MTH410 – Quantitative Business Analysis
Colorado State University–Global Campus
Introduction
Gulf Real Estate Properties, Inc. is a real estate firm located in southwest Florida. The company, which advertises itself as an expert in the real estate market, monitors condominium sales by collecting data on location, list price, sale price, and the number of days it takes to sell each unit. Each condominium is classified as Gulf View if it is located directly on the Gulf of Mexico, or No Gulf View if it is located on the bay or a golf course (near but not on the Gulf). Sample data from the Multiple Listing Service in Naples, Florida, provided sales data for 40 Gulf View condominiums and 18 No Gulf View condominiums. The data comprises of 3 categories: list price, selling price, and days to sell. The purpose of this analysis is to identify relationship amongst to variables as well as do some scenario analysis.
Descriptive Statistics
Interpretation of Results
Gulf View Condominium
Using a sample set of 40 customers, the total sale amounted to $20,631,900. The average listing and selling price per customer are $537,075 and $515,797.5 respectively which took an average of 149 days to be sold. Since the pattern of the listing is similar with selling price, the sale price will be used for interpretation because the statistics is centered on the actual amount earned and not the intrinsic value of the property. The lowest selling price was $150,900 while the highest selling price was $948,700. The shortest time it took to sell the condominium unit was 19 days while the longest took for almost a year with 275 days. Standard deviation is the measure of the plus minus spread away from the median based on the set of value. The established mean for selling price was around $500,000 and for this particular data, it’s dispersing by adding or deducting $219,874.87. In terms of days to sell, the data deviates from the mean by plus and minus 85 days. Table 1 summarizes the statistics of Gulf View Condominium.
Looking at Graph 1, the data is much dispersed. No concentration is seen which is why standard deviation is high. The selling price and days to sell both have similar patterns wherein there’s no determinate average pricing. Some condominiums will sell for almost $950,000, others about $150,000. This is pretty much the same for how long it took to be sold; some close to 300 days while the fastest turnaround was 19 days.
The confidence level is used to measure the fluctuations in the sample set (for it’s not possible to capture a whole population) and there’s always a degree of uncertainty, hence this gives statisticians a leeway to measure the actual value of the mean with room for error. Using a 95% confidence level, the confidence value of selling price is $70,319.40 while 27 for the days. Given the sample size is only 40, there’s a 95% probability that for the total population. The selling price would around $515,797.5 +/- $70,319.40 while the days to sell 149 days +/- 27 days.
Graph 1. Scatterplot chart
No Gulf View Condominium
Using a sample set of 18 customers, the total sale amounted to $3,699,500. The average listing and selling price per customer are $212,555.56 and $205,527.78 respectively which took an average of 194 days to be sold. The lowest selling price was $122,700 while the highest selling price was $278,700. The shortest time it took to sell the condominium unit was 65 days while the longest took more than year with 386 days. Contrary to the Gulf view, the No Gulf view is relatively cheaper if the comparison is with the mean and took longer to sell. Due to the disparity in sample set, it might not be safe to presume that the amount of customer is less in No Gulf View but if basing on the statistics, customers prefer condominium units facing Gulf of Mexico. The established mean for selling price was around $205,000 and for this particular data, it’s dispersing by adding or deducting $42,668.90. In terms of days to sell, the data deviates from the mean by plus and minus 115 days. Table 2 summarizes the statistics of No Gulf View Condominium.
Looking at Graph 2, the data is much dispersed. No concentration is seen which is why standard deviation is high. The selling price and days to sell both have similar patterns wherein there’s no determinate average pricing. Some condominiums will sell for almost $280,000, others about $150,000. This is pretty much the same for how long it took to be sold; some close to 400 days while the fastest turnaround was 65 days.
Using a 95% confidence level, the confidence value of selling price is $21,218.75 while 57 for the days. Given the sample size is only 18, there’s a 95% probability that for the total population, the selling price would around $205,527.28 +/- $21,218.75 while the days to sell 194 days +/- 57 days.
Graph 2. Scatterplot chart
Scenario Analysis
Assuming a margin of error of $40,000 for Gulf View and $15,000 for No Gulf View, the calculated ideal sample size given 95% confidence interval are 116 and 31 (refer to Excel workings).
Another scenario is when the listing price of Gulf View is $589,000 and of No Gulf View at $285,000. Calculating the mean of the spread between the listing price and selling price, there’s 4.01% and 3.34% division from listing price respectively. Hence, the selling price could be $565,372.71 for Gulf view while $275,267.36 for No GulfView. Those are estimates on the possible selling price. The calculation of days to sell would be represented by a linear regression in order to determine the correlation between the selling prices against days to sell.
Using the LINEST function in excel, the linear regression between days to sell against selling price is determined. Given the selling price is the independent variable and days to sell as the dependent variable.
Function of Gulf View:
Days to sell= -0.068571902*selling price+184 days
Function of No Gulf View:
Days to sell= 0.363857436*selling price+117 days
The estimated days to sell given the selling price would be 145 days for the Gulf View and 217 days for the No Gulf View.
Bibliography
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Microsoft. (2016). Description of the CONFIDENCE statistical functions in Excel. Retrieved from https://support.microsoft.com/en-us/kb/828124.
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