Cook's distance
= Cook's distance
{c}
{wiki}
If $\widehat\beta_{(i)}$ is the least-squares estimate after deleting observation $i$, Cook's distance is
$$
D_i=\frac{(\widehat\beta_{(i)}-\widehat\beta)^TX^TX
(\widehat\beta_{(i)}-\widehat\beta)}{p\widehat\sigma^2}
=\frac{\|\widehat Y_{(i)}-\widehat Y\|^2}{p\widehat\sigma^2}.
$$
It measures the deleted estimate in the same quadratic metric as the coefficient confidence ellipsoid.