Question

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 car’s mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub web site, February 24, 2012).

Miles (1000s)	Price ($1000s)
22	16.2
29	16.0
36	13.8
47	11.5
63	12.5
77	12.9
73	11.2
87	13.0
92	11.8
101	10.8
110	8.3
28	12.5
59	11.1
68	15.0
68	12.2
91	13.0
42	15.6
65	12.7
110	8.3

(b)	Develop an estimated regression equation showing how price is related to miles. What is the estimated regression model?
	Let x represent the miles.
	If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

For the model estimated in part (b), calculate the predicted price and residual for each automobile in the data. Identify the two automobiles that were the biggest bargains.
	If required, round your answer to the nearest whole number.
	The best bargain is the Camry # __ in the data set, which has __ miles, and sells for $__ less than its predicted price. The second best bargain is the Camry # __ in the data set, which has __ miles, and sells for $ __ less than its predicted price.

Answer 1

(b) The regression output is:

	r²	0.539
	r	-0.734
	Std. Error	1.541
	n	19
	k	1
	Dep. Var.	Price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	47.1580	1	47.1580	19.85	.0003
Residual	40.3893	17	2.3758
Total	87.5474	18
Regression output					confidence interval
variables	coefficients	std. error	t (df=17)	p-value	95% lower	95% upper
Intercept	16.4698
Miles	-0.0588	0.0132	-4.455	.0003	-0.0866	-0.0309

The estimated regression equation showing how price is related to miles is:

y = 16.4698 - 0.0588*x

The residual output is:

Observation	Price	Predicted	Residual
1	16.20	15.18	1.02
2	16.00	14.77	1.23
3	13.80	14.35	-0.55
4	11.50	13.71	-2.21
5	12.50	12.77	-0.27
6	12.90	11.94	0.96
7	11.20	12.18	-0.98
8	13.00	11.36	1.64
9	11.80	11.06	0.74
10	10.80	10.53	0.27
11	8.30	10.00	-1.70
12	12.50	14.82	-2.32
13	11.10	13.00	-1.90
14	15.00	12.47	2.53
15	12.20	12.47	-0.27
16	13.00	11.12	1.88
17	15.60	14.00	1.60
18	12.70	12.65	0.05
19	8.30	10.00	-1.70

The best bargain is the Camry # 12 in the data set, which has 28 miles, and sells for $2.32 less than its predicted price.

The second best bargain is the Camry # 4 in the data set, which has 47 miles, and sells for $ 2.21 less than its predicted price.