What is the linear correlation coefficient?

The purpose of the linear correlation coefficient is to determine the degree of intensity that exists between two data or variables. For this reason, the linear correlation coefficient serves to check when the relationship between two variables is linear.

The concept of linear correlation coefficient is also known as Pearson's coefficient and is part of a statistics whose objective is to verify the intensity that occurs between the two variables that it intends to define.

What is the formula for the linear correlation coefficient?

To calculate the Pearson correlation we have a formula that helps us determine two fundamental aspects, which are the covariance and the standard deviation. Next we will check what is the formula for the linear correlation coefficient and how it should be calculated, taking into account that said linear correlation will always be represented by the r.

How to calculate Pearson's coefficient


The properties of the Pearson coefficient

When defining the Pearson coefficient, it will be taken into account that the data cannot vary along its measurement scale. In particular, the linear correlation coefficient can never result in numbers between -1 and 1. In fact, we can speak of several types or results of the Pearson coefficient, which are the following:

  • The positive covariance, which will be given as long as the results indicate a direct correlation. This covariance will be considered strong as it approaches 1.
  • The negative covariance, we will talk about it when the result shows an inverse correlation. For its part, this covariance will be considered stronger as it approaches -1.
  • When the covariance is null, it occurs in all those cases whose calculation result does not allow correlation.

In all those cases in which the result of r is equal to 0, it will be when the correlation between the variables does not occur. Even so, for this type of case there could be another type of correlation, such as an exponential one.

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