Report on Making business decisions

The case is about the investigation of different factors that induce impact on the sale price of the oceanside condominium units. These condominium units were sold in the public auction. The sales were done after 20 years and the relationship was determined for different factors and sale prices (McClave, James, Benson, George, Sincich, Terry, 2001). The condominium complex was first completed in 1975 and because of recession sales became slow. In this case, the developer was forced to sell condominium units at the auctions. The aim of the present work is to conduct a regression analysis and regression model that can be used to predict the sale prices of the condominium unit sold at auction. The report presents the results of the analysis that include a graphical representation of independent variables in the model that affect the price of the auction (Sincich, 2000).   

Background of the case of Making business decisions

The ocean view is facing south side and faces the ocean and beach. Only a single elevator in the complex is located at the east end of the building 1. The people are moving to and from the high sides of building 2. The building units are ending on the number 11 and 14 that are apart from each other. The auction data is complete for the specific buyer and oriented over the estate sales data. There is a number of unsold units that are complex and furnished by the developer. The services were further provided to the rented auctions. The condominium complex is complex for the single elevator that is located at the end of the complex producers. The developers are unsure about the height of units, the distance between the units, presence of ocean view, the effect of the prices (McClave & Sincich, Statistics, 2009). The single elevator is in the complex process and it requires greater great effort for the management of private services and houses. The condominium complex is unique and produces a remarkable level of privacy. Consequently, the complex and unique infrastructure is developed with different heights of the unit. The data used in the analysis of 106 units sold at the auction include the sale price, flood height, distance from elevator, view of the ocean, end units and furniture. The layout of the condominium complex presented in figure 1. The relevant details of the condominium complex are listed below,

1.      There are eight identical floors of the complex.

2.      The size of the units is the same for the complex.

3.       The units are on the first floor towards the south and beach pool are known as an ocean view.

4.      The units on the other floor are towards the north and facing the parking lot and called bay-view.

5.      The single elevator of the building is complex, and it is located towards the east end of the building.

6.      Some of the units are end units that are viewed from the partially blocked region.

Purpose of the study of Making business decisions

The goal of the present work is to identify different factors that induce influence on the sales prices of condominium units. The report will find quantification of effects with the factors. The information is further used by the owner and help in identifying sales prices and possible rental rates in the future (Prentice-Hall Publishers, 2010). Before having analysis, anticipated effects for the explanatory variables are considered. The variables used in the analysis are listed below in table 1.

Table 1: Price and Unit sale price

Data analysis of Making business decisions

On every floor, the furnished and unfurnished units are sold to the customer. On three floors, the units are unfurnished. Half of the bay view units were sold furnished and one-third of the ocean view units were sold as furnished (McClave, James, Benson, George, Sincich, Terry, 2001).

Model 1: The “Naive” Regression of Making business decisions

In the analysis, the descriptive statistics are carried out for the marginal distributions of the variables. The variables used in the analysis are price, floor, distance from elevator, ocean, end unit and Furnish. The descriptive statistics include calculation of mean, median, standard deviation, minimum value and maximum value. The values are mentioned in table 2.

Table 2: Statistical analysis of price, floor, distance, view, end, furnish, and auction

The model includes five explanatory variables for the analysis and detail information is under statistical analysis. The variables used in the regression analysis are coefficient, standard deviation, t-value and P-value (McClave, James, Benson, George, Sincich, Terry, 2001).  The results of the statistical analysis carried out for the five explanatory variables in the raw forms are mentioned below in table 3. Table 3 provides a cross-tabulation of furnished units with both ocean view and floor levels. The correlation matrix is used to provide an idea about the interrelation of six variables.

Table 3: The results of statistical analysis including co-efficient, standard deviation, t-value, and the p-value of all the variables

 The regression statistics of the price floor, end, distance, furnished units and auction are mentioned in table 4, 5, 6, 7 and 8. The relation between the price and floor relation analysis are measured. The price probably drives the correlation between all the factor. The correlation matrix is used for the cross-tabulations. The negative correlation is measured between the other parameters with the price considerations. In the analysis negative correlation is observed between the floor and ocean view of the units (McClave & Sincich, 2009).

1.      Regression analysis of price and floor value

The plot indicates the observation regarding price and floor value in the analysis. In the analysis the floor value is the level of floor and location of the unit as 1, 2, . . .. 8. The graphical representation shows the fluctuation between changing the price and floor value in figure 1. The highest and lowest floor value is observed that define dropping values and other parameters. The multiple R-value for the price and floor relation is 0.24. The R – square value in the regression analysis is 0.059. The adjusted R square value is 0.05. The total number of observations in the analysis is 209 units. The standard error measured in the analysis is 32.95. The significant factor of the regression analysis is evaluated as 0.0003 with factor value as 13.03.  The values measured in the regression analysis are mentioned in table 4. The correlation between the floor and price is negative that means the positive effect of the lower floors on the price and it is measured by the regression analysis. The correlation defines the relationship between these variables. For instance, in case of negative correlation between ocean and floor, it means that on an average smaller number of units were sold on the high floors (Sincich, 2000).

Table 4: Regression statistics of price and floor relation analysis

Figure 1: Relation between price and floor value

2.      Regression analysis of price and floor value

The summary of regression statistics for price and end relation analysis of continuum units is mentioned below in table 5. According to the statistical analysis, the value of multiple R is 0.077, R square value is 0.006, and value of adjusted R-square is 0.001. The standard error value is 33.86. The total number of observations is the number of units that is 209 in the statistical analysis. The significant factor is 0.26 and regression factor is 1.26. The residual of analysis is 207. The graphical representation in figure 2 demonstrates the relation between the price of units and the end relation. The value of the end unit fluctuates between zero and one. In the end unit, the partial reduction is measured for the view of end units on the ocean side. The number of ending units reduces their sale price. In the case of end units of ocean view, the building is blocked under the building 2. The qualitative variable is under analysis with the dummy variable and the number end for 0 and 1. While comparing the values it is estimated that the FLOOR coefficient is not significant in the model (McClave, James, Benson, George, Sincich, Terry, 2001). The graphical representation shows non-linearity and the regression is used to underestimate the prices of first-floor units. The regression seems to demonstrate the prices that are overestimated for the third and fourth units of the floors. The residuals are accurate for the remaining floors. There are different methods to model the nonlinearity and floor effect that is linear spline and polynomial. The two indicators and variables under the addition with the linearity forms. According to the analysis, the first floor seems to be different from the remaining other floors. In the analysis, the fact of the higher floor may induce a positive impact on the value and price of the unit under the linearity model. The analysis shows that the variables of the first floor and second floor have positive and significant effects.   

Table 5: Regression statistics of price and end relation analysis

Figure 2: Relation between price and end unit

3.      Regression analysis of price and unit distance

The distance of the unit is measured in length from the elevator and it is a complex value that represents the number of condominium units. In this analysis, two units of distance are also added to the building number two. The measured length takes into account the walking distance of the units from the elevators (Sincich, 2000). The distance of unit 105 from the elevator is measured as 3. The distance between elevator and unit 113 is 9 and the variable values are changing in the analysis from level 1, 2, 3 . . .  15.

To allow the possibility of partial effect for the given variable, it is possible to vary the values with the levels of floor and another variable. In the model, we will introduce interaction terms. According to the results, one might expect a positive effect on the value of the floor by changing the ocean view and distance of the elevator for all the floor levels. The summary of regression analysis is mentioned in table 6. The regression analysis shows the value of multiple R is 0.31. The R- Square value and adjusted R square value is 0.097 and 0.093 respectively. The standard error was measured as 32.27 for 209 observations in the analysis. The significant factor is 4.2. The factor of regression is measured as 22.34. The coefficient measured in the relation between the price of the unit and the distance of the unit from the elevator is 183.36. The graphical representation in figure 3 demonstrates the relation between price and distance of the unit from the elevator.

Table 6: Regression statistics of price and distance relation analysis

Figure 3: Relation between price and unit distance

4.      Regression analysis of price and view of the ocean from the unit

In the analysis of the view of the ocean from the unit is also considered. The consideration includes the absence and presence of ocean view that is recorded for all the units and specified it by considering the dummy variable (McClave, James, Benson, George, Sincich, Terry, 2001). The value 1 is used in the unit processing system for units that have a view of the ocean and zero shows absence of ocean view from the unit. The data under investigation is not enough to evaluate the interaction between floor and ocean view from the unit. The interaction between the end unit and the ocean view is not accurate and authentic because no bay view end unit was sold in the current data. The summary of regression analysis for the price of units and the view of units from the ocean is mentioned below in table 7. The results of regression statistics show the value of Multiple regression as 0.57 and value of Regression square as 0.33. The adjusted R square value is 0.33 and the standard error was measured as 27.70 for 209 observations. The graphical representation in figure 4 shows the relation between the price of the unit and ocean view units in the building. The values fluctuate between highest as one and lowest as zero.

Table 7: Regression statistics of price and view of units under the relation analysis

Figure 4: Relation between price and ocean view

5.      Regression analysis of price and unit auction

The regression analysis for auction show relation between auction of units in the buildings and price for the units. The observation is not seeming strange for any reason. There is a significant influence of the evaluations on the regression that can cause the inclusion of the interaction terms (McClave & Sincich, 2009). In the regression statistics of price and unit auction, the value of multiple R is 0.28 and the value of R- the square is estimated as 0.08. The value of adjusted R – the square is 0.07. The analysis was based on 209 observations and the standard error of the regression statistics was measured as 32.56.

Table 8: Regression statistics of price and auction of units under the relation analysis

Figure 5: Relation between price and auction

6.      Regression analysis of price and furnished units

The consideration of price and furnished units deal with presence and absence of the furniture that is recorded for each unit. The single dummy variable is used in the process and regression analysis. the value of 1 shows that the unit is furnished and zero show that it is not furnished (McClave & Sincich, 2009). According to the economic theory, the interaction between the values of furnished units with the other variables must yield an estimate of zero. The main reason is that if any significant effect that is different from zero is observed for any value of the furnished unit's interaction terms it would lead to finding that is considered for the interest of owners. The analysis of data shows that all the furnished interactions are insignificant from zero that is already predicted in the economic theory. The value of end unit interaction is also considered as insignificant, but the regression shows a bit surprising result. The regression statistics of price and furnished units are provided below in table 9. According to the regression statistics the value of multiple regression factor is 0.005. The value of regression square is 2.76 with adjusted R square is 0.004. The standard error is measured as 33.97 for 209 observations. The graphical representation in figure 6 shows the relation between price and furnished units.  

Table 9: Regression statistics of price and furnished units under the relation analysis

Figure 6: Relation between price and furnished units

Conclusion of Making business decisions

The objective of present work was to develop a model that demonstrates the relation between price and other five variables including the distance of the units from the elevator, floor level, end unit, ocean view from the unit, and auction. The statistical analysis carried out in the report for these variables is regression analysis. Besides the regression analysis, the correlation between all the variables is measured by comparing mean, standard deviation, minimum value and maximum value. The graphical representation is used to show the relationship between all parameters and their significance. On the basis of the current analysis, we have settled different possible models that can be used to analyze the significance of the correlation between all variables. In different models, the different analysis was settled invariably. One of the important considerations is that the proposed model has captured all the main patterns of the data. In the whole analysis, first-floor units were considered different from the rest of the units. The distance of the elevator from the unit is also measured. The analysis shows that it will be more beneficial to drop the first-floor units from all the sample data and consider only the ground floor units. The results of statistical analysis should be applied to all the above units of the building in the case.  

References of Making business decisions

McClave, J. T., & Sincich, T. (2009). Statistics. Pearson Prentice Hall.

McClave, James, Benson, George, Sincich, Terry. (2001). Statistics for business and economics, Volume 1. Prentice-Hall.

Prentice-Hall Publishers. (2010). A First Course Business Statistics, 8th Ed, McClave-Benson-Sincich,: A First Course Business Statistics,. Bukupedia.

Sincich, T. (2000). Statistics by Example. Prentice Hall.