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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]
This is an important technique in the detection of outliers. ... line going through (0, 0) to the points (1, 4), (2, − ... Cook's distance – a measure of changes ...
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) ...
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.
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.
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 ...