# ECO 311 Midterm 2 Spring 2018 Solutions

53 views15 pages Eco311, Second Midterm Exam, Spring 2018.
Prof. Bill Even
-1-
Directions
so that it can easily be distinguished from your work. Round all numerical answers to the nearest 100th
(e.g. 1.23) unless specifically told otherwise. Each question is worth 4 points unless otherwise
indicated.
The formula sheet and tables with the standard normal CDF and F-distribution are attached to the end
of the exam.
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Eco311, Second Midterm Exam, Spring 2018.
Prof. Bill Even
-2-
Table 1 (provided in the attachment) provides the results of a regression of student grades in courses at
Miami University between 2008 and 2017. In addition to coefficients and standard errors, the model’s
total and residual sum of squares are provided along with the number of observations. The grade variable
is the standard numeric value assigned to letter grades and ranges from 0 (F) to 4 (A or A+) The control
variables used in table 1 include:
Female: dummy variable that equals one if the student is female; 0 otherwise.
Resident: dummy variable that equals one if the student is a resident of Ohio; 0 otherwise
High School GPA: The student’s grade point average in high school.
ACT Score: The student’s composite ACT score.
Use specification (1) to answer the questions below.
1) Construct a 95% confidence interval for the coefficient on the Ohio resident dummy variable.
(-.02,.00)
2) What is R2 in specification (1)?
.10
3) (6 points) If another control variable is added to the regression, indicate whether each of the following
statements is true (T) or false (F).
a) R2 cannot decrease. T
b) Adjusted R2 will decrease unless the new variable has a t-statistic with an absolute value greater
than one.T
c) Adjusted R2 will be less than R2 T
4) If the t-statistic for a coefficient is 1.50, what is the associated p-value for the null hypothesis that the
coefficient is zero? Give answer to nearest .01. (Note: the table for the standard normal distribution
is included attachments.) 0.13
5) Based on specification 1 in table 1, construct a t-statistic for the null hypothesis that Ohio residents
and non-residents earn the same grades.
a) What is the value of the t-statistic?
2.0
b) Can you reject the null hypothesis at the
i) .10 level of significance?
yes
ii) .01 level of significance?
no
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Eco311, Second Midterm Exam, Spring 2018.
Prof. Bill Even
-3-
6) In specification (2), a control for the person’s ACT score is added to the regression. You should also
note that the coefficient on the female dummy variable rises relative to the estimate in specification
(1). Based on this and how omitted variable bias works, it must be the case that:
a) On average, women have lower ACT scores than men.
b) On average, women have higher ACT scores than men.
c) Neither of the above is implied by the change in the estimated coefficient on the female dummy
variable.
7) Using specification (2), what is the predicted course grade for a non-resident female student who had
a 3.0 high school GPA, and a 25 on the ACT? Give your answer to the nearest .01.
.694+3(.483)+.198+25(.023)=2.92
8) In specification (3), an interaction term between the female dummy variable and the ACT Score is
added. Based on this specification, what is the marginal effect of a one point increase in the ACT
score for
a) a male student? .024 b) a female student? .021
9) Based on specification (3), we can conclude that as the ACT score rises, the predicted grade earned
a) Rises for men, but falls for women.
b) Rises for both men and women, but more for women than men.
c) Rises for both men and women, but more for men than women.
10) Based on specification (3), we can conclude that, holding the other controls variables constant,
a) Women have higher grades than men
b) The female grade advantage is greater among students with higher ACT scores.
c) Both a and b
d) Neither a or b.
11) Using the results in specification (3), calculate the t-statistic to test the null hypothesis that the
marginal effect of ACT scores on grades is identical for men and women.
a) What is the t-statistic?
3.0
b) Based on the t-statistic, can you reject the null hypothesis that the marginal effect of ACT scores
on grades is identical for men and women at
i) The .05 level___y___ ii) the .01 level___y_____
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