6.2 Table 5.7 shows a 2 x 2 x 6 contingency table for v = 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. Table 5.7 Data for Exercise 5.9 on admissions to Berkeley. Admitted, Male Department Yes Admitted, Female Yes 89 512 353 120 138 53 205 17 202 391 207 279 138 351 1493 131 Total 1198 Note: Based on data in P. Bickel et al., Science 187: 399 40 1278 0 When we add a gender effect, the estimated conditional odds ratio between admis- sions and gender (1 male, O female) is 0.90. The marginal table, collapsed over department, has odds ratio 1.84. Explain what causes these associations to differ so much. 6.2 Table 5.7 shows a 2 x 2 x 6 contingency table for v = 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. Table 5.7 Data for Exercise 5.9 on admissions to Berkeley. Admitted, Male Department Yes Admitted, Female Yes 89 512 353 120 138 53 205 17 202 391 207 279 138 351 1493 131 Total 1198 Note: Based on data in P. Bickel et al., Science 187: 399 40 1278 0 When we add a gender effect, the estimated conditional odds ratio between admis- sions and gender (1 male, O female) is 0.90. The marginal table, collapsed over department, has odds ratio 1.84. Explain what causes these associations to differ so much