S470/670 Mini-project 1: House prices and population growth solution

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Description

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The researcher’s major research question is: How have house prices in U.S. states changed
over the last few decades, and are changes in prices are related to population in some
way? This question may be difficult to answer, at least straight away. So she has brainstormed a
series of questions he would like you to address, which can be divided into groups:
1. House prices over time: How have house prices in the U.S changed since 1975, after
adjusting for inflation (i.e. relative to the CPI?) How have changes in prices varied by state?
Which states have seen the biggest increases in real house prices, and which have seen the
biggest decreases? Have changes in prices within each state mostly followed the same basic
pattern, and are there outliers to that pattern? Do the typical patterns vary between the
four regions (Northeast, Midwest, South, and West)?
2. Population density and changes in house prices: Does present-day population density
explain changes in house prices by state since 1975? Are there outliers to the relationship,
and if so, is there a principled reason to drop them? What does the relationship look like
after dropping or downweighting outliers? Does the relationship vary by region? If so, how?
3. Changes in population and changes in house prices: Is there a relationship between
changes in population and changes in house prices? To answer this, look at changes in each
state over three time periods: 1990 to 2000, 2000 to 2010, and 2010 to the present. Analyze
the three time periods separately. Has the relationship changed over the three time periods?
Are there variations by region?
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4. Conclusion: What does all of this tell you about the relationship between house prices and
population? Is there a plausible cause-and-effect story you can tell that’s consistent with the
data and with common sense?
Data
• Freddie Mac House Price Index (http://www.freddiemac.com/research/indices/
house-price-index.html): This tracks the average house price in each state (plus Washington, D.C. and a national average) since 1975. For each state, the index value is fixed at
100 in December 2000. Figures are seasonally-adjusted but not adjusted for inflation. The
data is in the spreadsheet State and US SA.xls.
• state abbrevs.txt (on Canvas): This contains the names, the two-letter code, and the
Census region (Northeast, Midwest, South, or Midwest) for each state in the U.S.
• Consumer Price Index, on Canvas in cpi.csv. This tracks how prices in general have
changed in the U.S. The data in the spreadsheet is the “All Urban Consumers (Current
Series),” seasonally adjusted, from www.bls.gov/cpi/data.htm.
• Census Data: You’ll need to get population data for each state in 2018, 2010, 2000, and
1990 from the Census and American Community Survey. We recommend you do this using the tidycensus R package. See https://walkerke.github.io/tidycensus/articles/
basic-usage.html for a description of how to use the package.
To use the package, you’ll need a Census Data API key. To sign up for one, enter your email
at https://api.census.gov/data/key_signup.html and they’ll send you a key (you’ll have
to wait a few minutes for it to activate.) The main population variable is P001001 in the
2010 and 2000 Censuses, and P0010001 in the 1990 Census. If you can’t get the data this
way, you can always get it directly from data.census.gov.
What to submit
Your submission should consist of:
• A report (PDF preferred) of no more than eight pages, excluding appendices. The report
should have the following sections:
– Executive summary stating your main findings (Note: Do NOT include this executive
summary in your initial submission, as you should only write it when you’re nearly
finished.)
– House prices over time
– Population density and changes in house prices
– Changes in population and changes in house prices
– Conclusions
• A .Rmd or other file containing your code.
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• Any other supplementary files required to reproduce your work.
We will give you feedback, then, working alone or in a pair, you will make a final submission
by a date to be announced. The grade for your final submission will be the one that counts.
Some constraints:
• The researcher is familiar with elementary methods like linear models, but not with nonparametric methods such as loess and gam. That means that if you want to use those more
fancy models, you need to briefly describe what those techniques are doing in words that a
non-statistician can understand.
• She is comfortable with transformations, but they would have to be interpretable.
• She took her statistics course from a lecturer who was highly skeptical about P-values, so any
P-values you show must be accompanied by a justification of why the P-value is necessary.
• She wants to be able to reproduce your work if required, but doesn’t want to see R code in
the main report.
• She is red-green colorblind.
Notes
• There is no one objectively right answer to the project, but there are many subjectively bad
answers.
• Make sure you justify your answers to the questions (don’t just state answers.)
• You do not necessarily need one overall model that describes all the data.
• Because there’s no correct model, you’re free to use multiple models for the same data and
question, if you feel that’s a good use of your time and page count.
• A large fraction of the points are for communication, so maintain a decent level of professionalism.
• Graphs must be big enough to be readable if the report were printed out.
• Additional technical graphs such as residual plots can be included in an appendix, which will
not count toward the page limit and which we might not bother to read. Submit your code
as a separate file. Also upload any additional sources required to reproduce your work.
• The best reports tell a clear story. Pay attention to the structure of your report and make
sure that you leave the reader with a clear idea of your answers to the questions.
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Grading
• House prices over time: 5 points
• Population density and changes in house prices: 5 points
• Changes in population and changes in house prices: 10 points
• Communication (including executive summary and conclusion): 10 points. Full credit for
communication requires a readable, informative, comprehensive, clearly labeled set of graphs,
and a comprehensible write-up with few glaring spelling and grammatical errors that makes
the main points of the analysis clear.
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