Department of Economics
Spring 2006
University of California
Prof. Woroch
Economics 140
MIDTERM #2 –
EXAM CODE #4
GENERAL INSTRUCTIONS
: Write your name,
your GSI’s name
and the above Exam Code
on
the front cover of two
blue books.
Mark one as “Blue Book #1” and the other as “Blue Book #2.”
Put Part I in blue book #1 and Part II in #2.
There is a total of 100 points with point assignments
given in the instructions for each part. You may want to make preliminary calculations on scratch
paper, but be sure to put all of your answers in the bluebook.
I.
AGREE, DISAGREE and EXPLAIN
: Choose 3 of the following 4 statements regarding a
research project involving regression analysis
. For each, decide whether you agree or disagree
with part or all of the statement and explain the reasoning behind your answer in a couple short
paragraphs
. Note that you may agree with part of the statement, but disagree with the rest.
Each question is worth 14 points for a total of 42.
1.
When estimating the demand for gasoline using data on consumption by state and by month, it
occurs to the researcher that weather conditions may be a significant explanatory variable. The
researcher should decide to include a measure of weather conditions if its coefficient estimate is
statistically significantly different from zero, or the R
2
increases as a result, or both.
An increase in R
2
is uninformative about whether the variable is a significant explanatory
variable because the R
2
always
increases when an additional variable is added to the model.
Looking at the adjusted R
2
is a valid way of comparing the restricted and unrestricted models
because, unlike the R
2
, the adjusted R
2
will decrease if variables that do not improve the fit are
added.
However, the test of statistical significance is typically preferred as the significance level
can be specified.
Because of this, I might exclude the weather variable if its coefficient is
insignificant but the adjusted R
2
is greater in the unrestricted model.
2.
Believing that advertising stimulates sales, a researcher regressed sales of breakfast cereal brands
against the amount spent on advertising by each brand.
If, in fact, the relationship between sales
and advertising was quadratic and not simply linear, then the coefficient on the researcher’s linear
regression will be biased, and is likely to be too small.
True.
If we don’t include the quadratic term then we have specified the functional form
incorrectly. In this case, the misspecification creates omitted variable bias in the parameter on the
linear term.
Let X
1
be the linear term and X
2
the quadratic term.
The OLS estimator of
β
1
in the
linear model can be expressed in terms of the population parameter and a bias term:
)
(
)
,
(
ˆ
1
2
1
2
1
1
X
Var
X
X
Cov
p
β
β
β
+
⎯→
⎯
The covariance between the linear and quadratic terms is positive as long as advertising spending
only takes on positive values.
β
2
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 Spring '08
 DUNCAN
 Economics, Regression Analysis, researcher

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