3.4.2 Correlation Coefcient Flashcards
(16 cards)
Why is covariance not ideal for comparing correlation between different variable pairs?
Covariance is affected by the scale of the variables — larger variances can inflate it even if correlation is weak.
What is the correlation coefficient?
A normalized measure of covariance that adjusts for the scale of each variable.
What is the symbol for the correlation coefficient?
ρ (rho), or Corr(X, Y)
What is the formula for the correlation coefficient of X and Y?
ρ = Cov(X, Y) / (σ_X * σ_Y)
What is the range of the correlation coefficient?
-1 ≤ ρ ≤ 1
What does ρ = 1 mean?
Perfect positive linear relationship between X and Y.
What does ρ = -1 mean?
Perfect negative linear relationship between X and Y.
What does ρ = 0 mean?
X and Y have no linear relationship.
What does a positive value of ρ indicate?
As X increases, Y tends to increase — a positive linear association.
What does a negative value of ρ indicate?
As X increases, Y tends to decrease — a negative linear association.
Can two variables have zero correlation and still be dependent?
Yes — ρ = 0 does not imply independence, just no linear relationship.
If X and Y are independent, what is their correlation coefficient?
ρ = 0
Is the converse true: If ρ = 0, are X and Y independent?
No — zero correlation does not imply independence.
Why is correlation better than covariance for comparison?
Because it’s unitless and scaled — unaffected by the size or units of the variables.
What’s a real-world scenario where correlation matters more than covariance?
Comparing two stocks: one with large price swings and another with small swings — covariance is misleading, but correlation shows strength of linear relationship.
What’s a shortcut for calculating Cov(X, Y) if you know ρ, σ_X, and σ_Y?
Cov(X, Y) = ρ * σ_X * σ_Y
