Much effort has been carried out to calibrate and revise asteroseismic relations, given their importance of relations in asteroseismology in determining fundamental parameters of stars. In this study, we statistically explore asteroseismic relations with partial correlation coefficients to determine the most fundamental parameters, separately analyzing asteroseismic data based on the evolutionary status of stars from main sequence up to core helium-burning red-clump stars. We have found that regardless of the evolutionary status of the sampled stars the surface gravity and density of stars strongly influence the observed correlations. More importantly, it is found that indirect correlations derived considering the influence of confounding parameters are subject to the evolutionary status. For example, the observed correlation of the large frequency separation Δν with the central frequency νmax is influenced by the stellar mass, radius, and luminosity only for main sequence stars. The observed correlation of the width of the Gaussian envelope δνenv with νmax is influenced by the stellar mass, effective temperature, radius, and luminosity for main-sequence and subgiant stars. The observed relation between Δν and the small frequency separation δν02 is influenced by the stellar mass, radius, and luminosity for main-sequence and subgiant stars. In contrast, effective temperature, metallicity, and age do not seem to significantly affect the observed correlations. Finally, we conclude by discussing implication of our findings.

In this study, the partial correlation between the expansion and the vertical displacement excluding the temperature and the correlation between the expansion and vertical displacement and the average temperature of the reinforced truss member was analyzed. The correlation coefficients between temperature and expansion, temperature and vertical displacement were .929 and .874, respectively. The correlation coefficient between vertical displacement and expansion was 0.860 and partial correlation coefficient excluding temperature effect was 0.268.