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 51F, the temperature at the time of the Challenger flight.

Test the hypothesis that temperature had no effect using the Wald statistic