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 =
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 =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
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 =
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