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 ($1,000) Landscaping Expenditures ($1,000) 241 8.2 322 10.7 199 12.1 340 16.1 300 15.7 400 18.8 800 23.5 200 9.5 522 17.5 548 22.0 436 12.2 463 13.5 635 17.8 357 13.8 (a) Develop a scatter diagram with home value as the independent variable. 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 (199, 21.8) to (800, 6.5). 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 (8.2, 199) 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 (199, 8.2) to (800, 23.5). 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 down and right from (6.5, 800) to (21.8, 199). 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 a positive linear relationship between home value and landscaping expenditures. The scatter diagram indicates a nonlinear relationship between home value and landscaping expenditures.The scatter diagram indicates no apparent 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 $475,000. (Round your answer to the nearest dollar.)

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 ($1,000) Landscaping Expenditures ($1,000) 241 8.2 322 10.7 199 12.1 340 16.1 300 15.7 400 18.8 800 23.5 200 9.5 522 17.5 548 22.0 436 12.2 463 13.5 635 17.8 357 13.8 (a) Develop a scatter diagram with home value as the independent variable. 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 (199, 21.8) to (800, 6.5). 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 (8.2, 199) 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 (199, 8.2) to (800, 23.5). 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 down and right from (6.5, 800) to (21.8, 199). 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 a positive linear relationship between home value and landscaping expenditures. The scatter diagram indicates a nonlinear relationship between home value and landscaping expenditures.The scatter diagram indicates no apparent 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 $475,000. (Round your answer to the nearest dollar.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...

See similar textbooks

Related questions

Question

100%

Home Value ($1,000)	Landscaping Expenditures ($1,000)
241	8.2
322	10.7
199	12.1
340	16.1
300	15.7
400	18.8
800	23.5
200	9.5
522	17.5
548	22.0
436	12.2
463	13.5
635	17.8
357	13.8

(a)

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

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 (199, 21.8) to (800, 6.5). 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 (8.2, 199) 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 (199, 8.2) to (800, 23.5). 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 down and right from (6.5, 800) to (21.8, 199). 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 a positive linear relationship between home value and landscaping expenditures. The scatter diagram indicates a nonlinear relationship between home value and landscaping expenditures.The scatter diagram indicates no apparent 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 $475,000. (Round your answer to the nearest dollar.)

Expert Solution

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here