Definition

1. Noun:
   • (Statistics) A measure of the joint variability of two random variables: Covariance quantifies how much two variables change together. A positive covariance indicates that the variables tend to move in the same direction, while a negative covariance indicates they tend to move in opposite directions. A covariance of zero suggests no linear relationship.

Usage Examples

• Noun:
  • The covariance between advertising spend and sales revenue was calculated to be positive.
  • A high covariance between two stocks suggests their prices often rise and fall together.
  • The researcher reported the covariance matrix for all variables in the study.

Advanced Usage

• "Covariance matrix": A square matrix that contains the covariances between all possible pairs of elements in a random vector. It is a key concept in multivariate statistics.

  • Principal component analysis is performed on the covariance matrix of the dataset.

• "Sample covariance": An estimate of the population covariance, calculated from a sample of data.

  • The formula for sample covariance divides by (n-1) rather than n.

Variants and Related Words

• Covary (verb): To exhibit covariance; to vary together.

  • These two economic indicators are known to covary strongly.

• Covariant (adjective): Changing in a corresponding way with something else.

  • The covariant shift in both metrics was unexpected.

Synonyms

• Joint variability (noun phrase): A descriptive synonym for the concept of covariance.
• Co-movement (noun): Informal term for variables moving together.

Related Phrases

• "Covariance structure": Refers to the pattern of covariances between variables in a model.
  • The analysis tested different assumptions about the covariance structure.

Notes

• Covariance is a foundational concept for understanding correlation, which is a standardized version of covariance. While covariance indicates the direction of a linear relationship, correlation measures both the direction and strength of that relationship on a standardized scale.

Noun

1. (statistics) the mean value of the product of the deviations of two variates from their respective means