  We use a sample of 1338 spectroscopically confirmed and photometrically
classified Type Ia Supernovae (SNe Ia), sourced from the CSP, CfA, SDSS-II, and
SNLS supernova samples, to examine the relationships between SNe Ia and the
galaxies that host them. Our results provide confirmation with improved
statistical significance that SNe Ia, after standardization, are on average
more luminous in massive hosts (significance $\rm > 5 \sigma$), and decline
more rapidly in massive hosts (significance $\rm > 9\sigma$) and in hosts with
low specific star formation rates (significance $\rm > 8\sigma$). We study the
variation of these relationships with redshift and detect no evolution. We
split SNe Ia into pairs of subsets that are based on the properties of the
hosts, and fit cosmological models to each subset. Including both systematic
and statistical uncertainties, we do not find any significant shift in the
best-fit cosmological parameters between the subsets. Among different SN Ia
subsets, we find that SNe Ia in hosts with high specific star formation rates
have the least intrinsic scatter ($\rm \sigma_{int}=0.08\pm0.01$) in luminosity
after standardization.
