Icy lakes: Following are data on maximum ice thickness in millimeters (y), average number of days per year of ice cover (x1), average number of days the bottom temperature is lower than 8°C(x2), and the average snow depth in millimeters (x3) for 13 lakes in Minnesota.

a. Construct the multiple regression equation

b. Predict the ice thickness for a lake which is covered by ice an average of 140 days per year, the bottom temperature is less than 8°C an average of 190 days per year, and the average snow depth is 60 millimeters.

c. Refer to part (b). Construct a 95% confidence interval for the ice thickness.

d. Refer to part (b). Construct a 95% prediction interval for the ice thickness.

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

f. Is the model useful for prediction? Why or why not? Use the α = 0.05 level.
g. Test H0: β1 = 0 versus H1: β1 ≠ 0 at the α = 0.05 level. Can you reject H0? Repeat for β2 and β3.

Transcribed Image Text:

y I x2 X3 730 152 198 91 760 173 201 81 850 166 202 69 840 161 202 72 720 152 198 91 730 153 205 91 840 166 204 70 730 157 204 90 650 136 172 47 850 142 218 59 740 151 207 88 720 145 209 60 710 147 190 63