Answered: Car manufacturers produced a variety of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	13	70.0
B	18	975.0
C	15	102.5
D	17	475.0
E	18	1,600.0
F	19	2,675.0
G	19	4,000.0
H	16	375.0
I	16	250.0
J	17	375.0
K	14	37.0
L	16	100.0
M	17	165.0
N	19	1,275.0
O	18	400.0

(a)

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

-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, 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.

Does a simple linear regression model appear to be appropriate? Explain.

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

-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.

(b)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x² 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 = ??

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