Unraveling the conditions at which Earth's metallic iron core formed yields important information about Earth's early accretion and differentiation history. Multi-variable statistical modeling of siderophile element partitioning between core-forming metallic liquids and silicate melts form the basis for physical models of core formation. While it seems clear that core segregation in a deep peridotitic magma ocean is generally consistent with many mantle siderophile element abundances, there is considerable disparity among extant physical models in terms of the key parameters of pressure, temperature and oxygen fugacity at which the core formed. Moreover, there is ongoing debate over whether simple single-stage equilibrium or more complex multi-stage accretion models are required by the partitioning data. Here we consider how variations in the statistical regression of partitioning data affect the outcomes of physical models for core formation. Taking extant experimental data sets for four well-studied siderophile elements (Ni, Co, W and V) as examples, we find that the regression model exerts a fundamental control on physical model outcomes. Further, the experimental data are currently too imprecise to discriminate among various single-stage and continuous core formation scenarios. Progress in the development of physical models requires better isolation of the independent variables that affect partition coefficients and verification of activity models at high pressure and temperature in order to reduce the global uncertainty in multi-variable statistical models.