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 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". 0.115 0.126 0.183 0.245 0.282 0.344 0.355 0.452 0.491 0.554 0.651 yl 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Coef SE Coef Constant 321.878 2.483 129.64 0.000 absorb 156.711 6.464 24.24 0.000 S- 3.60498 R-Sg - 98.5 R-Sq (adj) - 98.34 SOURCE DF MS Regression 7639.0 7639.0 0.000 587.81 9 Residual Error Total 117.0 13.0 10 7756.0 (a) Does the simple linear regression model appear to be appropriate? Explain. O Yes, a scatter plot of the data shows a strong, linear pattern, and - 98.5%. O Yes, a scatter plot of the data shows a weak, linear patterm, and - 98.5%. O No, a scatter plot of the data shows a strong, linear pattern, and - 98.5%. O No, a scatter plot of the data shows a weak, non-linear pattern, and - 98.5%. (b) What wrinkle resistance angle would you predict for a fabric specimen having an absorbance of 0.220? (Round your answer to two decimal places.) (c) What would be the estimate of the expected wrinkle resistance angle when absorbance is 0.220? (Round your answer to two decimal places.)
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 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". 0.115 0.126 0.183 0.245 0.282 0.344 0.355 0.452 0.491 0.554 0.651 yl 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Coef SE Coef Constant 321.878 2.483 129.64 0.000 absorb 156.711 6.464 24.24 0.000 S- 3.60498 R-Sg - 98.5 R-Sq (adj) - 98.34 SOURCE DF MS Regression 7639.0 7639.0 0.000 587.81 9 Residual Error Total 117.0 13.0 10 7756.0 (a) Does the simple linear regression model appear to be appropriate? Explain. O Yes, a scatter plot of the data shows a strong, linear pattern, and - 98.5%. O Yes, a scatter plot of the data shows a weak, linear patterm, and - 98.5%. O No, a scatter plot of the data shows a strong, linear pattern, and - 98.5%. O No, a scatter plot of the data shows a weak, non-linear pattern, and - 98.5%. (b) What wrinkle resistance angle would you predict for a fabric specimen having an absorbance of 0.220? (Round your answer to two decimal places.) (c) What would be the estimate of the expected wrinkle resistance angle when absorbance is 0.220? (Round your answer to two decimal places.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Related questions
Question
Transcribed Image Text: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 appropriate? Explain.
O Yes, a scatter plot of the data shows a strong, linear pattern, and r2 = 98.5%.
O Yes, a scatter plot of the data shows a weak, linear pattern, and r2 = 98.5%.
O No, a scatter plot of the data shows a strong, linear pattern, and r = 98.5%.
O No, a scatter plot of the data shows a weak, non-linear pattern, and r = 98.5%.
(b) What wrinkle resistance angle would you predict for a fabric specimen having an absorbance of 0.220? (Round your answer to two decimal places.)
(c) What would be the estimate of the expected wrinkle resistance angle when absorbance is 0.220? (Round your answer to two decimal places.)
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