25 Pages Posted: 3 Jul 2007
Date Written: September 7, 2007
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: 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