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

likelihood ratio test,
which is slightly involved and is therefore discussed in
the appendix to the chapter. For further discussion, see Theil, op. cit., pp. 179–184.
EXAMPLE 8.3
(
Continued
)
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Chapter 8
Multiple Regression Analysis: The Problem of Inference
253
We then fit the unconstrained and constrained models to the data and obtain the respec-
tive coefficients of determination, namely, 
R
2
UR
and 
R
2
R
. We note the df in the unconstrained
model (
=
n
−
k
) and also note the df in the constrained model (
=
m
), 
m
being the num-
ber of linear restriction (e.g., 1 in Eq. [8.6.16] or Eq. [8.6.18]) or the number of regressors
omitted from the model (e.g., 
m
=
4 if Eq. [8.6.18] holds, since four regressors are as-
sumed to be absent from the model). We then compute the 
F
ratio as indicated in Eq. (8.6.9)
or Eq. (8.6.10) and use this 
Decision Rule: If the computed F exceeds F
α
(
m
,
n
−
k
)
, where
F
α
(
m
,
n
−
k
)
is the critical F at the 
α
level of significance, we reject the null hypothesis:
otherwise we do not reject it.
Let us illustrate:
EXAMPLE 8.4
The Demand for
Chicken in the
United States,
1960–1982
In Exercise 7.19, among other things, you were asked to consider the following demand
function for chicken:
ln
Y
t
=
β
1
+
β
2
ln
X
2
t
+
β
3
ln
X
3
t
+
β
4
ln
X
4
t
+
β
5
ln
X
5
t
+
u
i