Project: Eruptions of the "Old Faithful" Geyser
(Estimation of the time interval between eruptions)
A geyser is a hot spring that occasionally becomes unstable and erupts hot water and steam into the air. The “Old Faithful” geyser at Yellowstone National Park in Wyoming is probably the most famous geyser in the world. Visitors to the park try to arrive at the geyser site to see it erupts without waiting too long; the name of this geyser comes from the fact that eruptions follow a relatively stable pattern. The National Park Service erects a sign at the geyser site predicting when the next eruption will occur. Thus, it is of interest to understand and predict the interval time until the next eruption.
A sample of inter-eruption times was taken during August 1-8. The data set is saved in the file p_ysgr.dat which is an ASCII file, and the SPSS file is p_ysgr.sav. The first column of the data set is for date, the second column is eruption duration time (in minutes) and the third column is inter-eruption time (minutes). How can we help the tourists? Try some exploratory techniques such as histogram, boxplot, scatter plot, ..., to see if there is any pattern.
**** To read ASCII file, in SPSS, click on FILE and select Read Text Data and locate the data file. ****
A characteristic of the geyser is the duration of the previous
eruption. We could think of our data as pairs of the form (duration of
eruption, time until next eruption). Do you see two subgroups in this
data set? Do you see that a longer duration tends to be followed by a
longer time interval until the next eruption? J. S. Rinehart, in a 1969
paper in the Journal of Geophysical Research, provides a mechanism for this
pattern based on the temperature level of the water at the bottom of a geyser
tube at the time the water at the top reaches the boiling temperature.
That a shorter eruption would be followed by a shorter inter-eruption time (and
a longer eruption would be followed by a longer inter-eruption time) is also
consistent with Rinehart's model, since a short eruption is characterized by
having more water at the bottom of the geyser being heated short of boiling
temperature, and left in the tube. This water has been heated somewhat,
however, so it takes less time for the next eruption to occur. A long
eruption results in the tube being emptied, so the water must be heated from a
colder temperature, which takes longer.
Answer the following questions: