Correlation vs Covariance
Student project for ECE302
by Blue
Introduction
Covariance and correlation are very similarly related. Correlation is used to identify the relationship of two random variables, X and Y. In order to determine the dependence of the two events, the correlation coefficient,$ \rho $, is calculated as:
$ \rho (X,Y) = \frac{cov(X,Y)}{ \sqrt{var(X)var(Y)} } $
The covariance is defined as: E(X-E[X])(Y-E[X]))
If X and Y are independent of each other, that means they are uncorrelated with each other, or cov(X,Y) = 0. However, if X and Y are uncorrelated, that does not mean they are independent of each other. 1, -1, and 0 are the three extreme points $ p\rho X,Y) $ can represent. 1 represents that X and Y are linearly dependent of each other. In other words, Y-E[X] is a positive multiple of X-E[X]. -1 represents that X and Y are inversely dependent of each other. In other words, Y-E[X] is a negative multiple of X-E[X].
Examples
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