PROBABILITY & STATS FOR ENGINEERING &SCI
9th Edition
ISBN: 9781285099804
Author: DEVORE
Publisher: CENGAGE L
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Chapter 13.4, Problem 44E
The accompanying Minitab regression output is based on data that appeared in the article “Application of Design of Experiments for Modeling Surface Roughness in Ultrasonic Vibration Turning” (J. of Engr. Manuf., 2009: 641–652). The response variable is surface roughness (μm), and the independent variables are vibration amplitude (μm), depth of cut (μm), feed rate (mm/rev), and cutting speed (m/min), respectively.
- a. How many observations were there in the data set?
- b. Interpret the coefficient of multiple determination.
- c. Carry out a test of hypotheses to decide if the model specifies a useful relationship between the response variable and at least one of the predictors.
- d. Interpret the number 18.2602 that appears in the Coef column.
- e. At significance level .10, can any single one of the predictors be eliminated from the model provided that all of the other predictors are retained?
- f. The estimated SD of
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removing fluids are used in machining operations to cool
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concern to OSHA, which has recently lowered substantially
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and y = the extent of mist droplets having diameters smaller
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89 177 189 354 362 442 965
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a. The investigators performed a simple linear regres-
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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…
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…
Chapter 13 Solutions
PROBABILITY & STATS FOR ENGINEERING &SCI
Ch. 13.1 - Suppose the variables x = commuting distance and y...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - As the air temperature drops, river water becomes...Ch. 13.1 - The accompanying scatterplot is based on data...Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Consider the following four (x, y) data sets; the...Ch. 13.1 - a. Show that i=1nei=0 when the eis are the...
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - If there is at least one x value at which more...Ch. 13.2 - No tortilla chip aficionado likes soggy chips, so...Ch. 13.2 - Polyester fiber ropes are increasingly being used...Ch. 13.2 - The following data on mass rate of burning x and...Ch. 13.2 - Failures in aircraft gas turbine engines due to...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Mineral mining is one of the most important...Ch. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Kyphosis refers to severe forward flexion of the...Ch. 13.2 - Prob. 25ECh. 13.3 - The following data on y 5 glucose concentration...Ch. 13.3 - The viscosity (y) of an oil was measured by a cone...Ch. 13.3 - Prob. 29ECh. 13.3 - The accompanying data was extracted from the...Ch. 13.3 - The accompanying data on y 5 energy output (W) and...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The following data resulted from an experiment to...Ch. 13.3 - The article The Respiration in Air and in Water of...Ch. 13.4 - Cardiorespiratory fitness is widely recognized as...Ch. 13.4 - A trucking company considered a multiple...Ch. 13.4 - Let y = wear life of a bearing, x1 = oil...Ch. 13.4 - Let y = sales at a fast-food outlet (1000s of ),...Ch. 13.4 - The article cited in Exercise 49 of Chapter 7 gave...Ch. 13.4 - The article A Study of Factors Affecting the Human...Ch. 13.4 - An investigation of a die-casting process resulted...Ch. 13.4 - Prob. 43ECh. 13.4 - The accompanying Minitab regression output is...Ch. 13.4 - The article Analysis of the Modeling Methodologies...Ch. 13.4 - A regression analysis carried out to relate y =...Ch. 13.4 - Efficient design of certain types of municipal...Ch. 13.4 - An experiment to investigate the effects of a new...Ch. 13.4 - Prob. 49ECh. 13.4 - Prob. 50ECh. 13.4 - The article Optimization of Surface Roughness in...Ch. 13.4 - Utilization of sucrose as a carbon source for the...Ch. 13.4 - Prob. 53ECh. 13.4 - Prob. 54ECh. 13.5 - The article The Influence of Honing Process...Ch. 13.5 - Prob. 56ECh. 13.5 - In the accompanying table, we give the smallest...Ch. 13.5 - Prob. 58ECh. 13.5 - Prob. 59ECh. 13.5 - Pillar stability is a most important factor to...Ch. 13.5 - Prob. 61ECh. 13.5 - Prob. 62ECh. 13.5 - Prob. 63ECh. 13.5 - Prob. 64ECh. 13 - Curing concrete is known to be vulnerable to shock...Ch. 13 - Prob. 66SECh. 13 - The article Validation of the Rockport Fitness...Ch. 13 - Feature recognition from surface models of...Ch. 13 - Air pressure (psi) and temperature (F) were...Ch. 13 - An aeronautical engineering student carried out an...Ch. 13 - An ammonia bath is the one most widely used for...Ch. 13 - The article An Experimental Study of Resistance...Ch. 13 - The accompanying data on x = frequency (MHz) and y...Ch. 13 - Prob. 74SECh. 13 - Prob. 75SECh. 13 - The article Chemithermomechanical Pulp from Mixed...Ch. 13 - Prob. 77SECh. 13 - Prob. 78SECh. 13 - Prob. 79SECh. 13 - Prob. 80SECh. 13 - Prob. 81SECh. 13 - Prob. 82SECh. 13 - Prob. 83SE
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