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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 ...
Specifically, for some matrix , the squared Mahalanobis distance of (where is row of ) from the vector of mean ^ = = of length , is () = (^) (^), where = is the estimated covariance matrix of 's. This is related to the leverage h i i {\displaystyle h_{ii}} of the hat matrix of X {\displaystyle \mathbf {X} } after appending a column vector of 1 ...
Even when a normal distribution model is appropriate to the data being analyzed, outliers are expected for large sample sizes and should not automatically be discarded if that is the case. [26] Instead, one should use a method that is robust to outliers to model or analyze data with naturally occurring outliers. [26]
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.
The outliers would greatly change the estimate of location if the arithmetic average were to be used as a summary statistic of location. The problem is that the arithmetic mean is very sensitive to the inclusion of any outliers; in statistical terminology, the arithmetic mean is not robust .
Outliers Influential observations. Leverage (statistics), ... DFFITS; Cook's distance; References This page was last edited on 29 November 2017, at 18:51 (UTC). ...
Galton's experimental setup "Standard eugenics scheme of descent" – early application of Galton's insight [1]. In statistics, regression toward the mean (also called regression to the mean, reversion to the mean, and reversion to mediocrity) is the phenomenon where if one sample of a random variable is extreme, the next sampling of the same random variable is likely to be closer to its mean.
reachability-distance k (A,B)=max{k-distance(B), d(A,B)} In words, the reachability distance of an object A from B is the true distance of the two objects, but at least the k -distance of B . Objects that belong to the k nearest neighbors of B (the "core" of B , see DBSCAN cluster analysis ) are considered to be equally distant.