15.12. Table 15.23 refers to individuals who applied for admission into graduate school at the University of California in Berkeley. Data10 are presented for five of the six largest graduate departments at the university. The variables are A: Whether admitted (yes, no).

S: Sex of applicant (male, female).

D: Department to which application was sent

(D1,D2,D3,D4,D5).

(a) Construct the two-way table for sex and whether admitted, collapsing the table over department. Find the odds ratio and interpret.

(b) Treating A as the response and D and S as categorical explanatory variables, fit the logistic model having main effects. Report the prediction equation. Interpret the coefficient of S in this equation by finding the estimated conditional odds ratio between A and S, controlling for D.

(c) Contrast the model estimated conditional odds ratio between A and S in

(b) with the odds ratio reported in

(a). Explain why they differ so much, satisfying Simpson’s paradox.

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TABLE 15.22 Parameter DF Estimate Std Err ChiSquare Pr > Chil INTERCEPT 1 -5.309 0.4752 124.820 0.0001 ALCOHOL yes 1 2.986 0.4647 41.293 0.0001 ALCOHOL no 0 0.000 0.0000 0. 0. CIGARETT yes 1 2.848 0.1638 302.141 0.0001 CIGARETT no 0 0.000 0.0000 0. 0.