Pearson correlation coefficient

This is a method discussed in Social Media Analysis 10-802 in Spring 2010.

Its a metric to measure dependence between two random variables. It is defined as follows :

 Corr(X,Y) =  cov(X,Y) / (var(X) * var(Y))
 where,
 *  Corr(X,Y) : Pearson correlation coefficient between X and Y
 *  cov(X,Y)  : Covariance between X and Y
 *  var(X)    : variance of variable X

• The correlation coefficient ranges from −1 to 1.
• A value of 1 implies that a linear equation describes the relationship between X and Y perfectly, with all data points lying on a line for which Y increases as X increases.
• A value of −1 implies that all data points lie on a line for which Y decreases as X increases.
• A value of 0 implies that there is no linear correlation between the variables.