90-786 Homework 2 Answer Key
Problems to be Handed In:
CHS:
1. (20 Points)
Ecuador
China
0.5
Vietnam
Log(92/91)
0.0
Peru
Cambodia
-0.5
-1.0
Romania
0
1
2
3
Log(91/88)
Homework 2 Answer Key
Page 1
2. Health Care Spending Case, CHS pg 32
a.
(20 Points) Does it appear that health care spending differs across different regions of the
country?
13
12
percent income
per capita spending
2500
2000
1500
11
10
9
8
7
1
2
3
4
5
6
reg number
1
2
3
4
5
6
7
8
9
7
8
9
1
2
3
4
5
6
7
8
9
reg number
North East
Middle Atlantic
South Atlantic
East North Central
East South Central
West South Central
West North Central
Mountain
Pacific
The health spending as a percentage of income exhibits a great deal of variation by
region. The minimum values range from 7.4% to 10.8%, while the maximums go from 9.1% to
12.9%. (These values can be determined by examining descriptive statistics by region.) The
mean health care per capita spending shows less variation, with most of the regional means near
$1,800. This suggests that the real difference in health care spending by regions stems not from
the nominal amount of spending on health care per capita, but on the “burden” that health care
spending places on residents of a particular region, in terms of its percentage of income. Thus,
the real difference among regions is in per capita income. The data may also suggest that the
costs of health care by region do not “adjust” to account for variations in per capita income.
Homework 2 Answer Key
Page 2
b.
(20 Points) Plot of per capita spending vs. per capita income, by region
The .regional scatter plots confirm the conclusions reached above by examining the boxplots.
We should expect that in those regions where health care spending is a lower proportion of percapita income, the boxplot will indicate an upward (positively-sloped) trend. Notice that this
does not necessarily mean that health care spending is nominally low; only that it is a more
moderate, and consistent, proportion of income. On the other hand, in those regions where
health care spending is a greater proportion of per capita income, we would expect the scatter
plot to exhibit less of a pattern, with at least some of the data points being clustered in or near the
upper-left quadrant of the plot (where per capita spending is a relatively high proportion of per
capita income).
Indeed, if we compare the boxplots for regions 1 and 9 (where health care spending is a
relatively low portion of income) to the plots for these regions, there is a general upward trend
among the data points. On the other hand, the scatter plots for regions 5, 6, and 7 (where health
care spending is a greater portion of income) the data is clustered more towards the left side of
the graph.
Per Capita Spending vs. Income
Per Capita Spending vs. Income
2500
Mid Atl p/c spending
North East p/c spending
2500
2000
1500
15000
20000
2000
1500
15000
25000
Per Capita Spending vs. Income
25000
Per Capita Spending vs. Income
2500
South Atl p/c spending
2500
Mountain p/c spending
20000
Mid Atl p/c income
North East p/c income
2000
1500
15000
20000
Mountain p/c income
25000
2000
1500
15000
20000
25000
South Atl p/c income
Homework 2 Answer Key
Page 3
Per Capita Spending vs. Income
Per Capita Spending vs. Income
2500
Pacific p/c spending
West N.C. p/c spending
2500
2000
1500
15000
20000
1500
25000
15000
20000
25000
West N.C. p/c income
Pacific p/c income
Per Capita Spending vs. Income
Per Capita Spending vs. Income
2500
East S.C. p/c spending
2500
East N.C. p/c spending
2000
2000
1500
15000
20000
25000
East N.C. p/c income
2000
1500
15000
20000
25000
East S.C. p/c income
Per Capita Spending vs. Income
West S.C. p/c spending
2500
2000
1500
15000
20000
25000
West S.C. p/c income
Homework 2 Answer Key
Page 4
c. (20 Points) Regroup subregions
Obviously, there are any number of ways that the states could be regrouped into regions. The
example here is based on combining the western states, the southern states, and the New England
states. The regrouping appears to have resulting in slightly less variation within some of the
regions, and the medians across regions are somewhat closer together.
Revised Regions
Census Regions
revised region
region
13
12
percent income
per capita spending
2500
2000
1500
11
10
9
8
7
1
3
4
5
revised
7
8
1
3
4
5
7
8
revised
Homework 2 Answer Key
Page 5
3.
(20 Points) International Adoption
In 1997, U.S. Citizens adopted 13,620 children from abroad, according to the U.S. State
Department Bureau of Consular Affairs’ website. The top two countries of origin were Russia
(3,816 children) and China (3,597 children). A White House press release found on the same
site gives the number as 13,621. Either answer will be given full credit, provided that an
appropriate reference is given.
Below is a plot of the number of Romanian children adopted between 1989 and 1997.
The most interesting thing to notice is the dramatic increase in 1991, and then a return to the
former levels in 1992 and beyond.
Adoption of Romanian Children
Romanian Adoptions
2500
2000
1500
1000
500
0
89
90
91
92
93
94
95
96
97
year
Homework 2 Answer Key
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