Department of Economics
Spring 2011
University of California
Prof. Woroch
Economics 140:
Problem Set 3
SUGGESTED SOLUTIONS
True/False/Uncertain and Explain.
1.
A researcher should go ahead and add a new regressor whenever adding it to the regression
model increases the adjusted
2
R
because that measure of goodness of fit corrects for the fact
that the usual
2
R
will always increase with inclusion of an additional variable.
False. Economic theory should be our guide when specifying which variables enter into the
population regression.
2
R
measures the linear relationship between dependent variable and
independent variables, but does not imply a causal relationship.
It is true that usual
2
R
will
always increase with inclusion of an additional variable, and so looking instead at the value of
the adjusted
2
R
will help identify the inclusion of irrelevant explanatory variables, but it not the
criterion to include a variable.
2.
A researcher is worried about multicollinearity in a multivariate regression model because the
correlation coefficient between two regressors,
2
X
and
3
X
, is equal to 0.89.
Her solution is to
drop one of the regressors,
3
X
,
expecting that the t stat value on the other remaining regressor,
2
X
, will get much larger.
True. Dropping one of the two collinear variables will remove the main symptom of
multicollinearity which is large standard errors of the individual regressors.
Accordingly, the
standard error on the remaining regressor will greatly diminish and so have a much larger t stat.
But keep in mind that, while dropping the regressor will have this effect, it is not advisable if
economic principles dictate that both variables should be in the regression.
3.
If you reject a joint null hypothesis using the
F
test in a multivariate linear regression model,
then you will reject the null hypotheses that each of the coefficients is equal to zero by
performing individual ttests on them.
False.
The size of the one at a time ttest is not the same as the size of the Ftest at a given
significance level.
If the tstatistics are correlated, the Ftest may reject the null hypothesis when
one or more of the ttest does not reject the null hypothesis.
MultiPart Questions.
1.
The Excel spreadsheet wages.xls contains data from a survey of 526 U.S. workers in 1976. The
dataset includes information on each worker’s age, hourly wage, years working for their current
employer (tenure), years of education, gender, and marital status.
a)
Estimate the following model using linear regression:
i
i
i
u
X
Y
1
1
0
(1)
where
i
Y
is the wage,
i
X
1
is the age, and
i
indexes the
i
= 1,
. . .,
526 workers.
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 Spring '08
 DUNCAN
 Economics, Econometrics, Regression Analysis, Null hypothesis, Statistical hypothesis testing, Los Angeles Dodgers

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