We want to study the determinants of house prices. We have collected a dataset with 43 observations in the same town in the South of California, which includes the following variables P: the price (in...

EC2010
    
We want to study the determinants of house prices. We have collected a dataset with 43 observations in the same town in the South of California, which includes the following variables
P: the price (in thousands of dollars) of the house.
S: the size (in square feet) of the house
N: the quality of the neighbourhood where the house (1=best; 4= worst) as rated by two local estate agents.
CA: dummy variable equal to 1 if the house has central air conditioning, 0 otherwise.
Y: the size of the garden (in square feet).
A: age of the house.
The estimation results that you are asked to consider are in table 1 (computed with EViews):
    Dependent Variable: P
    
    
    Method: Least Squares
    
    
    Date: 02/15/12 Time: 14:35
    
    
    Sample: 1 43
    
    
    
    Included observations: 43
    
    
    
    
    
    
    
    
    
    
    
    Variable
    Coefficient
    Std. E
o
    
    
    
    
    
    
    
    
    C
    100.9200
    25.89138
    S
    0.132459
    0.010390
    S*N
    -0.024494
    0.003219
    A
    -0.921926
    0.817800
    A^2
    0.006782
    0.008469
    Y
    0.005016
    0.001305
    CA
    -1.694856
    10.25875
    
    
    
    
    
    
    
    
    Total Sum of Squares
    263725.4
    
    
    Residual Sum of Squares
    16558.01
    
    
    
    
    
    
    
    
    
    
    
    
Table 1
1. What is the interpretation of the coefficient on CA? Is its sign consistent with your expectations?
[10%]
Ans: The coefficient (-1.694856 in thousands) is the average difference in the price of a house with and without central air conditioning. Since the coefficient is negative, it means that on average the price of a house with central air conditioning would be less than that of house without central air conditioning which is not consistent with my expectation as one would consider central air conditioning to be an extra amenity and hence would expect to have a positive impact on the price.
2. Test the individual significance of the coefficient of CA against the alternative that it is positive. Use a 5% significance level.
[10%]
Ans: The null hypothesis here is that coefficient of CA=0 against the alternative that it is positive.
The estimated coefficient is -1.694856 with standard e
or being 10.25875, so the t statistic is t= -1.694856/10.25875=-0.165210771. The absolute value of t is =0.165210771. The critical value of t with degrees of freedom (n-k-1),i.e. d.f =(43-7) =36 at 5% level of significance (one tailed test) is 1.688. Since 0.165210771< 1.6883, we do not reject the null of the coefficient of CA being significant against the alternative that it is positive.
    
    
3.What is the effect of the size of the house on its price? Discuss.
[10%]
Ans: The estimated regression is:
P=100.9200+0.132459*S-0.024494*S*N-0.921926*A+0.006782*A^2+0.005016*Y-1.6948567*CA
The main effect of the size of the house on the price is positive. One unit increase in the size (in square feet) of the house increases the price of the house by 0.132459 units (in thousand dollars).
However, the size of the house has an interaction term with the...