both the terms measure the relationship and the dependency between two variables. “Covariance” indicates the direction of the linear relationship between variables. “Correlation” on the other hand measures both the strength and direction of the linear relationship between two variables.

When it comes to choosing between Covariance vs Correlation, the latter stands to be the first choice as it remains unaffected by the change in dimensions, location, and scale, and can also be used to make a comparison between two pairs of variables. 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.

Covariance is a measure to indicate the extent to which two random variables change in tandem. Correlation is a measure used to represent how strongly two random variables are related to each other.

Covariance is nothing but a measure of correlation. Correlation refers to the scaled form of covariance.

Covariance indicates the direction of the linear relationship between variables. Correlation on the other hand measures both the strength and direction of the linear relationship between two variables.

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

Covariance is affected by the change in scale. If all the values of one variable are multiplied by a constant and all the values of another variable are multiplied, by a similar or different constant, then the covariance is changed. Correlation is not influenced by the change in scale.

Covariance assumes the units from the product of the units of the two variables. Correlation is dimensionless, i.e. It’s a unit-free measure of the relationship between variables.

Covariance of two dependent variables measures how much in real quantity (i.e. cm, kg, liters) on average they co-vary. Correlation of two dependent variables measures the proportion of how much on average these variables vary w.r.t one another.

Covariance is zero in case of independent variables (if one variable moves and the other doesn’t) because then the variables do not necessarily move together. Independent movements do not contribute to the total correlation. Therefore, completely independent variables have a zero correlation.

Dear Salman

Thanks a lot for detailed explanation.

Regards

Neda Mam Thanks a lot for information.

Regards

covariance = product of the variances of two or more variables.

correlation = covariance / product of standard deviations of two or more variables.

Both the terms measure the relationship and the dependency between two variables. Covariance indicate the direction of the linear relationship between the variables. Correlation measures both the strength and direction of the linear relationship between two variables.

Please refer the following article:

https://towardsdatascience.com/let-us-understand-the-correlation-matrix-and-covariance-matrix-d42e6b643c22

"Correlation is a statistical relationship of two or more random variables (or quantities that can be considered as such with some acceptable degree of accuracy). At the same time, changes in one or more of these quantities lead to a systematic change in another or other quantities. Mathematical measure of the correlation of two random variables. serves as the correlation coefficient.

Covariance in probability theory is a measure of the linear dependence of two random variables. "

The problem with covariance is that it is difficult to compare them: when you compute the covariance of the set and weights, expressed in (respectively) meters and kilograms, you get a different covariance than when you do it in other units (which already creates a problem for humans doing the same thing with or without metric!), but it will also be difficult to tell if (for example) height and weight are “more equal” than, say, the length of fingers and toes simply because “scale” is which the covariance is calculated is different.

The solution to this problem is to “normalize” the covariance: you divide the covariance by what represents the variety and scale in both covariates, and you end up with a value that is guaranteed to be in the -1 to 1 range: correlation. No matter what unit your original variables were in, you will always get the same result, and this also ensures that you can compare to some degree, “two” variables are correlated with the other two, simply by comparing their correlation.

Regards, Sergey Viktorovich Pushkin

All measures the dependent correlation between two variables

But

the Covariance measures the direction of the linear relationship between two variables

While correlation measures the strength and direction of the relationship

Thanks for these scientific questions Bodh R Sharma Sergey Viktorovich Pushkin Ranjan Parekh

You can use this paper

https://www.mygreatlearning.com/blog/covariance-vs-correlation/

In simple words, both the terms measure the relationship and the dependency between two variables. “Covariance” indicates the direction of the linear relationship between variables. “Correlation” on the other hand measures both the strength and direction of the linear relationship between two variables.

.https://towardsdatascience.com/let-us-understand-the-correlation-matrix-and-covariance-matrix-d42e6b643c22

When comparing data samples from different populations, covariance is used to determine how much two random variables vary together, whereas correlation is used to determine when a change in one variable can result in a change in another. Both covariance and correlation measure linear relationships between variables.

https://acadgild.com/blog/covariance-and-correlation

As covariance says something on same lines as correlation, correlation takes a step further than covariance and also tells us about the strength of the relationship. Both can be positive or negative. ... Correlation coefficient is the term used to refer the result of any correlation measurement methods.

https://towardsdatascience.com/getting-the-basics-of-correlation-covariance-c8fc110b90b4

You can use similar operations to convert a covariance matrix to a correlation matrix. First, use the DIAG function to extract the variances from the diagonal elements of the covariance matrix. Then invert the matrix to form the diagonal matrix with diagonal elements that are the reciprocals of the standard deviations.

https://blogs.sas.com/content/iml/2010/12/10/converting-between-correlation-and-covariance-matrices.html

Dear Prof. Sharma!

I found a website that gives examples and illustrations on the difference between the concept you spotted:

WallStreetMojo (2020). "Difference Between Covariance and Correlation -

Correlation vs Covariance Infographics" Copyright © 2020. CFA Institute Available at: https://www.wallstreetmojo.com/correlation-vs-covariance/

Yours sincerely, Bulcsu Szekely

Please see this link

https://www.mygreatlearning.com/blog/covariance-vs-correlation/

Dear Bodh R Sharma,

Correation measured the ralation between two variables. But, covariance calculated the relation between two variable according to their expected value E(X).

So, covariance = corrélation + E(X)

Respected Bara Mouslim; M.K. Tripathi; Mahammad Khuddush; Lamia Al-Naama; Chinaza Godswill Awuchi; Chinaza Godswill Awuchi; and other experts i extend my thanks for your valuable time and responses.

Bodh