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 
3.6914E10 

Residual 
17 
14964.95 
880.2914 

Total 
19 
192671.7 

Coefficients 
SE 
t Stat 
Pvalue 
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).
a. H_{0}: β_{1} = β_{2} = 0, The model is not significant
H_{1}: At least β_{i} = is not 0, The model is significant
pvalue (Significance F) = 0.000
Since pvalue is less than 0.05, we reject the null hypothesis.
So, the model is significant.
b. Adjusted Rsquare = 0.9223 = 92.23%
c. Dummy varible is Nicholas Falls.
H_{0}: β_{2} = 0, The dummy variable is not significant
H_{1}: β_{2} ≠ 0, The dummy variable is significant
pvalue = 0.0317
Since pvalue 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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