Question: Consider the slightly scary topic of business
Consider the slightly scary topic of business bankruptcies. Table 11.3.4 shows data for each state on the number of failed businesses and the population in millions.
a. Construct a scatterplot of business bankruptcies (Y) against population (X). Describe the relationship that you see. Does there appear to be some association?
b. Does the linear model appear to hold? Why or why not?
c. Find the logarithm of each data value, both for population and for business bankruptcies. You may choose either base 10 or base e, but use only one type.
d. Construct a scatterplot of the logarithms and describe the relationship.
e. Find the equation of the regression line to predict the log of business bankruptcies from the log of population.
f. Find the two-sided 95% confidence interval for the slope coefficient of the log relationship.
g. Testatthe5%leveltoseewhetherthereisasignificant relationship between the logs of bankruptcies and of population. Explain why the result is reasonable.
h. If the slope for the logs were exactly 1, then business bankruptcies would be proportional to population. A value larger than 1 would say that large states have proportionately more bankruptcies, and a slope less than1 would suggest that the smaller states have proportion a tely more bankruptcies. Test at the 5% level to see whether the populations lope for the logs is significantly different from 1 or not, and briefly discuss your conclusion.
Table 11.3.4:
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TABLE 11.3.4 Business Bankruptcies by State State Bankruptcies Population Alabama 395 4.662 Alaska 78 0.686 Arizona 691 6.500 Arkansas 429 2.855 California 4,697 36.757 Colorado 756 4.939 Connecticut 366 3.501 Delaware 361 0.873 District of Columbia 42 0.592 Florida 2,759 18.328 Georgia 1,714 9.686 Hawaii 51 1.288 Idaho 167 1.524 Illinois 1,178 12.902 Indiana 692 6.377 lowa 270 3.003 Kansas 244 2.802 Kentucky 390 4.269 Louisiana 571 4.411 Maine 154 1.316 Maryland 405 5.634 Massachusetts 334 6.498 Michigan 1,394 10.003 Minnesota 656 5.220 Mississippi 298 2.939 Missouri 534 5.912 Montana 71 0.967 Nebraska 221 1.783 Nevada 395 2.600 New Hampshire 318 1.316 New Jersey 925 8.683 New Mexico 185 1.984 New York 1,534 19.490 North Carolina 738 9.222 North Dakota 54 0.641 Ohio 1,436 11.486 Oklahoma 392 3.642 Oregon 283 3.790 Pennsylvania 1,078 12.448 Rhode Island 122 1.051 South Carolina 196 4.480 South Dakota 95 0.804 Tennessee 653 6.215 Texas 2,728 24.327 Utah 302 2.736 Vermont 52 0.621 Virginia 798 7.769 Washington 565 6.549 West Virginia 169 1.814 Wisconsin 525 5.628 Wyoming 42 0.533 Source: Data are from U.S. Census Bureau, Statistical Abstract of the United States: 2010 (129th edition), Washington, DC, 2009. Bankruptcies for 2008 were accessed at http://www.census.gov/ compendia/statab/cats/business_enterprise/establishments_ employees_payroll.html on July 5, 2010. Populations for 2008 are from Table 12, accessed from http://www.census.gov/compendia/statab/ Cals/populatiom.html on July 5, 2010.
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