Computational Statistics & Data Analysis 50 (2006) 1391 – 1397 www.elsevier.com/locate/csda Short Communication Least median of squares and regression through the origin  Humberto Barreto a , ∗ , David Maharry b a Department of Economics,Wabash College, Crawfordsville, IN 47933, USA b Department of Mathematics and Computer Science,Wabash College, Crawfordsville, IN 47933, USA Received 5 January 2005; accepted 6 January 2005 Available online 30 January 2005 Abstract An exact algorithm is provided for finding the least median of squares (LMS) line for a bivari- ate regression with no intercept term. It is shown that the popular Program for RObust reGRES- Sion (PROGRESS) routine will not, in general, find the LMS slope when the intercept is sup- pressed. A Microsoft Excel workbook that provides the code in Visual Basic is made available at http://www.wabash.edu/econexcel/LMSOrigin. © 2005 Elsevier B.V.All rights reserved. Keywords: LMS; Robust regression; PROGRESS 1. Introduction Rousseeuw (1984) introduced least median of squares (LMS) as a robust regression procedure. Instead of minimizing the sum of squared residuals, coefficients are chosen so as to minimize the median of the squared residuals. Unlike conventional least squares (LS), there is no closed-form solution with which to easily calculate the LMS line since the median is an order or rank statistic. A general non-linear optimization algorithm performs poorly because the median of squared residuals surface is so bumpy that merely local minima are often incorrectly reported as the solution.  Supporting files online at: http://www.wabash.edu/econexcel/LMSOrigin. ∗ Corresponding author. Tel.: +765 361 6315; fax: +765 361 6277. E-mail addresses: barretoh@wabash.edu (H. Barreto), maharryd@wabash.edu (D. Maharry). 0167-9473/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.csda.2005.01.005