Eruptions of the Old Faithful geyser in Yellowstone National Park typically last from 1.5 to 5 minutes. Between eruptions are dormant periods, which typically last from 50 to 100 minutes. A dormant period can also be thought of as the waiting time between eruptions. The durations in minutes for 60 consecutive dormant periods are given in the following table. It is desired to predict the length of a dormant period from the length of the dormant period immediately preceding it. To express this in symbols, denote the sequence of dormant periods T₁, . . . , T₆₀. It is desired to predict T_i+1from T_i.

a. Construct a scatterplot of the points (T_i, T_i+1), for i = 1, . . . , 59.

b. Compute the least-squares line for predicting T_i+1 from T_i. T₁, . . . , T₅₉, and the values of the dependent variable (y) are T₂, . . . , T₆₀.)

c. Find a 95% confidence interval for the slope β₁.

d. If the waiting time before the last eruption was 70 minutes, what is the predicted waiting time before the next eruption?

e. Find a 98% confidence interval for the mean waiting time before the next eruption when the time before the last eruption was 70 minutes.

f. Find a 99% prediction interval for the waiting time before the next eruption, if the time before the last eruption was 70 minutes.

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