In this exercise we investigate the effect of gender on the odds of getting a high GPA.

(a) Use gender to predict HIGPA using a logistic regression. Summarize the results.

(b) Perform a logistic regression using gender and the two SAT scores to predict HIGPA. Summarize the results.

(c) Compare the results of parts (a) and (b) with respect to how gender relates to HIGPA. Summarize your conclusions.

Died                                  63                                  16

Survived                           2037                                784

Total                                 2100                                800

And here are the more detailed data where the patients are categorized as being in good condition or poor condition:

Good condition               Hospital A                    Hospital B

Died                               6                                    8

Survived                        594                                592

Total                            600                                600

Poor condition               Hospital A                    Hospital B

Died                              57                                    8

Survived                       1443                                192

Total                            1500                                200

(a) Use a logistic regression to model the odds of death with hospital as the explanatory variable. Summarize the results of your analysis and give a 95% con?dence interval for the odds ratio of Hospital A relative to Hospital B.

(b) Rerun your analysis in (a) using hospital and the condition of the patient as explanatory variables. Summarize the results of your analysis and give a 95% con?dence interval for the odds ratio of Hospital A relative to Hospital B.

(c) Explain Simpson's paradox in terms of your results in parts (a) and (b).