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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 ...
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.
As illustrated by the figure, the q-relaxed intersection corresponds to the set of all x which belong to all sets except q of them. Sets X i that do not intersect the q-relaxed intersection could be suspected to be outliers. Figure 5. q-relaxed intersection of 6 sets for q=2 (red), q=3 (green), q= 4 (blue), q= 5 (yellow).
A regression diagnostic may take the form of a graphical result, informal quantitative results or a formal statistical hypothesis test, [2] each of which provides guidance for further stages of a regression analysis.
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
In the first couple of seconds, the measurements may be accurate to the nearest centimeter. After five minutes, the accuracy of the measurements may be good only to 100 m, because of the increased distance, atmospheric distortion, and a variety of other factors. So the measurements of distance may exhibit heteroscedasticity.
The following Python code returns x-squared values for a given N (first column) and n (top row) in Table 1 (m = 1) and Table 2 (m = 2) of Gould 1855. [5] Due to the Newton-method of iteration, look-up tables, such as N versus log Q (Table III in Gould, 1855) and x versus log R (Table III in Peirce, 1852 and Table IV in Gould, 1855) are no ...