# ECO 311 Midterm 2 2016 Solutions

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Department
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Eco311, Second Midterm Exam, Fall 2016.
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, Fall 2016.
Prof. Bill Even
-2-
The table below was generated from a regression of standardized math scores measured in the 12th grade
as a function of the following characteristics:
motheduc, fatheduc: years of education for the student’s parents
cathhs: a dummy variable that equals one if the student attended a Catholic high school
lfaminc: log of family income
female: a dummy variable that equals one if the student is female.
black: a dummy variable that equals one if the student is black.
1. Construct a 99% confidence interval for the effect of father’s education on the math score.
+.𝟖𝟖𝟕±2.57*.055 =(.746, 1.028)
2. Suppose that school funding improves math scores. Adding a control for school funding to the
regressions would cause the estimated coefficient on the black dummy variable to
a. Increase
b. Decrease
c. Increase only if black students are in schools with lower funding than white students
d. Decrease only if black students are in schools with lower funding than white students
3. Suppose that better school funding increases student test scores. Adding a control for school
funding to the regressions
a. Will definitely not decrease R2, but could decrease adjusted R2
b. Will definitely not decrease R2 or adjusted R2
c. Will definitely not increase R2 or adjusted R2
d. Will definitely not decrease adjusted R2, but could decrease R2
_cons 15.61951 1.32827 11.76 0.000 13.01572 18.22329
black -5.23345 .3896062 -13.43 0.000 -5.997189 -4.469712
female -1.069473 .1959767 -5.46 0.000 -1.453643 -.6853035
lfaminc 1.457989 .143305 10.17 0.000 1.177071 1.738908
cathhs 1.5192 .412244 3.69 0.000 .7110846 2.327315
fatheduc .8872497 .0553613 16.03 0.000 .7787258 .9957735
motheduc .7574657 .0613026 12.36 0.000 .6372952 .8776362
math12 Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 664709.043 7,429 89.4749015 Root MSE = 8.4235
Residual 526696.571 7,423 70.9546775 R-squared = 0.2076
Model 138012.472 6 23002.0787 Prob > F = 0.0000
F(6, 7423) = 324.18
Source SS df MS Number of obs = 7,430
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Eco311, Second Midterm Exam, Fall 2016.
Prof. Bill Even
-3-
4. Suppose that better school funding increases student test scores. Also, suppose that family
income is positively correlated with mother and father’s education, but is uncorrelated with the
student’s sex (female). Adding a control for student funding to the regressions will
a. Definitely increase the standard errors for the estimated coefficients on female,
motheduc, and fatheduc
b. Could increase or decrease the standard errors for any estimated coefficients, but is more
likely to increase the standard error for the coefficient on female than that on motheduc
or fatheduc.
c. Could increase or decrease the standard errors for any estimated coefficients, but is
more likely to increase the standard error for the coefficient on motheduc and fatheduc
than that on female.
d. Definitely decrease the standard errors for the estimated coefficients on female,
motheduc, and fatheduc
Other things being the same, indicate whether the standard error of the estimated coefficient on mother’s
education would be larger (L), smaller (S), or unaffected (U) if
5. Mother’s education (not the coefficient on mother’s education) had increased variance __S___
6. Mother’s education was more highly correlated with father’s education __L_____
7. The variance of the regression residual was greater __L___
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