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).

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