Checking for outliers in regression

According to Hoaglin and Welsch (1978) leverage values above 2(p+1)/n where p predictors are in the regression on n observations (items) are influential values. If the sample size is < 30 a stiffer criterion such as 3(p+1)/n is suggested.

Leverage is also related to the i-th observation's [:FAQ/mahal:Mahalanobis distance], $$\mbox{MD}_text{i}$$, such that for sample size, N

Leverage for observation i = $$\frac{\mbox{MD}_text{i}}{\mbox{N-1}} + \frac{\mbox{1}}{\mbox{N}}$$

so

Critical $$\mbox{MD}_text{i} = (\frac{\mbox{2(p+1)}}{\mbox{N}} - \frac{1}{\mbox{N}})(\mbox{N-1}) $$

(See Tabachnick and Fidell)

Other outlier detection methods using boxplots are in the Exloratory Data Analysis Graduate talk[:StatsCourse2009 here] or by using z-scores using tests such as Grubb's test - further details and an on-line calculator are located [http://www.graphpad.com/quickcalcs/Grubbs1.cfm here.]

Hair, Anderson, Tatham and Black (1998) suggest Cook's distances greater than 1 are influential.

References

Hair, J., Anderson, R., Tatham, R. and Black W. (1998). Multivariate Data Analysis (fifth edition). Englewood Cliffs, NJ: Prentice-Hall.

Hoaglin, D. C. and Welsch, R. E. (1978). The hat matrix in regression and ANOVA. The American Statistician 32, 17-22.

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