Index: The Book of Statistical ProofsModel Selection ▷ Goodness-of-fit measures ▷ R-squared ▷ Definition

Definition: Let there be a linear regression model with independent observations

\[\label{eq:mlr} y = X\beta + \varepsilon, \; \varepsilon_i \overset{\mathrm{i.i.d.}}{\sim} \mathcal{N}(0, \sigma^2)\]

with measured data $y$, known design matrix $X$ as well as unknown regression coefficients $\beta$ and noise variance $\sigma^2$.

Then, the proportion of the variance of the dependent variable $y$ (“total variance”) that can be predicted from the independent variables $X$ (“explained variance”) is called “coefficient of determination”, “R-squared” or $R^2$.


Metadata: ID: D21 | shortcut: rsq | author: JoramSoch | date: 2020-02-25, 11:41.