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.

Analysis of Variance

SOURCE	DF	Adj SS
Regression	1	41587.3
Error	7
Total	8	51984.1

Predictor	Coef	SE Coef	T-Value
Constant	20.000	3.2213	6.21
X	7.210	1.3626	5.29

Regression Equation

Y = 20.0 + 7.21 X

(a)

How many apartment buildings were in the sample?

(b)

Write the estimated regression equation.

ŷ =

(c)

What is the value of

s_b1?

(d)

Use the F statistic to test the significance of the relationship at a 0.05 level of significance.

State the null and alternative hypotheses.

H₀: β₁ ≥ 0
H_a: β₁ < 0H₀: β₁ = 0
H_a: β₁ ≠ 0    H₀: β₀ = 0
H_a: β₀ ≠ 0H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.Reject H₀. We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.     Reject H₀. We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.Do not reject H₀. We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.

(e)

Predict the selling price (in thousands of dollars) of an apartment building with gross annual rents of $55,000.----------

$  thousand

Answer 1

Answer: 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	Adj SS
Regression	1	41587.3
Error	7
Total	8	51984.1

Predictor	Coef	SE Coef	T-Value
Constant	20.000	3.2213	6.21
X	7.210	1.3626	5.29

Regression Equation

Y = 20.0 + 7.21 X

Solution:

a)How many apartment buildings were in the sample?

df = n-1

8 = n-1

Sample size, n = 9

b) Write the estimated regression equation.

ŷ = 20.0 + 7.21 X

c) What is the value of sb1?

From the given data output,

Standard error of b1,Sb1 = 1.3626

d) Use the F statistic to test the significance of the relationship at a 0.05 level of significance.

State the null and alternative hypotheses.

H0: β1 = 0

Ha: β1 ≠ 0

e) Predict the selling price (in thousands of dollars) of an apartment building with gross annual rents of $55,000.

X = 55 (in thousands of dollars)

ŷ = 20.0 + 7.21 X

ŷ = 20.0 + 7.21 * 55

ŷ = 416.55 (in thousands of dollars).