The following table lists values measured for 60 consecutive eruptions of the geyser Old Faithful in Yellowstone National Park. They are the duration of the eruption (x1), the duration of the dormant period immediately before the eruption (x2), and the duration of the dormant period immediately after the eruption (y). All the times are in minutes.

a. Construct the multiple regression equation ̂y = b0 + b1x1 + b2x2.

b. Predict the duration of dormant period immediately after an eruption, if the duration of the eruption is 3.0 minutes and the duration of the dormant period immediately before the eruption is 70 minutes.

c. Refer to part (b). Construct a 95% confidence interval for the duration of the dormant period immediately following the eruption.

d. Refer to part (b). Construct a 95% prediction interval for the duration of the dormant period immediately following the eruption.

e. What percentage of the variation in the duration is explained by the model?

f. Is the model useful for prediction? Why or why not? Use the α = 0.01 level.
g. Test H0: β1 = 0 versus H1: β1 ≠ 0 at the α = 0.05 level. Can you reject H0? Repeat for β2.

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x1 *2 y x1 *2 y x1 x2 y x1 x2 y 3.5 80 84 1.8 42 91 4.7 88 51 4.1 70 79 4.1 84 50 4.1 91 51 1.8 51 80 3.7 79 2.3 50 93 1.8 51 79 4.6 80 49 3.8 60 86 768 60 4.7 93 55 3.2 79 53 1.9 49 82 3.4 86 71 1.7 55 76 1.9 53 82 3.5 82 75 4.0 71 67 4.9 76 58 4.6 82 51 4.0 75 73 2.3 67 81 1.7 58 74 2.0 51 76 3.7 73 67 4.4 81 76 4.6 74 75 4.5 76 82 3.7 67 68 4.1 76 83 3.4. 75 80 3.9 82 84 4.3 68 86 4.3 83 76 4.3 80 56 4.3 84 53 3.6 86 72 3.3 76 55 1.7 56 80 2.3 53 86 3.8 72 75 2.0 55 73 3.9 80 69 3.8 86 51 3.8 75 75 4.3 73 56 3.7 69 57 1.9 51 85 3.8 75 66 2.9 56 83 3.1 57 90 4.6 85 45 2.5 66 84 4.6 83 57 4.0 90 42 1.8 45 88 4.5 84 R 70 1.9 57 71