Difference Between Covariance and Correlation

What is Covariance?

Statistically, covariance is a way of determining the direction of the relationship between independent variables and dependent variables (positive or negative). (Abdulhaleem , 2017)

A covariance relationship is a statistical term that describes a systematic relationship between two random variables, where a change in one variable reflects changes in the other.

A negative covariance value indicates a negative relationship, while a positive value indicates a positive relationship.

In general, the greater the covariance number, the stronger the relationship. Positive covariance indicates that it is a direct relationship.

Negative covariance, on the other hand, indicates an inverse relationship between two variables. Covariance is useful for defining the relationship type, but terrible for interpreting the magnitude.

What is Correlation?

A correlation is used to display the direction and strength of the relationship between a dependent variable and an independent variable, with a stronger correlation indicating better regression results. (Abdulhaleem , 2017)

In correlation analysis, two numerically measured, continuous variables are compared to determine the strength of their relationship.

In addition to showing the type of relationship (in terms of direction), it also shows how strong that relationship is. It is therefore possible to say that correlation values have standardized notions, whereas covariance values are not standardized. Due to the lack of direct significance of magnitude, they cannot be used to determine the strength or weakness of the relationship. A value of -1 to +1 can be assumed. 

Using standard deviations as a measure of covariance, we can determine whether there is a large or small covariance between the two variables. 

This is done by dividing the covariance by the ratio of standard deviations of the two variables, which provides a correlation between them.

Correlation coefficients are the main result of a correlation.

Difference Between Covariance and Correlation

In covariance, two random variables are measured by how much they change together, while in correlation, two variables are measured by how strong their relationship is.

The term covariance refers to a measure of correlation, whereas correlation is the scaled form of covariance.

Correlation measures both the strength and direction of the linear relationship between two variables, while covariance indicates the direction of the linear relationship.

Covariance can vary between -∞ and +∞ while Correlation ranges between -1 and +1

Covariance is affected by a change in scale. The covariance is changed if all the values of one variable are multiplied by a constant, while the correlation is not affected by the change in scale if all the values of another variable are multiplied by a constant.

Comparison Between Covariance and Correlation

 Parameter of ComparisonCovarianceCorrelation
ApplicationCovariance tells us the direction of the relationship between two variablesCorrelation provides an indication as to how strong the relationship between the two variables is, in addition to the direction of correlated variables
Range From +-∞ to +∞From +1 to -1
How They MeasureCovariance measures whether a variation in one variable results in a variation in another variable; for example, looking at whether an increase in one variable results in an increase, decrease, or no change in the other variable.Correlation measures the direction as well as the strength of the relationship between two variables (i.e. how strongly these two variables are related to each other).
Relationship constraintsCovariance deals with the linear relationship of only two variables in the datasetCorrelation can involve two or multiple variables or data sets and their linear relationships
Measurement UnitsCovariance is in units, which is formed by multiplying the unit of one variable by the unit of another variableCorrelation is dimensionless, i.e. it is a unit-free measure of the relationship between variables


Abdulhaleem, M. A. (2017, March). A NOVEL DATA MINING FRAMEWORK TO PREDICT STUDENTS’ MARKS IN SECONDARY EDUCATION, University of Medical Sciences & Technology, Graduate College, M.Sc. of Business Information System.