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				15				12.0
	2				10				10.1
	3				17				5.4
	4				19				4.9
	5				12				5.6
	6				11				12.6
	7				13				9.7
	8				17				9.0
	9				16				9.0
	10				19				4.9
	11				8				11.4
	12				8				9.9

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

2. A=___________ B=

3. Estimate the selling price of an 11-year-old car (in $000). (Round your answer to 3 decimal places.)

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

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
15	12	1.56	10.84	4.11
10	10.1	14.06	1.94	-5.22
17	5.4	10.56	10.95	-10.75
19	4.9	27.56	14.50	-19.99
12	5.6	3.06	9.66	5.44
11	12.6	7.56	15.15	-10.70
13	9.7	0.56	0.98	-0.74
17	9	10.56	0.09	0.95
16	9	5.06	0.09	0.66
19	4.9	27.56	14.50	-19.99
8	11.4	33.06	7.25	-15.48
8	9.9	33.06	1.42	-6.85

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	165	104.5	174.25	87.349	-78.575
mean	13.750	8.708	SSxx	SSyy	SSxy

a)

sample size ,   n =   12          
here, x̅ = Σx / n=   13.75   ,     ȳ = Σy/n =   8.71  
                  
SSxx =    Σ(x-x̅)² =    174.2500          
SSxy=   Σ(x-x̅)(y-ȳ) =   -78.6          
                  
estimated slope , ß1 = SSxy/SSxx =   -78.6   /   174.250   =   -0.45093
                  
intercept,   ß0 = y̅-ß1* x̄ =   14.90866          
                  
so, regression line is   Ŷ =   14.909 - 0.451   *x

b) a = 14.909 , b = -0.451
c) Predicted Y at X=   11   is                  
Ŷ =   14.9087   +   -0.4509   *   11   =   9.948

d) For each additional year, the car decreases $ 451 in value