Consider the following two regressions based on the U$.$S$.$ data for $1946$ to

$1975\mathrm{.}26($Standard errors are in parentheses.$)$

Ct $=26\mathrm{.}19+0\mathrm{.}6248$GNPt$-0\mathrm{.}4398$Dt

se $=(2\mathrm{.}73)(0\mathrm{.}0060)$

$(0\mathrm{.}0736)$

R$2=0\mathrm{.}999$

$1$

D

aC

GNP bt

$=25\mathrm{.}92$

$+0\mathrm{.}6246-0\mathrm{.}4315$

GNPt

GNPt

se $=(2\mathrm{.}22)(0\mathrm{.}0068)$

$(0\mathrm{.}0597)$

R$2=0\mathrm{.}875$

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 heteroscedas$-$

ticity, 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 R$2$ values of the two regressions? Why or why not?