Condition on Coefficient of Determination for Total Dependence

Theorem

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

The coefficient of determination of $Y$ upon $X$ is equal to $1$ if and only if $Y$ is totally dependent upon $X$.

Proof

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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)