We analyse spectroscopic measurements of 122 Type Ia supernovae (SNe Ia) with z <0.09 discovered by the Palomar Transient Factory, focusing on the properties of the Si II lambda 6355 and Ca II 'near-infrared triplet' absorptions. We examine the velocities of the photospheric Si II lambda 6355, and the velocities and strengths of the photospheric and high-velocity Ca II, in the context of the stellar mass (M-stellar) and star formation rate (SFR) of the SN host galaxies, as well as the position of the SN within its host. We find that SNe Ia with faster Si II lambda 6355 tend to explode in more massive galaxies, with the highest velocity events only occurring in galaxies with M-stellar > 3 x 10(9) M-circle dot. We also find some evidence that these highest velocity SNe Ia explode in the inner regions of their host galaxies, similar to the study of Wang et al., although the trend is not as significant in our data. We show that these trends are consistent with some SN Ia spectral models, if the host galaxy stellar mass is interpreted as a proxy for host galaxy metallicity. We study the strength of the high-velocity component of the Ca II near-IR absorption, and show that SNe Ia with stronger high-velocity components relative to photospheric components are hosted by galaxies with low M-stellar, blue colour, and a high sSFR. Such SNe are therefore likely to arise from the youngest progenitor systems. This argues against a pure orientation effect being responsible for high-velocity features in SN Ia spectra and, when combined with other studies, is consistent with a scenario where high-velocity features are related to an interaction between the SN ejecta and circumstellar medium local to the SN.