The article "The Undrained Strength of Some Thawed Permafrost Soils"† contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x 1 = depth (m) x 2 = water content (%)The predicted values and residuals were computed using the estimated regression equation ŷ = −152.62 − 16.16x1 + 13.58x2 + 0.091x3 − 0.255x4 + 0.492x5 wherex 3 =x 1 2,x 4 =x 2 2, andx 5 =x 1 x 2. y x 1 x 2 Predictedy Residual 14.7 8.8 31.6 23.49 −8.79 48.0 36.5 27.1 46.32 1.68 25.6 36.7 26.0 27.19 −1.59 10.0 6.2 39.0 11.43 −1.43 16.0 7.0 39.3 13.92 2.08 16.8 6.8 38.4 15.63 1.17 20.7 7.4 33.8 23.50 −2.80 38.8 8.3 33.7 25.16 13.64 16.9 6.4 27.8 15.64 1.26 27.0 8.1 33.2 24.52 2.48 16.0 4.6 26.4 15.49 0.51 24.9 10.0 37.9 29.72 −4.82 7.3 3.0 34.7 15.15 −7.85 12.8 2.1 36.3 8.34 4.46 (a) Use the given information to calculate SSResid, SSTo, and SSRegr. (Round your answers to four decimal places.) SSTo=SSResid=SSRegr= (b) CalculateR 2 for this regression model. (Round your answer to three decimal places.) R 2 = (c) Use the value ofR 2 from part (b) and a 0.05 level of significance to carry out a model utilityF test. Calculate the test statistic and calculate the P-value. (Round your answer to two decimal places.) F = P-value =

The article "The Undrained Strength of Some Thawed Permafrost Soils"† contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x 1 = depth (m) x 2 = water content (%)...

The article "The Undrained Strength of Some Thawed Permafrost Soils"† contained the accompanying data on the following.

The predicted values and residuals were computed using the estimated regression equation

ŷ = −152.62 − 16.16x₁ + 13.58x₂ + 0.091x₃ − 0.255x₄ + 0.492x₅

wherex
₃ =x
₁
²,x
₄ =x
₂
², andx
₅ =x
₁
x
₂.

y	x ₁	x ₂	Predictedy	Residual
14.7	8.8	31.6	23.49	−8.79
48.0	36.5	27.1	46.32	1.68
25.6	36.7	26.0	27.19	−1.59
10.0	6.2	39.0	11.43	−1.43
16.0	7.0	39.3	13.92	2.08
16.8	6.8	38.4	15.63	1.17
20.7	7.4	33.8	23.50	−2.80
38.8	8.3	33.7	25.16	13.64
16.9	6.4	27.8	15.64	1.26
27.0	8.1	33.2	24.52	2.48
16.0	4.6	26.4	15.49	0.51
24.9	10.0	37.9	29.72	−4.82
7.3	3.0	34.7	15.15	−7.85
12.8	2.1	36.3	8.34	4.46

(a)

Use the given information to calculate SSResid, SSTo, and SSRegr. (Round your answers to four decimal places.)

SSTo=SSResid=SSRegr=

(b)

CalculateR
² for this regression model. (Round your answer to three decimal places.)

R
² =

(c)

Use the value ofR
² from part (b) and a 0.05 level of significance to carry out a model utilityF test.

Calculate the test statistic and calculate the P-value. (Round your answer to two decimal places.)

F =

P-value =

Jun 09, 2022