Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
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.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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 = -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…
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…
Chapter 14 Solutions
Introduction To Statistics And Data Analysis
Ch. 14.1 - Prob. 1ECh. 14.1 - The authors of the paper Weight-Bearing Activity...Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - The relationship between yield of maize (a type of...
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...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- A. 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) 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 particular article presented data on y = tar content (grains/100 ft³) of a gas stream as a function of x₁ = rotor speed (rev/min) and x₂ = gas inlet temperature (°F). The following regression model using X₁, X2, X3 = ×₂² and ×4 = X₁X₂ was suggested. (mean y value) = 86.5 – 0.121x₁ +5.07x2 - 0.0706x3 + 0.001x4 (a) According to this model, what is the mean y value (in grains/100 ft³) if x₁ = 3,400 and x₂ = 55. grains/100 ft³ (b) For this particular model, does it make sense to interpret the value of ₂ as the average change in tar content associated with a 1-degree increase in gas inlet temperature when rotor speed is held constant? Explain. Yes, since there are no other terms involving X2. O Yes, since there are other terms involving X₂. ● No, since there are other terms involving X2. O No, since there are no other terms involving X2.arrow_forward
- A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 0arrow_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_forwardIdentify two graphs used in a residual analysis to check the Assumptions 1–3 for regression inferences, and explain the reasoning behind their use.arrow_forward
- 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 9-145.41-14.24x, +12.70x₂ +0.079x,-0.236 +0.441x where x₂-x₂²x₂-x₂², and x ₁2 Y 14.7 *2 9.1 31.6 48.0 36.5 27.1 25.6 36.7 25.8 10.0 6.0 39.2 16.0 7.0 39.3 16.8 7.0 38.4 20.7 7.4 34.0 38.8 8.3 33.7 16.9 6.4 28.0 27.0 8.1 33.0 16.0 4.6 26.4 24.9 9.8 37.9 7.3 2.8 34.5 12.8 1.9 36.3 Predicted y Residual 23.83 47.07 26.46 10.77 14.57 16.88 23.38 25.07 16.23 24.31 15.06 28.64 15.08 8.15 -9.13 0.93 -0.86 -0.77 1.43 -0.08 -2.68 13.73 0.67 2.69 0.94 -3.74 -7.78 4.65 (a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.) SSTO- 1x |x SSResid- SSRegr - Ix (b) Calculate R² for this regression model. (Round your answer to three decimal places.) R²-X How would you…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 = −145.41 − 14.24x1 + 12.70x2 + 0.079x3 − 0.236x4 + 0.441x5 where x3 = x12, x4 = x22, and x5 = x1x2. y x1 x2 Predicted y Residual 14.7 9.0 31.6 23.83 −9.13 48.0 36.5 27.1 47.07 0.93 25.6 36.7 25.8 26.46 −0.86 10.0 6.0 39.2 10.77 −0.77 16.0 7.0 39.3 14.57 1.43 16.8 7.0 38.4 16.88 −0.08 20.7 7.4 34.0 23.38 −2.68 38.8 8.3 33.7 25.07 13.73 16.9 6.4 28.0 16.23 0.67 27.0 8.1 33.0 24.31 2.69 16.0 4.6 26.4 15.06 0.94 24.9 9.8 37.9 28.64 −3.74 7.3 2.8 34.5 15.08 −7.78 12.8 1.9 36.3 8.15 4.65 (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_forward1. Perform regression analysis based on linear and logarithmic regression models for normal stress data (x-axis) and peak shear stress (y-axis). Show the calculation in tabular form. Also determine the value of the correlation coefficient of the two data 2. Determine the best regression between the two models. Show the calculation in tabular form.arrow_forward
- A particular article presented data on y = tar content (grains/100 ft3) of a gas stream as a function of x1 = rotor speed (rev/min) and x2 = gas inlet temperature (°F). The following regression model using x1, x2, x3 = x22 and x4 = x1x2 was suggested. (mean y value) = 86.5 − 0.124x1 + 5.07x2 − 0.0708x3 + 0.001x4 a.) According to this model, what is the mean y value (in grains/100 ft3) if x1 = 3,200 and x2 = 55. grains/100 ft3arrow_forward1. Data was collected on 82 vehicles of different models to study the relationship between the weight of a vehicle (wt) and the miles per gallon (mpg) of the vehicle. The output from a regression analysis of the data is attached to the end of the sheet. a)Use the estimated linear regression model for predicting miles per gallon from weight to predict the miles per gallon for a vehicle with a weight of 40. b)Given that the mean weight of vehicles in the sample was 30.9, and that the corrected sum of squares (Sxx ) for weight was 5369., compute an interval estimate of the miles per gallon for an individual vehicle with a weight of 40. c) Here is a listing for a subset of the vehicle data: mpg wt 40.9 22.5 38.4 25.0 33.2 30.0 31.4 30.0 23.6 40.0 19.5 45.0 For this subset of the data, list the Y and X matrices that would be used in the matrix-based approach to regression for predicting miles per gallon from weight. Assume that the simple linear regression model yi = B0 +…arrow_forwardA researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 3.3 +12.7x Coefficients (Intercept) X Estimate Std. Error Test statistic O Ho: B₁: = 0 Ha: B₁ 0 O Ho: B₁ = 0 Ha: B₁ 0 12.7 2.2 6.4 1.5 1.98 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a positive linear relationship exists between x and y. 0.08 0.03arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY