Table 3.6 refers to a sample of subjects randomly selected for an Italian study on the relation between income and whether one possesses a travel credit card

(such as American Express or Diners Club). At each level of annual income in millions of lira, the table indicates the number of subjects sampled and the number of them possessing at least one travel credit card. (Note: one million lira at the time of the study is currentlyworth aout 500 euros.) Software provides the following results of using logistic regression to relate the probability of having a travel credit card to income, treating these as independent binomial samples.

Parameter Estimate Standard error Intercept −3.5561 0.7169 Income 0.0532 0.0131

a. Report the prediction equation.

b. Interpret the sign of ˆ β.

c. When ˆπ = 0.50, show that the estimated logit value is 0. Based on this, for these data explain why the estimated probability of a travel credit card is 0.50 at income = 66.86 million lira.