(Chapter Opener Revisited) In the discussion that introduced this chapter, we looked at a plot that displayed the relationship between the duration of an Old Faithful eruption and the time to its next eruption. The plot was based on data from January, 2003, which is displayed in the following table.
Duration d (seconds) | 110 | 147 | 174 | 231 | 243 | 273 |
Times to Next Eruption T (minutes) | 66 | 73 | 81 | 92 | 96 | 101 |
a. It is known that the time to the next Old Faithful eruption can be predicted using the duration of an eruption and an appropriate regression model.
Use the table of values to find the best-fitting linear model T(d) that gives the time (in minutes) to the next eruption based on the duration (in seconds) of an eruption.
b. Use your model to predict the time to the next eruption if an eruption lasted 90 seconds.
c. Use your model to predict the time to the next eruption if an eruption lasts 260 seconds.
d. Complete the following table by finding the times to next eruption predicted by your linear model in part (a) and the corresponding errors. (Round your predicted values to the nearest whole minute.)
Duration (seconds)
110
147
174
231
243
273
Times to Next Eruption (minutes)
66
73
81
92
96
101
Predicted Value T(d) (minutes)
Error (Actual-Predicted)
e. According to Ralph Taylor, who has logged and analyzed much of the Old Faithful data, in recent years there have been more eruptions lasting longer than 90 seconds and fewer eruptions of shorter duration. Therefore, most predictions are made using two different regression models–one for longer durations and one for shorter durations. (Adjustments are made for the very few durations that fall in between.) The following table gives the time to next eruption predicted in the Old Faithful Visitor Center (OFVC) Logbook for each of our data points. Complete the table to find the errors for the Logbook predictions.
Duration (seconds)
110
147
174
231
243
273
Times to Next Eruption (minutes)
66
73
81
92
96
101
Time Predicted in OFVC Logbook (minutes)
65
65
84
94
94
94
Error (Actual-Predicted)
f. Find the SSEs for your model and for the Logbook predictions. Based on the SSEs, which predictions are better? (Note that our model is based on a very small set of very linear data.)
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.