Fog computing has emerged as a computing paradigm aimed at addressing the issues of latency, bandwidth and privacy when mobile devices are communicating with remote cloud services. The concept is to offload compute services closer to the data. However many challenges exist in the realisation of this approach. During offloading, (part of) the application underpinned by the services may be unavailable, which the user will experience as down time. This paper describes work aimed at building models to allow prediction of such down time based on metrics (operational data) of the underlying and surrounding infrastructure. Such prediction would be invaluable in the context of automated Fog offloading and adaptive decision making in Fog orchestration. Models that cater for four container-based stateless and stateful offload techniques, namely Save and Load, Export and Import, Push and Pull and Live Migration, are built using four (linear and non-linear) regression techniques. Experimental results comprising over 42 million data points from multiple lab-based Fog infrastructure are presented. The results highlight that reasonably accurate predictions (measured by the coefficient of determination for regression models, mean absolute percentage error, and mean absolute error) may be obtained when considering 25 metrics relevant to the infrastructure.