Stat 537: Statistics for Research 1
Simple Regression Homework
The time between eruptions of Old Faithful geyser
in Yellowstone National Park is random but related
to the duration of the last eruption. The table to the
right shows these times for 21 consecutive
eruptions. Let us see how we can predict time to
the next eruption. (You can find an Excel file
containing these data here. Remember that JMP
opens Excel files.)
a. Make a scatter plot of Next versus Last.
Does the relationship appear linear?
b. Fit a least squares regression line
c. Analyze the residuals of the model in
(b) to determine if the model is
adequate. Do you find any outliers
or influential observations?
d. What proportion of the variability in Next is accounted for by Last? Is Last a good predictor
of Next?
e. Calculate the mean square error estimates of σ.
f.
Calculate a 95% prediction of the time to the next eruption if the last eruption lasted 3
minutes.
g. Calculate a 95% confidence interval for the mean time to the next eruption for a last
eruption lasting 3 minutes. Compare this confidence interval with the prediction obtained in
(e).
h. Repeat (e) if the last eruption lasted 1 minute. Do you think this prediction is reliable? Why
or why not?