Adjustors 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:
-(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?

Question

Adjustors 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: 
-(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?

Quizplus · Accepted Answer

The Answer of Adjustors 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: 
-(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?

Adjustors Working for a Large Insurance Agency Are Each Given