  (Abridged) We assemble a sample of 3258 low-redshift galaxies from the SDSS
DR6 with complementary photometric observations by GALEX, 2MASS and IRAS at
far-ultraviolet and infrared wavelengths. We use a recent, simple but
physically motivated model to interpret the observed spectral energy
distributions of the galaxies in this sample in terms of statistical
constraints on physical parameters describing the star formation history and
dust content. The focus on a subsample of 1658 galaxies with highest S/N
observations enables us to investigate most clearly several strong correlations
between various derived physical properties of galaxies. We find that the
typical dust mass of a star-forming correlates remarkably well with the star
formation rate (SFR). We also find that the dust-to-stellar mass ratio, the
ratio of dust mass to star formation rate and the fraction of dust luminosity
contributed by the diffuse interstellar medium all correlate strongly with
specific SFR. A comparison with recent models of chemical and dust evolution of
galaxies suggests that these correlations could arise, at least in part, from
an evolutionary sequence. As galaxies form stars, their ISM becomes enriched in
dust, while the drop in gas supply makes the specific SFR decrease.
Interestingly, as a result, a young, actively star-forming galaxy with low
dust-to-gas ratio may still be highly dusty because it contains large amounts
of interstellar gas. This may be important for the interpretation of the
infrared emission from young, gas-rich star-forming galaxies at high redshift.
Our study provides a useful local reference for future statistical studies of
the star formation and dust properties of galaxies at high redshifts.
