Properties of Pearson's r
Prerequisites
Linear
Transformations, Introduction to Bivariate
Data
Learning Objectives
 State the range of values for Pearson's correlation
 State the values that represent perfect linear relationships
 State the relationship between the correlation of Y with X and the
correlation of X with Y
 State the effect of linear transformation on Pearson's correlation
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.
