Your classmate Kim would like to buy a used Volkswagon Eurovan for an extended road trip this summer. Her neighbor Tim has offered to sell her his Eurovan. Tim's Eurovan is has 75,000 miles on it. Kim and Tim agree that the van is in average condition. Tim has asked her to come up with a fair price. Your classmate has never heard of "blue book value" and sets out to estimate the value using her newly acquired knowledge of regression analysis. She checks the Seattle Times and finds a long list of Eurovans for sale.She selects a random sample of 10 vans, ranging in mileage from 59,000 to 129,000 miles. For each Eurovan, she enters the mileage (in 1000s) and the offered sales price (in $1000s) into R. She runs a regression predicting asking price in thousands based on mileage in thousands.She determines the relationship between mileage and asking price and also runs some estimates for the price of a Eurovan with 75,000 miles on it. The data for this example is found on Canvas, Eurovan.jmp or Eurovan.xlsx.

1. What is the estimated regression equation?

2. To what extent is variation in the prices of the vans explained by differences in their mileage?

3. Give a 95% confidence interval for the coefficient on mileage.

4. Interpret the confidence interval calculated in question 3. Exactly what does it tell you?

5. Sketch a graph illustrating the estimated relationship between mileage and a van's price.

6. Give a point estimate of the predicted price for a Eurovan in average condition with 75,000 miles on it.

7. Give a 95% confidence interval for the average price of Eurovans with 75,000 miles on them.

8. Give a 95% confidence interval (prediction interval) for the price of an individual Eurovan with 75,000 miles on it.

9. Explain carefully why the confidence interval you gave for the individual van is wider that that you gave for the average van.

10. Assuming that your classmate and Tim agree that his van is in average condition, what price should she offer him? What is the price you would consider fair? Explain.

11. The sample contains a Eurovan with 81,718 thousand miles on it. Assuming that the price given accurately reflects the condition of the car, do you think this van is likely to be in below-average, average, or above average condition, given its mileage? Explain your answer.

12. Does the residual plot give any suggestion that one of the assumptions of the regression model may be violated? If not, why not? If so, which of the assumptions may be violated, and what in the residual plot indicates this.

13. Conduct a t-test at a 0.05 significance level as to whether mileage has a statistically significant relationship to the price of a van.Be sure to provide the hypotheses, test statistics, p-value and conclusion. Summarize the test result in a non-technical sentence.

14. Now suppose a researcher wanted to provide evidence using a 0.05 significance level, that the price of a van declines by more than $250 for each additional 1,000 on the odometer. What would be the appropriate hypotheses? The test statistic? The p-value?The conclusion?

Year	Age	Mileage (1000s)	Price (1000s)	Type (full camper/MV)
2000	9	64	30	FC
2000	9	82.345	28	MV
1997	12	59	27	FC
2001	8	76.767	24.9	MV
2001	8	69.218	21.992	MV
2002	7	88.275	19.988	MV
1995	14	108.077	15	FC
2000	9	110.608	13.995	MV
2001	8	81.718	10.999	MV
2000	9	129.591	8.888	MV