Change in the minimum-χ² PEP solution for ¹³CO spectra as a function of T_kin. The model is a 10 M_⊙ BE sphere with T_kin = 20 K. Frame a shows the minimum value of χ² (solid lines) and the χ² value for the reference parameter values (dashed lines). Frame b shows the predicted density and frame c the predicted column density. The cyan, magenta, and red colours correspond, respectively, to the analysis using two, three, or four transitions.