News / Blog: Knowledge Base

Covariance between Variables

Covariance is a measure of how two variables change together. It indicates the extent to which deviations from the means of the two variables occur together. Covariance can be interpreted as positive, negative, or neutral (close to zero).

Calculation of Covariance:

The covariance between variables \(X\) and \(Y\) is calculated using the following formula:

\[ \text(X, Y) = \frac{1}{N} \sum_{i=1}^{N} (X_i - \bar{X})(Y_i - \bar{Y}) \]

where \(N\) is the number of observations, \(X_i\) and \(Y_i\) are individual data points, and \(\bar{X}\) and \(\bar{Y}\) are the means of the variables.

Interpretation of Covariance:

• Positive: Positive covariance indicates that larger values of \(X\) tend to occur with larger values of \(Y\), and smaller values of \(X\) tend to occur with smaller values of \(Y\).
• Negative: Negative covariance indicates that larger values of \(X\) tend to occur with smaller values of \(Y\), and vice versa.
• Near Zero: Covariance close to zero suggests that there is no clear linear relationship between the two variables.

Example:

Suppose we have data on advertising expenses (\(X\)) and generated revenues (\(Y\)) for a company. A positive covariance would suggest that higher advertising expenses are associated with higher revenues.