Numerical Analysis in Least Squares Regression with an Application to the Abortion-Crime Debate

25 Pages Posted: 3 Jul 2007  

William Anderson

Cornell University - School of Operations Research and Information Engineering

Martin T. Wells

Cornell University - Law School

Date Written: September 7, 2007

Abstract

Concepts of numerical analysis with applications to least squares problems are introduced in a manner which the practitioner can readily apply to their research problems, especially in the social sciences. Numerical analysis is mainly concerned with the accuracy and stability of numerical algorithms. We frame these concerns in terms of forward and backward error, two important concepts in helping to understand the quality of the computed answers. The goal of numerical computing is to get correct, approximate answers to the true solution. We extended this forward and backward error framework to issues in least squares problems and check the condition of the regression problem via condition numbers. The more ill-conditioned the data are, the more sensitive the computed solution is to perturbations in the data, and the more unstable the computed solutions become. Condition numbers can also be used to signal the presence of solution degrading collinearity in regression problems. We apply the various numerical analysis tools outlined with some model diagnostics to the abortion-crime debate, and show the regression analysis used in various papers addressing the abortion-crime debate cannot be trusted.

Suggested Citation

Anderson, William and Wells, Martin T., Numerical Analysis in Least Squares Regression with an Application to the Abortion-Crime Debate (September 7, 2007). 2nd Annual Conference on Empirical Legal Studies Paper. Available at SSRN: https://ssrn.com/abstract=997912 or http://dx.doi.org/10.2139/ssrn.997912

William Anderson (Contact Author)

Cornell University - School of Operations Research and Information Engineering ( email )

414A Rhodes Hall
Ithaca, NY 14850
United States
607-254-4875 (Phone)

HOME PAGE: http://www.orie.cornell.edu

Martin T. Wells

Cornell University - Law School ( email )

Comstock Hall
Ithaca, NY 14853
United States
607-255-8801 (Phone)

Paper statistics

Downloads
338
Rank
71,020
Abstract Views
2,356