1. You use a random sample of 1,002 individuals and estimate the following
OLS model
����! = 10.6 + 1.2 ∗ ��ℎ������
Where wage is measured in dollars per hour and schooling is measured in the
number of years of education. You have also calculated TSS = 8,000 and SER
= 2.00.
a. If a person increases the number of years of schooling by 4 years,
what is the predicted effect on their wage?
b. The sample average for years of schooling is 12. What is the sample
average for wage?
c. The sample covariance for wage and schooling is 2.15. What is the
sample standard deviation for years of schooling?
d. What is the R2?
e. If the education variable is in months of schooling rather than years
(assume a year of schooling is 12 months), what are R2, SER and �!?
2. You are interested in the effect of household income on the amount of
mortgage debt held. You collect a random sample and use OLS to estimate
the following model
����!
= 1.0
(1.2)
+ 0.25
(0.10)
×������!, �! = 0.34, ��� = 425.00
where Debt is mortgage debt in one hundred thousands and Income is
measured as total annual household income in ten thousands.
a. What is your conclusion regarding the effect household income on
mortgage debt?
b. On average, how much mortgage debt will a household with \$100,000
of annual income have?
3. Use the CA test scores data on Cougars Courses. Provide the STATA output
along with your answers to the following questions.
a. You are asked by the Department of Education to determine the effect
of subsidized lunch on student achievement. What is your conclusion
regarding the effect of the percentage of students qualifying for
reduced-price lunch on average test scores?
b. Do you believe your results are useful for policy (can you use the
results to suggest a change that may improve test scores)? Why, or
why not?
c. Interpret the R2 from your regression.