Hi, everyone. PS6 has been graded, and will be in your Littauer mailbox
Tuesday morning. Non-GovGrads should make an appointment to stop by to
pick up their solution sets soon (or in section Tuesday evening). On the
whole, these solutions were quite good, and most rewrites are quite minor.
Congratulations! I advise everyone to read the solution notes below,
especially problems 2 and 6, as PS6 forms the backbone of our multiple
linear regression work. Let me know if you have questions of any kind.
Cheers,
Ryan
Gov1000, PS6 Solution Notes
Problem 1. R^2 is the RegSS/TSS, not TSS/RegSS. Several papers stated
the latter relationship.
Problem 2. In a regression table, be sure to include coefficient
estimates, measures of uncertainty, and the number of observations or
degrees of freedom. R^2 and the standard error of the regression will
often be required as well. In either the table or a caption, describe the
dependent variable.
Visually, avoid unnecessary griding. Work to make your table as legible
and attractive as possible. Sometimes reviewers or readers will only look
at your tables and figures, so make them as informative as you can.
Presentation will be especially important on the final exam.
Problem 3. In part b), the regression of residuals on residuals yields
intercept zero because of the construction of the residuals themselves.
For those who need to rewrite this portion, think about how we define the
residuals' distribution in OLS, and submit a rewrite by email, if you
wish.
Problem 5. As Alison noted in section, showing that the terms are 1x1
does not justify the simplification Fox writes out. It is necessary, but
not sufficient. See section notes for details on how to ensure equality,
not just conformability.
Problem 6. I required a very particular sort of interpretation of
regression coefficients on Problems 3 and 7 of Problem Set 4. Because of
that, I am a bit more lenient here with what constitutes "interpreting the
coefficients". I strongly recommend that you review the interpretations
required in PS4, and ask if you have any questions at all. These
interpretations centered around describing the conditional expectation of
y for x=0 (the intercept), and of y for changes in x (the bivariate
slope), both in the appropriate units of x and y. Similar interpretations
are appropriate for this problem, as they will be for final exams and
papers. In Part b), these interpretations should have at least some sort
of "controlling for the other x's" statement. To make such a statement
more precise, see the interpretations of problem 3 on this Problem Set.
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Ryan T. Moore ~ Government & Social Policy
Ph.D. Candidate ~ Harvard University
Homepage:
http://www.people.fas.harvard.edu/~rtmoore/
Gov1000:
http://www.courses.fas.harvard.edu/~gov1000/