On this Picostat.com statistics page, you will find information about the SiegelsEx data set which pertains to Siegel's Exact Fit Example Data. The SiegelsEx data set is found in the robustbase R package. You can load the SiegelsEx data set in R by issuing the following command at the console data("SiegelsEx"). This will load the data into a variable called SiegelsEx. If R says the SiegelsEx data set is not found, you can try installing the package by issuing this command install.packages("robustbase") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the SiegelsEx R data set. The size of this file is about 50 bytes.

Siegel's Exact Fit Example Data

Description

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.

Usage

data(SiegelsEx)

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)

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Dataset imported from https://www.r-project.org.