Left: residuals of a Gaussian fit of the beam-average line profiles, as a function of the sub-beam column density field β_W index. The sample of 1000 toy clouds is divided in eight equally sized bins of column density field β_W index. The full lines and filled range show the mean and standard deviation of the bins. Each colour represents a different emission line. Right: residuals of a Gaussian fit of the beam-average line profiles, as a function of the sub-beam velocity field β_v index, in a similar fashion to the left plot.