The following associations can be described by generalized linear models.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

QUESTION 1

The following associations can be described by generalized linear models. For each one, identify the response variable and the explanatory variables, select a probability distribution for the response (justifying your choice) and write down the linear component.

(a) The effect of age, sex, height, mean daily food intake and mean daily energy expenditure on a person's weight. (3) (b) The proportions of laboratory mice that became infected after exposure to bacteria when five different exposure levels are used and 20 mice are exposed at each level. (3)

(c) The association between the number of trips per week to the supermarket for a household and the number of people in the household, the household income and the distance to the supermarket.

QUESTION 2

(a) For a negative binomial random variable Y~ NBin(r, q), find E(Y) and var(Y).

(b) Notice that for a random variable Y following the Poisson distribution E(Y) = var(Y), for a random variable Y following the binomial distribution E(Y) > var(Y) and for a random variable Y following the negative binomial distribution, E(Y) < var(Y). How might these, results affect your choice of a model?

QUESTION 3

Show that the following probability density functions belong to the exponential family:

(a) Pareto distribution with probability density function f(y; 0) = 0yo-1

(b) Exponential distribution probability density function f(y; 0) = 0e-

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