Question

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 Coef SE Coef T 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-Sq(adj) = 98.3%
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

(b) what wrinkle resistance angle would you predict for a fabric specimen having an absorbance of 0.370? (round your answer to two decimal places.

Answer 1

Rounded to two decimal places, the predicted wrinkle resistance angle for a fabric specimen with an absorbance of 0.370 is approximately 379.86

To predict the wrinkle resistance angle for a fabric specimen with an absorbance of 0.370, we can use the regression equation provided in the Minitab output. The equation is:

y = constant + absorb * x

where y represents the wrinkle resistance angle and x represents the absorbance.

From the Minitab output, we can see that the constant value is 321.878 and the coefficient for absorb is 156.711.

To find the predicted wrinkle resistance angle, we substitute the given absorbance value (0.370) into the equation:

y = 321.878 + 156.711 * 0.370

Calculating this expression gives us:

y = 321.878 + 57.97857

y ≈ 379.85657

Rounded to two decimal places, the predicted wrinkle resistance angle for a fabric specimen with an absorbance of 0.370 is approximately 379.86.