Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.2, Problem 21E
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 absorbence, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinke resistance angle was read from a graph in the paper “Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy” (Textile Res. J., 1999: 145–151).
| x | .115 | .126 | .183 | .246 | .282 | .344 | .355 | .452 | .491 | .554 | .651 |
| y | 334 | 342 | 355 | 363 | 365 | 372 | 381 | 392 | 400 | 412 | 420 |
Here is regression output from Minitab:
| Predictor | Coef | SE Coef | T | P |
| Constant | 321.878 | 2.483 | 129.64 | 0.000 |
| absorb | 156.711 | 6.464 | 24.24 | 0.000 |
| source | DF | SS | 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 appropriate? Explain.
- b. What wrinkle resistance angle would you predict for a fabric specimen having an absorbance of .300?
- c. What would be the estimate of expected wrinkle resistance angle when absorbance is .300?
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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