Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 8.3, Problem 14E
a.
To determine
Construct a multiple linear regression model
Plot the residuals versus fitted line plot for the obtained model.
Check whether the model is appropriate.
b.
To determine
Construct a multiple linear regression model
Plot the residuals versus fitted line plot for the obtained model.
Check whether the model is appropriate.
c.
To determine
Find the predicted value of y when
d.
To determine
Explain whether the model used in part (c) is improved by including an interaction term.
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a.
Fit the linear model y = Bo + B1x + ɛ. For each coefficient, test the hypothesis that the
coefficient is equal to 0.
b. Fit the quadratic model y = Bo + Bịx + B2x² + ɛ. For each coefficient, test the hypothesis
that the coefficient is equal to 0.
%3D
Fit the cubic model y = Bo + B1x +
B2x? + B3x + E. For each coefficient, test the
C.
hypothesis that the coefficient is equal to 0.
d.
Which of the models in parts (a)…
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…
Chapter 8 Solutions
Statistics for Engineers and Scientists
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