1. The table below outlines the degree of injury in automobile accidents. The response categories are (1) not injured, (2) injured but not transported by emergency medical services, (3) injured and transported by emergency medical services but not hospitalized, (4) injured and hospitalized but did not die, and (5) injured and died. SAS output of a cumulative logit model is listed in the table below. (20 marks) Response on Injury Outcome 2 3 4 Gender Location Seat Belt 1 5 Female Urban No Yes No Yes 175 126 73 94 720 577 710 564 91 48 159 82 10 8 31 17 Rural 7,287 11.587 3,246 6,134 10.381 10.969 6,123 6,693 Male Urban No Yes No Yes 136 83 141 74 566 259 710 353 96 37 188 74 14 1 45 12 Rural DF 1 1 1 1 1 1 0 Parameter Intercepti Intercept 2 Intercept 3 Intercept 4 gender gender location location seatbelt seat belt location'seat belt location'seatbelt location' seatbelt location seatbelt 1 0 1 female male rural urban no yes rural rura2 urban urban Estimate 3.3074 3.4818 5.3494 7.2563 -0.5463 0.0000 -0.6988 0.0000 -0.7602 0.0000 -0.1244 0.0000 0.0000 0.0000 Std Error 0.0351 0.0355 0.0470 0.0914 0.0272 0.0000 0.0424 0.0000 0.0393 0.0000 0.0548 0.0000 0.0000 0.0000 0 no 1 yes no yes 0 0 0 0 a) Why are there four intercepts? Explain how they determine the estimated response distribution for males in urban areas wearing seat belts. Calculate the probability of each response. (6 marks) b) Construct a Wald 95% confidence interval for the effect of gender, given seat belt use and location. Interpret. (6 marks) c) Find the estimated cumulative odds ratio between the response and seatbelt use for those in rural locations and for those in urban locations, given gender. Based on this, explain 2 Name: Student ID: how the effect of seat-belt use varies by region, and explain how to interpret the interaction estimate, -0.1244. (6 marks) d) The score test (output not provided) is reported to have a chi-squared value of 136.1 on 12 df, P