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. Test at the 5% level to see whether there is a significant 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 than 1 would suggest that the smaller states have proportionately more bankruptcies. Test at the 5% level to see whether the population slope for the logs is significantly different from 1 or not, and briefly discuss your conclusion.
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TABLE 113.4 Business Bankruptcies by State Bankruptcies Population Alabama Alaska Arizona Arkansas Califonia Colorado Connecticut Delaware Distrid of Columbia42 4.662 6.500 36.757 0.873 18328 Georgia Hawali Idaho 1,714 1,288 lowa Kansas Kentucky Louisiana Maine Maryland 4.411 154 1316 Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota 1,394 10003 1783 318 8.683 1.984 19.490 11.486 3 76199483 2 321406420761 238 538228 95205 3 2 2 32011 51 in V