  The present study deals with the problem of deriving the coefficients of the
fundamental plane (FP) of early-type galaxies.
  We introduce statistical models of the FP and relative fitting methods: the
MIST (Measurement errors and Intrinsic Scatter Three dimensional) fits. The
MIST fits account for the measurement errors on the variables and their
correlations as well as for the intrinsic scatter. We show that the lack of a
model of the intrinsic scatter of the FP is the origin of the systematic
differences between the various fitting methods.
  We also address the problem of estimating the uncertainties of the FP
coefficients and determine a simple relation between the sample size and the
expected accuracy of the coefficients.
  The present study leads to define a `minimum sample size' for a correct
estimate of the uncertainties. For N < 30, both theoretical formulae and
re-sampling techniques, like the bootstrap, do not give reliable estimates.
  The question of the 'universality' of the FP is addressed by applying the
MIST fits to ten samples of cluster galaxies. The FP slopes are actually
consistent between the different samples, but, due to the large uncertainties,
they could also hide significant systematic differences.
  The feasibility of the measurement of the possible variations of the FP
slopes as a function of redshift is also proved.
