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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 ...
An outlier may be defined as a data point that differs markedly from other observations. [6] [7] A high-leverage point are observations made at extreme values of independent variables. [8] Both types of atypical observations will force the regression line to be close to the point. [2]
Therefore, the authors suggest investigating those points with DFFITS greater than . 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]
A frequent cause of outliers is a mixture of two distributions, ... using a measure such as Cook's distance. [30] If a data point (or points) ...
High-leverage points, if any, are outliers with respect to the independent variables. That is, high-leverage points have no neighboring points in R p {\displaystyle \mathbb {R} ^{p}} space, where p {\displaystyle {p}} is the number of independent variables in a regression model.
Outliers Influential observations. Leverage (statistics), ... DFFITS; Cook's distance; References This page was last edited on 29 November 2017, at 18:51 (UTC). ...
For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%. Shown percentages are rounded theoretical probabilities intended only to approximate the empirical ...
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.