What is covariance?

Covariance measures the linear relationship between two variables. The covariance is similar to the correlation between two variables, however, they differ in the following ways:
  • Correlation coefficients are standardized. Thus, a perfect linear relationship results in a coefficient of 1. The correlation measures both the strength and direction of the linear relationship between two variables.
  • Covariance values are not standardized. Therefore, the covariance can range from negative infinity to positive infinity. Thus, the value for a perfect linear relationship depends on the data. Because the data are not standardized, it is difficult to determine the strength of the relationship between the variables.

You can use the covariance to understand the direction of the relationship between variables. Positive covariance values indicate that above average values of one variable are associated with above average values of the other variable and below average values are similarly associated. Negative covariance values indicate that above average values of one variable are associated with below average values of the other variable.

The correlation coefficient is a function of the covariance. The correlation coefficient is equal to the covariance divided by the product of the standard deviations of the variables. Therefore, a positive covariance always results in a positive correlation and a negative covariance always results in a negative correlation.

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