Question

The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car				Age (years)				Selling Price ($000)
	1				11				12.2
	2				8				11.0
	3				16				4.9
	4				18				4.1
	5				9				6.7
	6				8				13.6
	7				10				11.1
	8				16				9.0
	9				14				9.0
	10				18				4.2
	11				6				12.1
	12				6				10.4

1. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

a =
b =

2. Estimate the selling price of an 7-year-old car (in $000). (Round your answer to 3 decimal places.)

Selling price

3. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)

For each additional year, the car decreases

in value.

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Selling Price
Independent Variable: Age
Selling Price = 15.72003 - 0.5731454 Age
Sample size: 12
R (correlation coefficient) = -0.78121953
R-sq = 0.61030395
Estimate of error standard deviation: 2.1708211

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	15.72003	1.8021335	≠ 0	10	8.7230108	<0.0001
Slope	-0.5731454	0.14482873	≠ 0	10	-3.9574013	0.0027

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	73.802023	73.802023	15.661025	0.0027
Error	10	47.124644	4.7124644
Total	11	120.92667

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
7	11.708012	0.92168439	(9.6543711, 13.761653)	(6.4532089, 16.962815)

Hence,

1. Regression equation:

a = 15.720

b = -0.573

2. Selling price of 7-year old car = 11.708

3. For each additiona year, the car decreases $ 573 in value