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 = -152.59 - 16.12x₁ + 13.55x₂ + 0.092x3-0.255x4 + 0.493x5 where x3 = x₁²₁x₁ = x₂², and x5 = X₁X₂¹ y X1 14.7 8.8 31.4 F= x2 48.0 36.5 26.9 25.6 36.7 25.8 10.0 6.0 39.0 16.0 7.0 39.1 16.8 7.0 38.4 20.7 7.4 33.8 38.8 8.3 33.7 16.9 6.6 27.8 27.0 7.9 33.2 16.0 4.6 26.4 7.3 24.9 9.8 37.7 12.8 2.8 34.5 2.1 36.3 Predicted y 23.41 46.39 27.12 10.61 14.63 16.54 23.65 25.40 15.46 24.39 15.39 29.46 15.09 7.96 Residual -8.71 1.61 -1.52 -0.61 1.37 0.26 -2.95 13.40 1.44 2.61 0.61 -4.56 -7.79 4.84 (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? 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 observed variation in water content that can be explained by the fitted 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.) Use technology to calculate the P-value. (Round your answer to four decimal places.) 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 y = -152.59 - 16.12x₁ + 13.55x₂ + 0.092x3-0.255x4 + 0.493x5 where x3 = x₁²₁x₁ = x₂², and x5 = X₁X₂¹ y X1 14.7 8.8 31.4 F= x2 48.0 36.5 26.9 25.6 36.7 25.8 10.0 6.0 39.0 16.0 7.0 39.1 16.8 7.0 38.4 20.7 7.4 33.8 38.8 8.3 33.7 16.9 6.6 27.8 27.0 7.9 33.2 16.0 4.6 26.4 7.3 24.9 9.8 37.7 12.8 2.8 34.5 2.1 36.3 Predicted y 23.41 46.39 27.12 10.61 14.63 16.54 23.65 25.40 15.46 24.39 15.39 29.46 15.09 7.96 Residual -8.71 1.61 -1.52 -0.61 1.37 0.26 -2.95 13.40 1.44 2.61 0.61 -4.56 -7.79 4.84 (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? 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 observed variation in water content that can be explained by the fitted 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.) Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value =
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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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 = -152.59 - 16.12x₁ + 13.55x₂ +0.092x3 -0.255x4 + 0.493x5
2
x3 = x₁²₁x₁ = x₂², and x5 = X₁X₂
X
where X3
y
88
14.7 8.8 31.4
48.0 36.5
10.0 6.0
16.0
X1
25.6 36.7 25.8
16.8
x2
38.8 8.3
16.0
16.9 6.6
26.9
20.7 7.4 33.8
7.3
7.0 39.1
12.8
39.0
7.0 38.4
27.0 7.9 33.2
33.7
27.8
24.9 9.8 37.7
4.6 26.4
2.8 34.5
2.1 36.3
Predicted y Residual
23.41
46.39
27.12
10.61
14.63
16.54
23.65
25.40
15.46
24.39
15.39
29.46
15.09
7.96
-8.71
1.61
-1.52
-0.61
1.37
0.26
-2.95
13.40
1.44
2.61
0.61
-4.56
-7.79
4.84
(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?
● 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 observed variation in water content that can be explained by the fitted 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 =
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