Standard Article

Least Squares

Statistical and Numerical Computing

  1. John Haslett

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.val009

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Haslett, J. 2006. Least Squares. Encyclopedia of Environmetrics. 3.

Author Information

  1. Trinity College, Ireland

Publication History

  1. Published Online: 15 SEP 2006

Abstract

Developed about 200 years ago, the method – more formally, the criterion – of Least Squares (LS) seems likely to remain at the heart of the statistician's toolbox for the twenty first century. Virtually every text on elementary statistical methods gives some exposition and it lies at the heart of very many algorithms routinely used in modern data analysis, most notably in regression. To avoid confusion, only the criterion and the method more formally known as Ordinary Least Squares (OLS) are discussed in this article. As OLS is so strongly associated with the statistical modeling procedure of linear regression, it is appropriate to include an introduction to regression under the heading of OLS. In addition, the solution of the numerical equations associated with this model has almost become synonymous with OLS, and therefore the solution itself is also discussed in this article, as are some extensions.