The article "Air Pollution and Medical Care Use by Older Americans" (Health Affairs [2002]: 207-214) gave data on a measure of pollution (in micro- grams of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographical regions of the United States:
| Region |
Pollution |
Cost of Medical Care |
| 6.17 |
|
-0.08 |
| 8.06 |
|
0.25 |
| 8.62 |
|
-0.14 |
| 10.56 |
|
0 |
| 12.45 |
|
0.08 |
| 11.99 |
|
0.03 |
| 12.5 |
|
-0.07 |
| 17.98 |
|
0.29 |
| 18.29 |
|
0.23 |
| 19.89 |
|
0.24 |
| 20.25 |
|
0.19 |
| 19.07 |
|
0.14 |
| 17.73 |
|
0.05 |
| 19.62 |
|
0.07 |
Mean Temperature (x) Net Directionality (y)
|
North
|
30.0
|
915
|
|
Upper South
|
31.8
|
891
|
|
Deep South
|
32.1
|
968
|
|
West South
|
26.8
|
972
|
|
Big Sky
|
30.4
|
952
|
|
West
|
40.0
|
899
|
a. Construct a scatterplot of the data. Describe any interesting features of the scatterplot.
b. Find the equation of the least-squares line describing the relationship between y 5 medical cost and x 5 pollution.
c. Is the slope of the least-squares line positive or negative? Is this consistent with your description of the relationship in Part (a)?
d. Do the scatterplot and the equation of the least- squares line support the researchers' conclusion that elderly people who live in more polluted areas have higher medical costs? Explain.