Equations · Probability and statistics
Pearson correlation coefficient
How closely two quantities move together in a straight line, on a scale from −1 to 1.
ρ = Cov(X, Y) / (σ_X σ_Y)
Aethel says
rho equals the covariance of X and Y, over the quantity sigma sub X sigma sub Y
What it says
The covariance measures whether X and Y tend to be above their means at the same time. Dividing by both standard deviations removes the units, leaving a number between −1 and 1.
A value of 1 is a perfect rising line, −1 a perfect falling line, and 0 no linear relationship. A strong correlation alone does not show that one quantity causes the other.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| ρ | rho | the correlation coefficient |
| Cov(X, Y) | the covariance of X and Y | the average product of the deviations from the two means |
| σ_X, σ_Y | sigma sub X, sigma sub Y | the standard deviations of X and of Y |
Where you meet it
Statistics, finance (asset correlations) and the sciences.
Questions
How do you say Pearson correlation coefficient out loud?
ρ = Cov(X, Y) / (σ_X σ_Y) is read: “rho equals the covariance of X and Y, over the quantity sigma sub X sigma sub Y.” That is exactly what Aethel says when it meets the formula in a book.
What does ρ mean in Pearson correlation coefficient?
ρ (said “rho”) is the correlation coefficient.
What does Cov(X, Y) mean in Pearson correlation coefficient?
Cov(X, Y) (said “the covariance of X and Y”) is the average product of the deviations from the two means.
Can I listen to the equations in my own textbook like this?
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