1.) Using the assumption that Y = β0 + β1X1 + β2X2 + U,
a.) Derive the population regression function and state the necessary assumptions.
b.) What are β0, β1, β2, and U, in the above equation? What do they show? Explain.
c.) How can you estimate this population regression function using the Method of Mo-
ments? State the terms that will be data, and the terms that you will have to estimate,
and describe how the estimation process works, step by step for this equation. State the
population equations as well as the sample equations, explain how you reach them.
d.) How can you estimate this population regression function using the Ordinary Least
Squares? Describe how the estimation process works, in general.
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2.) Using the population equation below, we run a regression of wages on experience and
education, using a random sample of size 1000.
W age = β0 + β1Experience + β2Education + U
We know that wages are monthly wages measured in 1000 US dollars, experience shows years
of work experience, and education shows years of schooling. The estimation output for the
OLS estimates is provided below.
Using the given information, answer the following.
Table 1: Regression Output:
R Code: reg2< −lm(wage ∼ experience+education)
summary(reg2)
Coefficients
Intercept
experience
education
R2
Estimate
3.4012
0.0423
0.0824
0.0411
a.) What is β0? What does it show? Interpret this result using the measurement units
provided, in terms of this example (NOT in general).
b.) What is β1? What does it show? Interpret this result using the measurement units
provided, in terms of this example (NOT in general).
c.) What is β2? What does it show? Interpret this result using the measurement units
provided, in terms of this example (NOT in general).
d.) According to the results above, what would be the predicted wage for the individuals
with 10 years of experience and 5 years of schooling?
e.) What is the R2 value of the above regression? How can we interpret this value?./
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