Correlation

Correlation is used to identify the strength as well as the magnitude of the relationship between two variables. It is an important measure as it provides a fair indication of the predictive relationship between the variables. Correlation is quantified by the correlation coefficient ρ, which ranges from -1 to +1. The correlation coefficient indicates the degree of correlation between the two variables. The value of +1 means there exists a perfect positive correlation between the two variables, -1 means there is a perfect negative correlation and 0 means there is no correlation.

A perfect positive correlation is when one variable moves in either up or down direction, the other variable also moves in the same direction with the same magnitude while a perfect negative correlation is when one variable moves in the upward direction, the other variable moves in the downward (i.e. opposite) direction with the same magnitude.

The correlation coefficient for two variable is given by

Correlation(X,Y) = ρ = COV(X,Y) /  SD(X).SD(Y)

where, cov (X, Y) is the covariance between X & Y while SD (X) and SD(Y) denotes the standard deviation of the respective variables.