WebAssign for Devore's Probability and Statistics for Engineering and the Sciences, 9th Edition [Instant Access], Single-Term
9th Edition
ISBN: 9780357893104
Author: Devore; Jay L.
Publisher: Cengage Learning US
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Textbook Question
Chapter 12.2, Problem 22E
Calcium phosphate cement is gaining increasing attention for use in bone repair applications. The article “Short-Fibre Reinforcement of Calcium Phosphate Bone Cement” (J. of Engr. in Med., 2007: 203–211) reported on a study in which polypropylene fibers were used in an attempt to improve fracture behavior. The following data on x = fiber weight (%) and y = compressive strength (MPa) was provided by the article’s authors.
x | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 1.25 | 1.25 | 1.25 |
y | 9.94 | 11.67 | 11.00 | 13.44 | 9.20 | 9.92 | 9.79 | 10.99 | 11.32 |
x | 2.50 | 2.50 | 2.50 | 2.50 | 2.50 | 5.00 | 5.00 | 5.00 | 5.00 |
y | 12.29 | 8.69 | 9.91 | 10.45 | 10.25 | 7.89 | 7.61 | 8.07 | 9.04 |
x | 7.50 | 7.50 | 7.50 | 7.50 | 10.00 | 10.00 | 10.00 | 10.00 |
y | 6.63 | 6.43 | 7.03 | 7.63 | 7.35 | 6.94 | 7.02 | 7.67 |
- a. Fit the simple linear regression model to this data. Then determine the proportion of observed variation in strength that can be attributed to the model relationship between strength and fiber weight. Finally, obtain a point estimate of the standard deviation of e, the random deviation in the model equation.
- b. The average strength values for the six different levels of fiber weight are 11.05, 10.51, 10.32, 8.15, 6.93, and 7.24, respectively. The cited paper included a figure in which the average strength was regressed against fiber weight. Obtain the equation of this regression line and calculate the corresponding coefficient of determination. Explain the difference between the r2 value for this regression and the r2 value obtained in (a).
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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
WebAssign for Devore's Probability and Statistics for Engineering and the Sciences, 9th Edition [Instant Access], Single-Term
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