  Supersonic gas turbulence is a ubiquitous property of the interstellar
medium. The level of turbulence, quantified by the gas velocity dispersion
($\sigma_{\rm g}$), is observed to increase with the star formation rate (SFR)
of a galaxy, but it is yet not established whether this trend is driven by
stellar feedback or gravitational instabilities. In this work we carry out
hydrodynamical simulations of entire disc galaxies, with different gas
fractions, to understand the origins of the SFR-$\sigma_{\rm g}$ relation. We
show that disc galaxies reach the same levels of turbulence regardless of the
presence of stellar feedback processes, and argue that this is an outcome of
the way disc galaxies regulate their gravitational stability. The simulations
match the SFR-$\sigma_{\rm g}$ relation up to SFRs of the order of tens of
M$_\odot$ yr$^{-1}$ and $\sigma_{\rm g}\sim 50$ km s$^{-1}$ in neutral hydrogen
and molecular gas, but fail to reach the very large values ($>100$ km s$^{-1}$)
reported in the literature for rapidly star-forming galaxies. We demonstrate
that such high values of $\sigma_{\rm g}$ can be explained by 1) insufficient
beam smearing corrections in observations, and 2) stellar feedback being
coupled to the ionised gas phase traced by recombination lines. Given that the
observed SFR-$\sigma_{\rm g}$ relation is composed of highly heterogeneous
data, with $\sigma_{\rm g}$ at high SFRs almost exclusively being derived from
H$\alpha$ observations of high redshift galaxies with complex morphologies, we
caution against analytical models that attempt to explain the SFR-$\sigma_{\rm
g}$ relation without accounting for these effects.
