Pivot Points in Bivariate Linear Regression

Abstract

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.