Consider the following two regressions based on the U.S. data for 1946 to 1975.26 (Standard errors are in parentheses.)

where C = aggregate private consumption expenditure
GNP = gross national product
D = national defense expenditure
t = time
The objective of Hanushek and Jackson's study was to find out the effect of defense expenditure on other expenditures in the economy.
a. What might be the reason(s) for transforming the first equation into the second equation?
b. If the objective of the transformation was to remove or reduce heteroscedasticity, what assumption has been made about the error variance?
c. If there was heteroscedasticity, have the authors succeeded in removing it? How can you tell?
d. Does the transformed regression have to be run through the origin? Why or why not?
e. Can you compare the R2 values of the two regressions? Why or why not?

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C; = 26.19 + 0.6248GNP,-04398D; se = (2.73) (0.0060) (0.0736) R2 = 0.999 = 25.92 + 0.6246-0.4315 GNP ): 25.92 GNP /t GNP GNP se = (2.22)(0.0068) (0.0597) R2 = 0.875