Determine the Relationship between Variables Using Covariance and Correlation

By Alan Anderson

You can determine the relationship between two variables with two measures of association: covariance and correlation. For example, if an investor wants to understand the risk of a portfolio of stocks, then he can use these measures to properly determine how closely the returns on the stocks track each other.

Covariance is used to measure the tendency for two variables to rise above their means or fall below their means at the same time. For example, suppose that a bioengineering company finds that increasing research and development expenditures typically leads to an increase in the development of new patents. In this case, R&D spending and new patents would have a positive covariance. If the same company finds that rising labor costs typically reduce corporate profits, then labor costs and profits would have a negative covariance. If the company finds that profits are not related to the average daily temperature, then these two variables will have a covariance that is very close to zero.

Correlation is a closely related measure. It’s defined as a value between –1 and 1, so interpreting the correlation is easier than the covariance. For example, a correlation of 0.9 between two variables would indicate a very strong positive relationship, whereas a correlation of 0.2 would indicate a fairly weak but positive relationship. A correlation of –0.8 would indicate a very strong negative relationship; a correlation of –0.3 would indicate a weak negative relationship. A correlation of 0 would show that two variables are unrelated (that is, independent).