Instructor’s Manual
Answers to Odd-numbered Exercises
Chapter 1
1-3. (a) The coefficient of Li represents the change in the percentage chance of making a putt when
the length of the putt increases by one foot. In this case, the percentage chance of making the
putt decreases by 4.1 for each foot longer the putt is.
(b) The equations are identical. To convert one to the other, note thatˆP i = Pi – ei, which is true
because ei = Pi -ˆP i (or more generally, ei = Yi –ˆYi ).
(c) 42.6 percent, yes; 79.5 percent, no (too low); -18.9 percent, no (negative!).
(d) One problem is that the theoretical relationship between the length of the putt and the
percentage of putts made is almost surely non-linear in the variables; we’ll discuss models
appropriate to this problem in Chapter 7. A second problem is that the actual dependent
variable is limited by zero and one but the regression estimate is not; we’ll discuss models
appropriate to this problem in Chapter 13.
1-5. (a) βʏ is the change in S caused by a one-unit increase in Y, holding G constant and βG is the
change in S caused by a one-unit increase in G, holding Y constant.
(b) +, -
(c) Yes. Richer states spend at least some of their extra money on education, but states with
rapidly growing student populations find it difficult to increase spending at the same rate as
the student population, causing spending per student to fall, especially if you hold the wealth
of the state constant.
(d) Ŝi = -183 + 0.1422Yi - 59.26Gi. Note that 59.26 ∙ 10 = 5926 ∙ 0.10, so nothing in the
equation has changed except the scale of the coefficient of G.
1-7. (a) β2 represents the impact on the wage of the ith worker of a one-year increase in the education
of the ith worker, holding constant that worker’s experience and gender.
(b) β3 represents the impact on the wage of the ith worker of being male instead of female,
holding constant that worker’s experience and education.
(c) There are two ways of defining such a dummy variable. You could define COLORi = 1 if the
ith worker is a person of color and 0 otherwise, or you could define COLOR1 = 1 if the ith
worker is not a person of color and 0 otherwise. (The actual name you use for the variable
doesn’t have to be “COLOR.” You could choose any variable name as long as it didn’t
conflict with the other variable names in the equation.)
(d) We’d favor adding a measure of the quality of the worker to this equation, and answer iv, the
number of employee of the month awards won, is the best measure of quality in this group.
As tempting as it might be to add the average wage in the field, it would be the same for each
employee in the sample and thus wouldn’t provide any useful information.

2 Studenmund • Using Econometrics, Seventh Edition
Chapter 2
2-3. (a) The squares are “least” in the sense that they are being minimized.
(b) If R2 = 0, then RSS = TSS, and ESS = 0. If R2 is calculated as ESS/TSS, then it cannot be
negative. If R2 is calculated as 1 – RSS/TSS, however, then it can be negative if RSS > TSS,
which can happen ifˆY is a worse predictor of Y thanY (possible only with a non-OLS
estimator or if the constant term is omitted).
(c) positive.
(d) We prefer Model T because it has estimated signs that meet expectations and also because it
includes an important variable that Model A omits. A higher R2 does not automatically mean
that an equation is preferred.
2-5. (a) Even though the fit in Equation A is better, most researchers would prefer equation B
because the signs of the estimated coefficients are as would be expected. In addition, X4 is a
theoretically sound variable for a campus track, while X3 seems poorly specified because an
especially hot or cold day would discourage fitness runners.
(b) The coefficient of an independent variable tells us the impact of a one-unit increase in that
variable on the dependent variable holding constant the other explanatory variables in the
equation. If we change the other variables in the equation, we’re holding different variables
constant, and so theˆ
 has a different meaning.
2-7. (a) Yes. We’d expect bigger colleges to get more applicants, and we’d expect colleges that used
the common application to attract more applicants. It might seem at first that the rank of a
college ought to have a positive coefficient, but the variable is defined as 1 = best, so we’d
expect a negative coefficient for RANK.
(b) The meaning of the coefficient of SIZE is that for every increase of one in the size of the
student body, we’d expect a college to generate 2.15 more applications, holding RANK and
COMMONAP constant. The meaning of the coefficient of RANK is that every one-rank
improvement in a college’s USNews ranking should generate 32.1 more applications,
holding SIZE and COMMONAP constant. These results do not allow us to conclude that a
college’s ranking is 15 times more important than the size of that college because the units of
the variables SIZE and RANK are quite different in magnitude. On a more philosophical
level, it’s risky to draw any general conclusions at all from one regression estimated on a
sample of 49 colleges.
(c) The meaning of the coefficient of COMMONAP is that a college that switches to using the
common application can expect to generate 1222 more applications, holding constant RANK
and SIZE. However, this result does not prove that a given college would increase
applications by 1222 by switching to the common application. Why not? First, we don’t
trust this result because there may well be an omitted relevant variable (or two) and because
all but three of the colleges in the sample use the common application. Second, in general,
econometric results are evidence that can be used to support an argument, but in and of
themselves they don’t come close to “proving” anything.
(e) If you drop COMMONAP from the equation,2
R falls. This is evidence (but not proof) that
COMMONAP belongs in the equation.

An Additional Interactive Regression Learning Exercise 3
Chapter 3
3-3. (a) A male professor in this sample earns $817 more than a female professor, holding constant
the other independent variables in the equation.
(b) Most students will expect a negative coefficient, so they will call this an unexpected sign.
Most professors and administrators will expect a positive sign because of the growing
competition among colleges for African-American professors, so they will call this an
expected sign. A key point here is not to change expectations based solely on this result.
(c) R is not a dummy variable because it takes on more than two values. For each additional year
in rank, the ith professor’s salary will rise by $406, holding constant the other independent
variables in the equation.
(d) Yes. The coefficient is large and, as we’ll learn in Chapter 5, statistically significantly
greater than zero. (In addition, it’s quite robust.)
(e) There’s no measure of the quality of the professor in the equation as it stands, so good
suggestions might the number of articles published by the ith professor or the average
teaching evaluation (on a standard scale) of the ith professor.
3-5. (a) A male student’s GRE subject score in Economics is likely to be 39.7 points higher than a
female’s, holding constant their GPA and SATs.
(b) This result is evidence of, but not proof of, bias. If we were sure that we had the best
possible specification (the topic of Chapter 6) and if this result turned out to be statistically
significant (the topic of Chapter 5), and if we were able to reproduce this result in other
samples, we’d be much closer to a “proof.” Even then, there still would be a possibility that
some factor other than bias was the cause of these results.
(c) Possible variables include the number of upper division economics courses taken, the number
of mathematics classes taken, and dummy variables measuring whether the student had taken
econometrics or international economics (two fields frequently covered in the test). It’s vital
that any suggested variable be cross-sectional by student.
(d) The equation would becomei
GRE = 212.1 – 39.7Gi + 78.9GPAi + 0.203SATMi +
0.110SATVi..
3-7. (a) The best way to handle three discrete conditions is to specify two dummy variables. For
example, one dummy variable could =1 if the iPod is new (and 0 otherwise) and the other
dummy variable could =1 if the iPod is used but unblemished (and 0 otherwise). The omitted
condition, that the iPod is used and scratched, would be represented by both dummy
variables equaling zero.
(b) Positive, negative, positive
(c) In theory, the narrower the time spread of the observations, the better the sample, but three
weeks probably is a short enough time period to ensure that the observations are from the
same population. If the three weeks included a major shock to the iPod market, however,
then the friend would be right, and the sample should be split into “before the shock” and
“after the shock” subsamples.
(d) Yes, they match with the answer to part b.

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4 Studenmund • Using Econometrics, Seventh Edition
(e)2
R is missing!
(f)2
R is .431.
Chapter 4
4-3. Pair “c” clearly violates Assumption VI, and pair “a” probably violates it for most samples.
4-5. (a) Yes, Yes. In particular, there’s no measure of prices in the equation.
(b) Yes
(c) Yes, Very unlikely
(d) No
(e) No
(f) No
(g) The nightclub should hire a dancer because the estimated coefficient is higher.
Chapter 5
5-3. (a) H0:β1 0, HA:β1 > 0
(b) H0:β1 ≥ 0, HA:β1 < 0; H0:β2 ≤ 0, HA:β2 > 0;
H0:β3 ≤ 0, HA:β3 > 0 (The hypothesis for β3 assumes that it is never too hot to go jogging.)
(c) H0:β1 0, HA:β1 > 0; H0:β2 ≤ 0, HA:β2 > 0;
H0:β3 ≥ 0, HA:β3 < 0; (The hypothesis for β3 assumes you’re not breaking the speed limit.)
(d) H0:βG = 0; HA:βG 0 (G for grunt.)
5-5. (a) t2 = (200 – 160)/25.0 = 1.6; tc = 2.052; therefore cannot reject H0. (Notice the violation of the
principle that the null hypothesis contains that which we do not expect.)
(b) t3 = 2.37; tc = 2.756; therefore cannot reject the null hypothesis.
(c) t2 = 5.6; tc = 2.447; therefore reject H0 if it is formulated as in the exercise, but this poses a
problem because the original hypothesized sign of the coefficient was negative. Thus, the
alternative hypothesis ought to have been stated: HA: β2 < 0, and H0 cannot be rejected
because the sign of t2 doesn’t agree with the sign in the alternative hypothesis.
5-7. (a) For both, H0: β ≤ 0 and HA: β > 0. For WIN, we cannot reject H0, even though the sign agrees
with the sign implied by HA, because |+1.00| < 1.697, the 5 percent one-sided critical t-value
for 30 degrees of freedom. For FREE, we can reject H0 at the 5 percent level of significance
because |2.00|> 1.697 and because 2.00 has the sign implied by HA.

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Solution Manual for Using Econometrics: A Practical Guide, 7th Edition

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