What can covariance be used for?

Question

Quinn Allen · Accepted Answer

One use of co-variance is to study the correlation.

When we have sample data relating to two dependent variables, the co-variance becomes relevant. Co-variance is a measure of the effect of variation between the two variables. When we have two dependent variables say X and Y, we can study the variation within the values of X - this is #sigma_x^2# the variation within the values of Y is the variance of y #sigma_y^2#. The study of the simultaneous variation between X and Y is called COV(X,Y) or #sigma_(xy)#.

Josiah Allen · Answer

undefined Covariance can be used to measure the degree to which two variables change together. It indicates the direction of the linear relationship between two variables. A positive covariance suggests that the variables tend to increase or decrease together, while a negative covariance indicates that one variable tends to increase as the other decreases. However, covariance does not provide information about the strength of the relationship between variables, as it is influenced by the scale of the variables. Therefore, it is often standardized to obtain the correlation coefficient, which measures the strength and direction of the linear relationship between variables on a scale from -1 to 1.