MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A landscaping company has collected data on home values (in thousands of $) and expenditures (in thousands of $) on landscaping with the hope of developing a predictive model to help marketing to potential new clients. Suppose the following table represents data for
14 households.
Home
Value
Landscaping
Expenditures
($1,000)
($1,000)
241
8.2
322
10.7
197
12.1
340
16.3
300
15.7
400
18.8
800
23.5
200
9.5
522
17.5
546
22.0
438
12.2
463
13.5
635
17.8
357
13.8
(a) Develop a scatter diagram with home value as the independent variable.
900
900
800
800
20
20
700
700
600
600
15
15
500
500
400
400
300
300
200
200
100
100
100 200 300 400 500 600 700 800 900
10
15
20
25
100 200 300 400 500 600 700 800 900
5
10
15
20
25
Home Value ($1,000)
Landscaping Expenditures ($1,000)
Home Value ($1,000)
Landscaping Expenditures ($1,000)
Landscaping Expenditures ($1,000)
Home Value ($1,000)
Landscaping Expenditures ($1,000)
Home Value ($1,000)
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Transcribed Image Text:A landscaping company has collected data on home values (in thousands of $) and expenditures (in thousands of $) on landscaping with the hope of developing a predictive model to help marketing to potential new clients. Suppose the following table represents data for 14 households. Home Value Landscaping Expenditures ($1,000) ($1,000) 241 8.2 322 10.7 197 12.1 340 16.3 300 15.7 400 18.8 800 23.5 200 9.5 522 17.5 546 22.0 438 12.2 463 13.5 635 17.8 357 13.8 (a) Develop a scatter diagram with home value as the independent variable. 900 900 800 800 20 20 700 700 600 600 15 15 500 500 400 400 300 300 200 200 100 100 100 200 300 400 500 600 700 800 900 10 15 20 25 100 200 300 400 500 600 700 800 900 5 10 15 20 25 Home Value ($1,000) Landscaping Expenditures ($1,000) Home Value ($1,000) Landscaping Expenditures ($1,000) Landscaping Expenditures ($1,000) Home Value ($1,000) Landscaping Expenditures ($1,000) Home Value ($1,000)
(b) What does the scatter plot developed in part (a) indicate about the relationship between the two variables?
O The scatter diagram indicates no apparent relationship between home value and landscaping expenditures.
O The scatter diagram indicates a positive linear relationship between home value and landscaping expenditures.
O The scatter diagram indicates a nonlinear relationship between home value and landscaping expenditures.
O The scatter diagram indicates a negative linear relationship between home value and landscaping expenditures.
(c) Use the least squares method to develop the estimated regression equation. (Let x = home value (in thousands of $), and let y = landscaping expenditures (in thousands of $). Round your numerical values to five decimal places.)
(d) For every additional $1,000 in home value, estimate how much additional will be spent (in $) on landscaping. (Round your answer to the nearest cent.)
$
(e) Use the equation estimated in part (c) to predict the landscaping expenditures (in $) for a home valued at $475,000. (Round your answer to the nearest dollar.)
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Transcribed Image Text:(b) What does the scatter plot developed in part (a) indicate about the relationship between the two variables? O The scatter diagram indicates no apparent relationship between home value and landscaping expenditures. O The scatter diagram indicates a positive linear relationship between home value and landscaping expenditures. O The scatter diagram indicates a nonlinear relationship between home value and landscaping expenditures. O The scatter diagram indicates a negative linear relationship between home value and landscaping expenditures. (c) Use the least squares method to develop the estimated regression equation. (Let x = home value (in thousands of $), and let y = landscaping expenditures (in thousands of $). Round your numerical values to five decimal places.) (d) For every additional $1,000 in home value, estimate how much additional will be spent (in $) on landscaping. (Round your answer to the nearest cent.) $ (e) Use the equation estimated in part (c) to predict the landscaping expenditures (in $) for a home valued at $475,000. (Round your answer to the nearest dollar.)
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