Effect of Punishment Regimes on Crime Rates

Description

Criminologists are interested in the effect of punishment regimes on crime rates. This has been studied using aggregate data on 47 states of the USA for 1960. The data set contains the following columns:

Variable	Description

M	percentage of males aged 14–24 in total state population
So	indicator variable for a southern state
Ed	mean years of schooling of the population aged 25 years or over
Po1	per capita expenditure on police protection in 1960
Po2	per capita expenditure on police protection in 1959
LF	labour force participation rate of civilian urban males in the age-group 14-24
M.F	number of males per 100 females
Pop	state population in 1960 in hundred thousands
NW	percentage of nonwhites in the population
U1	unemployment rate of urban males 14–24
U2	unemployment rate of urban males 35–39
Wealth	wealth: median value of transferable assets or family income
Ineq	income inequality: percentage of families earning below half the median income
Prob	probability of imprisonment: ratio of number of commitments to number of offenses
Time	average time in months served by offenders in state prisons before their first release
Crime	crime rate: number of offenses per 100,000 population in 1960

Données ici.

Analyse 1

(a) La réponse est « Crime » et les variables explicatives sont « Ineq » et « Wealth ». Faire une régression avec ces deux variables et une autre avec « Ineq » seulement. Expliquer l'apparente contradiction dans un langage le plus clair possible. On s'aidera de tracés.

(b) Pour tester la linearité de l'influence de « Wealth », on propose de rajouter le carré de « Wealth » en variable explicative. Comparer les résultats de « summary » selon que l'on recentre ou non la variable « Wealth ». Donner une explication heuristique. Comparer ensuite avec anova. Quelle est la conclusion au final ?

Analyse 2

(a) L'élimination des variables conduit à un modèle additif: Crime~M+Ed+Po1+U2+Ineq+Prob
Que se passe-t-il si l'on ajoute Po2? Expliquer.

(b) La criminalité augmente-t-elle avec l'investissement dans la police?

(d) Essayer d'introduire la variable Soc en interaction.

Source

OzDASL
Ehrlich, I. (1973) Participation in illegitimate activities: a theoretical and empirical investigation. Journal of Political Economy 81, 521–565.
Vandaele, W. (1978) Participation in illegitimate activities: Ehrlich revisited. In Deterrence and Incapacitation, eds A. Blumstein, J. Cohen and D. Nagin, National Academy of Sciences, Washington DC, pp. 270–335.
Venables, W., and Ripley, B. (1998). Modern Applied Statistics with S-Plus, Second Edition. Springer-Verlag.

The data given here is rounded data taken from Vandaele (1978). The column scales differ somewhat from Venables and Ripley (1998). The data was originally collected by Ehrlich from the Uniform Crime Report of the FBI and other US government sources.