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The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and condition. To investigate the relationship between the cars mileage and the sales price for Camrys, a data scientist collects the the mileage and sale price for 124 recent sales of Toyota Camrys.

	Miles (1000s)	Price ($1000s)	Miles (1000s)	Price ($1000s)	Miles (1000s)	Price ($1000s)	Miles (1000s)	Price ($1000s)
1	116.53	25.5	57.89	20.5	51.38	38.1	59.43	27.5
2	100.27	19.1	94.41	22.5	53.26	33.3	16.70	36.7
3	29.93	46.2	50.73	19.1	15.61	31.2	56.94	23.8
4	25.47	24.7	41.88	23.4	101.39	23.5	18.20	40.2
5	49.96	39.3	110.06	25.1	77.04	29.7	70.19	29.9
6	83.68	32.7	22.25	41.3	86.47	17.4	23.13	31.1
7	62.53	23.4	57.00	29.6	119.18	16.2	42.49	27.8
8	85.54	33.7	15.73	26.9	35.96	34.5	43.91	29.4
9	27.93	37.1	99.87	23.8	99.38	29	37.75	33.4
10	89.31	26.5	98.30	33.1	103.17	35.1	95.43	15.6
11	59.89	24.4	90.12	18.4	37.72	24.3	118.85	24.1
12	17.87	21.5	31.55	34.4	75.59	21.3	10.82	34.6
13	20.35	27.1	30.47	30.5	55.73	35.9	58.99	21.9
14	116.65	27.6	33.28	37.9	61.24	31.4	49.95	29.9
15	63.18	23.1	52.94	18.2	88.32	32	108.77	18.5
16	30.54	39.9	17.60	31.5	97.54	29.5	86.98	25
17	51.36	18.5	88.29	35.5	59.46	36.6	88.41	24.6
18	34.83	46.1	90.98	21.7	51.19	32.3	113.97	22.6
19	93.06	24	75.39	26.9	80.54	29.1	68.14	23.9
20	116.49	15.8	28.20	22.4	17.71	35.3	13.77	31.8
21	68.08	21.4	102.03	29.2	70.23	33.7	71.62	34.2
22	29.90	29.7	28.38	29.3	21.03	23.8	76.41	22.6
23	39.98	24.5	45.44	39.2	49.85	33.7	35.10	24.9
24	98.06	24.3	44.82	38.3	85.38	25.6	80.65	19.7
25	44.43	22.9	74.81	27.4	33.30	32.1	96.51	22.6
26	22.90	41.8	33.22	43.8	102.52	24	97.28	25.6
27	52.13	31.4	29.30	26.2	82.67	33.8	62.20	32.5
28	57.72	18.9	17.73	36	17.86	28.3	33.28	36
29	67.89	21.7	53.33	34.8	57.61	24.1	89.62	33.1
30	61.77	39.5	31.54	42.6	12.31	22.1	17.00	25
31	46.90	22.7	30.83	41.3	62.43	29.8	21.04	23.6

(a)

A scatter chart of the data with miles as the independent variable is shown below. Does a linear relationship appear reasonable? Explain.

A scatter chart title is Line Fit Plot. The horizontal axis is labeled Miles, in thousands of miles, with values from 0 to 140. The vertical axis is labeled Price, in thousands of dollars, with values from 0 to 50. The chart has a collection of 124 points. A pattern starts at approximately 11 thousands of miles and 47 thousands of dollars then goes down and right to approximately 120 thousands of miles and 16 thousands of dollars. The points are scattered widely from the pattern.

The scatter chart reveals a - Select your answer -horizontalnegativepositiveverticalItem 1 - Select your answer -linearnon-linearItem 2 relationship between a Camrys miles and its price.

(b)

A regression output of the data, with miles as the independent variable x, is shown below. What is the estimated linear regression equation that can be used to predict how price is related to miles?

Round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.

= + x

(c)

Use the plot of residuals versus distance to work shown below to check the conditions necessary for valid inference in regression.

A scatter chart with title Residual Plot shows the residuals of a simple regression model. The horizontal axis is labeled Miles, in thousands of miles, with values from 0 to 140. The vertical axis is labeled Residuals with values from negative 15 to 20. The chart has a collection of 124 points. The points are scattered widely from approximately 11 to approximately 120 thousands of miles on the horizontal axis and from approximately negative 12 to approximately 15 on the vertical axis.

The plot of residuals shows - Select your answer -one horizontal banda funnel patterntwo horizontal bandsa curvatureItem 5 . Because there is - Select your answer -nostrongweakItem 6 significant evidence of a violation of the conditions, we - Select your answer -may proceedshould be cautiousItem 7 with our inference.

Test whether ₀ is significant at = 0.01.

H₀ : - Select your answer - 0 1 b0 b1 Item 8 - Select your answer ->=

H₁ : - Select your answer - 0 1 b0 b1 Item 11 - Select your answer ->=

The p-value - Select your answer ->Item 14 0.01. - Select your answer -RejectDo not rejectAcceptItem 15 H₀ . We - Select your answer -cancannotItem 16 conclude that the - Select your answer -interceptslopeItem 17 of the regression - Select your answer -doesdoes notItem 18 significantly contribute to the price.

What is the interpretation of ₀?

The - Select your answer -pricemileageItem 19 is expected to - Select your answer -be equal todecrease byincrease byItem 20 - Select your answer -dollar(s)mile(s)Item 22 when the - Select your answer -mileagepriceItem 23 - Select your answer -is equal todecrease byincrease byItem 24 - Select your answer -mile(s)dollar(s)Item 26 .

Is the interpretation of ₀ reasonable?

The interpretation is - Select your answer -meaninglessreasonableItem 27 because the y-intercept has been estimated through - Select your answer -extrapolationinterpolationItem 28 .

Test whether ₁ is significant at = 0.05.

H₀ : - Select your answer - 1 0 b1 b0 Item 29 - Select your answer ->=

H₁ : - Select your answer - 1 0 b1 b0 Item 32 - Select your answer ->=

The p-value - Select your answer ->Item 35 0.05. - Select your answer -RejectDo not rejectAcceptItem 36 H₀ . We - Select your answer -cancannotItem 37 conclude that there is - Select your answer -anoItem 38 significant linear relationship between a Camry's miles and price.

What is the interpretation of ₁?

The - Select your answer -pricemileageItem 39 is expected to - Select your answer -increase bybe equal todecrease byItem 40 - Select your answer -dollar(s)mile(s)Item 42 when the - Select your answer -mileagepriceItem 43 - Select your answer -increase bydecrease byis equal toItem 44 - Select your answer -mile(s)dollar(s)Item 46 .

Is the interpretation of ₁ reasonable?

The interpretation is - Select your answer -reasonablemeaninglessItem 47 because the price is expected to - Select your answer -decreaseincreaseItem 48 as the mileage - Select your answer -increasesdecreasesItem 49 .

(d)

How much of the variation in the sample values of price does the model estimated in part (b) explain?

If required, round your answer to one decimal place.

%

(e)

For the model estimated in part (b), where in the scatter chart and the plot of residuals would you expect to find the automobiles representing the biggest bargains?

The biggest bargains are to be found - Select your answer -at the bottomat the topto the leftto the rightin the middleItem 51 of the scatter chart and plot of residuals because those data points correspond to those Camrys with an actual price that is - Select your answer -lowerhighersimilarItem 52 than the price the model predicts.

(f)

Suppose that you are considering purchasing a previously owned Camry that has been driven 110,000 miles. Use the estimated regression equation entered in part (b) to predict the price for this car. Is this the price you would offer the seller?

If required, round your answer to one decimal place. Do not round intermediate calculations. Enter your answer in dollars. For example, 12 thousand should be entered as 12,000.

Depending on other factors not considered in the model (various options, the physical condition of the body and interior, etc.), a $ asking price - Select your answer -cancannotItem 54 be reasonably expected to be paid for a Camry that has been driven 110,000 miles.

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