# Determine the Relationship between Variables Using Covariance and Correlation

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).