Category:Coefficient of Determination

This category contains results about Coefficient of Determination.
Definitions specific to this category can be found in Definitions/Coefficient of Determination.

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

Let $r$ denote the product moment correlation coefficient of $X$ and $Y$.

Let a set of data consist of $n$ pairs of observations $\tuple {x_i, y_i}$ from $X$ and $Y$ respectively.

Let a least-squares linear regression of $Y$ on $X$ be fitted.

The proportion of the total variance of the $y_i$ which can be attributed to dependence on $x$ (as opposed to independent variance) is equal to $r^2$.

This coefficient is known as the coefficient of determination.