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9
CHAPTER 3
SOLUTIONS TO PROBLEMS
3.2
(i)
hsperc
is defined so that the smaller it is, the lower the student’s standing in high
school.
Everything else equal, the worse the student’s standing in high school, the lower is
his/her expected college GPA.
(ii) Just plug these values into the equation:
n
colgpa
= 1.392
−
.0135(20) + .00148(1050) = 2.676.
(iii) The difference between A and B is simply 140 times the coefficient on
sat
, because
hsperc
is the same for both students.
So A is predicted to have a score .00148(140)
≈
.207
higher.
(iv) With
hsperc
fixed,
n
colgpa
Δ
= .00148
Δ
sat
.
Now, we want to find
Δ
sat
such that
n
colgpa
Δ
= .5, so .5 = .00148(
Δ
sat
) or
Δ
sat
= .5/(.00148)
≈
338.
Perhaps not surprisingly, a
large ceteris paribus difference in SAT score – almost two and onehalf standard deviations – is
needed to obtain a predicted difference in college GPA or a half a point.
3.4
(i) If adults trade off sleep for work, more work implies less sleep (other things equal), so
1
β
< 0.
(ii) The signs of
2
and
3
are not obvious, at least to me.
One could argue that more
educated people like to get more out of life, and so, other things equal, they sleep less (
2
< 0).
The relationship between sleeping and age is more complicated than this model suggests, and
economists are not in the best position to judge such things.
(iii) Since
totwrk
is in minutes, we must convert five hours into minutes:
Δ
totwrk
=
5(60) = 300.
Then
sleep
is predicted to fall by .148(300) = 44.4 minutes.
For a week, 45
minutes less sleep is not an overwhelming change.
(iv) More education implies less predicted time sleeping, but the effect is quite small.
If
we assume the difference between college and high school is four years, the college graduate
sleeps about 45 minutes less per week, other things equal.
(v) Not surprisingly, the three explanatory variables explain only about 11.3% of the
variation in
sleep
.
One important factor in the error term is general health.
Another is marital
status, and whether the person has children.
Health (however we measure that), marital status,
and number and ages of children would generally be correlated with
totwrk
.
(For example, less
healthy people would tend to work less.)
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10
3.6
(i) No.
By definition,
study
+
sleep
+
work
+
leisure
= 168.
Therefore, if we change
study
,
we must change at least one of the other categories so that the sum is still 168.
(ii) From part (i), we can write, say,
study
as a perfect linear function of the other
independent variables:
study
= 168
−
sleep
−
work
−
leisure
. This holds for every observation,
so MLR.3 violated.
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 Spring '11
 Suzuki
 Econometrics, Regression Analysis, prior consent

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