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 + 7.23 X
Predictor	Coef	SE Coef	T
Constant	20.000	3.2213	6.21
X	7.230	1.3625	5.29
Analysis of Variance
SOURCE	DF	SS
Regression	1	41,587.4
Residual Error	7
Total	8	51,984.2

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 s_b1 (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? Use Table 1 of Appendix B.
p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6

What is your conclusion?
SelectConclude that the selling price is related to annual gross rents.Cannot conclude that the selling price is related to annual gross rents.Item 7

e. Predict the selling price of an apartment building with gross annual rents of $60,000 (to 1 decimal).
$ thousands.

Answer 1

The regression equation is
Y = 20.0 + 7.23 X
Predictor	Coef	SE Coef	T
Constant	20.000	3.2213	6.21
X	7.230	1.3625	5.29
Analysis of Variance

ANOVA
	df	SS	MS	F
Regression	1	41587.4	41587.4	28.00013
Residual	7	10396.8	1485.257
Total	8	51984.2

a. 9 apartment buildings were in the sample?

b. the estimated regression equation
ŷ =20.00 +7.23  x

c. the value of sb1 is 1.3625

d) the F test statistic = 28.00

the p-value.
p-value is less than .01

Conclude that the selling price is related to annual gross rents

e. the selling price of an apartment building with gross annual rents of $60,000

ŷ =20.00 +7.23*60 =453.8 $ thousands.