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Normal linear model

Normal linear-model confidence ellipsoid

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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.


Cook's distance

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Regression diagnostics

Residual-versus-fitted plot

Cook's distance

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Cook's distance

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