Introduction to Categorical Data Analysis

PROBLEMS 93
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 currently worth 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 ˆβ.
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.
Table 3.6. Data for Problem 3.9 on Italian Credit Cards
No. Credit No. Credit No. Credit No. Credit
Inc. Cases Cards Inc. Cases Cards Inc. Cases Cards Inc. Cases Cards
24 1 0 34 7 1 48 1 0 70 5 3
27 1 0 35 1 1 49 1 0 79 1 0
28 5 2 38 3 1 50 10 2 80 1 0
29 3 0 39 2 0 52 1 0 84 1 0
30 9 1 40 5 0 59 1 0 94 1 0
31 5 1 41 2 0 60 5 2 120 6 6
32 8 0 42 2 0 65 6 6 130 1 1
33 1 0 45 1 1 68 3 3
Source: Based on data in Categorical Data Analysis, Quaderni del Corso Estivo di Statistica e Calcolo
delle Probabilità, no. 4, Istituto di Metodi Quantitativi, Università Luigi Bocconi, by R. Piccarreta.
3.10 Refer to Problem 4.1 on cancer remission. Table 3.7 shows output for fitting a
probit model. Interpret the parameter estimates (a) finding the remission value
at which the estimated probability of remission equals 0.50, (b) finding the
difference between the estimated probabilities of remission at the upper and
lower quartiles of the labeling index, 14 and 28, and (c) using characteristics
of the normal cdf response curve.
3.11 An experiment analyzes imperfection rates for two processes used to fabricate
silicon wafers for computer chips. For treatment A applied to 10 wafers, the
numbers of imperfections are 8, 7, 6, 6, 3, 4, 7, 2, 3, 4. Treatment B applied to
10 other wafers has 9, 9, 8, 14, 8, 13, 11, 5, 7, 6 imperfections. Treat the counts