Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 14.2, Problem 29E
The article “The Undrained Strength of Some Thawed Permafrost Soils” (Canadian Geotechnical Journal [1979]: 420–427) contained the accompanying data on y = Shear strength of sandy soil (kPa), x1 = Depth (m), and x2 = Water content (%). The predicted values and residuals were calculated using the estimated regression equation
where
- a. Use the given information to calculate SSResid, SSTo, and SSRegr.
- b. Calculate R2 for this regression model. How would you interpret this value?
- c. Use the value of R2 from Part (b) and a 0.05 level of significance to carry out a model utility F test.
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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 + 0.100x3 -0.258x4 +0.496x5
₁², x₁ = x₂², and x5 = X1X2•
where x3 =
y
X1
14.7 8.8 31.4
48.0 36.5 26.9
25.6 36.9 25.8
x2
10.0 6.2 39.2
16.0 6.8 39.3
20.7
16.8 7.0 38.4
7.4 33.8
38.8 8.3 33.9
16.9 6.4
27.0 8.1 33.2
24.9 10.0
12.8
28.0
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…
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…
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…
Chapter 14 Solutions
Introduction To Statistics And Data Analysis
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Ch. 14.1 - Prob. 11ECh. 14.1 - A manufacturer of wood stoves collected data on y...Ch. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - State as much information as you can about the...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - The ability of ecologists to identify regions of...Ch. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - Prob. 28ECh. 14.2 - The article The Undrained Strength of Some Thawed...Ch. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - When Coastal power stations take in large amounts...Ch. 14.3 - Prob. 39ECh. 14.3 - The article first introduced in Exercise 14.28 of...Ch. 14.3 - Data from a random sample of 107 students taking a...Ch. 14.3 - Benevolence payments are monies collected by a...Ch. 14.3 - Prob. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Exercise 14.26 gave data on fish weight, length,...Ch. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - The article The Analysis and Selection of...Ch. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.4 - This exercise requires use of a statistical...Ch. 14.4 - Prob. 62ECh. 14 - Prob. 63CRCh. 14 - Prob. 64CRCh. 14 - The accompanying data on y = Glucose concentration...Ch. 14 - Much interest in management circles has focused on...Ch. 14 - Prob. 67CRCh. 14 - Prob. 68CRCh. 14 - Prob. 69CRCh. 14 - A study of pregnant grey seals resulted in n = 25...Ch. 14 - Prob. 71CRCh. 14 - Prob. 72CRCh. 14 - This exercise requires the use of a statistical...
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- The article "The Undrained Strength of Some Thawed Permafrost Soils"+ contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x₂ = depth (m) x₂= water content (%) The predicted values and residuals were computed using the estimated regression equation ŷ-140.14 13.15x₁ + 12.22x₂ + 0.070x3 -0.227x4 + 0.413x5 where x3 = x₁²₁x4x₂², and x = x1x2. y X1 14.7 8.8 31.6 48.0 36.7 27.1 x2 25.6 36.7 25.8 10.0 6.0 39.0 16.0 6.8 39.1 16.8 7.0 38.4 20.7 7.2 33.8 38.8 8.5 33.7 16.9 6.6 27.0 7.9 33.0 7.3 27.8 16.0 4.6 26.2 24.9 10.0 37.7 2.8 34.5 12.8 2.1 36.5 Predicted y 23.92 46.76 26.79 11.42 14.23 16.77 23.03 25.48 16.21 24.09 15.00 29.13 14.88 7.79 Residual -9.22 1.24 -1.19 -1.42 1.77 0.03 -2.33 13.32 0.69 2.91 1.00 -4.23 -7.58 5.01 (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…arrow_forwardA. Do these data provide sufficient evidence that there is a positive linear relationship between the two variables? B. What does R^2 imply? C. Using the regression model, predict the blood pressure level associated with a sound pressure of 7.5 decibels.arrow_forwardThe 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…arrow_forward
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