Use the dataset low

Use the dataset low

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 1. (10 points) Use the dataset low_birth_weight_infants.dta.

a. (1.5) Do a linear regression to model birth weight as the dependent variable and gestational age as the independent variable:

The equation is: bw=-932.40+70.31ga

The coefficient of determination is: 0.435517682

The p-value for the slope is: 8.15E-14

b. (2.5) Add length as another independent variable to the above regression model.

The equation is: _____________________

The coefficient of determination is: ______________________

The p-value for the gestage coefficient is: ___________________

The p-value for the length coefficient is: ___________________

Do you think the model improves by adding length as an independent variable (yes/no)

_____? Explain.

c. (2) Compute a 95% confidence interval for the true mean of birth weight with a gestational age of 31 weeks and a length of 40 cm. Round off to whole numbers.

d. (2) Create an interaction term by multiplying gestational age and length. Add the interaction term to the model that already includes gestage and length. Fill in the table (left column without interaction, right column with interaction term).

Independent variables

gestage, length

gestage, length, gestlength

p-value, gestage coefficient

Std error, gestage coefficient

p-value, length coefficient

Std error, length coefficient

Coefficient of determination

e. (1) What principle accounts for the changes in p-value and standard error?

f. (1) Since the coefficient of determination rose slightly, would you include the interaction

term in the model? Why or why not?

2. (8 points) Use the stenosis.dta or stenosis.xls file that you used in both Chapter 16 and

Chapter 20 homeworks.

a. (2) Generate two tables: one for smokers and another for nonsmokers.

b. (2) What is the odds ratio for developing stenosis for males relative to females

(smokers only)?

c. (2) What is the Mantel-Haenszel combined odds ratio for males developing stenosis

relative to females, combining both smokers and nonsmokers?

d. (2) Perform a logistic regression with stenosis as the outcome and sex and smoking

status as the explanatory variables. What is the equation?

3. (4 points) Looking at the following life table (WHO), estimate that probability that a 40-year

old will survive to age 80.

Liberia - 2006

both sexes

Age range

<1

1-4

5-9

10-14

15-19

20-24

25-29

30-34

35-39

40-44

45-49

50-54

55-59

60-64

65-69

70-74

75-79

80-84

85-89

90-94

95-99

100+

nMx

0.17631

0.02447

0.00541

0.00289

0.00330

0.00635

0.00835

0.01047

0.01316

0.01523

0.01704

0.02051

0.02761

0.03494

0.05052

0.07571

0.11134

0.16298

0.23262

0.32390

0.44023

0.88600

nqx

0.15694

0.09245

0.02669

0.01436

0.01636

0.03125

0.04089

0.05103

0.06370

0.07336

0.08170

0.09756

0.12914

0.16066

0.22428

0.31830

0.43550

0.57898

0.73541

0.82137

0.86632

1.00000

lx

100000

84306

76512

74470

73400

72199

69942

67082

63659

59604

55231

50719

45771

39860

33456

25953

17692

9987

4205

1113

199

27

ndx

15694

7794

2042

1070

1201

2256

2860

3423

4055

4373

4512

4948

5911

6404

7504

8261

7705

5782

3092

914

172

27

nLx

89014

318518

377454

369674

363997

355353

342562

326853

308158

287088

264875

241225

214078

183291

148522

109111

69198

35480

13293

2821

391

30

Tx

4420987

4331972

4013454

3636000

3266326

2902329

2546975

2204414

1877560

1569403

1282315

1017440

776215

562138

378847

230324

121213

52015

16535

3242

421

30

ex

44.2

51.4

52.5

48.8

44.5

40.2

36.4

32.9

29.5

26.3

23.2

20.1

17.0

14.1

11.3

8.9

6.9

5.2

3.9

2.9

2.1

1.1

4. (10 points) The data set pef.dta contains data from a German study published in 2007 in the

journal Pneumologie (61: 83-85). The English translation of the title is, “Improvement in

Expiratory Peak Flow (PEF) of COPD Patients due to “Lung” Sport for 12 Months.” The data

measures expiratory peak flow (PEF) from the lungs before and after 12 months. There were

seven patients in the aerobic exercise group (beforeex, afterex) and 10 patients in a control

group (beforecon and aftercon).

a. (2) Perform a sign test on the exercise group. The p-value of the two-sided test is:

________________.

b. (2) Perform a sign test on the control group. The p-value of the two-sided test is:

___________.

c. (2) Perform a Wilcoxon signed-rank test on the exercise group. The Z score is ______ and

the p-value is ___________________

d. (2) Perform a Wilcoxon signed-rank test on the control group. The Z score is ______ and

the p-value is ___________________. The conclusion is:

e. (2) Use the percviner column to test the difference in the % increase between the control group and the exercise group. Perform a Wilcoxon rank sum test for the hypothesis

test. The Z score is _____ and the p-value is _______________.

5. (10 points) A 2007 study of women in Miami (Brewer et al., Ann Epidemiol. 17:533-539) examined the link between HIV status and high-risk sexual activity. Eligible participants were

female, at least 18 years of age, English-speaking, self-reported having vaginal or anal sex in

the past 30 days, and self-reported having smoked crack or snorted or injected cocaine or

heroin in the last 30 days and having not been in drug treatment in the last 30 days. The

data set HIVrisk.dta contains two columns: risk for unprotected sex and HIV for HIV status.

Each woman knew her HIV status.

a. (2) What proportion of the women was HIV-positive? _____What proportion was

HIV-negative? _______

b. (2) What proportion engaged in unprotected sex (regardless of HIV-status)?

_____________

c. (2) What proportion of the HIV-positive group engaged in unprotected sex? Provide a

95% CI for the true proportion.____________; ____________________

d. (2) What proportion of the HIV-negative group engaged in unprotected sex? Provide

a 95% CI for the true proportion. _____________; ________________________

e. (2) Test the null hypothesis that the proportion of HIV-positive women having unprotected sex is equal to the proportion of HIV-negative women having unprotected sex

(group proportion comparison). Provide the p-value and state the conclusion.