In type Ia supernovae (SNe Ia) cosmology, a well-established correlation exists between the mass of host galaxies and the Hubble residual (HR) of SNe Ia. In order to investigate the origin of this correlation, we used low-resolution spectroscopic data of early-type host galaxies obtained from our YOnsei Nearby Supernovae Evolution Investigation (YONSEI) project. We measured velocity dispersions and Lick/IDS absorption line indices from these fully calibrated spectra. These indices were used to estimate the luminosity-weighted mean age, metallicity and mass of host galaxies. We found a tight correlation between host mass and population age, which is consistent with the "downsizing" trend in early-type galaxies. This suggests that the well-established correlation between HR and host mass is most likely due to the difference in population age. More observations, which are in progress, are required to understand the impact of luminosity evolution on SNe Ia cosmology.