© 2018 The Author(s). The early star-forming Universe is still poorly constrained, with the properties of high-redshift stars, the first heating sources and reionization highly uncertain. This leaves observers planning 21-cm experiments with little theoretical guidance. In this work, we explore the possible range of high-redshift parameters including the star formation efficiency and the minimal mass of star-forming haloes; the efficiency, spectral energy distribution and redshift evolution of the first X-ray sources; and the history of reionization. These parameters are only weakly constrained by available observations, mainly the optical depth to the cosmic microwave background. We use realistic semi-numerical simulations to produce the global 21-cm signal over the redshift range z = 6-40 for each of 193 different combinations of the astrophysical parameters spanning the allowed range. We show that the expected signal fills a large parameter space, but with a fixed general shape for the global 21-cm curve. Even with our wide selection of models, we still find clear correlations between the key features of the global 21-cm signal and underlying astrophysical properties of the high-redshift Universe, namely the Ly α intensity, the X-ray heating rate and the production rate of ionizing photons. These correlations can be used to directly link futuremeasurements of the global 21-cm signal to astrophysical quantities in a mostly model-independent way. We identify additional correlations that can be used as consistency checks.