(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.
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