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In statistics, Cook's distance or Cook's D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. [1] In a practical ordinary least squares analysis, Cook's distance can be used in several ways: to indicate influential data points that are particularly worth checking for validity; or to indicate regions of the design space where it ...
Although the raw values resulting from the equations are different, Cook's distance and DFFITS are conceptually identical and there is a closed-form formula to convert one value to the other. [ 3 ] Development
The usual estimate of σ 2 is the internally studentized residual ^ = = ^. where m is the number of parameters in the model (2 in our example).. But if the i th case is suspected of being improbably large, then it would also not be normally distributed.
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The formula then divides by () to account for the fact that we remove the observation rather than adjusting its value, reflecting the fact that removal changes the distribution of covariates more when applied to high-leverage observations (i.e. with outlier covariate values). Similar formulas arise when applying general formulas for statistical ...
As well as there being several algebraically equivalent expressions there are also several different modified versions of "Cook's distance". Melcombe 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:
Tim Cook, CEO of Apple, at the company’s Fifth Avenue store in Manhattan, Sept. 20, 2024. (Victor J. Blue—Bloomberg/Getty Images)
The Mahalanobis distance is a measure of the distance between a point and a distribution, introduced by P. C. Mahalanobis in 1936. [1] The mathematical details of ...