## 4 Results
### Regression Analysis  
Stepwise multiple linear regression analysis was performed to design a model that predicts each affective dimension through acoustic parameters. Since the VIF (variance influence factor) values of all designed models were less than 10, it was found that there was no multi-collinearity. The results of the regression analysis for each range of RPM are shown in Tables 8-10. All the results in the table are shown only for the case where the R\({}^{2}\) is highest among the results obtained through the stepwise regression analysis. First, regression analysis for the range of entire RPM from 2000 to 5000 shows that SPL, sharpness, and fluctuation are included in the predictive model for 'Refined'. When the sharpness and fluctuation decreased and SPL increased, the value of perceived refined increased. In the case of 'Powerful', roughness, SPL, and SPL-A constituted the model. At the value of the standardization beta, the parameter that has the greatest influence on 'Powerful' is SPL-A. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Acoustic Parameter** & **Refined** & **Powerful** \\ \hline \hline \multirow{4}{*}{Refined} & \multirow{4}{*}{Constant} & \multirow{4}{*}{0.635} & \multirow{4}{*}{0.461} \\  & SPL\({}_{2000-5000}\) & & & \\ \cline{1-1}  & Sharpness\({}_{2000-5000}\) & & & \\ \cline{1-1}  & Fluctuation\({}_{2000-5000}\) & & & \\ \cline{1-1}  & Tonality\({}_{2000-5000}\) & & & \\ \cline{1-1}  & SPL\({}_{2000-5000}\) & & & \\ \cline{1-1}  & SPL-A\({}_{2000-5000}\) & & & \\ \cline{1-1}  & SPL-A\({}_{2000-5000}\) & & & \\ \cline{1-1}  & SPL-A\({}_{2000-5000}\) & \(-\)0.382 * & 0.597 ** \\ \cline{1-1}  & Roughness\({}_{2000-3500}\) & & & 0.575 ** \\ \cline{1-1}  & Fluctuation\({}_{2000-3500}\) & & & 0.517 ** \\ \cline{1-1}  & Tonality\({}_{2000-3500}\) & & & 0.475 ** \\ \cline{1-1}  & SPL-A\({}_{2000-3500}\) & & & & \\ \cline{1-1}  & SPL-A\({}_{2000-3500}\) & 0.489 ** & & 0.563 ** \\ \cline{1-1}  & SPL-C\({}_{2000-3500}\) & & & 0.467 ** \\ \cline{1-1}  & Loudness\({}_{5000-5000}\) & & & 0.606 ** \\ \cline{1-1}  & Sharpness\({}_{5000-5000}\) & \(-\)0.449 * & & 0.629 ** \\ \cline{1-1}  & Roughness\({}_{3500-5000}\) & \(-\)0.340 * & & 0.577 ** \\ \cline{1-1}  & Fluctuation\({}_{3500-5000}\) & & & & \\ \cline{1-1}  & Tonality\({}_{3500-5000}\) & & & 0.549 ** \\ \cline{1-1}  & SPL-A\({}_{3500-5000}\) & & & & \\ \cline{1-1}  & SPL-A\({}_{3500-5000}\) & & & 0.577 ** \\ \cline{1-1}  & SPL-C\({}_{3500-5000}\) & & & 0.489 ** \\ \hline \hline \end{tabular} Note. *: \(p<0.05\), **: \(p<0.01\).  
\end{table} 
Table 8: Results of regression analysis of affective dimensions for acoustic parameters from 2000 to 5000 RPM. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Affective** & **Acoustic Parameter** & **B** & **Error** & \(\beta\) & **F** & \(p\) & **VIF** & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{Refined} & Constant & 0.635 & 0.461 & & 1.379 & 0.178 & \multirow{4}{*}{0.858} \\  & SPL\({}_{2000-5000}\) & 0.064 & 0.005 & 0.885 & 8.782 & 0.000 & 0.813 \\ \cline{1-1}  & Sharpness\({}_{2000-5000}\) & \(-\)2.370 & 0.232 & \(-\)0.736 & \(-\)5.210 & 0.000 & 0.883 \\ \cline{1-1}  & Fluctuation\({}_{2000-5000}\) & \(-\)0.369 & 0.114 & \(-\)0.231 & \(-\)3.232 & 0.003 & 0.898 \\ \hline \multirow{4}{*}{Powerful} & Constant & 9.845 & 0.711 & & 13.851 & 0.000 & \multirow{4}{*}{0.907} \\  & Roughness\({}_{2000-5000}\) & 0.059 & 0.113 & 0.055 & 5.520 & 0.000 & 3.746 \\ \cline{1-1}  & SPL\({}_{2000-5000}\) & \(-\)0.158 & 0.012 & \(-\)1.341 & \(-\)12.699 & 0.000 & 3.717 \\ \cline{1-1}  & SPL-A\({}_{200-5000}\) & 0.133 & 0.012 & 1.706 & 11.284 & 0.000 & 7.616 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of correlation analysis between affective dimension and acoustic parameter. Second, regression analysis was performed based on the parameters of RPM divided by 2000 to 3500 and 3500 to 5000. In the case of 'Refined', the regression model consisted of SPL\({}_{3500}\)-5000, sharpness\({}_{3500}\)-5000, and roughness\({}_{3500}\)-5000.