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Cook's distance

If

β_{(i)}

is the least-squares estimate after deleting observation

i

, Cook's distance is

D_{i} = \frac{( β _{(i)} - β ) ^{T} X ^{T} X ( β _{(i)} - β )}{p σ ^{2}} = \frac{∥ Y _{(i)} - Y ∥ ^{2}}{p σ ^{2}} .

It measures the deleted estimate in the same quadratic metric as the coefficient confidence ellipsoid.

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