Observational studies are showing that the galaxy-wide stellar initial mass function (IMF) is top-heavy in galaxies with high star formation rates (SFRs). Calculating the integrated galactic stellar initial mass function (IGIMF) as a function of the SFR of a galaxy, it follows that galaxies which have or which formed with SFRs >10 M⊙ yr-1 would have a top-heavy IGIMF in excellent consistency with the observations. Consequently and in agreement with observations, elliptical galaxies would have higher mass-to-light ratios as a result of the overabundance of stellar remnants compared to a stellar population that formed with an invariant canonical stellar IMF. For the Milky Way, the IGIMF yields very good agreement with the disc- and the bulge IMF determinations. Our conclusions are that purely stochastic descriptions of star formation on the scales of a parsec and above are falsified. Instead, star formation follows the laws, stated here as axioms, which define the IGIMF theory. We also find evidence that the power-law index β of the embedded cluster mass function decreases with increasing SFR. We propose further tests of the IGIMF theory through counting massive stars in dwarf galaxies.