Question

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).

Answer 1

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

H₁: At least β_i = 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