Data for this problem are in the table below. These data enable you to apply the methods that we are studying to the real estate area to answer this two-part question.

The data set contains information about apartment prices and characteristics for a central area of a city. The data include sale price (PRICE) in $, floor area (SQFT) in square feet, number of bedrooms (BED), number of bathrooms (BATH), number of floors in the building (FLOORS), and distance from a crowded and busy city landmark, the 'Presidential Tower' (PDIST) in feet.

The type of model that we study in this problem (regressing price against characteristics of dwelling and location) is commonly used for automating property tax assessments.

(a) Your friend owns a parcel of land on a Street exactly half a mile (one mile is equal to 5280 feet) from the Presidential Tower and the friend wishes to construct an apartment building. The friend has decided to build the building with all apartments having two bedrooms and one bathroom. However, no decision has been made on how many floors to build. A city ordinance however stipulates that one cannot build more than 20 floors in the building.

From past experience it is known that construction cost per square foot (for the type of building you friend plans to build) increases with the number of floors according to the following cost equation:

Cost = 100*FLOORS + 15*FLOORS².

Revenue per square foot per floor is given by PRICE/SQFT. Hence, revenue per square foot with more than one floor is given by FLOORS*(PRICE/SQFT). Using the regression you just ran, how many floors would you suggest your friend to build to maximize the revenue per square foot of developed property? That is, find the number of floors to maximize:

Profit = FLOORS*(PRICE/SQFT) - (100*FLOORS + 15*FLOORS²)

Hint:Substitute your estimated equation for price per square foot (from the second regression) for the type of apartment units that the building will contain. The only unknown in the resulting expression will then be the number of floors. You can then simply compute profit for each possible value of FLOORS from 1 floor till 20 floors (since the city ordinance prevents construction beyond 20 floors). Your answer would be the number of floors at which the profit is maximum.

Also remember:

\f\f