Comparison between the best-fit two-population model and the supernova data in the Hubble flow. The panels show supernova absolute magnitudes obtained from the standard linear corrections in stretch and supernova colour as a function of the colour parameter (left) and the stretch parameter (right). For a more direct comparison with the noisy data, the dashed lines show the best-fit model predictions, which take into account noise due to measurement uncertainties (omitted for the solid lines). The data on the left panel are restricted to supernovae with x₁ > 0.5 or x₁ < −0.8 representing high-purity samples of the underlying young and old populations. The apparent difference between the slopes of the colour correction at c > 0 in the two populations reflects the difference in the derived mean extinction coefficients, R_B. The right y-axis of the right panel shows the fraction of supernova host galaxies with log₁₀(M_⋆/M_⊙) > 10. This demonstrates a close connection (although not equivalence) between the two-population model and the traditional mass-step correction (see also Briday et al. 2022; Wiseman et al. 2023). The old population is dominated by high-stellar-mass hosts, whereas the young population is widely distributed over host-galaxy stellar masses.