Table 5.7 shows a 2 × 2 × 6 contingency table for y = whether admitted to graduate school at the University of California, Berkeley, for fall 1973, by gender of applicant for the six largest graduate departments.

a. Fit the logistic model that has department as the sole explanatory variable for y.

Use the standardized residuals to describe the lack of fit.

b. When we add a gender effect, the estimated conditional odds ratio between admissions and gender (1 = male, 0 = female) is 0.90. The marginal table, collapsed over department, has odds ratio 1.84. Explain what causes these associations to differ so much.