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Due Friday, January 26.
Turn in all of the following problems.
- Problem 1:
- For simple linear regression, show that . This fact has an interesting geometric
interpretation, and will be proven later using matrix methods.
- Problem 2:
- The data frame faithful in the library
MASS has 272 observations on two paired variables,
eruptions and waiting. A value of
eruptions represents the duration (in minutes) of an
eruption of the Old Faithful geyser, and the corresponding value of
waiting gives the waiting time until the next eruption.
Suppose that the an eruption of duration 4 minutes and 30 seconds
has just been observed. Compute a 95% prediction interval for the
waiting time until the next eruption. What assumptions are needed
to justify this interval? Can you think of any likely violations of
these assumptions? Do residual plots reveal anything?
- # 1.9 (this can be done by hand if you wish), 1.10,
Thu Apr 18 15:52:37 EDT 1996