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Question
NARRBEGIN: SA_135_140Adjustors working for a large insurance agency are each given a company car which they use on the job to travel to client locations to inspect damage to homes and automobiles that are covered by the agency. Although the cars are owned by the agency, maintenance is currently left up to the discretion of the adjustors, who are reimbursed for any costs they report. The agency believes that the lack of a maintenance policy has led to unnecessary maintenance expenses. In particular, they believe that many agents wait too long to have maintenance performed on their company cars, and that in such cases, maintenance expenses are inordinately high. The agency recently conducted a study to investigate the relationship between the reported cost of maintenance visits for their company cars (Y) and the length of time since the last maintenance service (X). The sample data are shown below:
NARREND
(A) Estimate a simple linear regression model with Service Interval (X) and Maintenance Cost (Y). Interpret the slope coefficient of the least squares line as well as the computed value of
.(B) Do you think this model proves the agency's point about maintenance? Explain your answer.
(C) Obtain a residual plot vs. Service Interval. Does this affect your opinion of the validity of the model in (A)?
(D) Obtain a scatterplot of Maintenance Cost vs. Service Interval. Does this affect your opinion of the validity of the model in (A)?
(E) Use what you have learned about transformations to fit an alternative model to the one in (A).
(F) Interpret the model you developed in (E). Does it help you assess the agency's claim? What should the agency conclude about the relationship between service interval and maintenance costs?
Answer
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NARRBEGIN: SA_79_80
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NARREND
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NARRBEGIN: SA_55_62A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future profits if oil is discovered. The landowner is also tempted to develop the field herself, believing that the interest in her land is a good indication that oil is present. In that case, she will have to contract a local drilling company to drill an exploratory well on her own. The cost for such a well is $750,000, which is lost forever if no oil is found. If oil is discovered, however, the landowner expects to earn future profits of $7,500,000. Finally, the landowner estimates (with the help of her geologist friend) the probability of finding oil on this site to be 60%.NARREND(A) Construct a decision tree to help the landowner make her decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.(B) What should the landowner do? Why?(C) Suppose the landowner is uncertain about the reliability of her geologist friend's estimate of the probability that oil will be found on her land. If she thinks the probability could be anywhere between 40% and 80%, would that change her decision?(D) Suppose that, in addition to the uncertainty about the probability of finding oil, the landowner is also uncertain about the cost of the exploratory well (could vary +/- 25%) and the future profits (could vary +/- 50%). To which of these variables is the expected value most sensitive?(E) What does the risk profile show about the relative risk levels for the landowner's two options?(F) Suppose the landowner suspects that she may be a somewhat risk-averse decision maker, because the she doesn"t feel there is as much of a difference between the two options as their expected values would indicate. She consults with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1) a gamble with equal probabilities of winning an amount $X and losing an amount "$X/2, and 2) doing nothing, with a payoff of $0. The point at which she cannot decide between 1) and 2) is when X=$1,500,000. What is her risk tolerance if she uses an exponential utility function to model her preferences?(G) Apply the risk tolerance given in your answer to the previous question to the landowner's decision tree in (A). What is the optimal decision in this case? What is the resulting certainty equivalent?(H) If the landowner could hire an expert geologist prepare a report to help her make her decision, what is the most that information could be worth? Assume the geologist's information is perfectly reliable.
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