Covariance measures the joint variability of two random variables.
⚠Both datasets must have the same number of values. Covariance is scale-dependent; use correlation for standardized comparison.
What is Covariance?
Covariance measures how two variables change together. A positive covariance indicates that larger values of one variable tend to be associated with larger values of the other. A negative covariance indicates the opposite.
Positive Covariance
Cov > 0: Variables tend to increase together (e.g., height & weight)
Negative Covariance
Cov < 0: When one variable increases, the other decreases
Zero Covariance
Cov = 0: No linear relationship between variables
Sample vs Population
Sample uses n-1 (unbiased), population uses n (biased)
Covariance measures how two variables vary together. Positive covariance means variables tend to increase together. Negative covariance means when one increases, the other tends to decrease.
Population vs sample covariance?▼
Population covariance divides by n. Sample covariance divides by n-1 (Bessel's correction) to give an unbiased estimator of population covariance.
How is covariance related to correlation?▼
Correlation = Covariance / (σₓ × σᵧ). Correlation normalizes covariance to range -1 to +1, making it easier to interpret strength of relationship.
What does covariance value mean?▼
Magnitude depends on variable scales. Sign matters: positive = variables move together, negative = move opposite. Use correlation for standardized comparison.
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