90-786 Homework 2 Answer Key

Problems to be Handed In:

CHS:

1. (20 Points)

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?

1 2 3 4 5 6 7 8 9

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.

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 per-capita 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.

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.

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.