Department of Economics
W3412
Columbia University
Spring 2010
SOLUTION TO
Problem Set 4
Introduction to Econometrics
Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD
Spring 2010
1.
Use Table 2 to answer the following questions. Table 2 presents the results of four
regressions, one in each column.
Estimate the indicated regressions and fill in the values
(you may either handwrite or type the entries in; if you choose to type up the table, an
electronic copy of Table 2 in .doc format is available on the course Web site).
For example,
to fill in column (2), estimate the regression with colGPA as the dependent variable and
hsGPA and skipped as the independent variables, using the “robust” option, and fill in the
estimated coefficients
a)
Fill out the table with necessary numbers, some will be on STATA output some you will
need to calculate yourself.
b)
Common sense predicts that your high school GPA (hsGPA) and the number of classes
you skipped (skipped) are determinants of your college GPA (colGPA).
Use regression
(2) to test the hypothesis (at the 5% significance level) that the coefficients on these two
economic variables are all zero, against the alternative that at least one coefficient is
nonzero.
at least one coef. is nonzero
The pvalue for the Fstatistic =.00<.05, thus we reject
at the 5% significance level. We tend
to conclude at least one coefficient is nonzero.
c)
Find the Fstatistic for regression (3) and explain what is it testing?
The Fstatistic for regression (3) is 12.07; it is jointly testing whether all of the coefficients are
equal to 0, that is  if all the regressors jointly have no explanatory power.
d)
Find the Fstatistics for regression (4) and explain what is it testing?
The Fstatistic for regression (4) is 11.14 (this is not from the table); it is jointly testing whether
all of the coefficients are equal to 0, that is  if all the regressors jointly have no explanatory
power.
e)
Are bgfriend (whether you have a boy/girlfriend) and campus (whether you live on
campus) jointly significant determinants of college GPA? Use regression (2) and (4) to
test your hypothesis. (i.e. use homoskedasticityonly F stat formula, eq.7.14 in the book,
instead of directly testing with STATA)
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View Full Documentat least one coef. is nonzero
where
and
are obtained from regression (4) and (2) respectively; the number of
restrictions
is q
=2;
is the number of regressors in the unrestricted regression;
q
and
are degrees of freedom for the F distriction (here we perform nonrobust regressions).
F
(2, 135, α=0.05) =3.06>2.62, thus we cannot reject
at the 5% significance level. We tend to
conclude that
bgfriend
and
campus
jointly have no explanatory power. Alternatively, we can use
the Stata command: di fprob(2, 135, 2.62) to find the associated pvalue = .077>.05, again we
cannot reject
at the 5% significance level.
Table 1
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 Fall '11
 SeyhanArkonac
 Econometrics, Regression Analysis, Statistical hypothesis testing, significance level, colGPA

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