A sample of 43 houses that were purchased in the Southern California town Monrovia within a month was collected. We are interested in the study of the relationships between Price and a set of factors which are believed to influence it. The data is saved in file House-price.sav. The variables in the data are:

P = the price (in thousands of dollars) of the house

S = the size (in square feet) of the house

N = the quality of the neighborhood of the house (1 = best, 4 = worst) as rated by two local real estate agents

A = the age of the house in years

CA = a dummy variable equal to 1 if the house has central air conditioning, 0 otherwise

SP = a dummy variable equal to 1 if the house has a pool, 0 otherwise

Y = the size of the yard around the house

Develop a multiple regression analysis for the data and answer the following question,

A) Does model fit the data? Test at 5% significance level.

B) Are all the regression coefficients significant on 5% level? Explain your results verbally.

C) Is there any difference in price between a house with swimming pool and without? If yes, what is the difference?

D) Is multicollinearity a problem here?