The article "The Undrained Strength of Some Thawed Permafrost Soils"† contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x1 = depth (m) x2 = 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 where x3 = x12, x4 = x22, and x5 = x1x2. y x1 x2 Predicted y 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) Calculate R2 for this regression model. (Round your answer to three decimal places.) R2 = (c) Use the value of R2 from part (b) and a 0.05 level of significance to carry out a model utility F test. Calculate the test statistic and calculate the P-value. (Round your answer to two decimal places.) F = P-value =

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 92E

Related questions

Question

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

where x₃ = x₁², x₄ = x₂², and x₅ = x₁x₂.

y	x₁	x₂	Predicted y	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)

Calculate R² for this regression model. (Round your answer to three decimal places.)

R² =

(c)

Use the value of R² from part (b) and a 0.05 level of significance to carry out a model utility F test.

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

F =

P-value =

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 1 images