Normal linear model
Definition taught in Functions of random variables and limit theorems, part of Probability
Normal linear model
| Type | Definition |
| Taught in | Functions of random variables and limit theorems |
| Part | Probability |
A normal linear model for a response vector \mathbf{Y}\in\mathbb{R}^n says
\mathbf{Y}=A\boldsymbol\beta+\boldsymbol\varepsilon, \qquad \boldsymbol\varepsilon\sim\operatorname{N}(\mathbf{0},\,\sigma^2 I_n),
with A a known n\times p matrix of full column rank, \boldsymbol\beta\in\mathbb{R}^p an unknown coefficient vector, and \sigma^2>0.
Used in
- Taught in Functions of random variables and limit theorems, where the derivation and examples are.
- All 21 questions on Functions of random variables and limit theorems
See also
Transformation rule · Multivariate normal distribution · Affine images of normal vectors · Law of large numbers · Central limit theorem