If we use Minitab to regress Diagnosis against Age for the data in Figure 1.7 we get the output shown in Figure 23.6.

(a) Is age significant?

(b) Use the Minitab values to write down the estimated logistic regression model.

(c) Calculate the probability that the diagnosis will be malignant, that is, p(Y =1), for women aged:

(i) 45 and (ii) 50.

(d) Calculate [1 − p(Y =1)] in each case, and hence calculate the odds ratio for a malignant diagnosis in women aged 45 compared to women aged 50. Explain your result.

(e) Confirm that the antiloge of the coefficient on Age is equal to the odds ratio.

(f) What effect does an increase in Age of 10 years have on the odds ratio?