MAT 240 Project One: Median Housing Price Prediction Model for D. M. Pan National Real Estate Company PDF

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Project One: Median Housing Price Prediction Model for D. M. Pan National Real Estate Company; This report aims to show if square footage of a home is a good indicator of what the listing price should be....

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Median Housing Price Prediction Model for D. M. Pan National Real Estate Company

Report: Median Housing Price Prediction Model for D. M. Pan National Real Estate Company Southern New Hampshire University

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Median Housing Price Model for D. M. Pan National Real Estate Company

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Introduction This report will provide D.M. Pan National Real Estate Company with predictions for median house prices for homes sold in 2019. This report aims to show if square footage of a home is a good indicator of what the listing price should be. Using a linear regression is most appropriate when predicting values of variables based on the values of other variables. In this case, we will be predicting median listing prices for homes based on the square footage. The expectation for the scatterplot is that there is a positive correlation between the variable. This means that as the square footage of the home increases the listing price also increases. The response or dependent variable (y-axis) is the variable being modeled or predicted which is the median listing price in this case. The predictor or independent variable (x-axis) is the variable used to predict the response, which is the square footage, for this report.

Data Collection From the Real Estate County Data in the spreadsheet, I chose to work with the East North Central regional data. I selected all properties that were listed in the East North Central region and transferred them to a separate sheet. I then added a column preceding the data where each field had a random number assigned, using the formula =RAND(). From there, I sorted those numbers from smallest to largest and I selected the first 50 properties listed. This ensured that I would be working with a truly random sample. The predictor variable is the square footage of the of the property and the response variable is what the median listing price should be based on the square footage.

Median Housing Price Model for D. M. Pan National Real Estate Company

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Median Sq Ft vs Median Listing Price $500,000.00 $450,000.00

Median Listing Price

$400,000.00 $350,000.00 $300,000.00 $250,000.00 $200,000.00 $150,000.00 $100,000.00 $50,000.00 $0.00 500.00

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Median Square Feet

Data Analysis Before creating a linear regression model there are certain assumptions or conditions that must be met. For the data, the true relationship is linear, errors have equal variance around the line, errors are normally distributed, and the observations are independent. The predictor variable is the square footage of the of the property and the response variable is what the median listing price should be based on the square footage.

Median Housing Price Model for D. M. Pan National Real Estate Company

Median Listing Price

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Median Square Foot

Mean

$218,757.96

1878.181429

Median

$199,148.57

1809.241071

$84,701.10

417.4150084

Standard Deviation

The first histogram, which shows the median square feet, is skewed right. This shows that most homes in this sample are less than 2,689 square feet. There are two outliers which are homes that are 3,482 square feet and 3,099 square feet. The house that is 3,482 square feet is surprisingly priced lower than the next largest home, at 3,099 square feet. This tells us that the count of Hamilton has a lower cost of living compared to Delaware county, which appears to be the most expensive county in the sample. The second histogram, displaying median listing price, shows the same shape as the previous histogram. The data is skewed right as there are few houses priced above $318,820. Houses in the East North Central region have a median price of $105 per square foot. In the national housing market, the median price per square foot is $142. This information shows that homes on average cost less per square foot in this region than the

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median price per square foot on the national housing market. It’s also worth noting that the median square footage of homes in the East North Central region is 1,809 square feet. For the national housing market, the median square footage is 1,901. This information shows that comparatively, homes in the East North Central region are slightly smaller on average when compared to the national housing market. This information tells us that our data is not representative of the national housing market as the cost of living in the East North Central region would be lower than that of the national averages.

Median Sq Ft vs Median Listing Price $500,000.00 $450,000.00

R² f(x)==0.55 150.91 x − 64683.78

Median Listing Price

$400,000.00 $350,000.00 $300,000.00 $250,000.00 $200,000.00 $150,000.00 $100,000.00 $50,000.00 $0.00 500.00

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The Regression Model

Based on the scatterplot above, a regression model can be developed for the data. This can be accomplished because the data has a positive correlation and is a true linear relationship. We see this in the trendline, as the square footage of the house increases, the price of the house also increases. While there us a moderate correlation in the data, it is still a positive correlation.

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The r value of 0.55 supports the positive correlation in that as one variable increases, the other does based on that increase. The Line of Best Fit Regression Equation: y = 150.91x-64684 This equation tells us what the median listing price (y) of a home should be when x is replaced with the square footage. For a house with zero square footage, the median listing price is -64,684. This value is negative and does not make sense as a house would not sell for a negative amount of money. This means that the y-intercept is not able to be interpreted. For a house that is 1,500 square feet, the equation would be y=150.91(1500)-64684, which means the median listing price should be $161,681. Conclusions Using the data above, I was able to determine that it would be suitable to determine what the median listing price of a home should be based on the square footage. This is what I thought I would initially find in the data and sample used. This was confirmed once built into the scatterplots and histograms above. It would be interesting to research how this region used above compares to another specific region in the nation, opposed to comparing the data or sample to the nation. Once compared, would the data from the East North Central region be representative of that new region selected....