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

FIGURE 11.13
Residuals (
a
) and squared residuals (
b
) on sales.
Glejser Test
| ˆ
u
i
| = −
1003
+
0.04639 Sales
i
se
= 
(2316) (0.0128)
(11.7.5)
t
=
(
−
0.43) (3.62)
r
2
=
0
.
522
The Glejser test also suggests that there is a systematic relationship between the absolute
values of the residuals and sales, raising the possibility that the regression (11.7.3) suffers
from heteroscedasticity.
White Test
ˆ
u
2
i
= −
46,746,325
+
578 Sales
i
+
0.000846 Sales
2
i
se
=
(112,224,348)
(1308)
(0.003171)
(11.7.6)
t
=
(
−
0.42)
(0.44)
(0.27)
R
2
=
0.435
Using the 
R
2 
value and 
n
=
14, we obtain 
n R
2
=
6.090. Under the null hypothesis of no
heteroscedasticity, this should follow a chi-square distribution with 2 df (because there are
two regressors in Eq. [11.7.6]). The 
p
value of obtaining a chi-square value of as much as
6.090 or greater is about 0.0476. Since this is a low value, the White test also suggests that
there is heteroscedasticity.
EXAMPLE 11.10
(
Continued
)
guj75772_ch11.qxd 14/08/2008 10:01 AM Page 398

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Chapter 11
Heteroscedasticity: What Happens If the Error Variance Is Nonconstant?
399
In sum, then, on the basis of the residual graphs and the Park, Glejser, and White tests,
it seems that our R&D regression (11.7.3) suffers from heteroscedasticity. Since the true
error variance is unknown, we cannot use the method of weighted least squares to obtain
heteroscedasticity-corrected standard errors and 
t
values. Therefore, we would have to
make some educated guesses about the nature of the error variance.
To conclude our example, we present below White’s heteroscedasticity-consistent
standard errors, as discussed in Section 11.6.
R & D
i
=
1337.87
+
0.0437 Sales
i
se
=
(4892.447)
(0.0411)