We present the dependences of the properties of type Ia Supernovae (SNe Ia) on their host galaxies by analyzing the multi-band lightcurves of 118 spectroscopically confirmed SNe Ia observed by the Sloan Digital Sky Survey (SDSS) Supernova Survey and
the spectra of their host galaxies. We derive the equivalent width of the rm{H}$alpha$ emission line, star formation rate, and gas-phase metallicity from the spectra and compare these with the lightcurve widths and colors of SNe Ia. In addition, we compare host properties with the deviation of the observed distance modulus corrected for lightcurve parameters from the distance modulus determined by the best fit cosmological parameters. This allows us to investigate uncorrected systematic effects in the magnitude standardization. We find that SNe Ia in host galaxies with a higher star formation rate have synthesized on average a larger $^{56}$Ni mass and show wider lightcurves. The $^{56}$Ni mass dependence on metallicity is consistent with a prediction of Timmes et al. 2003 based on nucleosynthesis. SNe Ia in metal-rich galaxies ({$log_{10}(O/H)+12>8.9$) have become 0.13 $pm$ 0.06 magnitude brighter after corrections for their lightcurve widths and colors, which corresponds to up to 6% uncertainty in the luminosity distance. We investigate whether parameters for standardizing SN Ia maximum magnitude differ among samples with different host characteristics. The coefficient of the color term is larger by 0.67 $pm$ 0.19 for SNe Ia in metal-poor hosts than those in metal-rich hosts when no color cuts are imposed.
