Definition: Coefficient of determination
Index: The Book of Statistical Proofs ▷ Model Selection ▷ Goodness-of-fit measures ▷ R-squared ▷ Definition
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Metadata: ID: D21 | shortcut: rsq | author: JoramSoch | date: 2020-02-25, 11:41.
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 $R^2$.
- 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.