Correlation

Pronunciation: /ˌkɒr.əˈleɪ.ʃən/ Explain

A correlation is the strength and direction of the relationship between two variables.^[2] A correlation is measured with a correlation coefficient. A correlation coefficient of 1 means the variables are perfectly related to each other in a positive manner (y ≈ ax + b, a > 0). A correlation coefficient of 0 means the variables are not related to each other (y ≠ x). A correlation coefficient of -1 means the variables are perfectly related to each in a negative manner (y ≈ ax + b, a < 0).

Correlation can be considered the amount of 'noise' in a dataset. This noise can be measurement error or complicating factors.

Figure 1: Several sets of (x, y) points, with the correlation coefficient of x and y for each set.

References

1. McAdams, David E.. All Math Words Dictionary, correlation. 2nd Classroom edition 20150108-4799968. pg 48. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Correlation. 4/18/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/correlation.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.
• Several sets of (x, y) points, with the correlation coefficient of x and y for each set: Imagecreator, https://en.wikipedia.org. This work has been released into the public domain by its author, Imagecreator at English Wikipedia. https://en.wikipedia.org/wiki/File:Correlation_examples.png.

Revision History

4/16/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (McAdams, David E.)
1/21/2010: Added "References". (McAdams, David E.)
12/2/2008: Initial version. (McAdams, David E.)