What Are the Seven Properties of the Linear Correlation Coefficient?

••• BananaStock/BananaStock/Getty Images

The linear correlation coefficient is a big part of math and science. The linear correlation coefficient is the ratio between the covariance and the product of standard deviations of both variables. This article will explain the properties of a correlation coefficient and what they mean.

Property 1

The correlation coefficient does not change the measurement scale. This rule only applies if the height is expressed in meters or feet; then the correlation coefficient does not change.

Property 2

The sign of the linear correlation coefficient is shared by the covariance. A covariance is a measure of how much two variables change together.

Property 3

The linear correlation coefficient is a real number between −1 and 1. A real number is one that represents a point along a continuum, such as an integer or a rational number that is not an integer.

Property 4

If the linear correlation coefficient takes values closer to −1, the correlation is strong and negative, and will become stronger the closer it approaches −1.

Property 5

If the linear correlation coefficient takes values close to 1, the correlation is strong and positive, and thus will become stronger the closer it approaches to 1.

Property 6

If a correlation coefficient takes values closer to 0, the correlation is weak.

Property 7

If r = 1 or r = −1 (r being the variable for a linear correlation coefficient), there is perfect correlation, and the line on the scatter plot is increasing or decreasing. If r = 0 then there is no linear correlation.

Related Articles

What Are the Different Types of Correlations?
Linear Factors of Polynomials
How to Identify Linear & Nonlinear Equations
How to Calculate Percent Relative Range
How to Calculate Significant Figures
How to Calculate CV Values
How to Calculate Ramp Length
How to Find the X Intercept of a Function
What is the Identity Property of Multiplication?
How to Convert Square Meters to Linear Yards
Difference Between Velocity Time Graph & Position Time...
How to Do Linear Equations in Math
Basic Pythagorean Theorem
Characteristics of Aquatic Plants
How to Convert 55 X 40 X 20 CM to Inches
The Difference Between Linear & Nonlinear Equations
How to Find the Angle of a Curve
How to Calculate Statistical Mean
How to Find a Z Score
How to Interpret a Scatter Plot