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.

1. What is wrong with the regression runs she did not use?

1. Specify the equation used by her? Why?

1. Which variables are significant in determining the price of a lot? Which is most significant?

1. If she were to set a price with 99% confidence on a lot with excellent view, 10^o slope, 20,000 square feet area and 200 feet elevation, what will it be?

(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