Statistics 401D,XE
Spring, 2008
Laboratory 7
The data used in this analysis are shown in Table 9.1 on page 256 in Agresti and Finlay.
Use the results from
the following output to answer the questions for problem 1 below.
The variables in the data set are defined as follows.
All variables were compiled from the
Statistical Abstract
of the United States
.
state = state (including the District of Columbia, or DC), using two-letter postal codes,
violent = violent crime rate,
murder = murder rate,
metro = percent in metropolitan areas,
white = percent white,
hs = percent high school graduates,
poverty = percent below the poverty level,
single = percent of families headed by a single parent.
The output consists of the results of estimating a model predicting violent crime rate by the percentage of
persons below the poverty level.
The results on pages 1-3 include DC, for a total of 51 observations; questions a-f below
are related to those first 3 pages of the output.
Pages 4-6 of the output provide comparable results, but omitting DC;
question g below asks you to compare the two sets of results.
The SAS program file (
lab7
on putty) that produced these
results is at the end of this document.
a.
Compare the square of the correlation coefficient between violent crime and poverty with the value of r
2
for the
model in which poverty predicts violent crime.
What do you conclude?
For that same model, compare the calculated t-
statistics used in testing H
0
:
β
1
= 0 and H
0
:
ρ
xy
= 0.
Also compare the squares of these t values to the calculated F-
statistic for testing H
0
:
β
1
= 0, and state your conclusions.
b.
Using the results from PROC CORR, find the critical value for testing H
0
:
ρ
xy
= 0 against Ha :
ρ
xy
0, with
α
= .01.
What do you conclude?
c.
Test H
0
:
ρ
= .50 against H
a
:
ρ
.50, with
α
= .01, for the relationship between violent and poverty.
State the
conclusion of your test.
d.
Using the results on your printout for the relationship between violent and poverty, show that r = b
1
(s
x
/ s
y
)
e.
What is the estimated mean level of violent crime for any and all states in which poverty equals 10.3?
Construct a 95% confidence interval around this point estimate.
f.
What is the predicted level of violent crime for any one state (say, Iowa) in which poverty equals 10.3?
Construct a 95% prediction interval around this point estimate, and comment on how this result compares with that in
question 1e.
g.
Comment on the consequences of deleting DC from the data analysis.
Would you conclude that it is better to
analyze the relationship between violent crime and poverty with or without DC included?
Explain your answer, based
on your comparison of the detailed results for the two models.