Coefficient of determination

Index: The Book of Statistical Proofs ▷ Model 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 $R^2$.

Sources:

Wikipedia (2020): "Coefficient of determination"; in: Wikipedia, the free encyclopedia, retrieved on 2020-02-25; URL: https://en.wikipedia.org/wiki/Mean_squared_error#Proof_of_variance_and_bias_relationship.

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