Stat 401B
Lab 6: Due October 18
Fall 2005
1
1. A sociologist is interested in the relationship between the homicide rate per 100,000 population
(Y ) and a city’s population (X1 ) in thousands of people, the percentage of families with yearly
incomes less than $10,000 (X2 ), and the rate of unemployment (X3 ). Data are provided for
a random sample of 20 cities.
City
1
2
3
4
5
6
7
8
9
10
Y
11.2
13.4
40.7
5.3
24.8
12.7
20.9
35.7
8.7
9.6
X1
587
643
635
692
1248
643
1964
1531
713
749
X2
16.5
20.5
26.3
16.5
19.2
16.5
20.2
21.3
17.2
14.3
X3
6.2
6.4
9.3
5.3
7.3
5.9
6.4
7.6
4.9
6.4
City
11
12
13
14
15
16
17
18
19
20
Y
14.5
26.9
15.7
36.2
18.1
28.9
14.9
25.8
21.7
25.7
X1
7895
762
2793
741
625
854
716
921
595
3353
X2
18.1
23.1
19.1
24.7
18.6
24.9
17.9
22.4
20.2
16.9
X3
6.0
7.4
5.8
8.6
6.5
8.3
6.7
8.6
8.4
6.7
The data are on the class web page
http://www.public.iastate.edu/∼wrstephe/stat401.html
Use JMP to fit the models necessary to answer the following questions. Be sure to support
your answers with the appropriate information from the JMP output. Turn in the JMP
output with your answers.
(a) Is there a statistically significant relationship between homicide rate and the percentage
of families with yearly incomes less than $10,000?
(b) Does unemployment rate add significantly to the model that already contains population?
(c) Does population add significantly to the model that contains the two variables percentage
of families with yearly incomes less than $10,000 and unemployment rate?
(d) There are three models that satisfy the first two criteria for being the “best” model.
Summarize the models that are both statistically useful and have all explanatory variables adding significantly. In your summaries give:
• The explanatory variables in the model.
• The test statistic and P-value for the test of model utility.
• The test statistic and P-value for each of the explanatory variables that add significantly to the model.
• R2 , adjR2 , and the Root Mean Square Error.
(e) Of the three models summarized in d), which is the “best” model? Explain briefly.
(f) For the “best” model look at the plot of residuals versus predicted values and the analysis
of the distribution of residuals. Indicate what you see in the plots and what this tells
you about the conditions necessary for conducting the statistical analysis.