Network slicing is a key concept in 5G networking. It enables an infrastructure provider (InP) to support heterogeneous services over a common platform by creating a customized slice for each one of them. Once in operation, the slices can be dynamically scaled up/down to match the variation of service requirements. Although an InP generates revenue by accepting a slice request, however it might need to pay a penalty (proportional to the level of service degradation) if a slice cannot be scaled up when required. Hence, it becomes crucial to decide which slice requests should be accepted in order to maximize the net profit of an InP. This paper presents a slice admission strategy based on big data analytics (BDA) predictions. The intuition is to accept a slice request only when it is estimated that no service degradation will take place for both the incoming slice request and the slices already in operation. In this way, the penalty paid by an InP is contained, with beneficial effects on the overall net profit. Apart from simulations, the performance of the proposed admission policy has also been evaluated using emulation. Simulation results show that, in the presence of a high penalty due to service degradation, using BDA predictions brings up to 50.7% increase in profit, as compared to a slice admission policy without BDA. Emulation results for a small network scenario show a profit increase of up to 383% with only a small impact on the slice provisioning time (i.e., due to the processing of BDA predictions).