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.

  • CreatedNovember 11, 2015
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