This quantity measures how much the entire regression function changes when the i-th observation is deleted. Should be comparable to F_p,n-p: if the 'p-value' of D_i is 50 percent or more, then the i-th point is likely influential: investigate this point further. Cook's distance (D_i) is an influence measure based on the difference between the regression parameter estimates b and what they become if the i-th data point is removed, b_-1.
The usual criterion is that a point is influential if D_i exceeds the median of the F_p,n-p distribution, where p is the number of regression coefficients (including the intercept) and n the number of data.
D - matrix data (=[X Y]) (last column must be the Y-dependent variable). (X-independent variable entry can be for a simple [X], multiple [X1,X2,X3,...Xp] or polynomial [X,X^2,X^3,...,X^p] regression model).
A complete summary (table and/or plot) of the Cook's influence index. For the graph, the cross-hair can be positioned with the mouse at the selected location.
NOTE.-One should be careful. This procedure it is not a conclusive test to detect any outliers on regression models, but unusual observations by its very high leverage and high influence values. For such a case you should to check it under the appropriate assumptions.
Antonio Trujillo-Ortiz (2022). Cookdist (https://www.mathworks.com/matlabcentral/fileexchange/8716-cookdist), MATLAB Central File Exchange. Retrieved .
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