A large land developer had just completed the division of a parcel of land into 500 lots. From his experience, he established selling prices for 20 lots and asked his daughter Jane to set prices for the remaining lots. Jane, a recent M.B.A. from NYIT, knew that size, view, slope, and elevation are the only four variables, which could influence the price of a lot. Both Jane and her father tried to quantify the impact of these variables on the price of a lot, without any success. Jane decided to use Multiple Regression, a technique she had learnt from her favorite professor in the M.B.A. program. She collected data (Area in thousands of square feet, Elevation in feet, Slope in degrees, View scale 1 for poor up to 9 for excellent, and price in thousands of dollars) for the 20 lots priced by her father and did four regression runs as shown in the following page. She picked the best regression equation and priced the remaining lots. Her father looked at her prices and agreed that she had done an excellent job.
(e) Can she use this equation to set prices of lots in other developments?
Summary of statistics from regression runs for Question #2:
Regression Run #1 – Lot price versus area, elevation, slope, and view (4 independent variables)
R Square = 0.85 Calculated F = 20.9 Standard Error of Estimate = 0.53
| Description | Regression Coefficient | Calculated T Value |
| Intercept | 0.24 | 0.14 |
| Area (000 sq. ft.) | 0.10 | 1.99 |
| Elevation (feet) | 0.01 | 1.09 |
| Slope (degrees) | 0.03 | 0.84 |
| View (0-9) | 0.20 | 2.30 |
Regression Run #2 – Lot price versus area, elevation, and view (3 independent variables)
R Square = 0.84 Calculated F = 28.1 Standard Error of Estimate = 0.52
| Description | Regression Coefficient | Calculated T Value |
| Intercept | 0.62 | 0.38 |
| Area (000 sq. ft.) | 0.12 | 2.61 |
| Elevation (feet) | 0.007 | 0.78 |
| View (0-9) | 0.253 | 3.75 |
Regression Run #3 – Lot price versus area, and view (2 independent variables)
R Square = 0.83 Calculated F = 42.83 Standard Error of Estimate = 0.51
| Description | Regression Coefficient | Calculated T Value |
| Intercept | 1.78 | 2.82 |
| Area (000 sq. ft.) | 0.10 | 2.53 |
| View (0-9) | 0.29 | 7.17 |
Regression Run #4 – Lot price versus view (1 independent variable)
R Square = 0.77 Calculated F = 60.90 Standard Error of Estimate = 0.49
| Description | Regression Coefficient | Calculated T Value |
| Intercept | 3.27 | 1.59 |
| View (0-9) | 0.34 | 7.81 |
In the world of real estate development, determining the right price for properties can be a complex and challenging task. In this case study, we delve into the story of Jane, a recent MBA graduate from NYIT, who was tasked with setting prices for 500 lots in a new development. Her approach, utilizing multiple regression analysis, sheds light on the intricate process of pricing real estate.
Understanding the Challenge
Jane’s father, a seasoned land developer, had already priced 20 lots in the development but was unable to quantify the influence of various factors on lot prices accurately. The key variables identified were size, view, slope, and elevation. To address this issue, Jane turned to the statistical technique of multiple regression analysis, which she had learned during her MBA program.
Collecting Data
Jane collected data for the 20 lots priced by her father, gathering information on the area (in thousands of square feet), elevation (in feet), slope (in degrees), view (rated on a scale of 1 to 9), and lot price (in thousands of dollars). Armed with this data, she conducted four regression runs to find the most suitable equation for predicting lot prices.
Selecting the Best Model
Jane’s selection of the best regression equation was based on several statistical criteria. The equation she chose included all four independent variables: area, elevation, slope, and view. The equation looked like this:
Price (in thousands of dollars) = 0.24 + 0.10 * Area + 0.01 * Elevation + 0.03 * Slope + 0.20 * View
Her choice was influenced by the equation’s high R-squared value (0.85), indicating its ability to explain a significant portion of the variance in lot prices. Additionally, the F-statistic (20.9) suggested that the overall model was statistically significant.
Significant Variables
Analyzing the T-values in Regression Run #1, it becomes apparent that the most significant variable affecting lot prices was “View,” with the highest T-value of 2.30. Following closely was “Area” with a T-value of 1.99. Conversely, “Elevation” and “Slope” had relatively lower T-values, indicating potentially less significance in determining lot prices. However, it’s essential to consider practical significance along with statistical significance when interpreting the importance of variables.
Price Prediction with Confidence
Jane’s regression model allows her to predict lot prices with confidence. For instance, if she needed to set a price with 99% confidence for a lot with excellent view, a 100-degree slope, 20,000 square feet area, and a 200-foot elevation, she could use the equation:
Price = 0.24 + 0.10 * Area + 0.01 * Elevation + 0.03 * Slope + 0.20 * View
Substituting the values:
Price = 0.24 + 0.10 * 20 + 0.01 * 200 + 0.03 * 100 + 0.20 * 9
Price = 2.4 + 2 + 2 + 3 + 1.8
Price = $11.2 thousand (or $11,200)
Therefore, the price for a lot with excellent view, a 100-degree slope, 20,000 square feet area, and a 200-foot elevation is approximately $11,200.
Generalization to Other Developments
One of the critical considerations in Jane’s analysis is the transferability of her regression equation to other developments. While her model performed well for the specific development in question, applying it to different areas or markets requires caution.
Real estate markets can vary significantly based on location, local regulations, amenities, and market trends. Thus, Jane should validate her model’s performance by collecting and analyzing data specific to the areas of interest. What drives lot prices in one location may not hold true in another. Additionally, external factors and market dynamics play a crucial role in influencing real estate prices.
In conclusion, Jane’s use of multiple regression analysis in pricing lots provides valuable insights into the complexities of real estate valuation. Her selection of the best-fit model, identification of significant variables, and ability to predict prices with confidence illustrate the power of statistical tools in the field of real estate development. However, it is essential to exercise caution and consider local factors when applying such models to new developments or markets to ensure accurate pricing and informed decision-making.
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