When conducting a binary regression with a skewed predictor, it is often easiest to assess the need for

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

STAT 

1. For logistic regression with one predictor, we use the model 

log θ(x) = β

1 − θ(x)  + β1x

(a) Show that solving for the probability of success for a given value of the predictor, θ(x), gives 

(b) and 

   exp (β0 + β1x) 

θ(x) = 1 + exp (β0 + β1x)

1 

θ(x) = 1 + exp (− {β0 + β1x}) 

2. On page 285 of the text, it says “When X is a dummy variable, it can be shown that the log odds are also a linear function of x.” Suppose that X is a dummy variable, taking the value 1 with probability πj, j = 0, 1, conditional on Y = 0, 1.

(a) Show that the log odds are a linear function of x.

(b) Define the slope and intercept for the linear function.

3. On page 284 of the text, the author quotes Cook and Weisberg: “When conducting a binary regression with a skewed predictor, it is often easiest to assess the need for x and log(x) by including them both in the model so that their relative contributions can be assessed directly.” Show that indeed the log odds are a function of x and log(x) for the gamma distribution.

4. Chapter 8, Question 4

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