Homework Assignment 1: What’s That Got to
Do with the Price of Condos in California?
36-402, Advanced Data Analysis
Due at the start of class, Tuesday, 18 January 2011
The Census Bureau divides the country up into “tracts” of approximately
equal population. For the 1990 Census, California was divided into 20640 tracts.
One of the standard data sets (housing on lib.stat.cmu.edu; accompanying
this problem set) records the following for each tract in California: Median house
price, median house age, total number of rooms, total number of bedrooms, total
number of occupants, total number of houses, median income (in thousands of
dollars), latitude and longitude.
Do not give raw computer output as your main answer to any question; do
include R code in an appendix. Do not report numbers to more significant digits
than is warranted. Remember that providing a clear and reasonable justification
of your answers is at least as important as getting the answer right.
1. (10 points) Make a plot of median house prices over space (i.e., a map).
The xaxis should be longitude and the yaxis latitude; show price either
as a zaxis in a 3D plot, or by color or grey-scale intensity; make sure the
results are legible when printed out before turning the assignment in.
2. (20 points) Use the lm command to linearly regress price on all the other
variables. Report the coefficients, R2, and the mean squared error. Ex-
plain, in words, what the estimated coefficients mean.
3. (20 points) Which variables seem most important? Why? Do they make
sense?
4. (10 points) Use a Q−Qplot to check if your residuals have a Gaussian
distribution. Do they?
Extra credit (10 points): find and apply an appropriate formal test of
normality to the residuals.
5. (10 points) Make a map of your residuals. Do they look uniform over
space? Should they? If they are not uniform, where, geographically, does
the regression tend to over-predict prices, and where does it under-predict?
6. (20 points) For each input variable, make a scatter plot of the features vs.
residuals. Add a kernel smoothing curve to each scatter plot. (See the
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