An essential component of galaxy formation theory is the stellar initial mass function (IMF) that describes the parent distribution of stellar mass in star-forming regions. We present observational evidence in a sample of early-type galaxies (ETGs) of a tight correlation between central velocity dispersion and the strength of several absorption features sensitive to the presence of low-mass stars. Our sample comprises ˜40 000 ETGs from the Spheroids Panchromatic Investigation in Different Environmental Regions survey (z ≲ 0.1). The data - extracted from the Sloan Digital Sky Survey - are combined, rejecting both noisy data, and spectra with contamination from telluric lines, resulting in a set of 18 stacked spectra at high signal-to-noise ratio (S/N ≳ 400 Å-1). A combined analysis of IMF-sensitive line strengths and spectral fitting is performed with the latest state-of-the-art population synthesis models (an extended version of the MILES models). A significant trend is found between IMF slope and velocity dispersion, towards an excess of low-mass stars in the most massive galaxies. Although we emphasize that accurate values of the IMF slope will require a detailed analysis of chemical composition (such as [α/Fe] or even individual element abundance ratios), the observed trends suggest that low-mass ETGs are better fitted by a Kroupa-like IMF, whereas massive galaxies require bottom-heavy IMFs, exceeding the Salpeter slope at σ ≳ 200 km s-1.