# Properties of Pearson's r

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## Abstract

Connexions module: m10951 1 Properties of Pearson's r ∗ David Lane This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License 1.0 † A basic property of Pearson's r is that its possible range is from −1 to 1. A correlation of −1 means a perfect negative linear relationship, a correlation of 0 means no linear relationship, and a correlation of 1 means a perfect linear relationship. Pearson's correlation is symmetric in the sense that the correlation of X with Y is the same as the correlation of Y with X. For example, the correlation of Weight with Height is the same as the correlation of Height with Weight. A critical property of Pearson's r is that it is unaffected by linear transformations. This means that multiplying a variable by a constant and/or adding a constant does not change the correlation of that variable with other variables. For instance, the correlation of Weight and Height does not depend on whether Height is measured in inches, feet, or even miles. Similarly, adding five points to every student's test score would not change the correlation of the test score with other variables such as GPA. Glossary Definition 1: Linear Transformation A linear transformation is any transformation of a variable that can be achieved by multiplying it by a constant, and then adding a second constant. If Y is the transformed value of X, then Y = aX + b. ∗ Version 2.2: Jul 21, 2003 12:30 pm +0000 † http://creativecommons.org/licenses/by/1.0 http://cnx.org/content/m10951/2.2/

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