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?
What is the Identity Property of Multiplication?
Basic Pythagorean Theorem
Characteristics of Aquatic Plants
Algebra 1 Substitution Method
How to Solve a Parabola
How to Find the Slope of Linear Equations
How to Find the X Intercept of a Function
How to Convert Square Meters to Linear Yards
How to Interpret a Scatter Plot
How to Convert an Area to Square Feet
Linear Factors of Polynomials
How to Do Exponents Outside of the Parenthesis
How to Calculate Significant Figures
How to Find the Height of a Rectangular Pyramid
How to Identify Linear & Nonlinear Equations
Associative & Commutative Properties of Multiplication
How to Find the Sum of Residuals
How to Calculate Regression Coefficient
How to Solve Absolute Value Equations With a Number...