Question

The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.

The regression equation is
Y =20.0 + 7.21 X
Predictor	Coef	SE Coef	T
Constant	20.000	3.2213	6.21
X	7.210	1.3628	5.29
Analysis of Variance
SOURCE	DF	SS
Regression	1	41,587.6
Residual Error	7
Total	8	51,984.6

a. How many apartment buildings were in the sample?

b. Write the estimated regression equation (to 2 decimals if necessary).
ŷ = ________ + ___________x

c. What is the value of sb1 (to 4 decimals)?

d. Use the F statistic to test the significance of the relationship at a .05 level of significance.

Compute the F test statistic (to 2 decimals).

What is the p-value?
p-value is Select less than .01

between .01 and .025

between .025 and .05

between .05 and .10

greater than .10

What is your conclusion?
Select Conclude that the selling price is related to annual gross rents.

Cannot conclude that the selling price is related to annual gross rents.

e. Predict the selling price of an apartment building with gross annual rents of $50,000 (to 1 decimal).
$ ________thousands.

Answer 1

Answer to the question is as follows. Please write back in case of doubts:

a . Since total df = n-1 and df = 8 we have n = 9, which is the number of apartment buidlings in the sample

b. Y =20.0 + 7.21*X is the estimated regression equation

c.Value of sB1 is basically SE for X: 1.3628

d. Fstatistic = MS regression/MS residual error = ( (41.587.6/1)/( 51.9846-41.5876)/7) 27.999 or 28.00 to 2 decimals.

The p-value for P(F,df1,df2) = P(28, 1,7) = .001134. The result is significant at p < .05

e. The selling price of an apartments with gross annual rents of $50,000 is $360,5 or $360 thousand dolalrs