Although these two terms are used for establishing a relationship and dependency between any two random variables, the following are the differences between them :
Correlation : This technique is used to measure and estimate the quantitative relationship between two variables and is measured in terms of how strong are the variables related.
Covariance : It represents the extent to which the variables change together in a cycle. This explains the systematic relationship between pair of variables where changes in one affect changes in another variable.
Mathematically, consider 2 random variables, X and Y where the means are represented as and respectively and standard deviations are represented by and respectively and E represents the expected value operator, then:
covarianceXY = E[(X-),(Y-)]
correlationXY = E[(X-),(Y-)]/()
correlation(X,Y) = covariance(X,Y)/(covariance(X) covariance(Y))
Based on the above formula, we can deduce that the correlation is dimensionless whereas covariance is represented in units that are obtained from the multiplication of units of two variables.
