3. 1/3 points I Previous Answers My Notes Ask You Wrinkle recovery angle and ten

Question

3. 1/3 points I Previous Answers My Notes Ask You 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 xabsorbance and = 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 365372 392 400 412 420 Here is regression output from Minitab Predictor Constant absorb Coef 321.878 156.711 SE Coef 2.483 6.464 129.64 24.24 0.000 0.000 S 3.60498 R-Sq 98.5% R-Sq (adj) 98.3% = SOURCE Regression Residual Error Total MS DE 1 7639.0 7639.0587.81 0.000 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 pattern, and 98.5% O No, a scatter plot of the data shows a strong, linear pattern, and r -98.5%. O No, a scatter plot ofthe 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 0.255? (Round your answer to two decimal places.) (c) What would be the estimate of the expected wrinkle resistance angle when absorbance is 0.255? (Round your answer to two decimal places.)

Explanation / Answer

(b) Here absorbance = 0.255

The linear fitted line

y^ = 321.878 + 156.711 * absorabance

y^ = 321.878 + 156.711 * 0.255 = 361.84

HEre it may be calculated by linear line equation:

y^ = [(365 - 363)* (0.255 - 0.246)/ (0.282 - 0.246)] + 363 = 363.50

(c) Here the estimate of the expected wrinkle resistance angle when absorbance is 0.255 would be the same as predicted value

y^ = 361.84

{note : Please see the answer is the bold value]

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