Question A
The data in the file CRIME are crime-related and demographic statistics for 47 US states in 1960. The data were collected from the FBI's Uniform Crime Report and other government agencies.
These are the variables in the dataset:
1 R: Crime rate: # of offenses reported to police per million population
2 Age: The number of males of age 14-24 per 1000 population
3 S: Indicator variable for Southern states (0 = No, 1 = Yes)
4 Ed: Mean # of years of schooling x 10 for persons of age 25 or older
5 Ex0: 1960 per capita expenditure on police by state and local government
6 Ex1: 1959 per capita expenditure on police by state and local government
7 LF: Labor force participation rate per 1000 civilian urban males age 14-24
8 M: The number of males per 1000 females
9 N: State population size in hundred thousands
10 NW: The number of non-whites per 1000 population
11 U1: Unemployment rate of urban males per 1000 of age 14-24
12 U2: Unemployment rate of urban males per 1000 of age 35-39
13 W: Median value of transferable goods and assets or family income in tens of $
14 X: The number of families per 1000 earning below 1/2 the median income
SEE APPENDIX A FOR DESCRIPTIVE STATS
Answer the following questions. For all questions (unless otherwise specified) give Model A/C, null and alternative hypotheses, PRE, F*, pa-pc, n-pa, interpret the relevant beta(s) and a substantive conclusion
1 Did police expenditures in 1960 predict crime rates?
Model A
Ri=β0 + β1Ex0i + ei
Model C
Ri=β0 + ei
H0 β1=0 H1 β10 PRE
.473
F*
40.36
F Critical Values
(1,45) = 4.06
PA-PC
1 n-PA 45
Beta
Value
Interpretation.
b0
14.45
The value of Ri when the value of Ex0 is 0. b1 .895
The change in Ri when the value of Ex0 increases by 1.
Conclusion:
We conducted GLM analysis on a dataset of 47 states to examine the relationship between police expenditures in 1960 (M=85.00, SD=29.72) and Crime Rate(M=90.51, SD=38.68). We found that police expenditures in 1960 was a significant predictor of Crime Rate F (1,45) = 40.36, PRE=.473 p=.000. Model predicted that for every increase of 1 unit in police expenditures, there was a .895 increase in crime rate. (See Appendix A)
2 (For this question only complete the Model A/C and hypotheses) Did expenditures in 1960 have a different impact on crime than expenditures in 1959?
Model A
Ri=β0 + β1Ex0i + β2 Ex1i + ei
Model C
Ri=β0 + β1Ex0i + β1 Ex1i + ei
H0 β1= β2
H1
β1 β2
3 Did states with higher income inequality (variable X) have higher crime rates?
Model A
Ri=β0 + β1Xi + ei
Model C
Ri=β0 + ei
H0 β1=0 H1 β10 PRE
.032
F*
(1,45) 1.490
F Critical Values
(1,45) = 4.06
PA-PC
1 n-PA 45
Beta
Value
Interpretation
b0
124.18
The expected value of Ri when Xi is 0 b1 -1.74
The predicted change in Ri when Xi increases by 1.
Conclusion:
We conducted GLM analysis on a dataset of 47 states to examine the relationship between income inequality (M=194.00, SD=39.90) and Crime Rate (M=90.51, SD=38.68). We found that income inequality was not a significant predictor of Crime Rate F (1,45) = 1.49, PRE=.032 p=.229. (See Appendix B)
4 Controlling for expenditures in 1960 did states with higher income inequality (variable X) have higher crime rates?
Model A
Ri=β0 + β1Ex0i + β2Xi ei
Model C
Ri=β0 + β1Ex0i + ei
H0 β2=0 H1 β20 PRE
.204
F*
(1,44) = 11.27
F Critical Values
(1,40) = 4.08
PA-PC
1 n-PA 44
Beta
Value
Interpretation
b0
-94.47
The expected value for Ri when Ex0i and Xi is 0 b1 1.241
The expected change in Ri when Ex0i increases by 1 controlling for the change in Xi. b2 .410
The expected change in Ri when Xi increases by 1 controlling for the change in Ex0i
We conducted GLM analysis on a dataset of 47 states to examine the relationship between income inequality (M=194.00, SD=39.90), Police and State Expenditures in 1960 (M=85.00, SD=29.719) and Crime Rate (M=90.51, SD=38.68). We found that income inequality was a significant predictor of Crime Rate when controlling for Police
