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final07 - Stat 500 Final Exam 11 Dec 2007 page 0 of 6...

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Stat 500 Final Exam – 11 Dec 2007 page 0 of 6 Please read this page but Do not open the exam until I tell you to start. Please put your name on the back of your answer book . Do NOT put it on the front. Thanks. The exam is closed book, closed notes. Use only the formula sheet and tables I provide today. You may use a calculator. Write your answers in your blue book. Ask if you need a second (or third) blue book. You have 2 hours (120 minutes) to complete the exam. Stop working when the end of the exam is announced. Points are indicated for each question. There are 160 total points. Important reminders: budget your time. Some parts of each question should be easy; others may be hard. Make sure you do all parts you can. notice that some parts do not require any computations. show your work neatly so you can receive partial credit. Good luck!
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Stat 500 Final Exam – 11 Dec 2007 page 1 of 6 1. 40 pts – Warranty claims on cars. A major car manufacturer is interested in modeling the number of warranty claims per month for two different car TYPEs, A and B. Their data include: TIME: the number of months since the type was introduced CLAIMS: the number of warranty claims for that type that month. For each of these two scenarios, described in words and pictures, construct an appropriate model. Briefly explain any additional X variables that you construct. Indicate what parameters (or combinations of parameters) estimate the quantity (or quantities) of interest. (a) 10 pts. There are no claims in month 0, but then claims increase linearly with time, perhaps at a different rate for the two car types. The quantity of interest is the difference in claims (between car types) in month 12. (b) 15 pts. There is an initial spike in claims in month 1. After that, claims increase linearly. The quantities of interest are: a) the difference in slopes from month 1 to 12, and b) the difference in claims in month 12. The number of warranty claims is associated with many other factors not included in the previous models. The company has over 1500 observations from many months, many car types, and many geographic regions. They want a model to predict monthly warranty claims. The data set includes a total of 28 possible variables, including all the variables you constructed in part 1c. These X variables are named X1, X2, · · · , X28. The next page includes output from a stepwise regression ( α include = 0 . 15 and α leave = 0 . 15) and selected parts of an all subsets regression. The all subsets regression includes the best 10 models using the C p criterion and a few additional models. (d) 10 pts. Which variables would you include in a regression model to predict monthly warranty claims? Briefly explain your choice.
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