STA 242/ENV 255

Optional Homework 5

Due Monday, April 22, 2002 by 5pm to 223 C Old Chemistry

1. Critique of 2 MP Presentations Follow the instructions given in class to submit a critique of 2 MP presentations. That is, for each project give:
   1. Name of presenter
   2. Title of project (rough title is fine)
   3. Research question
   4. What assumptions were necessary for the model chosen?
   5. Did the application of the model to these data raise any issues with assumptions?
   6. Measures of uncertainty for parameters critical to the research question: were they given? were they appropriate for the problem at hand?
   7. Model selection: Was any done? Was the process briefly described or justified?
   8. Model uncertainty: Did the author address the issue of model uncertainty either qualitatively or quantitatively?

   Each critique should be about a paragraph in length.

2. What is the impact of the emergency locator transmitter (ELT) for aircraft?

   70% of light aircraft that disappear in airspace are discovered. Of those that are discovered, 60% have an ELT. Of those that are not discovered, 90% do not have an ELT.

   1. What is the probability that an aircraft equipped with an ELT is not discovered?
   2. What is the probability that an aircraft without an ELT is discovered?

   Further reading: p. 355-6 of Moore and McCabe

3. In lab you performed a simulation exercise (#1,Lab 4/10/02). I also passed out Splus results from this exercise in class on April 11th.
   1. Sum the posterior probabilities for the top 5 models, and make a statement about the amount of model uncertainty in this problem. You may use language similar to that in the "Bayesian Model Averaging:A Tutorial" paper.
   2. Let's say you are using a variable selection technique when the number of explanatory variables is a substantial proportion of the sample size.
      1. What is the impact on the d.f. for model error?
      2. In this situation, compare the penalty terms for BIC and AIC for fixed MSE. Which criterion will favor a more parsimonious model?

4. The following questions apply to the reading handed out entitled "Chapter 4: Criteria for Choice of Best Model" (from Myers, "Classical and Modern Regression with Applications"). Note that a 6-parameter model is fit to the data on page 168.
   1. Refer to the small table on the top of page 169. We will focus on site 17. What do the numbers -466 and -3675 represent for site 17?
   2. A model is used to compute each of the above quantities for site 17. Give the associated error degrees of freedom for each model.
   3. At site 17, does the ordinary residual overstate or understate the true prediction error?
   4. What does PRESS say about observation 17 with respect to its influence?

5. Exercise 11 on p. 592, based on the space shuttle data. These are the original data; there are errors with the Sleuth data.

   Updated 4/19

   Turn in only these three parts:

   1. Part (a)
   2. Part (e)
   3. How do the estimated odds of failure change with each 5 degree increase in temperature?

   It may be helpful for you to refer to the text on page 577 "Example of Confidence Interval for a Multiple .... ". For this homework, I am interested in your interpretations of estimates. Don't worry about confidence intervals for these exercises.

   
   

Splus hints:

Fit a logistic regression with failure as the Response and temp as the explanatory variable. This is how:

• Go to Statistics, Regression and Generalized Linear Models

• Under Model Family, specify binomial. The default link is logit; leave that alone for now.

• The model formula is specified the same as in linear regression; in this case : failure ~ temp

click OK to run

## read in the shuttle data, let's call it "shuttle"
reduced.mod_glm(failure~temp,family=binomial,data=shuttle)
full.mod_glm(failure~temp+pressure,family=binomial,data=shuttle)
summary.glm(reduced.mod)
summary.glm(full.mod)
anova.glm(reduced.mod,full.mod,test="Chisq")