  Aims. Recently it has been reported that the intrinsic dispersion at constant
magnitude of the structural relations from 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. In this work we study the intrinsic dispersion of
the Faber-Jackson relation as function of the 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 of 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 of
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 those 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 of
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 along their life times,
such as collapse, accretion, interaction and merging.
