# The Correlation Coefficient

The degree or level of correlation is measured with the help of the correlation coefficient or coefficient of correlation. For population data, the correlation coefficient is denoted by . The joint variation of and is measured by the covariance of and . The covariance of and denoted by is defined as:

The may be positive, negative or zero. The covariance has the same units in which and are measured. When is divided by and, we get the correlation coefficient . Thus , is free of the units of measurement.

It is a pure number and lies between and . If , it is called a perfect correlation. If , it is called perfect negative correlation. If there is no correlation between and , then and are independent and . For sample data, the correlation coefficient denoted by “” is a measure of strength of the linear relation between and variables, where “” is a pure number and lies between and . On the other hand Karl Pearson’s coefficient of correlation is: