man/Detroit.Rd

% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/data.R
\docType{data}
\name{Detroit}
\alias{Detroit}
\title{Detroit Homicide Data for 1961-1973}
\format{
A data frame with 13 observations on the following 14 variables.
\describe{ 
 \item{\code{Police}}{Full-time police per 100,000 population}
 \item{\code{Unemp}}{Percent unemployed in the population}
 \item{\code{MfgWrk}}{Number of manufacturing workers in thousands}
 \item{\code{GunLic}}{Number of handgun licences per 100,000 population}
 \item{\code{GunReg}}{Number of handgun registrations per 100,000 population} 
 \item{\code{HClear}}{Percent of homicides cleared by arrests}
 \item{\code{WhMale}}{Number of white males in the population}
 \item{\code{NmfgWrk}}{Number of non-manufacturing workers in thousands}
 \item{\code{GovWrk}}{Number of government workers in thousands}
 \item{\code{HrEarn}}{Average hourly earnings} 
 \item{\code{WkEarn}}{Average weekly earnings} 
 \item{\code{Accident}}{Death rate in accidents per 100,000 population} 
 \item{\code{Assaults}}{Number of assaults per 100,000 population} 
 \item{\code{Homicide}}{Number of homicides per 100,000 of population} 
}
}
\source{
\url{https://lib.stat.cmu.edu/datasets/detroit}
}
\description{
The data set \code{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.
}
\details{
The data were originally 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 doesn't state
clearly which variables he used as predictors and which is the dependent
variable.  (\code{Homicide} was the dependent variable, and the predictors
were \code{Police} \dots{} \code{WkEarn}.)  The data were obtained from
StatLib.

A similar version of this data set, with different variable names appears in
the \code{bestglm} package.
}
\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)

\donttest{
plot3d(dridge, radius=0.5, labels=dridge$df)

# transform to PCA/SVD space
dpridge <- pca(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)
}


}
\references{
Fisher, J.C. (1976). Homicide in Detroit: The Role of Firearms.
\emph{Criminology}, \bold{14}, 387--400.

Gunst, R.F. and Mason, R.L. (1980). \emph{Regression analysis and its
application: A data-oriented approach}.  Marcel Dekker.

Miller, A. J. (2002). \emph{Subset Selection in Regression}. 2nd Ed. Chapman
& Hall/CRC. Boca Raton.
}
\keyword{datasets}