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### 17.7 Problems

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A real estate agency has developed a regression model for setting sale prices for new residential home listings.

SalesPrice = 23839 + 91.17SquareFootage + 3650Fireplace

where Fireplace = -1 if the house does not have a fireplace +1 if the house does have a fireplaceUse the regression equation to predict the sales price for a 2500 square foot house without a fireplace.

Use the regression equation to predict the sales price for a 2500 square foot house with a fireplace.

What is the estimate of the average difference between the price of a house with a fireplace and a house without a fireplace?

A property tax assessor is concerned with the value that an in-ground swimming pool adds to a home. A multiple regression analysis based on a random sample he collected is given as follows:

HousePrice = 47648 + 125.6SquareFootage + 2826Pool + 6.2(SquareFootage*Pool)

where Pool = -1 if the house does not have a swimming pool +1 if the house does have a swimming poolWrite down the regression equation for a house with a swimming pool.

Use the equation to predict sales prices for a 2500 square foot house with a pool.

Write down the equation for a house without a swimming pool.

Use the equation to predict sales prices for a 2500 square foot house without a pool.

A real estate agent has created a regression model to help in understanding the value that a garage adds to a house. The capacity of the garage is categorized as No Garage, 1 Car Garage, or >2 Car Garage.

SalesPrice = 52765 + 127.8SquareFootage + 3209[1 car] + 5190[>2 car]

where the coded variables are as follows:

1 car 2 car 1 Car Garage +1 0 >2 Car Garage 0 +1 No Garage -1 -1 What is the effect on sales price for a house with a one-car garage?

What is the effect on sales price for a house with a three-car garage?

What is the effect on sales price for a house without a garage?

A municipality wishes to compare the response time (in minutes) between the public and private ambulance service. JMP output from a multiple regression relating distance to the call and the nominal variable, type of ambulance service, to response time is shown below:

Write down the multiple regression equation.

Is there a significant difference in response time between the two ambulance services? Set up and conduct an appropriate test of hypothesis.

Parameter Estimates

Term Estimate Std Error t Ratio Prot»|t| Intercept 2.454023 0.885174 2.77 0.0217 Distance (miles) 2.2068966 0.171884 12.84 <0001 Ambulance Service[Private] -1.821839 0.516248 -3.53 0.0064 A producer and seller of organically grown turkeys wants to evaluate the productivity of farms located in different regions of the country. Turkeys are raised for periods from 20 to 35 weeks and their weight is measured in kilograms. Of interest is whether there is a consistent difference in weight between turkeys raised in the North and in the South. Data on 13 turkeys are contained in the file turkey_weights.jmp. Construct a multiple regression to predict the weights of turkeys by age and region of origin.

In the Fit Model platform, enter the column "Weight (kg)" as the Y and the columns "Age (weeks)" and "Origin" as the model effects.

Write down the multiple regression equation.

Assess the goodness-of-fit of the regression model.

Is there a significant difference in the weights of turkeys based on region of origin? Explain!

An environmental advocacy organization wishes to investigate the claim that automobile fuel consumption is greater for front-wheel drive cars as compared to rear-wheel drive cars. The file FuelConsumptionDriveSystem.jmp contains the fuel efficiency (in miles/gal) and fuel consumption (in gal/mile) as reported by the Environmental Protection Agency for 18 randomly selected two-wheel drive cars. Also included are the car class, manufacturer, curb weight, and drive system (front-or rear-wheel). Curb weight is defined as the weight of a vehicle, without cargo, driver, and passengers, but including the maximum amounts of fuel, oil, coolant and standard equipment (e.g., the spare tire).

Describe the data.

Construct a regression model for highway fuel consumption using curb weight and drive system as the independent variables. What conclusion can be drawn from the model with regard to drive system and highway fuel consumption?

A corporate ethics office is investigating a claim that year-end bonuses are inequitably distributed between two sales divisions–residential and commercial. Sales_Bonus.jmp contains a random sample with three variables pertinent to the analysis for each sampled person: Experience (years), the Sales Division (Commercial, Residential), and the size of the Bonus ($). Use this data to construct a regression model that relates bonuses to sales division and experience. Is the claim of inequity supported by the data? Write a memo that summarizes the data, analysis, and findings.

A credit card company is evaluating factors that relate to the percentage of outstanding credit card balances paid. The company has obtained the FICO credit scores for 150 randomly selected cardholders in three age groups. FICO credit scores range from 300 for the poorest credit risk to 850 for the best credit risk. The age groups are defined as follows:

Young Adult = ages 21-35 years

Middle = 36-60 years

Senior = over 60 yearsThe data are contained in CreditCardPayments.jmp.

Construct a multiple regression equation that relates percentage of outstanding credit card balance to the independent variables age group and FICO score.

Use the Connecting Letters Report to describe differences between the three age groups.

Check the residuals for normality. Could you use the regression equation to predict the percentage of outstanding credit card balance for a Young Adult with a FICO score of 700? Explain!

Collegiate Gifts sells customized novelty items such as sweatshirts, T-shirts, and baseball hats to schools, civic organizations, and small businesses. The items are imprinted with an organization's logo or slogan. Typically, the lot sizes are relatively small, less than 100. The file, CollegiateGifts.jmp, contains information pertaining to Collegiate's profits in dollars per lot size for both sweatshirts and T-shirts.

Write down the multiple regression model to fit two lines with different slopes based on a nominal X-variable. Fit a multiple regression that accounts for different intercepts and slopes between lot size as a continuous X-variable and sweatshirts and T-shirts as levels of a nominal X-variable. (Use uncentered polynomials by clicking on the red triangle in the Fit Model window and unchecking Centered Polynomial.)

Check the R

^{2}and RMSE, as well as residual and leverage plots, to make sure this is a good equation. Are the slopes of the sweatshirts and T-shirt lines significantly different? (Explain why you can conclude that!)Write down the fitted multiple regression model. Explain the coefficients. (Hint for simplified analysis: Click on the red triangle of the Fit Model output. Go to Save Columns and Save Prediction Formula. Click on the heading of the newly saved column and bring up the Formula window. The Formula of the regression equation is right there.)

Could you have obtained the same results by fitting two individual simple regression lines? (Do this with the Fit Y by X platform by alternately excluding rows for sweatshirts and T-shirts.)