Title: On the link between column density distribution and density scaling relation in star formation regions,
Abstract: We present a method to derive the density scaling relation $\langle n\rangle
\propto L^{-\alpha}$ in regions of star formation or in their turbulent
vicinities from straightforward binning of the column-density distribution
($N$-pdf). The outcome of the method is studied for three types of $N$-pdf:
power law ($7/5\le\alpha\le5/3$), lognormal ($0.7\lesssim\alpha\lesssim1.4$)
and combination of lognormals. In the last case, the method of Stanchev et al.
(2015) was also applied for comparison and a very weak (or close to zero)
correlation was found. We conclude that the considered `binning approach'
reflects rather the local morphology of the $N$-pdf with no reference to the
physical conditions in a considered region. The rough consistency of the
derived slopes with the widely adopted Larson's (1981) value $\alpha\sim1.1$ is
suggested to support claims that the density-size relation in molecular clouds
is indeed an artifact of the observed $N$-pdf.