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

Group of answer choices

27%

64%

16%

70%

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

Group of answer choices

(-0.33, -0.20)

(-0.43,-0.10)

(-0.53, -0.20)

(-0.43, 0.10)

3)Give a point estimate of the predicted price (in thousand dollars) for a Eurovan in average condition with 75,000 miles on it.

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

Group of answer choices

(29,819, 36,686)

(19,619, 27,686)

(19,819, 26,686)

(9,819, 6,686)

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

Group of answer choices

from $11,729 to $34,777

from $10,729 to $35,777

from $12,729 to $33,777

from 21,729 to $34,777

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

Group of answer choices

a)The confidence interval is wider for individual van because we have a more precise estimate of the value than if it was just the average van.

b)The individual van is much more specific being that the van has 75,000 miles and is in "average" condition. There may end up being a wider value range for this type of vehicle leading to a larger range in price. With more data points the values are likely to converge and paint a more accurate picture. This is a reason why the confidence interval for an individual van may be wider than the average.

c)The confidence interval for the individual value also takes into account that the model includes an error term. The price is not determined only by the mileage: vans with the same mileage might cost different amounts for other reasons: condition, features, etc. That is, we don't expect the value of each van to fall exactly on the line - we recognize that the price of each van may differ from its predicted price by some random amount.

d)Because the number of samples used for calculating average van is larger than used for calculating the confidence interval for the individual van, which resulted in a more spreaded data distribution and a relatively lower height of the curve that represents the individual van, and at the same time the curve for the average van is more likely to be a normal distribution. This resulted in a wider confidence interval for the individual van.

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.

Group of answer choices

If the van is average in every way (except mileage), they should look at the prediction interval for an individual Eurovan to determine the price: $11,729 to $34,777.She could offer him a price in this range with 95% confidence that the average price of vans with that mileage falls in that range.

7)Kim should offer no more than $ 23.25217 for Tim 's van based on the sample predicted estimates of regression coefficients.

If the van is average in every way (except mileage), they should look at confidence interval for the coefficient on mileage to determine the price: from$100 to $430. She could offer him a price in this range with 95% confidence that the average price of vans with that mileage falls in that range.

If the van is average in every way (except mileage), they should look at the confidence interval for the mean to determine the price: $19,819 to $26,686. She could offer him a price in this range with 95% confidence that the average price of vans with that mileage falls in that range.

8)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?

Group of answer choices

not enough information

in above-average condition

in average condition

in below-average condition

9)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.

Group of answer choices

a)I would not say that the residual plot gives indication that any assumptions are violated. The residual plots look random, the errors add up to 0, and the points look independent from other points.

b)Since there are not many data points, it is hard to tell.

c)The residual plot above does not give any suggestion that one of the assumptions of the regression model has been violated.To begin with, the plots indicate linearity, with only two outliers that do not significantly affect the linear relationship. The model has only one independent variable thus no multicollinearity and multivariate normality. It can also be noted that the residuals are independent from each other hence no autocorrelation. Lastly, the data on the scatter plot are homoscedastic that is the variances are seen to be homogeneous.

d)Moving from left to right, the residual plot seems to fan out. This suggests that there is more variation in price among the vans with higher predicted prices (lower mileage) than among those with lower predicted prices. This would be a violation of the "constant variance" assumption.

10)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. Provide the hypotheses

Group of answer choices

Ho: = 0

Ha: 0

Ho: = 0

Ha: <0

Ho: 0

Ha: =0

Ho: >= 0

Ha: <0

11)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?

Group of answer choices

Ho:A decline of more than $250 for each additional 1,000 on the odometer is not statistically significant. Ha: A decline of more than $250 for each additional 1,000 on the odometer is statistically significant.

Ho: = -.25 (price decrease by 250 for each additional 1000 miles on the odometer)

Ha: >-0.25 (price decreases by more than $250 for every 1000 miles on the odometer)

Ho: -.25 (price decrease by 250 or less for each additional 1000 miles on the odometer)

Ha: < -0.25 (price decreases by more than $250 for every 1000 miles on the odometer)

Ho: Price decline $250 if 1,000 added on odometer Ha: Price decline $250 if 1,000 added on odometer

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