
The variability explained by each model, as indicated by the R Square test, suggests that the models are robust, particularly models 2 and 3, which account for a large proportion of the variance in the acoustic absorption class and its performance. By applying a machine learning method based on the decision tree with the chi-square automatic interaction detector (CHAID) and the growing method with the same dependent and independent variables as the abovementioned regression models, we wanted to validate/confirm (or not) the predictors of regression models for acoustic comfort (Figure 4), absorption acoustic class (Figure 5) and acoustic class performance (Figure 6). Figure 4: Decision tree for acoustic comfort. Figure 5: Decision tree for the absorption acoustic class. The tree illustrates the distribution of class materials in relation to acoustic comfort, divided into two main categories: without acoustic comfort and with acoustic comfort. Node 0 shows the overall distribution, where 19.4% of the materials are without acoustic comfort and 80.6% are with acoustic comfort. The class materials are further divided into Node 1 and Node 2 based on their types. Node 1 includes metals, glass-based materials, plastic/polymer-based materials and textile materials, with 11.3% without acoustic comfort and 88.7% with acoustic comfort. Node 2 includes wood-based materials and elastic polymers, with 48.1% without acoustic comfort and 51.9% with acoustic comfort. The adjusted \(p\)-value is 0.000, with a Chi-square value of 36.066 and one degree of freedom, indicating a significant relationship between class material and acoustic comfort.