Relating observations of cluster galaxies or the gas content to the total mass of the underlying dark matter halos is a key challenge in the current cluster cosmology community. Additionally, accurate measurement of hot and cold phase baryon covariance in clusters will offer important constraints on hydrodynamic models of cluster formation. This property covariance has been predicted by hydrodynamics simulations of Farahi et al. (2017). Farahi et al. (2017) predict massive dark-matter halos are essentially ``Closed Box'' that retain all their gaseous and stellar matter. We develop a hierarchical Bayesian model by which the mass-observable scaling relation and the full property covariance are constrained. With this model, we consider the effect of measurement error, the covariance between measurement errors and sample selection. We, then, present results of this method applied to multi-wavelength observations of clusters from the Local Cluster Substructure Survey (LoCuSS), and provide the first empirical evidence for this predicted covariance.