A paper by Harmut Traunm\"uller [1] showed from statistical studies of observational data that the most adequate equation to represent observations on magnitude and redshift from 892 type 1a supernovae is $\mu = 5\,log[(1+z)\,ln(1+z)] + const.$ Comparing the Hubble diagram calculated from the observed redshift data of 280 supernovae with Hubble diagrams inferred on the basis of two cosmological models in the range of z = 0.0104 to 8.1, Laszlo Marosi [2] found in a quite independant study that the best fit function to represent observations is $\mu= 44.109769 \,z^{0.059883}$. Noting that differences between the different cosmological models become more pronouced in a photon time-of-fligth $t_s$ vs. $z$ repr\'esentation, he also noted that the best equation to account for observations may also be written $z = -1+e^{2.024\,\,10^{-18} \,\,ts}$. In the light of these observational data, we compare the theoretical Hubble diagram obtained with the flat $\Lambda CDM$ model to the ones we have obtained few years ago [3, 4, 5] from a model that we call here the "light model" for the sake of clarity. Our conclusions are that values calculated on the basis of the $\Lambda CDM$ model exhibit poor agreement with the presently available data while the light model agrees exactly with observations and conclusions of statistical studies [1] and [2] (independently of the values of $\Omega_k$, $\Omega_M$ or $\Omega_{\Lambda}$). Our model giving no accelerating expansion of the universe, we conclude that this latter is not necessary and that models can exist which lead exactly to observations without having to consider any accelerating expansion of the universe. In an Appendix, we discuss some aspects of the model and we present a brief overview of some of its key results., Comment: 24 pages, 9 figures