Question

1. 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.

Analysis of Variance SOURCE DF Regression 1 Error 7 Total 8

Predictor Coef Constant 20.000 X

Adj SS 41587.3

51984.1

SE Coef T-value 3.2213 6.21 1.3626 5.29

(a) How many apartment buildings are in the sample?
(b) What is the value of b1.
(c) Write the estimated regression equation.
(d) Use the F statistic to test the significance of the relationship at a 0.05 level of

significance.
(e) Predict the selling price of an apartment with gross rents of $50 000.

Answer 1

(a) (3 marks) How many apartment buildings are in the sample?

df = 8

We know that df = n - 1 = 9 - 1 = 8

Therefore, there are 9 apartment buildings in the sample.

(b) (4 marks) What is the value of b1.

The value of b1 is 6.21

(c) (6 marks) Write the estimated regression equation.

The estimated regression equation is:

y = 20.000 + 6.21*x

(d) (6 marks) Use the F statistic to test the significance of the relationship at a 0.05 level of

significance.

The p-value for f statistic = 5.29 is 0.0550.

Since the p-value (0.0550) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the relationship is significant at a 0.05 level of significance.

(e) (3 marks) Predict the selling price of an apartment with gross rents of $50 000.

The estimated regression equation is:

y = 20.000 + 6.21*x

Put x = 50

y = 20.000 + 6.21*50

y = 330.5 (in thousands of dollars))

Or Selling price = $330500