Module 2-3 Assignment - NEW MAT 240 PDF

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For the new MAT 240 course beginning Jan 2021.
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Selling Price and Area Analysis for D.M. Pan National Real Estate Company

Report: Selling Price and Area Analysis for D.M. Pan National Real Estate Company James Gruening Southern New Hampshire University

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Selling Price Analysis for D.M. Pan National Real Estate Company

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Introduction As the newest junior analyst at D.M. Pan Real Estate Company, I assumed the task of preparing a report that examines the relationship between the selling price of properties and their size in square feet. I was able to utilize data from 2019 that covers 30 different counties in the Midwest (Illinois and Indiana). This report is designed to inform the company of the real estate markets in randomly selected counties in the Midwest to demonstrate the relationship between listing prices and square footage. Representative Data Sample

Selling Price Analysis for D.M. Pan National Real Estate Company

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In this sample I randomly chose 30 counties in the Midwest. Number values were taken for listing price, square footage, and price per square foot. I calculated the median, mean, and standard deviation for the data by using the following formulas: Mean: =AVG([selected cells]) Median: =MEDIAN([selected cells]) Standard Deviation: =STDEV([selected cells]) I plugged in these formulas to determine the values for the three critical columns: listing price, number of square feet, and price per square foot. I utilized the data analysis link on the data tab of Excel to create my descriptive statistics which showed all of the statistics on the numbers. These numbers matched my manually entered formulas listed above. I then formatted the cells to simplify and round the numbers for a better table. Data Analysis In comparing my data with the national market, there were clear variations and similarities. The sample data has a considerably lower mean, median, and standard deviation in all three columns of data than the national average. The single exception would be the standard deviation of median square feet. The similarity between these categories is a consistent strong, positive trendline. To be certain my sampling was random, I plugged in the random formula in Excel, =rand(). I then expanded this to include 50 total entries. I then sorted from smallest to largest and selected the first 30 entries as my sample data. This confirms that all of my data was randomized by Excel.

Selling Price Analysis for D.M. Pan National Real Estate Company

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Scatterplot

real estate chart $500,000

listing price of house

$450,000 $400,000 $350,000

f(x) = 146.52 x − 95610.85 R² = 0.71

$300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $0 1000

1500

2000

2500

3000

3500

4000

sqft of house

The Pattern In my graph, there is a clear pattern that emerges from the data, once the variables are understood. The Y- variable is the vertical side of the graph, titled Listing Price of House. The Xvariable is the horizontal side, titled SQFT of House. Having the price per square foot, however,

Selling Price Analysis for D.M. Pan National Real Estate Company

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is necessary for making accurate predictions. There is a direct association between the X and Y, demonstrated by the formula y=146.52x – 95611. Also, the least squares method shows the relationship of R2=0.713. There is a strong positive relationship between the X and Y, with only a few outliers. The X and Y variables represent the linear regression, where Y would expect to be given X, based on the linear relationship. This is demonstrated by the equation [y=mx+b] or (y=146.53x – 95611). This gives us the rise/run (or slope) of the equation. This equation can translate to: the expected value of Y equals the intercept parameter of Y plus the slope (rise / run). The relationship between X and Y can only be obtained if the data represents the whole population. For this data set, there is a clear linear shape that emerges. Therefore, with the whole data set plugged in as well as the formula, we can accurately predict information. For instance, if I had a 1200 square foot house to sell, based on the regression equation in the graph, I would utilize the equation for the known data to determine the unknown data. I know that I need to figure out Y, and that the slope (rise/run) is equal to 146.52. I also know that the X value in this equation is 1,200 square feet, and that the numerical value for X is $95,611. With this information I can write out the equation in two different ways:

Slope Intercept Formula Y=mx+b Y=146.52 (1200sqft) – $95,611 Y=$80,213

Regression Formula E ( Y )=β 0 +β 1 X 95,611 =β 0+ 146.52( 1200 ) 95,611 = β 0 + 175,824 β 0=$ 80,213

Therefore, the price that I would choose to list my 1,200 square foot house at would be roughly $80,213. Depending on the market, that number could fluctuate.

Selling Price Analysis for D.M. Pan National Real Estate Company

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My scatterplot does show outliers. These do not necessarily mean they’re not useful to the graph because there could be several reasons that could cause them. Some communities are much more expensive per square foot than others. Some communities have larger houses than others. The condition of the house could cause it to be an outlier as well. We can still use these outliers to better understand the full range of data. My scatterplot contains these outliers because they were among the random sample I pulled. Location, demand, market, and condition play into the square footage and price. These outliers represent the data that does not fall within range of the trendline and therefore lies outside the normal scope of data.

Selling Price Analysis for D.M. Pan National Real Estate Company References MAT 240: Applied Statistics Southern New Hampshire University zyBooks 2020 ISBN: 978-1-394-04892-2

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