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5.2 For the 23 space shuttle flights before the Challenger mission disaster in 1986, Table 5.12 shows the temperature at the time of the flight and whether at least one primary O-ring suffered thermal distress. a. Use logistic regression to model the effect of temperature on the probability of thermal distress. Plot a figure of the fitted model, and interpret. b. Estimate the probability of thermal distress at 310F, the tempera- ture at the place and time of the Challenger flight. c. Construct a confidence interval for the effect of temperature on the odds of thermal distress, and test the statistical significance of the effect. d. Check the model fit by comparing it to a more complex model. TABLE 5.12 Data for Problem 5.2" Ft Temp TD Ft Temp TD Ft Temp TD Ft Temp TD Ft Temp TD 1 66 C 70 69 4 C 5 67 C 68 6 72 0 73 70 0 9 57 1 10 63 11 70 12 78 13 67 0 14 53 15 67 16 75 17 70 0 18 81 19 76 0 20 79 HO 75 22 76 O 21 23 58 "Ft, flight number; Temp, temperature (F); TD, thermal distress (1, yes; 0, no). Source: Data based on Table 1 in J. Amer. Statist. Assoc., 84: 945-957, (1989), by S. R. Dalal, E. B. Fowlkes, and B. Hoadley. Reprinted with permission from the Journal of the American Statistical Association