Using the largest single-survey sample of Type Ia supernovae (SNe Ia) to date, we study the relationship between properties of SNe Ia and those of their host galaxies, focusing primarily on correlations with Hubble residuals (HRs). Our sample consists of 345 photometrically classified or spectroscopically confirmed SNe Ia discovered as part of the SDSS-II Supernova Survey (SDSS-SNS). This analysis utilizes host-galaxy spectroscopy obtained during the SDSS-I/II spectroscopic survey and from an ancillary program on the SDSS-III Baryon Oscillation Spectroscopic Survey that obtained spectra for nearly all host galaxies of SDSS-II SN candidates. In addition, we use photometric host-galaxy properties from the SDSS-SNS data release such as host stellar mass and star formation rate. We confirm the well-known relation between HR and host-galaxy mass and find a 3.6{sigma} significance of a nonzero linear slope. We also recover correlations between HR and host-galaxy gas-phase metallicity and specific star formation rate as they are reported in the literature. With our large data set, we examine correlations between HR and multiple host-galaxy properties simultaneously and find no evidence of a significant correlation. We also independently analyze our spectroscopically confirmed and photometrically classified SNe Ia and comment on the significance of similar combined data sets for future surveys.