Question

(Use R or excel) The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for 20 used sedans

SellingPrice	Age	Miles
13535	7	61453
13727	9	54313
22929	1	8227
15302	2	24822
16392	2	22055
16583	2	23697
16911	3	47375
18456	3	16821
18849	7	35441
19800	7	29613
11813	9	55757
14971	4	46216
15898	3	37040
16462	1	45549
9436	6	86927
12979	8	77211
15706	9	59641
10548	7	93213
8927	12	48217
11932	9	42417

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. Use the predict() function in R or use the regression output to predict the selling price of a seven-year-old sedan with 68,000 miles. (Round answer to 2 decimal places.)

Answer 1

By using R-software we can solve this question.

Enter data into R software.

a)

R codes and output:

sedan
SellingPrice Age Miles
1 13535 7 61453
2 13727 9 54313
3 22929 1 8227
4 15302 2 24822
5 16392 2 22055
6 16583 2 23697
7 16911 3 47375
8 18456 3 16821
9 18849 7 35441
10 19800 7 29613
11 11813 9 55757
12 14971 4 46216
13 15898 3 37040
14 16462 1 45549
15 9436 6 86927
16 12979 8 77211
17 15706 9 59641
18 10548 7 93213
19 8927 12 48217
20 11932 9 42417
> model<-lm(SellingPrice~Age+Miles,data = sedan)
> model

Call:
lm(formula = SellingPrice ~ Age + Miles, data = sedan)

Coefficients:
(Intercept) Age Miles
2.112e+04 -3.144e+02 -9.424e-02

summary(model)

Call:
lm(formula = SellingPrice ~ Age + Miles, data = sedan)

Residuals:
Min 1Q Median 3Q Max
-3875.4 -1621.9 -92.1 1312.8 3672.6

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.112e+04 1.223e+03 17.265 3.26e-12 ***
Age -3.144e+02 1.881e+02 -1.671 0.11304
Miles -9.424e-02 2.728e-02 -3.454 0.00303 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2265 on 17 degrees of freedom
Multiple R-squared: 0.6356,   Adjusted R-squared: 0.5927
F-statistic: 14.82 on 2 and 17 DF, p-value: 0.0001878

The sample regression equation is:

$\hat{y}$ = 21120 - 314.4*Age - 0.09424*Miles

b)

Age = 7

Miles = 68000

The predicted selling price is:

$\hat{y}$ = 21120 - 314.4*7 - 0.09424*68000 = 12510.88