Table 3.4, the Credit data file at the text website, shows data for a sample of 100 adults randomly selected for an Italian study on the relation between x = annual income and y = whether you have a travel credit card (1 = yes, 0 = no). At each level of x (in thousands of euros), the table indicates the number of subjects in the sample and the number of those having at least one travel credit card. Software provides the following results of using logistic regression:

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Estimate Std. Error

(Intercept) -3.5179 0.7103 x 0.1054 0.0262

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a. Report the prediction equation and interpret the sign of βˆ.

b. When Pˆ(Y = 1) = 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 = 33.4 thousand euros.

c. Show how to apply software to the Credit data file at the text website to obtain the logistic regression fit.

Table 3.4 Data on travel credit cards and income for exercise 3.9.

No. of Credit No. of Credit No. of Credit Income Cases Cards Income Cases Cards Income Cases Cards 12 1 0 21 2 0 34 3 3 13 1 0 22 1 1 35 5 3 14 8 2 24 2 0 39 1 0 15 14 2 25 10 2 40 1 0 16 9 0 26 1 0 42 1 0 17 8 2 29 1 0 47 1 0 19 5 1 30 5 2 60 6 6 20 7 0 32 6 6 65 1 1 Source: Thanks to R. Piccarreta, Bocconi University, Milan, for original form of data.