The tragedy of the Challenger space shuttle mission in 1986. Prior to January 1986, there were 23 space shuttle flights. These real data are in Exhibit A, which provides the ambient temperature (°F)...

The tragedy of the Challenger space shuttle mission in 1986. Prior to January 1986, there were 23 space shuttle flights. These real data are in Exhibit A, which provides the ambient temperature (°F) at the time of the flight along with the binary response o-ring distress (1=thermal distress present; 0= thermal distress absent). The tragedy happened at on a cold day in Florida; it was 31°F.
Three models were fit to the 23 data points. We refer to these as:
probit, logit, identity
A.Briefly explain (at least) one potential advantage of using model 2 “logit” instead of model 3 “identity”.

1. B. Is deviance a reliable measure of goodness-of-fit (GOF) for these models? If so, assess the GOF for these models; if not, explain why not and suggest an approach to assess the model fits.




2. C. The probit model can be used to provide a “tolerance distribution”. What is the distribution and its parameters? Then: Use this information to find a temperature value such that the probability of distress is (at most) 0.05.




3. D. For the logit model, estimate the EL50, and interpret this in context of the space shuttle data (if possible).




4. E. Is TEMP an important factor in the logit model based on a Wald test from the output? If the information is not on the output, then explain how you would obtain it. Provide the degrees of freedom for the test, and your conclusions.




5. F. For the logit model, provide a likelihood ratio test for TEMP using the output. If this information is not on the output then explain how you would perform such a test.




6. G. Assume that the temperature decreases by ten degrees (say from 41 to 31 degrees F). For the logit and identity models (models 2 and 3), use the estimate of ß in a meaningful fashion for scientific interpretation of this temperature impact.




7. H. For each of the probit, logit, and identity models, provide an estimate of the probability of distress at freezing (32 degrees F). You can leave your answers in raw numeric form.