Open and run the (data) script file geyser.asc to create the data set GEYSER. It gives the characteristics of 222 eruptions of the "Old Faithful Geyser" during August 1978 and 1979. The first column gives the duration (in minutes) of the eruption and the second column gives the time until the following eruption (in minutes). Make sure that the S-Plus object you use has 222 rows and 2 columns.

1. Perform a least squares linear regression of the second column on the first one and assess the significance (or lack thereof) of the regression. Give an interpretation to your results.

2. Perform several kernel regressions (say 5) using the normal kernel and varying values for the bandwidth in order to see the two extreme regimes (very small bandwidths and very large bandwidths) discussed in the text. Choose the value of the bandwidth which you find most reasonable, and compare the resulting regression curve to the result of part 2.