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Module by: Paul E Pfeiffer. E-mail the author

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 Name: Linear Regression ID: m23468 Language: English (en) Summary: Consider a pair {X,Y} with a joint distribution. A value X(ω) is observed. It is desired to estimate the corresponding value Y(ω). The best that can be hoped for is some estimate based on an average of the errors, or on the average of some function of the errors. The most common measure of error is the mean (expectation) of the square of the error. This has two important properties: it treats positive and negative errors alike, and it weights large errors more heavily than smaller ones. In general, we seek a rule (function) r such that the estimate is r(X(ω)). That is, we seek a function r such that the expectation of the square of Y - r(X) is a minimum. The problem of determining such a function is known as the regression problem. LINEAR REGRESSION: we seek the best straight line function (the regression line of Y on X) of the form u = r(t) + b, such that the mean square of Y - r(X) is a minimum. Matlab approximation procedures are compared with analytic results. More general linear regression is considered Subject: Mathematics and Statistics Keywords: Correlation coefficient, Estimates, Mean square error, Regression line License: Creative Commons Attribution License CC-BY 3.0 Authors: Copyright Holders: Maintainers: Latest version: 1.6 (history) First publication date: Apr 17, 2009 12:32 pm -0500 Last revision to module: Sep 18, 2009 1:15 pm -0500

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## Version History

 Version: 1.6 Sep 18, 2009 1:15 pm -0500 by Changes: `added google analytics tracking code` Version: 1.5 Jul 27, 2009 12:06 pm -0500 by Changes: `disjoint union fix` Version: 1.4 Jun 19, 2009 11:12 am -0500 by Changes: `m-file fixes, supplemental links, metadata updated` Version: 1.3 Jun 9, 2009 5:16 pm -0500 by Changes: `updated links, images and accessibility` Version: 1.2 May 26, 2009 4:35 pm -0500 by Changes: `fixed module names, and updated content structure` Version: 1.1 May 19, 2009 10:26 am -0500 by Changes: `Content`

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### American Chemical Society (ACS) Style Guide:

Pfeiffer, P. Linear Regression, Connexions Web site. http://cnx.org/content/m23468/1.6/, Sep 18, 2009.

### American Medical Assocation (AMA) Manual of Style:

Pfeiffer P. Linear Regression [Connexions Web site]. September 18, 2009. Available at: http://cnx.org/content/m23468/1.6/.

### American Psychological Assocation (APA) Publication Manual:

Pfeiffer, P. (2009, September 18). Linear Regression. Retrieved from the Connexions Web site: http://cnx.org/content/m23468/1.6/

### Chicago Manual of Style (Bibliography):

Pfeiffer, Paul. "Linear Regression." Connexions. September 18, 2009. http://cnx.org/content/m23468/1.6/.

### Chicago Manual of Style (Note):

Paul Pfeiffer, "Linear Regression," Connexions, September 18, 2009, http://cnx.org/content/m23468/1.6/.

### Chicago Manual of Style (Reference, in Author-Date style):

Pfeiffer, P. 2009. Linear Regression. Connexions, September 18, 2009. http://cnx.org/content/m23468/1.6/.

### Modern Languages Association (MLA) Style Manual:

Pfeiffer, Paul. Linear Regression. Connexions. 18 Sep. 2009 <http://cnx.org/content/m23468/1.6/>.