Correlation Coefficient

The correlation coefficient is a statistical measure of the degree of linear relationship between two variables. The correlation coefficient may take on any value between plus and minus one. The sign of the correlation coefficient (+ , -) defines the direction of the relationship, either positive or negative. A positive correlation coefficient means that as the value of one variable increases, the value of the other variable increases as well; as one decreases the other decreases too. Taking the absolute value of the correlation coefficient measures the strength of the relationship. Thus a correlation coefficient of zero indicates the absence of a linear relationship and correlation coefficients of one and minus one indicate a perfect linear relationship.

Where sX denotes standard deviation of the first variable, sY standard deviation of the second variable and where x and y are means of first and second variable.