The orthogonal fitting procedure for determination of the empirical
  {\Sigma} - D relations for supernova remnants: application to starburst
  galaxy M82
  The radio surface brightness-to-diameter ({\Sigma} - D) relation for
supernova remnants (SNRs) in the starburst galaxy M82 is analyzed in a
statistically more robust manner than in the previous studies that mainly
discussed sample quality and related selection effects. The statistics of data
fits in log {\Sigma} - log D plane are analyzed by using vertical (standard)
and orthogonal regressions. As the parameter values of D - {\Sigma} and
{\Sigma} - D fits are invariant within the estimated uncertainties for
orthogonal regressions, slopes of the empirical {\Sigma} - D relations should
be determined by using the orthogonal regression fitting procedure. Thus
obtained {\Sigma} - D relations for samples which are not under severe
influence of the selection effects could be used for estimating SNR distances.
Using the orthogonal regression fitting procedure {\Sigma} - D slope {\beta}
\approx 3.9 is obtained for the sample of 31 SNRs in M82. The results of
implemented Monte Carlo simulations show that the sensitivity selection effect
does not significantly influence the slope of M82 relation. This relation could
be used for estimation of distances to SNRs that evolve in denser interstellar
environment, with number denisty up to 1000 particles per cm3 .
