For the 23 space shuttle flights that occurred before the Challenger mission disaster in 1986, Table 5.10 shows the temperature (F) 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. Interpret the model fit.

b. Calculate the predicted probability of thermal distress at 31, the temper- ature at the time of the Challenger flight. At what temperature does the predicted probability equal .5? At that temperature, give a linear approx- imation for the change in the predicted probability per degree increase in temperature.

c. Interpret the effect of temperature on the odds of thermal distress. Test the hypothesis that temperature has no effect, using (i) the Wald test, (ii) the likelihood-ratio test.

Table 5.10 Ft Temp TD Ft Temp TD Ft Temp TD 1 66 0 9 57 1 17 70 2 70 1 10 63 1 18 81 0 3 69 0 11 70 1 19 76 0 4 68 0 12 78 0 20 79 0 5 67 13 67 0 21 75 1 6 72 14 53 1 22 7'1 0 7 73 0 15 67 0 23 58 8 70 0 16 75 0 = no). Note: Ft flight no., Temp = temperature, TD = thermal distress (1 = yes, 0 = Source: Data based on Table 1 in S. R. Dalal, E. B. Fowlkes, and B. Hoadley. J. Amer. Statist. Assoc, 84: 945-957 (1989). Reprinted with permission of the American Statistical Association.