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

(13.4.6)
where
Y
=
total cost and
X
=
output. Now if we plot the residuals
ˆ
u
i
obtained from this
regression against
ˆ
Y
i
, the estimated
Y
i
from this model, we get the picture shown in Fig-
ure 13.2. Although
ˆ
u
i
and
ˆ
u
i
ˆ
Y
i
are necessarily zero (why? see Chapter 3), the residu-
als in this figure show a pattern in which their mean changes systematically with
ˆ
Y
i
.
This
would suggest that if we introduce
ˆ
Y
i
in some form as a regressor(s) in Eq. (13.4.6), it
should increase
R
2
. And if the increase in
R
2
is statistically significant (on the basis of the
F
test discussed in Chapter 8), it would suggest that the linear cost function (13.4.6) was
23
It does not matter if we order 
ˆ
u
i
according to 
X
2
i
or 
X
3
i
since these are functions of 
X
i
, which is
already ordered.
24
J. B. Ramsey, “Tests for Specification Errors in Classical Linear Least Squares Regression Analysis,”
Journal of the Royal Statistical Society,
series B, vol. 31, 1969, pp. 350–371.
guj75772_ch13.qxd 16/08/2008 03:24 PM Page 479

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Part Two
Relaxing the Assumptions of the Classical Model
mis-specified. This is essentially the idea behind RESET. The steps involved in RESET are
as follows:
1. From the chosen model, e.g., Eq. (13.4.6), obtain the estimated 
Y
i
, that is,
ˆ
Y
i
.
2. Rerun Eq. (13.4.6) introducing 
ˆ
Y
i
in some form as an additional regressor(s). From
Figure 13.2, we observe that there is a curvilinear relationship between 
ˆ
u
i
and 
ˆ
Y
i
, suggest-
ing that one can introduce 
ˆ
Y
2
i
and 
ˆ
Y
3
i
as additional regressors. Thus, we run
Y
i
=
β
1
+
β
2
X
i
+
β
3
ˆ
Y
2
i
+
β
4
ˆ
Y
3
i
+
u
i