The article Multiple Linear Regression for Lake Ice and Lake Temperature Characteristics

Chapter 8, Problem 18

(choose chapter or problem)

The article “Multiple Linear Regression for Lake Ice and Lake Temperature Characteristics” (S. Gao and H. Stefan, Journal of Cold Regions Engineering, 1999:59–77) presents data on maximum ice thickness in mm \((y)\), average number of days per year of ice cover \(\left(x_{1}\right)\), average number of days the bottom temperature is lower than \(8^{\circ} \mathrm{C}\) \(\left(x_{2}\right)\), and the average snow depth in mm \(\left(x_{3}\right)\) for 13 lakes in Minnesota. The data are presented in the following table.

y	\(\left(x_{1}\right)\)	\(\left(x_{2}\right)\)	\(\left(x_{3}\right)\)	y	\(\left(x_{1}\right)\)	\(\left(x_{2}\right)\)	\(\left(x_{3}\right)\)
730	152	198	91	730	157	204	90
760	173	201	81	650	136	172	47
850	166	202	69	850	142	218	59
84	161	202	72	740	151	207	88
720	152	198	91	720	145	209	60
730	153	205	91	710	147	190	63
840	166	204	70

a. Fit the model \(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\varepsilon\). 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.

Equation Transcription:

Text Transcription:

(y)

(x_1)

8^{o}C

(x_2)

(x_3)

(x_1)

(x_2)

(x_3)

(x_1)

(x_2)