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A typical question for people dealing with administrative processes is: "When will my case be finished?". In this paper, we show how this question can be answered, using historic information in the form of event logs of the systems supporting these administrative processes. Many information systems record information about activities performed for past cases in logs. Hence, to provide insights into the remaining cycle time of a case, the current case can be compared to all past ones. The most trivial way of estimating the remaining cycle time of a case is by looking at the average cycle time and deducting the already past time of the case under consideration. However, in this paper we show how to compute the remaining cycle time using non-parametric regression on the data recorded in event logs. An experiment is presented that demonstrates that our techniques perform well on logs taken from practice.