Question

The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for 20 used sedans.

Selling Price	Age	Miles
13529	8	61452
13835	5	54323
22912	3	8292
15345	7	24865
16398	6	22132
16620	1	23658
16967	6	47373
18460	1	16828
18873	6	35404
19881	6	29616
11837	8	55840
14907	4	46167
15900	7	36969
16524	4	45492
9426	8	86931
12946	5	77202
15724	7	59699
10529	9	93204
8905	10	48262
11967	10	42372

a. Determine the sample regression equation that enables us to predict the price of a sedan on the basis of its age and mileage. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) [If you are using R to obtain the output, then first enter the following command at the prompt: options(scipen=10). This will ensure that the output is not in scientific notation.]

b. Interpret the slope coefficient of Age.

• The slope coefficient of Age is −528.13, which suggests that for every additional year of age, the predicted price of car decreases by $528.13.

• The slope coefficient of Age is −0.09, which suggests that for every additional year of age, the predicted price of car decreases by $0.09.

• The slope coefficient of Age is −528.13, which suggests that for every additional year of age, the predicted price of car decreases by $528.13, holding number of miles constant.

• The slope coefficient of Age is −0.09, which suggests that for every additional year of age, the predicted price of car decreases by $0.09, holding number of miles constant.

c. Predict the selling price of a seven-year-old sedan with 66,000 miles. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

PriceˆPrice^ = ?

Answer 1

Following is the output of multiple regression generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.825215361
R Square	0.680980392
Adjusted R Square	0.643448674
Standard Error	2125.176046
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	163891328.9	81945664.44	18.14413033	6.05965E-05
Residual	17	76778344.87	4516373.228
Total	19	240669673.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	22286.69926	1321.588364	16.86357105	4.7635E-12	19498.39157	25075.00695
Age, X1	-528.1340497	224.1212495	-2.356465756	0.03070809	-1000.988549	-55.27955053
Miles, X2	-0.08770487	0.025384628	-3.455038568	0.003024904	-0.141261754	-0.034147986

The regression equation is

y' = 22286.70 - 528.13*x1 - 0.09 * x2

(b)

The slope coefficient of Age is −528.13, which suggests that for every additional year of age, the predicted price of car decreases by $528.13, holding number of miles constant.

(c)

The required predicted price for x1=7 and x2 =66000 is

y' = 22286.6993 - 528.1340*7 - 0.0877 * 66000 = 12801.5613

Answer: 12801.56