(Solved): (1) This problem asks you to make use of the housebinary data set for a binary choice analysis. The ...
(1) This problem asks you to make use of the housebinary data set for a binary choice analysis. The data set is a slightly modified version of the data you analyzed previously, with 9,433 observations on 3 variables. A description of each of the three variables is provided below, in column-order: baths: Number of full baths in the home. sqft: Square footage of the home. morethan300: Indicator variable, equal to one (otherwise zero) if the sales price of the home was greater than
$300,000. With these variables defined, consider the probit model:
Pr( morethan 300_(i)=1| Sqft, Baths )=\Phi (\beta _(0)+\beta _(1) Sqft _(()()i)+\beta _(2) Bath _(()()i)).(1a) Suppose you believe that not all bathrooms are created equally. That is, you believe that going from 1 to to 2 bathrooms may have a very different effect on the likelihood of a sales price in excess of
$300Kthan going from, say, 2 to 3 or from 3 to 4 bathrooms. Discuss how you might elaborate the model to investigate that possibility. (1b) Estimate the model in equation (1) using STATA (and the .dta version of the data provided). Are the point estimates consistent with what you expected? (1c) Calculate a marginal effect estimate for sqft and baths using
mfx. Interpret the results you obtain. (1d) Use MATLAB, given the coefficient estimates you obtained in STATA from part (b), to estimate the probability that a 2,000 square foot home with 3 bathrooms will sell for more than
$300,000. (1e) Suppose you are the owner of a 2,500 square foot home, currently with 1 bathroom. You are considering adding an additional bathroom to the existing space (without changing the home's footprint, thus leaving sqft unchanged). You are wondering how such an addition might change the probability that your home will sell for more than
$300,000. Write down mathematically the expression for this change and use MATLAB to provide a point estimate of that change.
