Consider a binary logistic regression model using the following predictors:

age (years), sex, race (white, African-American, Hispanic, Oriental, other), blood pressure (mmHg). The fitted model is given by logit Prob[Y = 1|X] = Xβˆ = −1.36 + .03(race = African-American)

− .04(race = hispanic) + .05(race = oriental) − .06(race = other)

+ .07|blood pressure − 110| + .3(sex = male) − .1age + .002age2 +

(sex = male)[.05age − .003age2].

a. Compute the predicted logit (log odds) that Y = 1 for a 50-year-old female Hispanic with a blood pressure of 90 mmHg. Also compute the odds that Y = 1 (Prob[Y = 1]/Prob[Y = 0]) and the estimated probability that Y = 1.

b. Estimate odds ratios for each nonwhite race compared with the reference group (white), holding all other predictors constant. Why can you estimate the relative effect of race for all types of subjects without specifying their characteristics?

c. Compute the odds ratio for a blood pressure of 120 mmHg compared with a blood pressure of 105, holding age first to 30 years and then to 40 years.

d. Compute the odds ratio for a blood pressure of 120 mmHg compared with a blood pressure of 105, all other variables held to unspecified constants. Why is this relative effect meaningful without knowing the subject’s age, race, or sex?

e. Compute the estimated risk difference in changing blood pressure from 105 mmHg to 120 mmHg, first for age = 30 then for age = 40, for a white female. Why does the risk difference depend on age?

f. Compute the relative odds for males compared with females, for age = 50 and other variables held constant.

g. Same as the previous question but for females : males instead of males

: females.

h. Compute the odds ratio resulting from increasing age from 50 to 55 for males, and then for females, other variables held constant. What is wrong with the following question: What is the relative effect of changing age by one year?