This paper presents a method of interactively generating natural hand gesture animation using reduced dimensionality from multiple captured data sequences of finger motions conducting specific tasks. This method is achieved by introducing an estimation with multiple regression analysis. Even when the skeletal structure of the user who inputs the motion is different from that of the shape model in the computer, the motion that a user imagines is generated. Experimental results obtained from the interface applied to virtual object manipulation showed that the proposed method generates animation naturally, just as users would expect. This method enables us to make input devices that require minimal user training and computer calibration, and helps to make the user interface intuitive and easy to use.