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

For the above model, we have ran the regression analysis, excluding the non-statistically significant variable.
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)	104170,232	14201,019		7,335	,000
	Apartments	5788,922	1185,929	,344	4,881	,000
	Age	-949,657	228,659	-,116	-4,153	,001
	Size	1244,213	138,211	,589	9,002	,000
	Parking space	2887,733	1260,931	,094	2,290	,034
	Excellent	48275,937	15384,359	,099	3,138	,005
a. Dependent Variable: Sale price

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	,994a	,987	,984	26696,06519
a. Predictors: (Constant), Excellent, Apartments, Age, Parking Space, Size

Questions:
1. State the estimated regression equation.

2. Comment on the importance of regression rates.

3. Determine the coefficient of determination and explain its meaning.

4. Using the above estimated model , estimate the average selling price for an apartment of 100 sq.m., located in a 20-year-old building in moderate condition, without parking spaces that accommodates 25 apartments.

Answer 1

1)

As we can see the above output. So the estimated regression equation is :

2)

As we can see that p value corresponding to all variables is less than 0.05

i.e., P value < for all variables

which implies that all variables are statistically significant at level of significance.

3)

we are given with R2 in the above output and we can say

Coefficient of determination is  R2 = 0.987

As we can see that R square us 0.987 which implies that independent variables explain 98.7% if the variability in the model.

4)

we need to determine sale price for

Age = 20

size = 100

parking space = 25

Excellent = 1

So the estimated price from the model is :

so the estimated price is 231686.3 Euros