Siegel's Exact Fit Example Data

A small counterexample data set devised by Andrew Siegel. Six (out of nine) data points lie on the line \(y = 0\) such that some robust regression estimators exhibit the “exact fit” property.

data(SiegelsEx, package="robustbase")

Format

A data frame with 9 observations on the following 2 variables.

x

a numeric vector

y

a numeric vector

Source

Emerson and Hoaglin (1983, p.139)

References

Peter J. Rousseeuw and Annick M. Leroy (1987) Robust Regression and Outlier Detection Wiley, p.60–61

Examples

data(SiegelsEx)
plot(SiegelsEx, main = "Siegel's example for 'exact fit'")
abline(          lm(y ~ x, data = SiegelsEx))
abline(MASS::lqs(y ~ x, data = SiegelsEx, method = "lms"), col = 2)
legend("topright", leg = c("lm", "LMS"), col=1:2, lwd=1, inset = 1/20)