The article Multiple Linear Regression for Lake Ice and Lake Temperature Characteristics (S. Gao and H. Stefan,
Question:
The article Multiple Linear Regression for Lake Ice and Lake Temperature Characteristics (S. Gao and H. Stefan, Journal of Cold Regions Engineering, 1999:5977) presents data on maximum ice thickness in mm (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 mm (x3) for 13 lakes in Minnesota. The data are presented in the following table.
a. Fit the model y = β0+β1x1+β2x2+β3x3+ε. For each coefficient, find the P-value for testing the null hypothesis that the coefficient is equal to 0.
b. If two lakes differ by 2 in the average number of days per year of ice cover, with other variables being equal, by how much would you expect their maximum ice thicknesses to differ?
c. Do lakes with greater average snow depth tend to have greater or lesser maximum ice thickness? Explain.
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