This article presents an approach to estimating exercise energy expenditure based on acceleration measurements from a wrist-worn biaxial sensor. The method uses the linear mixed model that makes it possible to model both between-subject and within-subject variation in energy expenditure. More precisely, a random-intercepts model is used. The variance and mean of the acceleration signals at 15-second intervals as well as subject demographics (height, weight, body mass index, age and VO2max) are used. Energy expenditure is modelled in four different activities: walking, running, Nordic walking and bicycling. This study introduces an effective backward model selection procedure for selecting the fixed-effect variables in the model. The procedure uses leave-one-out cross-validation to be able to effectively exploit the available data set and to ensure the robustness of the model. Estimation accuracy in test sets is used as a criterion of model performance. The model selection procedure pr...