Neurorehabilitation in patients suffering from motor deficits relies on relearning or re-adapting motor skills. Yet our understanding of motor learning is based mostly on results from one or two-dimensional experimental paradigms with highly confined movements. Since everyday movements are conducted in three-dimensional space, it is important to further our understanding about the effect that gravitational forces or perceptual anisotropy might or might not have on motor learning along all different dimensions relative to the body. Here we test how well existing concepts of motor learning generalize to movements in 3D. We ask how a subject's variability in movement planning and sensory perception influences motor adaptation along three different body axes. To extract variability and relate it to adaptation rate, we employed a novel hierarchical two-state space model using Bayesian modeling via Hamiltonian Monte Carlo procedures. Our results show that differences in adaptation rate occur between the coronal, sagittal and horizontal planes and can be explained by the Kalman gain, i.e., a statistically optimal solution integrating planning and sensory information weighted by the inverse of their variability. This indicates that optimal integration theory for error correction holds for 3D movements and explains adaptation rate variation between movements in different planes.