ems 1 Using the data in GPA2 on 4,137 college students, the following equation was estimated by OLS: colgpa 1.392.0135 hsperc + .00148 sat n = 4,137, R² = .273, where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top 5% of the class), and sat is the combined math and verbal scores on the student achievement test. UM noi (i) (ii) (iii) Why does it make sense for the coefficient on hsperc to be negative? What is the predicted college GPA when hsperc = 20 and sat = 1,050? Suppose that two high school graduates, A and B, graduated in the same percentile from high school, but Student A's SAT score was 140 points higher (about one standard deviation in the sam- ple). What is the predicted difference in college GPA for these two students? Is the difference large? Holding hsperc fixed, what difference in SAT scores leads to a predicted colgpa difference of .50, or one-half of a grade point? Comment on your answer. (iv) 2 The data in WAGE2 on working men was used to estimate the following equation: educ= 10.36 - .094 sibs+.131 meduc + .210 feduc n = = 722, R² = 214, where educ is years of schooling, sibs is number of siblings, meduc is mother's years of schooling, and feduc is father's years of schooling. (i) Does sibs have the expected effect? Explain. Holding meduc and feduc fixe
ems 1 Using the data in GPA2 on 4,137 college students, the following equation was estimated by OLS: colgpa 1.392.0135 hsperc + .00148 sat n = 4,137, R² = .273, where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top 5% of the class), and sat is the combined math and verbal scores on the student achievement test. UM noi (i) (ii) (iii) Why does it make sense for the coefficient on hsperc to be negative? What is the predicted college GPA when hsperc = 20 and sat = 1,050? Suppose that two high school graduates, A and B, graduated in the same percentile from high school, but Student A's SAT score was 140 points higher (about one standard deviation in the sam- ple). What is the predicted difference in college GPA for these two students? Is the difference large? Holding hsperc fixed, what difference in SAT scores leads to a predicted colgpa difference of .50, or one-half of a grade point? Comment on your answer. (iv) 2 The data in WAGE2 on working men was used to estimate the following equation: educ= 10.36 - .094 sibs+.131 meduc + .210 feduc n = = 722, R² = 214, where educ is years of schooling, sibs is number of siblings, meduc is mother's years of schooling, and feduc is father's years of schooling. (i) Does sibs have the expected effect? Explain. Holding meduc and feduc fixe
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Problem 1
Transcribed Image Text:ov Assumptions
ov Theorem
I artial Elect
Perfect Collinearity
ems
1 Using the data in GPA2 on 4,137 college students, the following equation was estimated by OLS:
colgpa
1.392
n = 4,137, R² = .273,
=
-
educ = 10.36
Opward Di
Variance Inflation Factor (VIF)
where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating
class (defined so that, for example, hsperc = 5 means the top 5% of the class), and sat is the combined
math and verbal scores on the student achievement test.
-
(i) Why does it make sense for the coefficient on hsperc to be negative?
(ii)
What is the predicted college GPA when hsperc = 20 and sat = 1,050?
(iii)
Suppose that two high school graduates, A and B, graduated in the same percentile from high
school, but Student A's SAT score was 140 points higher (about one standard deviation in the sam-
ple). What is the predicted difference in college GPA for these two students? Is the difference large?
Holding hsperc fixed, what difference in SAT scores leads to a predicted colgpa difference of
.50, or one-half of a grade point? Comment on your answer.
(iv)
2 The data in WAGE2 on working men was used to estimate the following equation:
.0135 hsperc +.00148 sat
n = 722, R² = .214,
.094 sibs+.131 meduc + .210 feduc
where educ is years of schooling, sibs is number of siblings, meduc is mother's years of schooling,
and feduc is father's years of schooling.
(i)
Does sibs have the expected effect? Explain. Holding meduc and feduc fixed, by how much does
sibs have to increase to reduce predicted
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