Question

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 10.9 197 12.3 340 16.3 300 15.7 400 18.8 800 23.5 200 9.5 522 17.5 548 22.0 438 12.2 463 13.5 635 17.8 357 13.8 (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.) Û = = 6.42008 + 0.02119x (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.) $ 27.60 x (e) Use the equation estimated in part (c) to predict the landscaping expenditures (in $) for a home valued at $275,000. (Round your answer to the nearest dollar.) $ 5834 X

Answer 1

The additional landscaping expenditure for every $1,000 increase in home value is $21.19, and for a home valued at $275,000, the predicted landscaping expenditure is approximately $12,247.

Step-by-step explanation:

The student is asking about the least squares method for developing a regression equation using a given set of data with home values as the independent variable (x) and landscaping expenditures as the dependent variable (y). The estimated regression equation provided is Û = 6.42008 + 0.02119x. This means the intercept is $6,420.08 and the slope is $21.19, reflecting the change in landscaping expenditures for every thousand-dollar increase in home value.

For part (d), the additional amount spent on landscaping for every additional $1,000 in home value is $21.19. This is directly given by the slope of the regression equation.

For part (e), to predict the landscaping expenditures for a home valued at $275,000, we substitute the home value into the equation as x = 275 (since the values are in thousands). Calculation is as follows:

Û = 6.42008 + 0.02119(275) = Û = $6,420.08 + $5,827.25 = $12,247.33 (rounded to the nearest dollar). Therefore, the predicted expenditure is approximately $12,247.

Answer 2

The question involves using the least squares method to develop a regression model, predicting additional landscaping expenditure per $1,000 increase in home value, and estimating the expenditure for a particular home value.

Step-by-step explanation:

The question concerns the development of a predictive regression model in the context of a landscaping company looking to predict future expenditures based on home values. To develop the estimated regression equation, the least squares method is used, which minimizes the sum of the squares of the residuals (the differences between the observed and predicted values). The model provided, Û = 6.42008 + 0.02119x, suggests that for every additional $1,000 in home value, approximately an additional $21.19 is spent on landscaping. To predict the landscaping expenditure for a home valued at $275,000, we substitute x=275 into the regression equation to get Û = 6.42008 + (0.02119 * 275), which yields an estimated expenditure.

Calculation using the provided regression equation:

• Plugging in the value of x=275 into the equation gives us Û = 6.42008 + (0.02119 * 275).
• Performing the calculation yields Û = 6.42008 + 5.82725.
• Adding the two gives us Û = 12.24733 thousand dollars, or $12,247.33 when rounded to the nearest dollar.