There are
little-noticed points in the plane, which are artifacts of linear regression.
The points, which are called pivot points, are the intersections of sets of
regression lines. We derive the coordinates of the pivot point and explain its
sources. We show how a pivot point arises in a certain notable data set, which
has been analyzed often for points of high leverage. We obtain the application
of pivot points that shortens calculations when updating a set of bivariate
observations by adding a new point.
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