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	16	225.0
B	16	375.0
C	19	1,325.0
D	18	1,625.0
E	19	4,025.0
F	17	400.0
G	15	102.5
H	14	87.0
I	17	450.0
J	17	140.0
K	19	2,675.0
L	18	1,000.0
M	18	350.0
N	16	100.0
O	13	95.0

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

A scatter diagram has 15 points. The horizontal axis ranges from 12 to 20 and is labeled: Rating. The vertical axis ranges from 0 to 4500 and is labeled: Price. Moving from left to right, the first point is located at approximately (13, 4300), with the general trend of the next 5 points moving downward rapidly, ending around 750 on the vertical axis. The next 9 points move downward much more slowly in a diagonal direction, staying fairly clustered between 250 and 750 on the vertical axis.

A scatter diagram has 15 points. The horizontal axis ranges from 12 to 20 and is labeled: Rating. The vertical axis ranges from 0 to 4500 and is labeled: Price. Moving from left to right, the first point is located at approximately (13, 100) and the next 9 points stay fairly clustered between 0 and 500 on the vertical axis. The next 5 points move up rapidly, beginning at approximately 1000 on the vertical axis and ending with the last point around 4000 on the vertical axis.

A scatter diagram has 15 points. The horizontal axis ranges from 12 to 20 and is labeled: Rating. The vertical axis ranges from 0 to 4500 and is labeled: Price. Moving from left to right, the first point is located at approximately (13, 300) and the next 9 points stay fairly clustered between 250 and 750 on the vertical axis. The next 5 points move up rapidly, beginning at approximately 1250 on the vertical axis and ending with the last point around 4250 on the vertical axis.

A scatter diagram has 15 points. The horizontal axis ranges from 12 to 20 and is labeled: Rating. The vertical axis ranges from 0 to 4500 and is labeled: Price. Moving from left to right, the first point is located at approximately (13, 4000), with the general trend of the next 5 points moving downward rapidly, ending around 500 on the vertical axis. The next 9 points move downward much more slowly in a diagonal direction, staying fairly clustered between 0 and 500 on the vertical axis.

Does a simple linear regression model appear to be appropriate?

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

(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 =

(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) =

(d)

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

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

Answer 1

(a) The scatter diagram isa s follows:

Looking at the diagram, the relationship doesn't appear to be linear. The corerct option to be chosen is:

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

(b) To find the regression equation, we select the trend line option on the scatter plot and then select polynomial of order 2. The result is as shown below:

(c) To find the required equation, we select "Power" option in the choices for trendline. The result is as follows:

Log (y) = Log (8 x 10^-10) + 9.5558 x Log (x)

(d) Comparing the above two plots, we see that R² is higher in the equation shown in part (c). Hence the correct option to be chosen is: The model in part (c) is preferred because r² is higher and the p-value is lower.