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 13,554 7 61,477 13,713 8 54,368 22,970 2 8,242 15,260 2 24,882 16,386 1 22,126 16,639 7 23,654 16,902 2 47,397 18,485 3 16,820 18,830 7 35,376 19,828 3 29,634 11,896 8 55,775 14,937 6 46,198 15,879 3 37,035 16,467 7 45,548 9,478 8 86,924 12,994 6 77,257 15,710 7 59,600 10,517 9 93,215 8,940 10 48,217 11,953 10 42,411 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.) Priceˆ = + Age + Miles. b. Interpret the slope coefficient of Age. The slope coefficient of Age is −487.30, which suggests that for every additional year of age, the predicted price of car decreases by $487.30. The slope coefficient of Age is −0.08, which suggests that for every additional year of age, the predicted price of car decreases by $0.08. The slope coefficient of Age is −487.30, which suggests that for every additional year of age, the predicted price of car decreases by $487.30, holding number of miles constant. The slope coefficient of Age is −0.08, which suggests that for every additional year of age, the predicted price of car decreases by $0.08, holding number of miles constant. c. Predict the selling price of a eight-year-old sedan with 68,000 miles. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Priceˆ = $

Answer 1

Solution:

Required regression model is given as below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.820884885
R Square	0.673851994
Adjusted R Square	0.635481641
Standard Error	2142.593861
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	161242092.1	80621046.06	17.56178745	7.31181E-05
Residual	17	78042043.67	4590708.451
Total	19	239284135.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	21600.31106	1203.935645	17.94141668	1.75217E-12	19060.22891	24140.39322
Age	-487.3008636	216.8667893	-2.247005478	0.03820909	-944.8497899	-29.75193742
Miles	-0.080926525	0.027545698	-2.937900674	0.009192767	-0.139042867	-0.022810182

a. Determine the sample regression equation that enables us to predict the price of a sedan on the basis of its age and mileage.

Price = 21600.31 - 487.30*Age - 0.08*Miles

(by using above regression output)

b. Interpret the slope coefficient of Age.

We are given a slope coefficient of age as -487.30, so correct interpretation is given as below:

The slope coefficient of Age is −487.30, which suggests that for every additional year of age, the predicted price of car decreases by $487.30, holding number of miles constant.

c. Predict the selling price of a eight-year-old sedan with 68,000 miles.

We are given age = 8, Miles = 68000

Price = 21600.31 - 487.30*Age - 0.08*Miles

Price = 21600.31 - 487.30*8 - 0.08*68000

Price = 12261.91