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 16.52x₁ + 13.83x₂ + 0.100x3 -0.258x4 + 0.496x5 and x5 = X₁X₂ y = -156.50 where x3 = x₁², x4 = X₂², y X1 14.7 8.8 48.0 36.5 26.9 25.6 36.9 25.8 16.0 6.8 16.8 x2 10.0 6.2 39.2 31.4 39.3 7.0 38.4 20.7 7.4 33.8 38.8 8.3 33.9 16.9 6.4 28.0 24.9 10.0 12.8 27.0 8.1 33.2 16.0 4.4 26.2 37.9 7.3 2.8 34.7 1.9 36.5 Predicted y 22.86 46.10 27.38 11.23 13.47 16.80 23.55 25.24 15.75 24.47 15.19 29.93 15.51 8.00 Residual -8.16 1.90 -1.78 -1.23 2.53 0.00 -2.85 13.56 1.15 2.53 0.81 -5.03 -8.21 4.80 (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 = How would you interpret this value? O The value R² gives the percentage of observed variation in water content that can be explained by the fitted model. O The value R² gives the percentage of observed variation in shear strength of sandy soil that can be explained by the fitted model. O The value R² gives the percentage of water content values in the sample that are equal to the values predicted by the model. O The value R² gives the percentage of shear strength of sandy soil values in the sample that are equal to the values predicted by the model (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. (Round your answer to two decimal places.) F = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? O Reject Ho. We do not have convincing evidence that the multiple regression model is useful. O Fail to reject Ho. We have convincing evidence that the multiple regression model is useful. O Reject H. We have convincing evidence that the multiple regression model is useful. O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful.
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 16.52x₁ + 13.83x₂ + 0.100x3 -0.258x4 + 0.496x5 and x5 = X₁X₂ y = -156.50 where x3 = x₁², x4 = X₂², y X1 14.7 8.8 48.0 36.5 26.9 25.6 36.9 25.8 16.0 6.8 16.8 x2 10.0 6.2 39.2 31.4 39.3 7.0 38.4 20.7 7.4 33.8 38.8 8.3 33.9 16.9 6.4 28.0 24.9 10.0 12.8 27.0 8.1 33.2 16.0 4.4 26.2 37.9 7.3 2.8 34.7 1.9 36.5 Predicted y 22.86 46.10 27.38 11.23 13.47 16.80 23.55 25.24 15.75 24.47 15.19 29.93 15.51 8.00 Residual -8.16 1.90 -1.78 -1.23 2.53 0.00 -2.85 13.56 1.15 2.53 0.81 -5.03 -8.21 4.80 (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 = How would you interpret this value? O The value R² gives the percentage of observed variation in water content that can be explained by the fitted model. O The value R² gives the percentage of observed variation in shear strength of sandy soil that can be explained by the fitted model. O The value R² gives the percentage of water content values in the sample that are equal to the values predicted by the model. O The value R² gives the percentage of shear strength of sandy soil values in the sample that are equal to the values predicted by the model (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. (Round your answer to two decimal places.) F = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? O Reject Ho. We do not have convincing evidence that the multiple regression model is useful. O Fail to reject Ho. We have convincing evidence that the multiple regression model is useful. O Reject H. We have convincing evidence that the multiple regression model is useful. O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful.
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
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Transcribed Image Text: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
y = -156.50
16.52x₁ + 13.83x₂ + 0.100x30.258x4 + 0.496x5
X1 = X
X4
where X3
y
₂², and x5 = X₁X2
14.7 8.8 31.4
X1
48.0 36.5 26.9
X2
25.6 36.9 25.8
10.0 6.2 39.2
16.0 6.8 39.3
16.8 7.0 38.4
20.7 7.4 33.8
38.8 8.3 33.9
16.9 6.4 28.0
27.0 8.1 33.2
7.3
16.0 4.4 26.2
12.8
24.9 10.0 37.9
SSResid =
SSRegr =
2.8 34.7
1.9 36.5
Predicted y
22.86
46.10
27.38
11.23
13.47
16.80
23.55
25.24
15.75
24.47
15.19
29.93
15.51
8.00
Residual
-8.16
1.90
-1.78
-1.23
2.53
0.00
-2.85
13.56
1.15
2.53
0.81
-5.03
-8.21
4.80
(a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.)
SSTO =
(b) Calculate R² for this regression model. (Round your answer to three decimal places.)
R² =
How would you interpret this value?
O The value R² gives the percentage of observed variation in water content that can be explained by the fitted model.
O The value R² gives the percentage of observed variation in shear strength of sandy soil that can be explained by the fitted model.
O The value R² gives the percentage of water content values in the sample that are equal to the values predicted by the model.
O The value R² gives the percentage of shear strength of sandy soil values in the sample that are equal to the values predicted by the model.
(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. (Round your answer to two decimal places.)
F =
Use technology to calculate the P-value. (Round your answer to four decimal places.)
P-value =
What can you conclude?
O Reject Ho. We do not have convincing evidence that the multiple regression model is useful.
O Fail to reject Ho. We have convincing evidence that the multiple regression model is useful.
O Reject Ho. We have convincing evidence that the multiple regression model is useful.
O Fail to reject Ho. We do not have convincing evidence that the multiple regression model is useful.
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