Question

2: A real estate agent is interested in what factors determine the selling price of homes...

2: A real estate agent is interested in what factors determine the selling price of homes in Northwest Arkansas. She takes a random sample of 20 homes, and conducts a multiple regression analysis. The dependent variable is price of the home (in thousands of dollars), the square footage of the home, and whether the home is located in a new subdivision (0 = no; 1 = yes). The results of the multiple regression analysis are shown below. Answer the following questions (a to e) using this output.

Regression Statistics

Multiple R

0.9604

R Square

0.9223

Adjusted R Square

0.9132

Standard Error

29.67

Observations

20

ANOVA

df

SS

MS

F

Significance F

Regression

2

177706.8

88853.4

100.94

3.6914E-10

Residual

17

14964.95

880.2914

Total

19

192671.7

Coefficients

SE

t Stat

P-value

Lower 95%

Upper 95%

Intercept

10.6185

44.7725

0.2372

0.8154

-83.84

105.08

Sq Ft

0.1987

0.0142

14.0076

0.0001

0.17

0.23

Nicholas Falls

33.5383

14.3328

2.3400

0.0317

3.30

63.78

a: Is the regression model significant at the .05 significance level? Explain your decision with reference to the output.

b: What is the percentage of variation explained by the independent variables? Please round your answer to two decimal places (i.e., 12.13%).

c: What independent variables are significant at the .05 significance level?

d: Identify the dummy variable. Is the dummy variable significant? Explain your decision using the output. If significant, what is the dummy variable’s impact on the dependent variable?

e: Summarize the results of the multiple regression analysis by writing the fitted multiple regression equation (use two decimal places).

Homework Answers

Answer #1

a. H0: β1 = β2 = 0, The model is not significant

H1: At least βi = is not 0, The model is significant

p-value (Significance F) = 0.000

Since p-value is less than 0.05, we reject the null hypothesis.

So, the model is significant.

b. Adjusted R-square = 0.9223 = 92.23%

c. Dummy varible is Nicholas Falls.

H0: β2 = 0, The dummy variable is not significant

H1: β2 ≠ 0, The dummy variable is significant

p-value = 0.0317

Since p-value is less than 0.05, we reject the null hypothesis.

So, the dummy variable is significant.

Coefficient of dummy variable = 33.5383

If the home is located in a new subdivision, the selling price increases by 33.5383 units.

d. Selling Price of Home = 10.62 + 0.20*Sqaure Footage + 33.54*Nicholas Falls

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