Least-Squares Line

Pronunciation: /list skwɛərz laɪn/ Explain

A least-square line is a line that minimizes the distance between the data points it represents and the line itself. Manipulative 1 is an example of a least squares line fitted to data.

Click on the blue points and drag them to change the figure. Move the points to create a near-vertical line. Move the points to create a near-horizontal line. Manipulative 1 - Least Squares Line Created with GeoGebra.

How to Calculate a Least Squares Line

In the equations, N is the number of points. x is the x-coordinate of a point. y is the y-coordinate of a point. All calculated amounts are approximate.

Legend	x	y	x2	xy
A	0.3	1.8	0.09	0.54
B	0.8	2.2	0.64	1.76
C	1.9	2.6	3.61	4.94
D	2.2	2.1	4.84	4.62
E	3.3	2.9	10.89	9.57
F	3.9	2.5	15.21	9.75
Sum	12.4	14.1	35.28	31.18

References

1. McAdams, David E.. All Math Words Dictionary, least-squares line. 2nd Classroom edition 20150108-4799968. pg 107. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Least-Squares Line. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/leastsquareline.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/31/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
7/18/2018: Changed title to common format. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)