The data set Detroit was used extensively in the book by Miller (2002)
on subset regression.
The data are
unusual in that a subset of three predictors can be found which gives a
very much better fit to the data than the subsets found from the Efroymson
stepwise algorithm, or from forward selection or backward elimination.
They are also unusual in that, as time series data, the assumption of
independence is patently violated, and the data suffer from problems
of high collinearity.
As well, ridge regression reveals somewhat paradoxical paths of
shrinkage in univariate ridge trace plots, that are more comprehensible
in multivariate views.
Usage
data(Detroit)
Format
A data frame with 13 observations on the following 14 variables.
Police
Full-time police per 100,000 population
Unemp
Percent unemployed in the population
MfgWrk
Number of manufacturing workers in thousands
GunLic
Number of handgun licences per 100,000 population
GunReg
Number of handgun registrations per 100,000 population
HClear
Percent of homicides cleared by arrests
WhMale
Number of white males in the population
NmfgWrk
Number of non-manufacturing workers in thousands
GovWrk
Number of government workers in thousands
HrEarn
Average hourly earnings
WkEarn
Average weekly earnings
Accident
Death rate in accidents per 100,000 population
Assaults
Number of assaults per 100,000 population
Homicide
Number of homicides per 100,000 of population
Details
The data were orginally collected and discussed by Fisher (1976) but the complete dataset first
appeared in Gunst and Mason (1980, Appendix A).
Miller (2002) discusses this dataset throughout his book, but doeesn't state clearly
which variables he used as predictors and
which is the dependent variable. (Homicide was the dependent variable, and the
predictors were Police ... WkEarn.)
The data were obtained from StatLib.
A similar version of this data set, with different variable names appears
in the bestglm package.
Fisher, J.C. (1976). Homicide in Detroit: The Role of Firearms. Criminology, 14, 387–400.
Gunst, R.F. and Mason, R.L. (1980). Regression analysis and its application: A data-oriented approach.
Marcel Dekker.
Miller, A. J. (2002). Subset Selection in Regression. 2nd Ed. Chapman & Hall/CRC. Boca Raton.
Examples
data(Detroit)
# Work with a subset of predictors, from Miller (2002, Table 3.14),
# the "best" 6 variable model
# Variables: Police, Unemp, GunLic, HClear, WhMale, WkEarn
# Scale these for comparison with other methods
Det <- as.data.frame(scale(Detroit[,c(1,2,4,6,7,11)]))
Det <- cbind(Det, Homicide=Detroit[,"Homicide"])
# use the formula interface; specify ridge constants in terms
# of equivalent degrees of freedom
dridge <- ridge(Homicide~., data=Det, df=seq(6,4,-.5))
# univariate trace plots are seemingly paradoxical in that
# some coefficients "shrink" *away* from 0
traceplot(dridge, X="df")
vif(dridge)
pairs(dridge, radius=0.5)
plot3d(dridge, radius=0.5, labels=dridge$df)
# transform to PCA/SVD space
dpridge <- pca.ridge(dridge)
# not so paradoxical in PCA space
traceplot(dpridge, X="df")
biplot(dpridge, radius=0.5, labels=dpridge$df)
# show PCA vectors in variable space
biplot(dridge, radius=0.5, labels=dridge$df)