Define correlation coefficient. What are its properties?

Correlation Coefficient is a statistical concept, which helps in establishing a relation between predicted and actual values obtained in a statistical experiment. The calculated value of the correlation coefficient explains the exactness between the predicted and actual values.

Correlation Coefficient value always lies between -1 to +1. If correlation coefficient value is positive, then there is a similar and identical relation between the two variables. Else it indicates the dissimilarity between the two variables.

The covariance of two variables divided by the product of their standard deviations gives Pearson’s correlation coefficient. It is usually represented by ρ (rho). 

ρ (X,Y) = cov (X,Y) / σX.σY. 

Here cov is the covariance. σX is the standard deviation of X __________ __________ __________ ______ _________.
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