Covariance

Gist

Definition

Properties

1. Location invariance:
   $$ Cov(x,y) = Cov(x - a, y) $$
2. Multilinearity:
   $$ \lambda Cov(x,y) = Cov(\lambda x, y)$$
3. Symmetry:
   $$ Cov(x,y) = Cov(y , x) $$

Notes:

• Covariance is sensitive to the scale of the variables. Large values can inflate the result.
• Covariance does not indicate the strength of the relationship in a standardized way.
• Outliers can significantly affect the covariance calculation.

A correlation matrix is just standardized covariance

Notably: