Homework Assignment 3: Old Heteroskedastic
36-402, Data Analysis, Spring 2011
Due at the start of class, 1 February 2011
The data set geyser in the library MASS contains a series of consecutive ob-
servations on the “Old Faithful” geyser at Yellowstone National Park, famed for
the approximate regularity of its eruptions. There are two columns: duration,
the length of the latest eruption of the geyser (in minutes), and waiting, the
interval from the end of one eruption to the start of the next (also in minutes).
Begin by obtaining the library (if you don’t have it already) and loading the
data set. You should be able to reproduce this:
> summary(geyser)
waiting duration
Min. : 43.00 Min. :0.8333
1st Qu.: 59.00 1st Qu.:2.0000
Median : 76.00 Median :4.0000
Mean : 72.31 Mean :3.4608
3rd Qu.: 83.00 3rd Qu.:4.3833
Max. :108.00 Max. :5.4500
1. (5 points) Linearly regress waiting on duration. Plot the data points,
together with the regression line. Comment (briefly) on any noteworthy
features of the plot.
2. (5 points) Plot the squared residuals from the linear regression versus
duration. Comment.
3. (20 points) Using the method presented in the notes to the lecture for
25 January, estimate the variance as a function of duration. Add it to
the plot from the previous problem. Does the estimated variance function
seem compatible with homoskedastic noise?
4. (10 points) Re-do the linear regression with weighted least squares, mak-
ing the weights inversely proportional to the estimated variance function.
What happens to the linear regression coefficients? Are the changes sta-
tistically significant? Does it seem like they matter?
5. (5 points) Do a nonparametric kernel regression of waiting on duration.
Plot the results along with the raw data. Comment on how the results
differ from the linear regression.
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