# Talk:Cook's distance

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## Correct?

I believe the second equation to be incorrect, atleast when compared to my textbook .. can any one confirm ? —Preceding unsigned comment added by Thedreamshaper (talkcontribs) 17:51, 4 July 2010 (UTC)

It looks ok to me. There are probably several algebraically equivalent expressions, so your book may give a different one without either being incorrect. Qwfp (talk) 11:01, 5 July 2010 (UTC)
The second Eq. agrees with a source I have. Check whether you have a "studentized residual" rather than the "raw residual" here. As well as there being several algebraically equivalent expressions there are also several different modified versions of "Cook's distance". Melcombe (talk) 14:36, 5 July 2010 (UTC)
I can confirm that the 2nd equation is equivalent to that presented in Cook's original ref. However, the latter is a simpler formula and possibly preferable here:
D = (ri^2 / p) * (hi / (1-hi))
Where:
hi is the leverage of the ith obs.
p is the rank of the model
ri is the internally studentized residual ( ri = ei / (sigmahat*sqrt(1-hi)) )
[where ei is the raw residual, and sigmahat is the estimated residual sd of the model) — Preceding unsigned comment added by 130.126.55.118 (talk) 20:50, 13 March 2012 (UTC)

## Not Correct?

It's the third equation that's incorrect: the denominator should be p s^2, not (1+p) s^2. Primrose61 (talk) 18:52, 11 November 2013 (UTC)

The denumerator in the second equation should be p * s^2, and in the terms of MSE, s^2 = MSE * n / (n - p), where n is the number of observations, and p is the number of parameters, so the whole equation should be:

${\displaystyle D_{i}={\frac {e_{i}^{2}\ (n-p)}{p\ n\ \mathrm {MSE} }}\left[{\frac {h_{ii}}{(1-h_{ii})^{2}}}\right],}$

Keskival (talk) 12:30, 5 December 2014 (UTC)