Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 8.2, Problem 1E
In an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft·lb (y) was measured for 22 welds at 0°C, along with the lateral expansion at the notch in % (x1), and the brittle fracture surface in % (x2). The data are presented in the following table.
- a. Fit the model y = β0 + β1x1 + ε. For each coefficient, test the null hypothesis that it is equal to 0.
- b. Fit the model y = β0 + β1x2 + ε. For each coefficient, test the null hypothesis that it is equal to 0.
- c. Fit the model y = β0 + β1x1 + β2x2 + ε. For each coefficient, test the null hypothesis that it is equal to 0.
- d. Which of the models in parts (a) through (c) is the best of the three? Why do you think so?
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In an experiment to determine factors related to weld toughness, the Charpy V-notch impact
toughness in ft - 1b (v) was measured for 22 welds at 0°Č, along with the lateral expansion
at the notch in % (x,), and the brittle fracture surface in % (x2). The data are presented in the
following table.
X1
X2
y
32
20.0
28
39
23.0
28
20
12.8
32
21
16.0
29
25
10.2
31
20
11.6
28
32
17.6
25
29
17.8
28
27
16.0
29
43
26.2
27
22
9.6
32
22
15.2
32
18
8.8
43
32
20.4
24
22
12.2
36
25
14.6
36
25
10.4
29
20
11.6
30
20
12.6
31
24
16.2
36
18
9.2
34
28
16.8
30
a. Fit the model y = Bo + B1 X1 + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
b. Fit the model y = Bo + B, xz + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
c. Fit the model y = Bo + B1 X1 + Bzx2 + ɛ. For each coefficient, test the null hypothesis
that it is equal to 0.
d. Which of the models in parts (a) through (c) is the best of the three? Why do you think
%3D
+ E.
so?
Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA,
which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets
having diameters smaller than 10 µm (mg/m³):
90 177 180 354 365 442 964
y 0.38 0.60 0.47 0.66 0.62 0.69 0.91
(a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy?
shows a reasonable linear relationship.
O No, a scatter plot does not show a reasonable linear relationship.
(b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.)
(c) The investigators were particularly interested in…
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
Ch. 8.1 - In an experiment to determine the factors...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - The article Application of Analysis of Variance to...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Refer to Exercise 7. a. Find a 95% confidence...Ch. 8.1 - In a study of the lung function of children, the...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - The following MINITAB output is for a multiple...Ch. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - The following data were collected in an experiment...Ch. 8.1 - The November 24, 2001, issue of The Economist...Ch. 8.1 - The article Multiple Linear Regression for Lake...Ch. 8.1 - Prob. 19ECh. 8.2 - In an experiment to determine factors related to...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.3 - True or false: a. For any set of data, there is...Ch. 8.3 - The article Experimental Design Approach for the...Ch. 8.3 - Prob. 3ECh. 8.3 - An engineer measures a dependent variable y and...Ch. 8.3 - Prob. 5ECh. 8.3 - The following MINITAB output is for a best subsets...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - (Continues Exercise 7 in Section 8.1.) To try to...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - The article Ultimate Load Analysis of Plate...Ch. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - The article Modeling Resilient Modulus and...Ch. 8.3 - The article Models for Assessing Hoisting Times of...Ch. 8 - The article Advances in Oxygen Equivalence...Ch. 8 - Prob. 2SECh. 8 - Prob. 3SECh. 8 - Prob. 4SECh. 8 - In a simulation of 30 mobile computer networks,...Ch. 8 - The data in Table SE6 (page 649) consist of yield...Ch. 8 - Prob. 7SECh. 8 - Prob. 8SECh. 8 - Refer to Exercise 2 in Section 8.2. a. Using each...Ch. 8 - Prob. 10SECh. 8 - The data presented in the following table give the...Ch. 8 - The article Enthalpies and Entropies of Transfer...Ch. 8 - Prob. 13SECh. 8 - Prob. 14SECh. 8 - The article Measurements of the Thermal...Ch. 8 - The article Electrical Impedance Variation with...Ch. 8 - The article Groundwater Electromagnetic Imaging in...Ch. 8 - Prob. 18SECh. 8 - Prob. 19SECh. 8 - Prob. 20SECh. 8 - Prob. 21SECh. 8 - Prob. 22SECh. 8 - The article Estimating Resource Requirements at...Ch. 8 - Prob. 24SE
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