The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

downward
trend
in 
Y
.
For the expenditure on services data that we considered earlier, the results of fitting the
linear trend model (6.6.9) are as follows:
EXS
t
=
4111.545
+
30.674
t
(6.6.10)
t
=
(655.5628)
(44.4671)
r
2
=
0.9935
In contrast to Eq. (6.6.8), the interpretation of Eq. (6.6.10) is as follows: Over the quarterly
period 2003-I to 2006-III, on average, expenditure on services increased at the absolute
(
note:
not relative) rate of about 30 billion dollars per quarter. That is, there was an upward
trend in the expenditure on services.
The choice between the growth rate model (6.6.8) and the linear trend model (6.6.10)
will depend upon whether one is interested in the relative or absolute change in the expen-
diture on services, although for comparative purposes it is the relative change that is gen-
erally more relevant. In passing, 
observe that we cannot compare the r
2
values of models
(6.6.8) and (6.6.10) because the regressands in the two models are different.
We will show
in Chapter 7 how one compares the 
r
2
’s of models like (6.6.8) and (6.6.10).
The Lin–Log Model
Unlike the growth model just discussed, in which we were interested in finding the per-
cent growth in 
Y
for an absolute change in 
X
, suppose we now want to find the absolute
change in 
Y
for a percent change in 
X
. A model that can accomplish this purpose can be
written as:
Y
i
=
β
1
+
β
2
ln
X
i
+
u
i