Question

1. Multiple Regression:  A rental property owner in a midsized town of Appleton wants to determine the appropriate rent to charge in a new apartment complex and therefore wants to model the relationship between property Rent (Y)in dollars, the number of Bedrooms(x1), Square foot(x2) area of each apartment and whether the apartment comes with a Dishwasher(x3). Dishwasher is coded using a dummy variable that takes the value of 1 if the apartment comes with a dishwasher and 0 if it doesn’t. Using a random sample ofn = 60apartments in the area the owner obtains the following regression output. (15 points)

Model:   Y = b₀+ b₁Bedrooms+b₂Sqft+ b₃Dishwasher Dummy+e

Dishwasher Dummy 1   if Dishwasher included
                                   0   Otherwise

            

SUMMARY OUTPUT		Dependent Variable: Apartment Rent ($)
Regression Statistics
Multiple R	0.824
R Square	0.678
Adjusted R Square	0.661
Standard Error	92.757
Observations	60
ANOVA	df	SS	MS	F	Significance F
Regression	3	1015955.29	338651.76	39.36	8.11272E-14
Residual	56	481813.65	8603.82
Total	59	1497768.93
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	216.402	44.797	4.831	0.000	126.664	306.141
Bedrooms	59.936	27.504	2.179	0.034	4.838	115.033
Square feet area	0.276	0.069	3.981	0.000	0.137	0.415
Dishwasher	50.00	20.923	2.389	0.047	65.000	85.000

1. Write the equation for the regression equation in terms of the variables and the estimated coefficients? (include the t-stat below each coefficient value).

2. The value of R² and adjusted R², measure the goodness of fit of the model. Which is the appropriate estimate to use for multiple regression analysis? Explain what it means.

3. Given that Rent is measured in dollars, interpret the relationship between (a) number of Bedrooms and Rent and (b) Dishwasher and Rent. (Give your answerin the correct units)

4. Use the estimated equation in (A) to predict the Rent on a 2 Bedroom apartment, with 915 sqft area.
   1. With no Dishwasher

2. With Dishwasher

5. Conduct a test of hypothesis using a= 0.05, forb₁, b₂and b₃. Compare the model t-stats for each independent variable against the critical t-valuefor a 2-sided test and determine if the variable is significant in explaining home price.

                                          H₀:

                                          H_A:

            

Criticalt-value=

                        Show on a graph:

6. Use the t-statsfrom the Excel output to determine if you should accept or reject the H₀forb_1,b₂andb_3.

Are number of bedrooms significant in explaining apartment Rent? Square Feet Area?  

Answer 1