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

Sale Price = 98308.606 + 1215.251 * Apartments + 269.262 * Age + 142.945 * Size + 1313.465 * Parking Space + 19957.138 * Excellent + 16714.509 * Good

The sale price of the apartment increases based on the other variables in the regression equation namely apartment, age, size etc. The extent by which the sale price increases is determined by the regression rate in the table given above.

Interpretation of the regression coefficients:

Intercept: With all the other variables as 0, the minimum price of the apartment is equal to 98308.606

Apartment: An increase in one apartment in the building and with all other variables kept constant, the sale price increases by 1215.251.

Age: An increase in the age of the apartment by 1 year and with all other variables kept constant, the sale price increases by 269.262.

Size: An increase in the size by 1 sq meter and with all other variables kept constant, the sale price increases by 142.945.

Similar explanation can be given for coefficient of parking space.

Excellent: If the building condition is referred to as excellent the sale price will increase by 19957.138.

Good: If the building condition is referred to as good the sale price will increase by 16714.509.