b. a. a. a. c. a. c. a. b.

23. For the exponential model, , which does depend on x. A similar result holds for the power model. 25. The z ratio for b 1 is highly significant, indicating that the like- lihood of a level being acceptable does decrease as the level increases. We estimate that for each 1 dBA increase in noise level, the odds of acceptability decreases by a factor of .70.

27. b.

52.88, .12 c. .895 d. No e. 48.54, 57.22 f. 42.85, 62.91

29. a. b.

c. Yes. from Minitab d. individual confidence levels 96: level 1 joint confidence 98 t 5 2 6.55, P-value 5 .003 R 2 5 .995 SSE 5 16.8, s 5 2.048 V Y|x 5 a 2 e 2bx s 2

55. a.

The dependent variable is , and the predictors are and ; . b. Now regress against and . c. 1.24, 5.78

57. k

R 2 adj. R 2 C k 1 .676 .647 138.2 2 .979 .975 2.7 3 .9819 .976 3.2 4 .9824 4 a. The model with b. No 59. The model with predictors x 1 , x 3 , and x 5 61. No. All R 2 values are much less than .9. 63. The impact of these two observations should be further investigated. Not entirely. The elimination of observation 6 followed by re-regressing should also be considered.

65. a.

The two distributions have similar amounts of variability, are both reasonably symmetric, and contain no outliers. The main difference is that the median of the crack values is about 840, whereas it is about 480 for the no-crack values. A 95 t CI for the difference between means is 132, 557. b. for the simple linear regression model, , but one standardized residual is Including an indicator for crack–no crack does not improve the fit, nor does including an indicator and interaction predictor.

67. a.

When gender, weight, and heart rate are held fixed, we esti- mate that the average change in VO 2 max associated with a 1-minute increase in walk time is . b. When weight, walk time, and heart rate are held fixed, the esti- mate of average difference between VO 2 max for males and females is .6566.

c. d.

.706 e. , so there does appear to be a useful relationship.

69. a.

No. There is substantial curvature in the scatter plot. b. Cubic regression yields and a 95 PI of 261.98, 295.62, and the cubic predictor appears to be important . A regression of y versus has , but there is a very large standardized resid- ual and the standardized residual plot is not satisfactory.

71. a.

. pH is a candi- date for deletion. Note that there is one extremely large standardized residual. b. , adjusted c. , don’t reject . The group of second-order predictors does not appear to be useful. d. , and now all six predictors are judged important the largest P-value for any t -ratio is .016; the importance of pH 2 was masked in the test of c. Note that there are two rather large standardized residuals. R 2 5 .871, f 5 28.50, P-value 5 .000 b 20 5 H : b 6 5 c 5 f 5 1.08, P-value . .10 R 2 5 .774, f 5 6.29, P-value 5 .002 R 2 5 .920 R 2 5 .802, f 5 21.03, P-value 5 .000 r 2 5 .991 lnx P-value 5 .001 R 2 5 .998 f 5 9.0 4.89 5 F .01,4,15 3.669, 2.519 2 .0996 2 4.11 P -value for model utility 5 0 r 2 5 .577 k 5 2 x 2 5 b x 1 5 a lnq .1815, aˆ 5 4.7836, qˆ 5 18.27 gˆ 5 bˆ 2 5 bˆ 5 bˆ 1 5 .9450, x 2 5 lnb x 1 5 lna lnq .671,3.706, .00498, ⫺.00135 e. 69.531, 76.186, 66.271, 79.446, using software

31. a.

.980 b. .747, much less than .977 for the cubic model. c. Yes, since . d. 6.31, 6.57, 6.06, 6.81

e. t ⫽ ⫺

5.6, P-value ⫽ 0

33. a.

.9671, .9407

b. c.

, so the cubic term should be deleted. d. Identical e. .987, .994, yes

35. 37. a.

4.9 b. When number of deliveries is held fixed, the average change in travel time associated with a 1-mile increase in distance traveled is .060 hr. When distance trav- eled is held fixed, the average change in travel time associ- ated with one extra delivery is .900 hr. c. .9861

39. a.

77.3 b. 40.4 41. , so P-value . The cho- sen model appears to be useful.

43. a.

48.31, 3.69 b. No. If x 1 increases, either x 3 or x 2 must change. c. Yes, since P -value d. Yes, using , since and P-value .

45. a.

, so there does appear to be a use- ful linear relationship between y and at least one of the predictors. b. .935 c. 9.095, 11.087

47. b.

, so conclude that the model is useful. c. , so reject ; garbage does appear to provide additional useful information. d. 1479.8, 1531.1, reasonable precision e. A 95 PI is 1435.7, 1575.2.

49. a. b .

, s o reject H and conclude that the model is useful. c. 78.28, 115.38 d. 38.50, 155.16 e. 46.91, 140.66 f. No. , so cannot be rejected.

51. a.

No b. . There does appear to be a useful linear relationship. c. 6.16, 3.304, 16.67, 31.91 d. , so cannot be rejected. The quad- ratic terms can be deleted. H : b 3 5 b 4 5 b 5 5 f 5 3.44 , 4.07 5 F .05,3,8 f 5 5.04 3.69 5 F .05,5,8 H : b 1 5 P -value 5 .208 f 5 14.9 8.02 5 F .05,2,9 96.8303, 25.8303 H : b 3 5 P -value 5 .034 .05 5 a P -value 5 .000 f 5 87.6, P-value 5 0 5 .003 t 5 3.496 a 5 .01 5 .001. f 5 18.924, , .001 f 5 24.4 . 5.12 5 F .001,6,30 yˆ 5 7.6883e .1799x2.0022x 2 t 5 2 , 3.182 5 t .025,3 .96034944 .0000492x 3 2 .000446058x 2 1 .007290688x 1 t 5 14.18, P-value 5 0 2 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

73. a.

, so the model appears useful. b.