Question

A real estate agent in Athens used regression analysis to investigate the relationship between apartment sales prices and the various characteristics of apartments and buildings. The variables collected from a random sample of 25 compartments are as follows:
Sale price: The sale price of the apartment (in €)
Apartments: Number of apartments in the building
Age: Age of the building (in years)
Size: Apartment size (area in square meters)
Parking spaces: Number of car parking spaces in the building
Excellent building condition (Pseudo-variable): 1 if the condition of the building is
excellent, 0 different
Good building condition (Pseudo-variable): 1 if the condition of the building is
good, 0 different

We have the following results of regression analysis with the OLS method:

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	98308,606	22888,689		4,295	,000
	Apartments	5776,999	1215,251	,344	4,754	,000
	Age	-905,594	269,262	-,111	-3,363	,003
	Size	1237,643	142,945	,586	8,658	,000
	Parking space	2966,996	1313,465	,096	2,259	,037
	Excellent	52337,908	19957,138	,108	2,623	,017
	Good	5543,922	16714,509	,013	,332	,744
a. Dependent Variable: Sale price

Questions:
1. State the estimated regression equation.

2. Comment on the importance of the regression rates.

3. Give the interpretation of the regression coefficients.

Answer 1

The estimated regression equation, as sale is the depedent variable would be:

1. Sale = 22888689 + 1215251*Apartment + 269262*Age +142945*Size + 1313465*Parking Space + 19957138*Excellent + 16714509*Good

2. From the given output of the regression analysis, we found the P-Value (Sig.) of Apartment, Age, Size, Parking Space and Excellent as 0.000, 0.003, 0.000, 0.037, 0.017 respectively which is less than the level of significance 0.05, therefore we reject the null hypothesis and conclude that there is statistically significant impact on sale of the explanatory variables Apartment, Age, Size, Parking Space and Excellent.

3. As the one unit change in explanatory variables Apartment, Age, Size, Parking Space, Excellent and Good then there must be the sale 62501259 Euro.

Sale = 22888689 + 1215251*1 + 269262*1 +142945*1 + 1313465*1 + 19957138*1 + 16714509*1

Sale = 22888689 + 1215251 + 269262 +142945 + 1313465 + 19957138 + 16714509