14.1

1. 0.083.
2. 12.

14.3 Odds for private: 0.364; odds for public: 3.61.

14.5 Log odds for private: −1.011; log odds for public: 1.284.

14.7 Private: log(odds)=−1.011+2.295x; the odds ratio is 0.101.

14.9 e0.855=2.3154.

14.1

1. 543/1200.
2. 0.826.
3. 657/1200.
4. 1.21.
5. They are inverses of each other.

14.3 0.11, 0.24, 0.43, 0.67, 1,00, 1.50, 2.33, 4.00, and 9.00. The the odds increase with p and the plot is curved.

14.5

1. The log odds of cell phone use is a linear function of the indicator variable for age.
2. The regression coefficient is the log of the odds ratio.

14.7

1. The intercept is the log odds of an event when x=0.
2. The log odds of an event are the log of the probability of the event divided by 1 – the probability of the event.
3. The log odds of an event increase by 3.

14.9

1. 0.7166.
2. 0.7517.
3. 0.9178.

14.11

1. b0=−2.5083 and b1=0.1933.
2. The fitted model is log(odds)=−2.5083+0.1933x.
3. The odds ratio is 1.21.
4. The relative risk was 1.19, which is very close to the odds ratio.

14.13

1. log(odds)=−6.76382+4.41058x.
2. The 95% confidence interval is (4.17, 4.65).
3. H0:   β1=0, Ha:   β1≠0. The null corresponds to the probability of being rejected for service due to lack of teeth was not related to age. z=36.0053 and P-value<0.0001. This is overwhelming evidence that the probability of being rejected for service in the Spanish–American War depended on age.

14.15

1. Odds ratio=82.3172.
2. (64.7468, 104.65572).
3. Recruits over 40 were about 82.3 times more likely to be rejected for service due to bad teeth than recruits younger than 20.

14.17

1. Tested with a X2 test.
2. The log is normally distributed.
3. Two-sided alternative.
4. We do need to worry about intercorrelations.

14.19

1. G=9413.210, P-value<0.0005.
2. (5.5941, 9.2247), (13.5793, 22.1399), (27.5384, 44.7252), (41.3094, 66.8606), (64.7449, 104.65879).
3. H0:   βi=0, Ha:   βi≠0. Z=15.45, 22.82, 28.76, 32.25, 36. In all cases, P-value≈0.

14.21 (2.1096, 4.1080).

14.23

1. log(odds)=β0+β1x.
2. β1 is the average change in log(odds) of using the cell phone to ask for advice on a purchase for each year older the person is.
3. The model assumes the probability of using the cell phone to ask for advice on a purchase depends on age and that the change in log(odds) is a linear function of age.

14.25 Use stress to predict exergame. Students with stress were more likely to be exergamers, OR=1.62, 95% CI is (1.23, 2.15), X2=11.24, P=0.008.

14.27 e−2.56×e1.125(x+1)e−2.56×e1.125x=e1.125(x+1) − 1.125x=e1.125(x+1−x)=e1.125.

14.29

1. log(odds)=0.2009−0.0674team. 95% Confidence Interval of Odds Ratio : (0.426, 1.795).
2. log(odds)=0.3493+0.0694team−0.4168 shot. 95% Confidence Interval of Odds Ratio : (0.525, 2.512).
3. Answers will vary.

14.31

1. From software: The fitted model is log(odds)=−3.892+0.4157x, where x=1 for Hospital A and 0 for Hospital B. z=−1.47 or X2=2.16, P-value=0.1420. There is not enough evidence to show a significant difference in the percentage of deaths between the two hospitals. The odds ratio is 1.515, a 95% confidence interval yields (0.870, 2.639), which includes 1.
2. From software, the fitted model is log(odds)=−3.109−0.1320hospital−1.266condition. For hospital, the odds ratio is 0.876, the 95% confidence interval is (0.479, 1.602). Note that this also includes 1.
3. In either case, the Hospital effect tests insignificant, though we can see Simpson’s paradox in the odds ratios.

14.33

1. X2=30.652(df=3), P-value=0.000.
2. log(odds)=−7.759+0.1695HSM+0.5113HSS+0.1925HSE. 95% confidence intervals are (−0.1936, 0.5326), (0.0334, 0.9892), and (−0.2202, 0.6052).
3. Only the coefficient of HSS is significant.

14.35

1. X2=18.7174(df=3); P-value=0.0003.
2. X2=9.3738(df=2); P-value=0.0092.
3. For modeling the odds of HIGPA, both high school grades and SAT scores are useful.

14.37 All three models are significant, but the only significant predictor variable in any of the models is LOpening; thus, the best model is with LOpening alone.