Condo Sales Case Study

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University Of Charleston *

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Feb 20, 2024

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1 Condo Sales Case Dylan Harloff “The Condo Sales Case” STAT 4300 – Data Driven Decision Making April 30 th , 2023 Professor Benestad

2 Condo Sales Case Introduction In this case study, we delve into an examination of key variables that influence the selling price of oceanfront condominium units. The focus is on a contemporary condominium development comprising two interconnected eight-story buildings. Numerous factors contribute to the pricing of each individual unit, encompassing aspects such as the actual sale price, floor elevation, proximity to the elevator, ocean view, whether it is an end unit or not, the inclusion of furniture, and whether the unit was sold through auction. The primary aim of this case study revolves around formulating an optimal regression model that accurately forecasts the sale price of condominium units sold at auction. Variables In our multiple regression model, we incorporate various factors to analyze their impact on the sale price of each condominium unit. These factors encompass: Price, which represents the actual sale price of each unit, measured in hundreds of dollars; Floor, denoting the floor height or specific location of each unit on a scale ranging from 1 to 8; Distance, indicating the proximity of each unit to the nearest elevator; View, a binary variable where 1 signifies a unit with an ocean view and 0 denotes units without an ocean view; End Unit, a binary variable where 1 designates units located at the ends, specifically those ending in 11, and 0 represents units that are not end units; Furnish, a binary variable where 1 indicates units that are furnished and 0 signifies unfurnished units; Auction, a binary variable where 1 denotes units sold at auction and 0 represents units sold through other means. These variables collectively contribute to our comprehensive regression model for predicting condominium unit sale prices.

3 Condo Sales Case Relationship Between Dependent and Independent Variable In preparation for running a multiple regression analysis, there are a few crucial steps that must be taken beforehand. As previously mentioned, the first steps involve identifying potential dependent and independent variables and collecting relevant data for each. The subsequent step is to examine the relationship between each dependent variable and the independent variables using scatterplots and correlation analysis. If an independent variable is not correlated with a dependent variable, then it should not be included in the multiple regression model. To be

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4 Condo Sales Case included in the regression model, the dependent and independent variables must display a strong linear relationship and should be correlated. In this case study, the scatterplot analysis and correlation calculations demonstrate that the sale price of each condo does not exhibit a particularly strong linear relationship with each independent variable. However, the distance and view variables show a small linear relationship with the sale price of each condo. The floor variable displays a negative correlation, which is generally not ideal for inclusion in the regression, but further analysis may be necessary due to its categorical nature. The three dummy variables of end, furnish, and auction are challenging to test for multicollinearity with the dependent variable of sale price. Dummy variables often result in multicollinearity with the dependent variable, making it difficult to determine whether certain dummy variables should be included in the multiple regression. As of now, all the independent variables will be included in the regression, with further analysis required to determine their impact on the sale price of each condo. Relationship between Independent Variables Next, it is important to examine the relationships among the independent variables by employing scatterplots and correlation analysis. To avoid an excessive number of scatterplots, the correlations between each independent variable are presented in the provided table. The objective is to identify whether the scatterplots display a robust linear relationship or a high correlation close to 1, as this indicates potential multicollinearity. It is crucial to avoid including

5 Condo Sales Case variables that exhibit strong correlations, as they can introduce problems into the regression model. Upon inspecting the Excel image, it becomes evident that there are no variables demonstrating multicollinearity concerns with correlations near 1. The floor and auction variables display a relatively moderate correlation of 0.4608, which stands among the highest correlations observed. Nevertheless, this correlation value is not notably high and falls far from 1, suggesting that the floor and auction variables are not considered multicollinear. Consequently, none of the independent variables exhibit multicollinearity issues, thereby allowing for the inclusion of all independent variables in the multiple regression model based on this analysis. Multiple Regression Models The final step of the multiple regression process involves selecting the most suitable model using independent variables that are not redundant. Based on the previous stages, there are no apparent variables that should be disregarded when utilizing the multiple regression model. The Excel image above illustrates the summary results of the multiple regression. In the "Regression Statistics" section, an R-Square value of 59.76% is observed, with an adjusted R- Square of 58.56%. This signifies that the independent variables account for 58.56% of the variation in the dependent variable, namely the sale price. The relatively high R-Square score

6 Condo Sales Case suggests that this model performs reasonably well in predicting the sale price of each condominium unit. While the standard error of the mean is relatively high at 21.8163, it is not a major cause for concern. The F-test result indicates the model's significance, with a significantly low p-value of 2.26E-37. However, the high F-test value raises the possibility of potential combined significance issues among the independent variables. To further analyze the independent variables, we assess their individual impacts on the model. The four highlighted independent variables—distance, view, end, furnish, and auction— are all statistically significant, with p-values below the alpha level of 0.05. The only independent variable in this model that lacks statistical significance is the floor variable, with a p-value of 0.1303, exceeding the alpha value. Considering the inclusion of factors in the regression model, the floor variable does not appear to exhibit a significant relationship with the dependent variable, i.e., the sales price. After observing the absence of correlation between the floor variable and the dependent variable in the previous step, it was decided to exclude the floor variable from the multiple regression model. This decision was further reinforced by its lack of statistical significance in the model that included all the independent variables. In the provided multiple regression summary

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7 Condo Sales Case output, all the independent variables are now statistically significant, adhering to an alpha value of 0.05. However, both the R-Square and adjusted R-Square values are marginally lower than those obtained in the previous multiple regression model, which encompassed all the independent variables. The adjusted R-Square for the second regression stands at 58.29%, slightly higher than the adjusted R-Square result of 58.56% achieved in the regression that considered all the independent variables. Consequently, it appears that the first regression, which incorporated all the factors, slightly outperforms in its ability to forecast the sale price of each condominium unit. The multiple regression performed above excludes the floor and auction independent variables. The floor variable did not demonstrate statistical significance in the initial regression model that incorporated all the independent variables, thereby leading to its exclusion. Additionally, the auction variable, which exhibited the most substantial negative correlation with the dependent variable of selling price and a strong association with the floor variable, was omitted to mitigate potential multicollinearity concerns. In the Excel figure presented, the adjusted R-Square for the regression stands at 41.86%, which is lower than the adjusted R-Square of 58.56% obtained from the multiple regression

8 Condo Sales Case involving all the independent variables. However, even after excluding the floor and auction independent variables, there is no noticeable improvement in model performance compared to the other two models. The modified R-Square values continue to decline when additional independent variables are removed, as evident in the Excel spreadsheet. Thus, the multiple regression model encompassing all independent variables remains the most accurate in forecasting the sale price of a condominium unit sold at auction. Interpretation The most suitable model for predicting the sale price of a condo unit is the multiple regression model. The coefficients in the model hold significant meanings. If all the independent variables are set to 0, the sale price of a condo unit would be $186.99 (in hundreds of dollars), as indicated by the intercept coefficient. This $186.99 can be considered the base price for a condo unit without any specified components from the regression.

9 Condo Sales Case The floor variable coefficient of -1.16 suggests that the sale price of a condo unit would decrease by 1.16 units if there is an increase in floor level. This interpretation aligns with the notion that individuals may prefer lower floors for easier access to amenities such as the beach and pool. However, the floor variable itself has limited significance. The distance variable implies that for every unit increase in the distance between a condo unit and the elevator, the sale price of the condo unit would rise by 0.92 units. This interpretation may be debatable, as it contradicts the common belief that a condo unit's value increases if it is closer to the elevator. The assumption here is that increased distance provides more privacy and less foot traffic, thus boosting the value. The view variable, being a dummy variable, suggests that if a condo unit has an ocean view, the sale price would increase by 48.25 units. This interpretation is highly reasonable, as ocean views are generally desirable and can significantly enhance the value of the condo unit. The end variable, another dummy variable, indicates that if a condo unit is an end unit ending at room number 11, the sale price would decrease by 23.63 units. This interpretation also aligns with the expectation that end units lacking ocean views and instead facing another building would have lower value compared to units with better views. The furnish variable, as a dummy variable, suggests that if a condo unit is furnished, the sale price would rise by 6.95 units. This interpretation is logical, as a fully furnished unit saves potential buyers the hassle of purchasing furnishings separately, thereby increasing the overall value of the property. Lastly, the auction variable, being a dummy variable, indicates that if a condo unit was sold at auction, the sale price would decrease by 27.97 units. It is plausible that the condo unit was initially listed at a low starting bid to attract potential buyers, but this strategy may have resulted in a lower final sale price. Therefore, this explanation appears reasonable. Overall, these interpretations provide insights into how each independent variable influences the sale price of a condo unit within the multiple regression model. Conclusion The interpretations of the independent variables in the multiple regression model seem plausible and logical. Furthermore, when comparing the R-Square and adjusted R-Square values among the different regression models, it is evident that the model incorporating all the independent variables yields the highest values. This suggests that this multiple regression model

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10 Condo Sales Case is the most effective in accurately predicting the sale price of condominium units. Each independent variable plays a significant role in the model and is essential for achieving accurate predictions of the sale price for these condo units. References Pearson: Chapter 12 – Multiple Regression and Model Building