The accompanying table shows a portion of data consisting of the selling price,
ID: 3313216 • Letter: T
Question
The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for 20 used sedans. PictureClick here for the Excel Data File Selling Price Age Miles 13,611 4 61,508 13,779 9 54,308 22,987 3 8,276 15,349 7 24,893 16,393 2 22,109 16,596 2 23,716 16,930 6 47,443 18,489 3 16,867 18,842 1 35,371 19,813 1 29,625 11,850 6 55,769 14,977 5 46,235 15,913 3 37,024 16,492 5 45,533 9,453 10 86,891 12,972 4 77,268 15,705 6 59,603 10,519 9 93,254 8,912 11 48,233 11,913 9 42,423 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 answer to 2 decimal places.) 111formula9.mml = + Age + Miles. b. Interpret the slope coefficient of Age. The slope coefficient of Age is 621.80, which suggests that for every additional year of age, the predicted price of car decreases by $621.80. The slope coefficient of Age is 0.07, which suggests that for every additional year of age, the predicted price of car decreases by $0.07. The slope coefficient of Age is 621.80, which suggests that for every additional year of age, the predicted price of car decreases by $621.80, holding number of miles constant. The slope coefficient of Age is 0.07, which suggests that for every additional year of age, the predicted price of car decreases by $0.07, holding number of miles constant. c. Predict the selling price of a six-year-old sedan with 68,000 miles. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) 111formula9.mml = $
Explanation / Answer
Solution:
First of all we have to find the regression analysis for the given data for the predicted of the dependent variable selling price based on the age and mileage. The required regression output by using excel is given as below:
Data:
Price
Age
Mileage
13611
4
61508
13779
9
54308
22987
3
8276
15349
7
24893
16393
2
22109
16596
2
23716
16930
6
47443
18489
3
16867
18842
1
35371
19813
1
29625
11850
6
55769
14977
5
46235
15913
3
37024
16492
5
45533
9453
10
86891
12972
4
77268
15705
6
59603
10519
9
93254
8912
11
48233
11913
9
42423
Regression Statistics
Multiple R
0.875917874
R Square
0.767232122
Adjusted R Square
0.739847665
Standard Error
1814.915089
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
2
184571768.5
92285884.2
28.0170661
4.15763E-06
Residual
17
55996585.29
3293916.78
Total
19
240568353.8
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
21611.42148
978.1621428
22.093905
5.845E-14
19547.67977
23675.16319
Age
-621.8017059
166.5511329
-3.7333982
0.00165347
-973.1938774
-270.4095344
Mileage
-0.070739913
0.022529645
-3.1398591
0.0059716
-0.11827331
-0.023206517
Part a
Here, we have to write the sample regression equation for the prediction of the selling price which is given as below:
Selling price = 21611.42 – 621.80*Age – 0.07*Mileage
Part b
Interpret the slope coefficient of age.
The slope coefficient of Age is 621.80, which suggests that for every additional year of age, the predicted price of car decreases by $621.80, holding number of miles constant.
(Minus sign indicate decrement in dependent variable when other regressors are constant.)
Part c
Predict the selling price of a six-year-old sedan with 68,000 miles.
Age = 6
Mileage = 68000
Selling price = 21611.42 – 621.80*Age – 0.07*Mileage
Selling price = 21611.42 - 621.80*6 - 0.07*68000
Selling price = $13120.62
Price
Age
Mileage
13611
4
61508
13779
9
54308
22987
3
8276
15349
7
24893
16393
2
22109
16596
2
23716
16930
6
47443
18489
3
16867
18842
1
35371
19813
1
29625
11850
6
55769
14977
5
46235
15913
3
37024
16492
5
45533
9453
10
86891
12972
4
77268
15705
6
59603
10519
9
93254
8912
11
48233
11913
9
42423
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