Abstract
For many fitting methods for lines in the plane, each observation possesses an associated point in the plane, or at infinity for particular observations. These associated points are called “fixed points,” because properly chosen replacement points for the originally selected observation create other fitted lines that contain the same fixed point. Simple linear regression and orthogonal least-squares regression are investigated as examples. The phenomenon has been previously noted for simple regression, where the properly selected replacement points are related to regression diagnostics and the determination of outliers. Orthogonal regression lines are fundamental to principal component analysis. Mechanical devices for simple linear regression and for orthogonal regression are presented. The devices show the dependence of the fitted lines, which contain the fixed point, on the new replacement points.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Date
8-2026
Document Type
Article
Department, Program, or Center
Mathematics and Statistics, School of
College
College of Science
Recommended Citation
Farnsworth, David L., "Fixed Points for Fitted Lines" (2026). Journal of Probability and Staistical Science, 24 (2), 133-147. Accessed from
https://repository.rit.edu/article/2196
Campus
RIT – Main Campus
