Hence our Q statistics is as follows:
0.05
2,44 4 1
(44
4 1)
185.66 138.41
.
138.41
2
RESET
Q
F
0.05
2,39
185.66 138.41 39
.
138.41
2
RESET
Q
F
0.05
2,39
6.66
(
3.23)
RESET
Q
F
Since 6.66 is greater than 3.23, we can reject the null hypothesis that
the coefficients of the added variables are jointly zero, allowing us to
conclude that there is a specification error in Equation (5).
3. Information Criteria
A. Theil’s Adjusted
R
2
Criterion (
2
R
)
An important property of R
2
is that it is a non-decreasing function of
the number of explanatory variables present in the model; as the

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ECON 301 - Introduction to Econometrics I
May 2013
METU - Department of Economics
Instructor: Dr. Ozan ERUYGUR
e-mail:
[email protected]
Lecture Notes
10
number of explanatory variables increases, R
2
almost invariably
increases and never decreases. Stated differently, an additional X
variable will not decrease R
2
.
In view of this, in comparing two regression models with the same
dependent variable but differing number of X variables, one can
choose the model with highest R
2
.
To compare two R
2
terms, one must take into account the number of
X variables present in the model. This can be done readily if we
consider an alternative coefficient of determination, which is as
follows:
2
2
2
ˆ
(
1)
1
(
1)
t
t
u
T
k
R
y
T
(1)
where
k
= the number of parameters in the model excluding the
intercept term. The R
2
thus defined is known as the
adjusted R
2
,
denoted by
2
R
.
B. Akaike Information Criterion (AIC)
Imposing a penalty for adding explanatory variables to the model is
the basis of the AIC criterion: