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 (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.)
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 (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.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question
5h.
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 |
(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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