Use logistic regression for the data given below on launch temperature and O-ring failure for the 24 space shuttle launches prior to the Challenger disaster of January 1986. There are six O-rings used on the rocket motor assembly to seal field joints. The table below presents the launch temperatures. A '1' in the "O-Ring Failure" column indicates that at least one O-ring failure had occurred on that launch.
|
Temperature (0F)
|
O-Ring Failure
|
Temperature (0F)
|
O-Ring Failure
|
Temperature (0F)
|
O-Ring Failure
|
|
53
|
1
|
68
|
0
|
75
|
0
|
|
56
|
1
|
69
|
0
|
75
|
1
|
|
57
|
1
|
70
|
0
|
76
|
0
|
|
63
|
0
|
70
|
1
|
76
|
0
|
|
66
|
0
|
70
|
1
|
78
|
0
|
|
67
|
0
|
70
|
1
|
79
|
0
|
|
67
|
0
|
72
|
0
|
80
|
0
|
|
67
|
0
|
73
|
0
|
81
|
0
|
- Use logistic regression to model the effect of temperature on the probability of O-Ring Failure. How do you the results be interpreted? In particular how the effect of temperature on the odds of thermal distress should be interpreted?
- Examine the model fit.
- Calculate the predicted probability of O-Ring Failure at 51°F, the temperature at the time of the Challenger flight.
- Test the hypothesis that temperature had no effect using the Wald statistic