Gamma-ray bursts (GRBs) are characterised by a strong correlation between the instantaneous luminosity and
the spectral peak energy within a burst. This correlation, which is known as the hardness-intensity
correlation or the Golenetskii correlation, not only holds important clues to the physics of GRBs but is
thought to have the potential to determine redshifts of bursts. In this paper, I use a hierarchical Bayesian
model to study the universality of the rest-frame Golenetskii correlation and in particular, I assess its use
as a redshift estimator for GRBs. I find that using a power-law prescription of the correlation, the power-law
indices cluster near a common value, but have a broader variance than previously reported ($\sim 1−2$).
Furthermore, I find evidence that there is spread in intrinsic rest-frame correlation normalizations for the
GRBs in our sample ($\sim10^{51} − 10^{53}$ erg $s^{−1}$). This points towards variable physical settings of the
emission (magnetic field strength, number of emitting electrons, photospheric radius, viewing angle, etc.).
Subsequently, these results eliminate the Golenetskii correlation as a useful tool for redshift determination
and hence a cosmological probe.