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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
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 ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
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 ...
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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In regression problems, an alternative approach may be to only exclude points which exhibit a large degree of influence on the estimated coefficients, using a measure such as Cook's distance. [29] If a data point (or points) is excluded from the data analysis, this should be clearly stated on any subsequent report.
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