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Some body parts, such as the head and the hand, change their orientation during motion. Orientation can be conveniently and elegantly represented using quaternions. The method has several advantages over Euler angles in that the problem of gimbal lock is avoided and that the orientation is represented by a single mathematical object rather than a collection of angles that can be redefined in various arbitrary ways. The use of quaternions has been popular in animation applications for some time, especially for interpolating motions. We will introduce some new applications involving statistical methods for quaternions that will allow us to present meaningful averages of repeated motions involving orientations and make regression predictions of orientation. For example, we can model how the glancing behavior of the head changes according to the target of the reach and other factors.