Covariance vs Correlation

Difference Between Covariance and Correlation

Covariance and Correlation are two terms which are exactly opposite to each other, they both are used in statistics and regression analysis, covariance shows us how the two variables vary from each other whereas correlation shows us the relationship between the two variables and how are they related.

Correlation and covariance are two statistical concepts that are used to determine the relationship between two random variables. Correlation defines how a change in one variable will impact the other, while covariance defines how two items vary together. Confusing? Let’s dive in further to understand the difference between these closely related terms.

What is Covariance?

Covariance measures how the two variables move with respect to each other and is an extension of the concept of variance (which tells about how a single variable varies). It can take any value from -∞ to +∞.

  • The higher this value, the more dependent the relationship is. A positive number signifies positive covariance and denotes that there is a direct relationship. Effectively this means that an increase in one variable would also lead to a corresponding increase in the other variable provided other conditions remain constant.
  • On the other hand, a negative number signifies negative covariance, which denotes an inverse relationship between the two variables. Though covariance is perfect for defining the type of relationship, it is bad for interpreting its magnitude.

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What is the Correlation?

Correlation is a step ahead of covariance as it quantifies the relationship between two random variables. In simple terms, it is a unit measure of how these variables change with respect to each other (normalized covariance value).

  • Unlike covariance, the correlation has an upper and lower cap on a range. It can only take values between +1 and -1. A correlation of +1 indicates that random variables have a direct and strong relationship.
  • On the other hand, the correlation of -1 indicates that there is a strong inverse relationship, and an increase in one variable will lead to an equal and opposite decrease in the other variable. 0 means that the two numbers are independent.

Formula for Covariance and Correlation

Let’s express these two concepts, mathematically. For two random variables A and B with mean values as Ua and Ub and standard deviation as Sa and Sb respectively:

Effectively the relationship between the two can be defined as:

Formula

Both correlations and covariance find application in fields of statistical and financial analysis. Since correlation standardizes the relationship, it is helpful in comparison of any two variables. This help analyst in coming up with strategies like pair trade and hedgingHedgingHedging is a type of investment that works like insurance and protects you from any financial losses. Hedging is achieved by taking the opposing position in the market.read more for not only efficient returns on the portfolio but also safeguarding these returns in terms of adverse movements in the stock market.

Correlation vs Covariance Infographics

Let’s see the top difference between Correlation vs Covariance.

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Key Differences

Covariance vs Correlation Comparative Table

BasisCovarianceCorrelation
MeaningCovariance is an indicator of the extent to which 2 random variables are dependent on each other. A higher number denotes higher dependency.Correlation is an indicator of how strongly these 2 variables are related, provided other conditions are constant. The maximum value is +1, denoting a perfect dependent relationship.
RelationshipCorrelation can be deduced from a covariance.Correlation provides a measure of covariance on a standard scale. It is deduced by dividing the calculated covariance with standard deviation.
ValuesThe value of covariance lies in the range of -∞ and +∞.Correlation is limited to values between the range -1 and +1.
ScalabilityAffects covarianceCorrelation is not affected by a change in scales or multiplication by a constant.
UnitsCovariance has a definite unit as it is deduced by the multiplication of two numbers and their units.Correlation is a unitless absolute number between -1 and +1, including decimal values.

Conclusion

Correlation and covariance are very closely related to each other, and yet they differ a lot. Covariance defines the type of interaction, but correlation defines not only the type but also the strength of this relationship. Due to this reason, correlation is often termed as the special case of covariance. However, if one must choose between the two, most analysts prefer correlation as it remains unaffected by the changes in dimensions, locations, and scale. Also, since it is limited to a range of -1 to +1, it is useful to draw comparisons between variables across domains. However, an important limitation is that both these concepts measure the only linear relationship.

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This has been a guide to the Covariance vs Correlation. Here we discuss the top 5 differences between Covariance and Correlation along with infographics and a comparison table. You may also have a look at the following articles –

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Comments

  1. Mike Geddes says

    Great article where information is presented in a simple, accurate, and concise manner.

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