Index: The Book of Statistical ProofsModel Selection ▷ Goodness-of-fit measures ▷ Residual variance ▷ Definition

Definition: Let there be a linear regression model

\[\label{eq:mlr} y = X\beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \sigma^2 V)\]

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

Then, an estimate of the noise variance $\sigma^2$ is called the “residual variance” $\hat{\sigma}^2$, e.g. obtained via maximum likelihood estimation.


Metadata: ID: D20 | shortcut: resvar | author: JoramSoch | date: 2020-02-25, 11:21.