Logistic Regression
1. In a town, the number of children located per household is thought to correlate to motherâ€™s BMI, income level and age. The following data was obtained:

Age BMI Income level Number of Children
23    22.5             2                         4
30    25.1             1                         6
36    28.5             3                         2
40    24.6             1                         8
42    30.1             2                         7
44    28.2             1                         10
50    26.1             3                         2

Income level Key: 1-poor, 2-middle class, 3-rich
Using the SPSS software, enter the data and apply a logistic regression to the above data.
Print the results and write a report interpreting the output and the meaning of the output with respect to the variables and their relationships.
2. Question taken from: Based on Rosner 13.58-61

Logistic Regression
Cardiovascular Disease (Based on Rosner 13.58-61): Sudden death is an important, lethal cardiovascular endpoint. Most previous studies of risk factors for sudden death have focused on men. Looking at this issue for women is important as well. For this purpose, data were used from the Framingham Heart Study.
Several potential risk factors, such as age, blood pressure and cigarette smoking are of interest and need to be controlled for simultaneously. Therefore a multiple logistic regression was fitted to these data as shown below. The response is 2-year incidence of sudden death in females without prior coronary heart disease.

Risk Factor             Regression Coefficient (bj)    Standard Error (se(bj))
Constant                         -15.3
Blood Pressure (mm Hg) .0019                               .0070
Weight (% of study mean) -.0060                               .0100
Cholesterol (mg/100 mL) .0056                               .0029
Glucose (mg/100 mL)       .0066                               .0038
Smoking (cigarettes/day) .0069                               .0199
Hematocrit (%)                   .111                               .049
Vital capacity (centiliters) - .0098                            .0036
Age (years)                         .0686                               .0225

(a) Assess the statistical significance of the individual risk factors and explain the practical implications of your findings.
(b) Give brief interpretations of the age and vital capacity coefficients.
(c) Compute the odds ratios relating the additional risk of sudden death associated with (i) a 100-centiliter decrease in vital capacity and (ii) an additional year of age after adjusting for the other risk factors.
(d) Provide 95% confidence intervals for the odds ratios in part (c)
(e) Predict the probability of sudden death for a 50 year old woman with systolic blood pressure of 120 mmHg, a relative weight of 100% a cholesterol level of 250 mg/100mL, a glucose level of 100mg/100mL, a hematocrit of 40%, and a vital capacity of 450 centiliters who smokes 10 cigarettes per day. (Note that these numbers are near average for a healthy woman except for the cholesterol level which is high, and of course the number of cigarettes smoked.)

3. A case-control study is performed to study the relationship between esophageal cancer and an exposure (exposure A). Esophageal cancer is a very rare disease (prevalence <<< 1%) in the general population.
The cases were 100 persons with the cancer of whom 30 had exposure A. The cases were a random sample of individuals with cancer in the population. The controls were 200 persons without the cancer of whom 18 had exposure A The controls were a random sample of individuals without cancer in the population. Fisher's exact test gave a p-value of .01. What is the estimated odds ratio of cancer for those who had exposure A relative to those who did not have exposure A?

4. Principal components examines and identifies the most important variables that have an effect on the outcome/response variable.
True /False

5. The diagonal line in the ROC analysis reflects 50:50 probability of sensitivity versus specificity.
True/false

6. The factor analysis explores the effect of factors on the dependent variables, while weighting the factors.
True/false

7. The use of cronbach's alpha is to assess reliability only.
True/False

8. Principal component analysis ranks the variables based on their percentage explanation of the variance.
True/false

9. In the poisson lambda is equal to np.
True/False

10. Hoteling's T can be converted into an F statistics.
True/False

11. The use of the covariance assesses interaction between multiple variables and the magnitude of any associated errors.
True /False

12. Mancova considers covariance without goodness of fit test.
True/false

13. The ROC method explores maximum ability to determine sensitivity vs specificity.
True/false

Logistic Regression 1. In a town, the number of children located p...