What Are the Seven Properties of the Linear Correlation Coefficient?

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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.

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