CHAPTER 7
SOLUTIONS TO PROBLEMS
7.1
(i) The coefficient on
male
is 87.75, so a man is estimated to sleep almost one and onehalf
hours more per week than a comparable woman.
Further,
t
male
= 87.75/34.33
≈
2.56, which is
close to the 1% critical value against a twosided alternative (about 2.58).
Thus, the evidence for
a gender differential is fairly strong.
(ii) The
t
statistic on
totwrk
is
−
.163/.018
≈
−
9.06, which is very statistically significant.
The
coefficient implies that one more hour of work (60 minutes) is associated with .163(60)
≈
9.8
minutes less sleep.
(iii) To obtain
2
r
R
, the
R
squared from the restricted regression, we need to estimate the
model without
age
and
age
2
.
When
age
and
age
2
are both in the model,
age
has no effect only if
the parameters on both terms are zero.
7.3
(i) The
t
statistic on
hsize
2
is over four in absolute value, so there is very strong evidence that
it belongs in the equation. We obtain this by finding the turnaround point;
this is the value of
hsize
that maximizes
(other things fixed):
19.3/(2
ˆ
sat
⋅
2.19)
≈
4.41.
Because
hsize
is measured
in hundreds, the optimal size of graduating class is about 441.
(ii) This is given by the coefficient on
female
(since
black
= 0):
nonblack females have SAT
scores about 45 points lower than nonblack males.
The
t
statistic is about –10.51, so the
difference is very statistically significant.
(The very large sample size certainly contributes to
the statistical significance.)
(iii) Because
female
= 0, the coefficient on
black
implies that a black male has an estimated
SAT score almost 170 points less than a comparable nonblack male.
The
t
statistic is over 13 in
absolute value, so we easily reject the hypothesis that there is no ceteris paribus difference.
(iv) We plug in
black
= 1,
female
= 1 for black females and
black
= 0 and
female
= 1 for
nonblack females.
The difference is therefore –169.81 + 62.31 =
−
107.50.
Because the estimate
depends on two coefficients, we cannot construct a
t
statistic from the information given.
The
easiest approach is to define dummy variables for three of the four race/gender categories and
choose nonblack females as the base group.
We can then obtain the
t
statistic we want as the
coefficient on the black female dummy variable.
7.5
(i) Following the hint,
=
n
colGPA
0
ˆ
β
+
0
ˆ
δ
(1 –
noPC
) +
1
ˆ
hsGPA
+
2
ˆ
ACT
= (
0
ˆ
+
0
ˆ
)
−
0
ˆ
noPC
+
1
ˆ
hsGPA
+
2
ˆ
ACT
.
For the specific estimates in equation (7.6),
0
ˆ
= 1.26 and
0
ˆ
=
.157, so the new intercept is 1.26 + .157 = 1.417.
The coefficient on
noPC
is –.157.
(ii) Nothing happens to the
R
squared.
Using
noPC
in place of
PC
is simply a different way
of including the same information on
PC
ownership.
34
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View Full Document(iii) It makes no sense to include both dummy variables in the regression:
we cannot hold
noPC
fixed while changing
PC
.
We have only two groups based on
PC
ownership so, in
addition to the overall intercept, we need only to include one dummy variable.
If we try to
include both along with an intercept we have perfect multicollinearity (the dummy variable trap).
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 Spring '08
 BREMAN
 Econometrics, Regression Analysis, Statistical hypothesis testing, nettfa, ecobuy

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