Eco311, Second Midterm Exam, Spring 2018.

Prof. Bill Even

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Your Name (Please print) ______FORM 1__________________________________

Your section (Please circle) 8:30 10:05

Your row (Please circle) 1 2 3 4 5

Directions

Place your answers to all questions in the space provided. Clearly circle your answer to each question

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.

Eco311, Second Midterm Exam, Spring 2018.

Prof. Bill Even

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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

Eco311, Second Midterm Exam, Spring 2018.

Prof. Bill Even

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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_____