Answer Happy

Exercise 6.4
The accurate prediction of the timing of earthquakes is an
important
undertaking in the interests of public safety. In this exercise,
we
explore a regression model approach to this problem.
The first column of Table 6.32 shows the month and year of
all
earthquakes measuring 3.5 or larger on the Richter scale on a
small
island in the Pacific Ocean between December, 1990 and
November,
1997. The dates in first column of the table are con
verted to a ''month number" in the second column of the table
starting
with December, 1990 being month number 0. Thus, for example,
October, 1991 is month number 10, since this month is 10 months
after
December, 1990. The data in Table 6.32 is reproduced in the
spreadsheet
EARTHQUAKE.xls.
We might postulate that the time to the next earthquake might be
a
function of the number of months after the most recent
earthquake, as
well as the number of months after the second-most-recent
earthquake.
These numbers are shown in the third and fourth columns of Table
6.32.
For example, consider the earthquake that occurred in May, 1995.
The
most recent earthquake prior to that time was in February, 1995,
and so
the number of months after the most recent earthquake would be
3
months. Also, the number of months after the
second-most-recent
earthquake is 11 months, as the second-most-recent earthquake
took
place in June, 1994.
(a) Construct a regression model to predict the time when
earthquakes
occur based on the data in Table 6.32.
(b) What is the R2 of your regression model? Given the very
imperfect nature of earthquake prediction, do you consider this
value
of R2 to be high or low?
(c) Evaluate the validity of your regression model. Do the
regression
coefficients pass the significance test? Is there evidence
of
autocorrelation?
(d) Construct a smaller regression model based on your answers
to
part (c) and test the validity of this smaller model to ensure
that it
passes all evaluation tests.