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 + 7.25 X
Predictor	Coef	SE Coef	T
Constant	20.000	3.2213	6.21
X	7.250	1.3624	5.29
Analysis of Variance
SOURCE	DF	SS
Regression	1	41,587.3
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 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?

What is your conclusion?
A) Conclude that the selling price is related to annual gross rents. B) 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 $50,000 (to 1 decimal).
$ thousands.

Answer 1

Solution:

a)How many apartment buildings were in the sample?

We know df=n-1

8=n-1

n=9

So 9 apartment buildings were there in the sample.

b) Write the estimated regression equation.

Y = 20.0 + 7.25 X is the estimated regression equation.

c) What is the value of sb1?

The value of sb1=1.3624

d)Formula to find F statistic is given by

F statistic =SSR/(SSE/n-2)

Given:

Analysis of Variance
SOURCE	DF	SS
Regression	1	SSR=41587.3
Residual Error	7	SSE=10397.3
Total	8	SST=51984.6

So from the above table let us solve for F statistic.

F statistic =SSR/(SSE/n-2)

=41587.3/(10397.3/(9-1))

=28

P-value for 0.05 level of significance and df1=1 and df2=7 is 5.59 from the below table.

Conclusion:Since F statistic=28 is greater than F-critical value=5.59, we reject null hypothesis.

Therefore we conclude that the selling price is related to annual gross rent.

e)Predict the selling price of an apartment building with gross annual rents of $50,000

We know Y = 20.0 + 7.25 X

For X=50,000 the value of Y=20+(7.25*50)=380.5*1000=$380,500