Context. It has been reported that the intrinsic dispersion at constant magnitude in the structural relations of early-type galaxies is a useful tool to study the universality of these structural relations, that is to say, to study whether the structural relations depend on luminosity, wavelength, redshift, and/or environment. Aims: We study the intrinsic dispersion at approximately constant magnitude in the Faber-Jackson relation as a function of luminosity, mass, and redshift. Methods: We use a sample of approximately 90 000 early-type galaxies from the Sloan Digital Sky Survey (SDSS-DR7) spanning a magnitude range of 7 mag in both g and r filters. We calculate the intrinsic dispersion in the Faber-Jackson relation at approximately constant magnitude and compare this at different luminosities, masses, and redshifts. Results: The main results are the following: i) the intrinsic dispersion in the Faber-Jackson relation depends on the luminosity, mass, and redshift; ii) the distribution for brighter and more massive galaxies has smaller intrinsic dispersion than that for fainter and less massive galaxies; iii) the distribution of bright and massive galaxies at higher redshift has smaller intrinsic dispersion than similar galaxies at low redshift. Conclusions: Comparisons of the results found in this work with recent studies from the literature make us conclude that the intrinsic dispersion in the Faber-Jackson relation could depend on the history of galaxies, in other words, the intrinsic dispersion could depend on the number and nature of transformation events that have affected the galaxies during their life times, such as collapse, accretion, interaction, and merging.