Statistical & Quantitative Methods
Case Study of
The Condo Sales
This case investigates the factors that are affecting the sale price of Oceanside condominium units. The relationship between these factors and sale price has remained the same despite condo sale prices increasing drastically over the past 20 years.
Sales data were drawn from a new Oceanside condominium complex consisting of two adjacent and connected eight floor buildings. The 200 units in the complex are approximately 500 square feet each.
1. Ocean view units (south-facing), have a good view of the pool and face the beach and ocean. Bay view units (units to the rear of the building), face an area of land that borders a bay as well as the parking lot. Visibility of the bay is poor from the upper floors of these units. 2. There is only one elevator located at the east end of building 1, so are the office and the game room. People from the upper floors in building 2 would have to use the elevators to move through the passages to their units. These units are less convenient. However, the advantage that such units hold is that they are the most private as it has the least amount of human traffic. 3. Lower floored Oceanside which open to the beach, ocean and pool and also within easily accessible to the game room and parking area, are most suitable for active people. 4. Units 11 and 14 located in the centre of the complex have views that are partially blocked. 5. Sales were slow after the completion of the complex as it was at the time of the 1975 recession. The developer had to sell most of the units at auction 18 months after opening. The auction data are completely buyer-specified and hence customer-oriented. This is in contrast to other real estate sales data which are mostly seller and broker specified.
From the case study, it is obvious that it reveals that there are in total of 5 predictor variables of x and 1 response variable of Y. Since it is stated to construct a regression model to predict the sale price of a condominium unit sold at the auction. With this, it identifies that the sale price will be the variable of Y, which will be responded or reacted with any change in the other variables.
The other variables that cause changes to the response variable will be as follows: * Floor height;
* Distance from elevator;
* View of ocean;
* End unit;
A MINITAB scatter plot for the data relating Price to Distance from elevator, we are able to observe a linear trend.
A MINITAB scatter plot for the data relating Price to Floor from elevator, we are able to observe a linear trend.
From the 2 graphs above, we hence believe that the independent terms and dependent terms are linearly co-related.
Construction of Regression Model
Assuming that all variables are dependent, the regression model will be as follows:
Y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + β6x1x2 + β7x1x3 + β8x1x4 + β9x1x5 + β10x2x3 + β11x2x4 + β12x2x5 + β13x3x4 + β14x3x5 + β15x4x5 + ε
Sale price (in hundreds of dollars, adjusted for inflation)
Floor height (1< x1 <8 , x1 є integer)
Distance from elevator (1< x2 <15 , x2 є integer)
1 if the unit possessed an ocean view
0 if otherwise
1 if the unit has a unit number ending in 11
0 if otherwise
1 if the unit was furnished
0 if otherwise
Assumptions for random error ε
For any given set of values of x1, x2, x3, x4, x5, the random error ε has a normal probability distribution with mean equal to 0 and variance equal to σ2.
The random errors are independent (in a probabilistic sense).
Obtaining SPSS Output Procedures
The values for each dependent second-order variable in term of the respective sale prices are computed in Table 1:...
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