# Definition: Residual variance

**Index:**The Book of Statistical Proofs ▷ Model Selection ▷ Goodness-of-fit measures ▷ Residual variance ▷ Definition

**Definition:** Let there be a linear regression model

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.

**Sources:**

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