Economics 122B
Midterm 1
October 27, 209
Page 1 of 7
This is a closed book exam, except that you can have one 2sided sheet of notes.
Please
be sure to put your name and UCI ID# in the upper right corner of each sheet you
turn in, and don’t staple your sheets together since we will be scanning them.
Please completely fill out the Rapid Return Cover sheet – including your assigned
seat number.
Do not leave the exam room until you have turned in your exam and
your name has been checked off the class roster by the instructor or TA
.
Do not
write your answers on this exam –put them on separate sheets of paper.
Please use
black or dark blue ink or pencil.
Be sure to show your work for partial credit.
There
are 100 points possible, and the points for each subquestion are in parenthesis at the
beginning of the question.
PART 1 (50 points)
1.. (8 points) Suppose that instead of fitting the regression model
i
ii
YX
αβ
µ
=
++
, you
instead fit the model
i
YZ
γδ
ε
=
where
10 2
ZX
=
+
. How are the leastsquares
estimators ˆ
γ
and
ˆ
δ
for this second model related to the corresponding LS estimators
ˆ
α
and
ˆ
β
of the linear model? (In other words, obtain ˆ
and
ˆ
as a function of ˆ
and
ˆ
).
2. (12 points) Using a random sample of 670 individuals for the population of people in
the workforce in 1976, we want to estimate the impact of education on wages. Let wage
denote hourly wage in 1976 U.S. dollars and let
educ
denote years of schooling. We
obtain the following OLS regression line:
wage = 0.54 + 0.54educ
. How do you interpret
the slope of this regression line? What is the expected difference in the hourly wage
between a worker that finished four years of college and a worker with finished high
school? What is the predicted wage for a person with one year of education? Does that
make sense? If it is not, what is the name of this problem in econometrics? How do we
deal with it?
3. (30 points) Suppose you are interested in the effect of skipping classes on college GPA,
and collect a sample of economic variables from 400 college students to analyze the
problem. Included in your data are college GPA on a fourpoint scale (COLGPA), high
school GPA on a fourpoint scale (HSGPA), achievement test score (ATS), and the
average number of Economics 122B lectures missed per week (SKIP). Running a
regression of the dependent variable COLGPA on the other explanatory variables
including a constant (and homoskedastic errors) yields:
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Midterm 1
October 27, 209
Page 2 of 7
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 Spring '10
 DAVIDBROWNSTONE
 Economics, Regression Analysis, Variance, Null Hypothesis Summary, Statistic Fstatistic Chisquare, dependent var S.D.

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