Major research efforts have been recently made to develop resource orchestration solutions to flexibly link edge nodes with centralised cloud resources so as to maximise the efficiency with which such a continuum of resources can be accessed by users. In this context, we consider the case of Big Data analytics in which total task completion time reductions can be achieved by routing tasks initially to edge servers and subsequently to cloud resources. We demonstrate that the task complexity of the computational jobs, the Wide Area Network (WAN) speed and the potential overload of edge servers (as reflected by CPU workloads) are crucial for achieving total task completion time reductions by offloading from edge to cloud resources. The edge-cloud orchestrators are situated in the edge nodes and, therefore, require continuous access to the parameters of WAN speeds (and their fluctuations), edge server CPU workload and the task complexities in Big Data analytics requirements to make accurate edge-to-cloud offloading decisions. With favourable values for these three parameters, large reductions in completion times can result from transfer of large-scale data from edge nodes to cloud resources, which can reduce the completion times by up to 97% and meet client deadlines for computational tasks with responsive and agile solutions.