Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.3, Problem 33E
During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. The article “Composition Optimization of High-Strength Steels for Sulfide Cracking Resistance Improvement” (Corrosion Science, 2009: 2878–2884) reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line).
| x | 635 | 644 | 711 | 708 | 836 | 820 | 810 | 870 | 856 | 923 | 878 | 937 | 948 |
| y | 100 | 93 | 88 | 84 | 77 | 75 | 74 | 63 | 57 | 55 | 47 | 43 | 38 |
- a. What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables?
- b. Compute the estimated standard deviation
- c. Calculate a confidence interval using confidence level 95% for the expected change in stress associated with a 1 MPa increase in strength. Does it appear that this true average change has been precisely estimated?
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Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle
resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with
Infrared Spectroscopy".†
x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651
y 334 342 355 363
365 372 381 392
400 412 420
Here is regression output from Minitab:
Predictor
Constant
absorb
S = 3.60498
Coef
321.878
156.711
SOURCE
Regression
Residual Error
Total
SE Coef
2.483
6.464
R-Sq = 98.5%
DF
1
9
10
SS
7639.0
117.0
7756.0
T
129.64
24.24
0.000
0.000
R-Sq (adj) = 98.3%
MS
7639.0
13.0
F
P
587.81
(a) Does the simple linear regression model appear to be…
Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical
strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t
半
0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651
334 342
355
363
365
372
381
392
400
412
420
Here is regression output from Minitab:
Predictor
Coef
SE Coef
P
Constant
321.878
2.483
129.64
0.000
absorb
156.711
6.464
24.24
0.000
S = 3.60498
R-Sq = 98.5%
R-Są (adj) - 98.3%
SOURCE
DF
MS
F
P
Regression
1
7639.0
7639.0
587.81
0.000
Residual Error
9
117.0
13.0
Total
10
7756.0
(a) Does the simple linear regression model appear to be…
Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as
determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and
y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t
x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651
y
334 342 355
363
365 372 381
400
392
412 420
Here is regression output from Minitab:
Predictor
Constant
absorb
S = 3.60498
Coef
321.878
156.711
SOURCE
Regression
Residual Error
Total
R-Sq= 98.5%
DF
SE Coef
2.483
6.464
1
9
10
SS
7639.0
117.0
7756..0
T
129.64
24.24
P
0.000
0.000.
R-Sq (adj) 98.3%
MS
7639.0
13.0
F
587.81
(a) Does the simple linear regression model appear to be appropriate?…
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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