# Covariance

## Definition of Covariance

Covariance is a measure of how two variables change together. It is calculated as the variance of the product of the two variables divided by the product of their standard deviations

## What is Covariance used for?

Covariance is a measure of how two random variables vary together. It is used to understand the relationship between two or more variables and how they move relative to one another. For example, if one variable increases while the other decreases, then a negative covariance will be observed. On the other hand, if both variables increase or decrease together, then a positive covariance will be observed. The magnitude of the covariance measures how strong the relationship between two variables is: it can range from perfect positive correlation to perfect negative correlation.

In data science and machine learning, covariance is used to assess the degree of linear dependence between two or more variables. It can also help identify clusters of related features and uncover relationships that could otherwise not be seen by simply looking at raw data. Covariance can also be used in decision making processes like portfolio optimization as well as for forecasting models such as time series analysis. Additionally, it’s commonly used in areas such as pattern recognition and image processing for feature extraction purposes.