The Σ - D relation for Galactic planetary nebulae: Application of orthogonal fitting procedure

We estimate the parameters of the radio surface brightness to diameter (Σ - D) relation for the sample of Galactic planetary nebulae (PNe). The bootstrap re-sampling and orthogonal offsets fitting procedure are applied. The orthogonal fitting procedure provides that the parameter values of D - Σ and Σ - D fits are invariant within the estimated uncertainties. We discuss the probability statistics of the fitted (log Σ = log A - β log D) relation and the resulting fit parameters which is indicative for PN distance determination.