Question

6. A business owner is looking to purchase a new office, and is considering the sale of other offices across a city in order to determine what prices he can expect to pay. Using the following data, perform an ordinary least squares regression of building price on lot size, the number of stories in the building, and whether the building is air conditioned.

Latitude	Longitude	Price	Lot size	Stories	Air conditioning
44	16	1960	0.956	1	0
54	13	19982	7.948	1	0
51	9	11306	5.835	1	0
41	12	5860	1.563	1	0
47	13	17303	7.093	1	1
54	15	24418	9.073	2	0
53	6	16723	8.426	2	0
46	14	13431	5.507	1.5	1
45	11	3910	0.879	1.5	0
53	5	12028	5.156	1	0
32	6	26618	9.697	2	1
34	7	20201	8.092	1	1
35	11	8788	2.202	1	1
37	11	17242	6.608	1.5	0
26	20	22261	5.754	1.5	1

Give the regression equation. Do the residuals show signs of autocorrelation? Produce a graph of the residuals relative to their position in space.

7. Assume that the “neighbors” of the buildings are restricted to the closest observation. Create an added variable plot for the variable y_i* = sum(j = 1 to n) w_ijy_j. Does the plot show a significant correlation? Should the variable be included?

Answer 1

The Regression Equation is given as:

Price=2085.74*Lot Size+2076.15*Stories+2930.82*(Air Conditioning)-928.36

But the coefficients of Stories and Air conditioning are not significant at an alpha level of 5% and hence they can be ignored as part of our regression equation.

Lot size Residual Plot 10000 5000 Residuals 0 2 4 6 8 10 12 -5000 Lot size

Stories Residual Plot 10000 5000 Residuals 0.5 1.5 2 2.5 -5000 Stories

Air conditioning Residual Plot 10000 Residuals 0 0.2 0.4 0.6 0.8 1 -10000 Air conditioning

For question 7, more information is needed about the w, y, i and j variables as to what they represent.