Jack Sprague is the relocation specialist for a real estate firm in the town of Arlington, Massachusetts. He has been working with a client who wishes to purchase a single-family home in Arlington. After seeing the information that Jack provided, the client is perplexed by the variability of home prices in Arlington. She is especially puzzled by the premium that a colonial house commands. (A colonial house is a style dating back to the time of the American colonies, with a simple rectangular structure and a peaked roof.) Despite Jack's eloquent explanations, it seems that the client will not be satisfied until she understands the quantitative relationship between house prices and house characteristics. Jack decides to use a multiple regression model to provide the client with the necessary information. He collects data on the prices for 36 single-family homes in Arlington sold in the first quarter of 2009. Also included in the data is the information on square footage, the number of bedrooms, the number of bathrooms, and whether or not the house is a colonial (1 for colonial; 0 otherwise). A portion of the data is shown in the accompanying table.

Data for Case Study 17.2 Sales Information of Single-Family Homes in Arlington, MA

In a report, use the sample information to:

1. Estimate and interpret three models, where d is the colonial dummy variable.

Model 1: Price = β₀ + β₁Sqft + β₂Beds + β₃Baths + β₄d + ????.

Model 2: Price = β₀ + β₁Sqft + β₂Beds + β₃Baths + β₄(Sqft × d ) + ????.

Model 3: Price = β₀ + β₁Sqft + β₂Beds + β₃Baths + β₄d + β₅(Sqft × d) + ????.

2. Choose which model is more reliable in predicting the price of a house. Provide at least one reason for your choice. Are price differences between colonial homes versus other styles fixed and/or changing at the 5% significance level?

3. Use this model to make predictions for a colonial home versus other styles, given the average values of the explanatory variables.

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Price $840,000 822,000 Square feet 2,768 2,500 Baths 3.5 2.5 edrooms Colonial 4 4 307,500 拱词》 0