X1-189 (2025/07/03)
The linear fitting, the ellipsoid
The fitting of a hyper-plane to a set of data is studied. It is shown that each set of data corresponds to an ellipsoid: The center of the ellipsoid is the mean of the data set, and is on the hyper-plane; and the smallest axis of the ellipsoid is normal to the hyper-plane. If the data set corresponds to a thing ellipsoidal layer, the ellipsoid resulting from the fitting is the same as the ellipsoid of the data set.