Question

Car manufacturers produced a variety of classic cars that continue to increase in value. Suppose the following data is based upon the Martin Rating System for Collectible Cars, and shows the rarity rating (1–20) and the high price ($1,000) for 15 classic cars.

Model	Rating	Price ($1,000)
A	14	37.0
B	19	1,300.0
C	16	125.0
D	17	140.0
E	18	1,575.0
F	16	250.0
G	17	375.0
H	17	425.0
I	18	400.0
J	19	2,650.0
K	19	4,000.0
L	18	975.0
M	15	77.5
N	16	325.0
O	13	95.0

(a)

Develop a scatter diagram of the data using the rarity rating as the independent variable and price as the independent variable.

a

Does a simple linear regression model appear to be appropriate?

No, there doesn't appear to be a relationship between the two variables.

Yes, there appears to be a linear relationship between the two variables.    

No, there appears to be a curvilinear relationship between the two variables.

(b)

Develop an estimated multiple regression equation with x = rarity rating and

x²

as the two independent variables. (Round b₀ and b₁ to the nearest integer and b₂ to one decimal place.)ŷ =

34426−4645x+155.8x2 (Wrong)

(c)

Consider the nonlinear relationship shown by equation (16.7):

E(y) = β₀β₁^x

Use logarithms to develop an estimated regression equation for this model. (Round b₀ to three decimal places and b₁ to four decimal places.)

log(ŷ) =

−10.280+10.5200log(x) (Wrong)

(d)

Do you prefer the estimated regression equation developed in part (b) or part (c)? Explain.

The model in part (c) is preferred because r² is lower and the p-value is lower.

The model in part (c) is preferred because r² is higher and the p-value is lower.    

The model in part (b) is preferred because r² is higher and the p-value is lower. (wrong)

The model in part (b) is preferred because r² is lower and the p-value is lower.

Answer 1

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x	y	logx	logy
14	37	1.146128	1.568202
19	1300	1.278754	3.113943
16	125	1.20412	2.09691
17	140	1.230449	2.146128
18	1575	1.255273	3.197281
16	250	1.20412	2.39794
17	375	1.230449	2.574031
17	425	1.230449	2.628389
18	400	1.255273	2.60206
19	2650	1.278754	3.423246
19	4000	1.278754	3.60206
18	975	1.255273	2.989005
15	77.5	1.176091	1.889302
16	325	1.20412	2.511883
13	95	1.113943	1.977724