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In this paper we demonstrate the ability to predict changes to heart rate due to changes in levels of activity, up to an hour into the future. Activity levels are calculated from data collected by a worn accelerometer for a person performing daily activities outside a laboratory environment. People with congestive heart failure must take care not to excessively stress their heart. This can be a challenge due to the difficulty of predicting how much stress an activity is exerting on the heart. We propose to model the relationship between motion and heart rate and thus to enable the prediction of heart rate changes prior to performing an activity. We explored three methods to predict current and future heart rate from activity level: a continuous state Kalman Filter, two simple linear models, and a nonlinear model given in the literature . The results from healthy subjects and subjects with congestive heart failure show that using the proposed models, the heart rate can be predicted an hour into the future using accelerometer data.