Statistics
Covariance
A measure of how much two random variables change together.
What is Covariance?
Covariance calculates the directional relationship between two continuous variables. A positive covariance means the variables tend to move in the same direction, while a negative covariance means they move in opposite directions. Unlike correlation, covariance is not standardized, meaning its magnitude depends on the units of the variables being measured.
Why Covariance Matters
It is the mathematical foundation for calculating correlation, variance of portfolios in finance, and the parameters of ordinary least squares regression.
Example
A finance researcher calculates the covariance between the daily returns of two tech stocks to determine if they tend to rise and fall on the exact same days.
Common Mistakes
- Interpreting the magnitude of the covariance directly to determine the strength of the relationship, which requires standardizing it into a correlation coefficient.
- Assuming a covariance of zero means the variables are entirely independent (it only means there is no linear relationship).