Comments on: The History of Least Squares http://healthcare-economist.com/2009/03/23/the-history-of-least-squares/ Thu, 09 Feb 2012 06:19:13 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Will Dwinnell http://healthcare-economist.com/2009/03/23/the-history-of-least-squares/comment-page-1/#comment-1071 Will Dwinnell Tue, 24 Mar 2009 17:22:04 +0000 http://healthcare-economist.com/?p=1985#comment-1071 It's also worth noting one important (and historical) reason that least-squares regression is so much more commonly employed than least-absolute-errors regression (or any other regression): the calculus is easier. Computation of the LS regression is straightforward, easy to program and quick to compute. In contrast, LAE regression is an iterative process with a few possible pitfalls along the way (non-unique solutions, for instance). However, from a practical standpoint, LS regression not only pays more attention to points which lie farther from the regression line, but it actually emphasizes them! Whether squared errors are even an appropriate measure of model fit is very often not even questioned. While there are good theoretical reasons to prefer LS regression in some circumstances, there are also historical reasons for its popularity. It’s also worth noting one important (and historical) reason that least-squares regression is so much more commonly employed than least-absolute-errors regression (or any other regression): the calculus is easier. Computation of the LS regression is straightforward, easy to program and quick to compute. In contrast, LAE regression is an iterative process with a few possible pitfalls along the way (non-unique solutions, for instance).

However, from a practical standpoint, LS regression not only pays more attention to points which lie farther from the regression line, but it actually emphasizes them! Whether squared errors are even an appropriate measure of model fit is very often not even questioned. While there are good theoretical reasons to prefer LS regression in some circumstances, there are also historical reasons for its popularity.

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