A real estate analyst is studying the relationship between home sales prices and living space (square footage) in a local housing market. The reason for this study is strategic: When offering a home for sale, it is important to choose a starting sales price that is close to the market price for homes of a similar characteristics. Why? If a home is first offered at a selling price that is too far below the market price, the seller will not be able to realize the full value of selling his or her home. If a home is first offered at a selling price that is too far above the market price, the home will not be likely to attract any buyers and the seller will be forced to make subsequent price reductions. In turn, these price reductions will be interpreted by buyers as desperation on the part of the seller, and buyers will act on this desperation by waiting for further price reductions. Again, this will leave the seller less likely to realize the full value of selling his or her home. It should be noted that this same strategic question is basis for the financial analysis of initial public offeringsor IPOsof corporate stocks.

The model underlying this study is based on practical real estate experience: The two most important characteristics of a home are its location and living space, and since all of the homes of interest are in the same geographic area, the remaining characteristic of importance is size. Presumably, a larger living space will command a higher price, so the research question is not whether or not these two quantitative properties of a home sale are related, but more specifically the exact quantitative nature of the relationship. That is, given a homes size, what is a reasonable selling price to expect? To address this question, the analyst has conceptually constructed the linear model

Sales Price = (b* Size) + c

wherebrepresents the differential pricing applied to the square footage of the home being offered for sale.

Based on this conceptual model, and motivated by the desire to have a strategic advantage in constructing home selling offers for her clients, the analyst has collected the sales history of twenty-five homes sold in the town over a three-month period. These data included prices, in thousands of dollars, and living spaces, in square footages. Applying a statistical software package to the data, the analyst has found the following results.

Mean Sales Price = $296,360

Mean Square Footage = 1647.04

Furthermore, she found the following linear relationship:

Sales Price = 200 (Square Footage) 33,574

1. What is the typical sales price for the community?

2. How large is the typical home?

3. What is the slope of the linear model?

What does the slope represent?

4. What is the constant of the linear model?

What does the constant represent?

5. If Home A is 1400 square feet, what is the expected sales price?

6. A builder is interested in constructing a home in the community. As she considers the prospective home size, for every additional square foot, how much can the builder expect the sales price to differ?