Definition:Coefficient of Determination/Measure of Independence

Definition

Let $X$ and $Y$ be random variables.

Let $r^2$ denote the coefficient of determination of $Y$ upon $X$.

The coefficient $1 - r^2$ provides a measure of the independence of $X$ and $Y$, where:

$1$ indicates full independence of $X$ and $Y$

$0$ indicates total dependence of $Y$ on $X$.

Also see

• Results about the coefficient of determination can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): coefficient of determination
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): coefficient of determination (index of determination)