  We explore the dependence of dust attenuation, as traced by the $\rm
H_{\alpha}/\rm H_{\beta}$ Balmer decrement, on galactic properties by using a
large sample of SDSS spectra. We use both Partial Correlation Coefficients
(PCC) and Random Forest (RF) analysis to distinguish those galactic parameters
that directly and primarily drive dust attenuation in galaxies, from parameters
that are only indirectly correlated through secondary dependencies. We find
that, once galactic inclination is controlled for, dust attenuation depends
primarily on stellar mass, followed by metallicity and velocity dispersion.
Once the dependence on these quantities is taken into account, there is no
dependence on star formation rate. While the dependence on stellar mass and
metallicity was expected based on simple analytical equations for the
interstellar medium, the dependence on velocity dispersion was not predicted
and we discuss possible scenarios to explain it. We identify a projection of
this multi-dimensional parameters space which minimises the dispersion in terms
of the Balmer decrement and which encapsulates the primary and secondary
dependences of the Balmer decrement into a single parameter defined as the
reduced mass $\mu = \log {\rm M}_{\star} +3.67 [{\rm O/H}] + 2.96 \log
(\sigma_v/100~km~s^{-1})$. We show that the dependence of the Balmer decrement
on this single parameter also holds at high redshift, suggesting that the
processes regulating dust production and distribution do not change
significantly through cosmic epochs at least out to z$\sim$2.

Astrophysics of Galaxies