David's Landscaping 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. Data for 14 households may be found in the file Landscape.

Home
Value
($1,000) Landscaping
Expenditures
($1,000)

242 8.1

321 10.8

198 12.2

340 16.2

300 15.6

400 18.9

800 23.5

200 9.5

521 17.5

547 22.0

437 12.1

464 13.5

635 17.9

356 13.9

(a)

Develop a scatter diagram with home value as the independent variable.

A scatter diagram has a horizontal axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25 and a vertical axis labeled "Home Value ($1,000)" with values from 0 to 900. The scatter diagram has 14 points. A pattern goes down and right from (6.5, 800) to (21.9, 198). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25 and a vertical axis labeled "Home Value ($1,000)" with values from 0 to 900. The scatter diagram has 14 points. A pattern goes up and right from (8.1, 198) to (23.5, 800). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "Home Value ($1,000)" with values from 0 to 900 and a vertical axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25. The scatter diagram has 14 points. A pattern goes up and right from (198, 8.1) to (800, 23.5). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "Home Value ($1,000)" with values from 0 to 900 and a vertical axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25. The scatter diagram has 14 points. A pattern goes down and right from (198, 21.9) to (800, 6.5). The points are scattered moderately from the pattern.

(b)

What does the scatter plot developed in part (a) indicate about the relationship between the two variables?

The scatter diagram indicates a negative linear relationship between home value and landscaping expenditures.The scatter diagram indicates no apparent relationship between home value and landscaping expenditures. The scatter diagram indicates a nonlinear relationship between home value and landscaping expenditures.The scatter diagram indicates a positive 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.)

ŷ =

(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 $575,000. (Round your answer to the nearest dollar.)

$

Question

David's Landscaping 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. Data for 14 households may be found in the file Landscape.

Home Value ($1,000)	Landscaping Expenditures ($1,000)
242	8.1
321	10.8
198	12.2
340	16.2
300	15.6
400	18.9
800	23.5
200	9.5
521	17.5
547	22.0
437	12.1
464	13.5
635	17.9
356	13.9

(a)

Develop a scatter diagram with home value as the independent variable.

A scatter diagram has a horizontal axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25 and a vertical axis labeled "Home Value ($1,000)" with values from 0 to 900. The scatter diagram has 14 points. A pattern goes down and right from (6.5, 800) to (21.9, 198). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25 and a vertical axis labeled "Home Value ($1,000)" with values from 0 to 900. The scatter diagram has 14 points. A pattern goes up and right from (8.1, 198) to (23.5, 800). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "Home Value ($1,000)" with values from 0 to 900 and a vertical axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25. The scatter diagram has 14 points. A pattern goes up and right from (198, 8.1) to (800, 23.5). The points are scattered moderately from the pattern.

A scatter diagram has a horizontal axis labeled "Home Value ($1,000)" with values from 0 to 900 and a vertical axis labeled "Landscaping Expenditures ($1,000)" with values from 0 to 25. The scatter diagram has 14 points. A pattern goes down and right from (198, 21.9) to (800, 6.5). The points are scattered moderately from the pattern.

(b)

What does the scatter plot developed in part (a) indicate about the relationship between the two variables?

The scatter diagram indicates a negative linear relationship between home value and landscaping expenditures.The scatter diagram indicates no apparent relationship between home value and landscaping expenditures. The scatter diagram indicates a nonlinear relationship between home value and landscaping expenditures.The scatter diagram indicates a positive 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.)

ŷ =

(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 $575,000. (Round your answer to the nearest dollar.)

$

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