Covariance vs Correlation

Difference Between Covariance Vs Correlation

Covariance and correlation measure the relationship and the dependency between two variables. Covariance calculates the direction of the linear regression between variables, whereas correlation calculates the strength and direction of the linear regression between two variables. Correlation is a function of covariance.  Correlation is a change in one variable that impacts another variable, while covariance evaluates the variation of two items.

Covariance and correlation are the mathematical concepts used in statistics. The Covariance vs Correlation is very similar in probability theory and statistics. The correlation between two variables is determined by calculating the covariance and dividing it by the product of their standard deviations. Covariance can take on three values: positive, negative, or zero. A positive covariance indicates that the two variables increase or decrease together, while a negative covariance indicates that the two variables move in opposite directions. The correlation between two variables measures how closely they are related. The correlation is positive if they tend to move in the same direction. If they tend to move in opposite directions, the correlation is negative. And if there is no relationship between the two variables, the correlation is zero.

Key Takeaways
  • Correlation and Covariance are similar as they measure the linear relationships between two variables. When the correlation coefficient is 0, the covariance is also 0. The location change cannot affect both correlation and covariance calculation.
  • Correlation is mostly used over Covariance to measure the relationship between variables because correlation does not get affected by the change in scale. 
  • Covariance shows the direction of the linear relationship between variables.
  • Correlation measures the strength and direction of the linear relationship between two variables.
  • Correlation values are standardized whereas Covariance values are not standardized.

What Is Covariance?

Covariance is a statistical measure that determines the relationship between two variables. It is an extension of the concept of variance and can take on any value from negative infinity to positive infinity. The higher the value, the stronger the relationship between the variables. A positive covariance indicates a direct connection between the variables. This means that an increase in one variable would increase the other variable while all other conditions remain constant. On the other hand, a negative covariance signifies an inverse relationship between the two variables. This means that an increase in one variable would result in a decrease in the other variable. Understanding covariance is essential in analyzing data and making informed decisions.

Covariance Formula And Example

Covariance Formula

xi =data value of x

yi = data value of y

x¯= mean of x

y¯= mean of y

N = number of data values

What is Covariance

What Is Correlation?

Correlation is similar to covariance and calculates the relationship between two random variables. It measures the behavior of these variables with each other. The correlation consists of upper and lower cap ranges. The values between +1 and -1 are used in the calculation of Correlation. If the value is near +1 indicates that variables have a strong relation, and if the value is near -1 indicates that variables have a strong inverse relation. When one variable increases, it will result in a corresponding decrease in the other variable. This relationship is known as an inverse correlation. When the value of one variable is zero, it indicates that the two variables are independent.

Correlation Formula And Example

Correlation Formula

Cov = Covariance

 σx = Standard Deviation of x

 σy = Standard Deviation of y

Correlation Vs Covariance – Key Differences

  • Covariance is a statistical measure that evaluates the relationship between two random variables. On the other hand, correlation measures the strength of this relationship. The correlation value ranges between +1 and -1, with +1 indicating a strong positive correlation and -1 indicating a strong negative correlation. In contrast, the range of covariance is indefinite, making it a less precise measure of the relationship between variables. Understanding the difference between covariance and correlation is important when analyzing data and making informed decisions.
  • Covariance is a measure of how two variables change together. If we change the scale of one variable, it will affect the covariance between the two variables. On the other hand, correlation is a measure of how strong the relationship is between two variables. Changing the scale of one variable will not affect the correlation between the two variables.
  • Correlation is a powerful tool for measuring the relationship between two variables, regardless of their units or dimensions. It provides a unit-free measurement that allows for easy comparison of values. On the other hand, covariance is not unit-free and can be more difficult to interpret. Understanding these two measurements’ differences is crucial for accurate data analysis and decision-making.

Covariance Vs Correlation Comparative Table

BasisCovarianceCorrelation
Definition  Covariance is a statistical measure that assesses the relationship between two interdependent random variables. A higher covariance value indicates a stronger dependency between the variables.  Correlation is a statistical measure that evaluates the strength of the relationship between two variables, assuming that all other conditions remain constant. The maximum value that can be obtained is +1, which indicates a perfect dependent relationship between the two variables.
RelationshipCorrelation can be calculated with Covariance.Correlation is measured by covariance on a standard scale. 
ValuesThe value of covariance is from the range -∞ to +∞.The value of correlation is from the range -1 to +1.
ScalabilityCovariance is affected by the change in scale.Correlation is not affected by the change in scale.
UnitsCovariance is a definite unit.Correlation is an absolute unitless.
OutputDirection only.Direction and Magnitude.

This has been a guide to Covariance vs Correlation. Here we correlation & covariance with their formulas, key differences and a comparative table. You can learn more from the following articles –

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