Content deleted Content added
Corrected formula of projection matrix. |
Added annihilator matrix as synonym of residual maker matrix |
||
Line 14:
The formula for the vector of [[errors and residuals in statistics|residual]]s <math>\mathbf{r}</math> can also be expressed compactly using the projection matrix:
:<math>\mathbf{r} = \mathbf{y} - \mathbf{\hat{y}} = \mathbf{y} - \mathbf{P} \mathbf{y} = \left( \mathbf{I} - \mathbf{P} \right) \mathbf{y}.</math>
where <math>\mathbf{I}</math> is the [[identity matrix]]. The matrix <math>\mathbf{M} \equiv \mathbf{I} - \mathbf{P}</math> is sometimes referred to as the '''residual maker matrix''' or the '''annihilator matrix'''.
The [[covariance matrix]] of the residuals <math>\mathbf{r}</math>, by [[error propagation]], equals
| |||