Fixed Points in Linear Regression

Abstract

There is a set of points in the plane whose elements correspond to the observations that are used to generate a simple least-squares regression line. Each value of the independent variable in the observations matches up with one of these points, which are called pivot or fixed points. The coordinates of the fixed points are derived, and the properties of the points are explored. All points in the plane that yield each of the fixed points are found. The role that fixed points play in regression diagnostics is investigated. A new mechanical device that uses linkages to model the role of fixed points is described. A numerical example is presented.