Question

The owner of Maumee Ford-Mercury-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)	Car	Age (years)	Selling Price ($000)
1	15	12.0	7	13	9.7
2	10	10.1	8	17	9.0
3	17	5.4	9	16	9.0
4	19	4.9	10	19	4.9
5	12	5.6	11	8	11.4
6	11	12.6	12	8	9.9

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

      

a =

b =

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

Selling price

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

       

  For each additional year, the car decreases $   in value.

Answer 1

(a)

Independent variable: Age

Dependent varibale: selling price

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	15	12	225	144	180
	10	10.1	100	102.01	101
	17	5.4	289	29.16	91.8
	19	4.9	361	24.01	93.1
	12	5.6	144	31.36	67.2
	11	12.6	121	158.76	138.6
	13	9.7	169	94.09	126.1
	17	9	289	81	153
	16	9	256	81	144
	19	4.9	361	24.01	93.1
	8	11.4	64	129.96	91.2
	8	9.9	64	98.01	79.2
Total	165	104.5	2443	997.37	1358.3

Sample size: n =12

Now

Slope of the regression equation is

and intercept of the equation will be

The requried regression equation is

y ' = 14.909-0.451x

(b)

The selling price of a 11-year-old car (in $000) is

y ' = 14.909-0.451*11 = 9.948

So required estimated selling price is $9.948..

(c)

For each additional year, price of dollar decreased by (0.451*1000) = $451