Normal linear-model confidence ellipsoid

With ${\hat{\sigma }}^2=\Vert Y-X\hat{\beta }{\Vert }^2/(n-p)$, a simultaneous $(1-\alpha )$ confidence region for $\beta$ is

If ${\hat{\beta }}_{(i)}$ is the least-squares estimate after deleting observation $i$, Cook's distance isIt measures the deleted estimate in the same quadratic metric as the coefficient confidence ellipsoid.