MAT 240 Project One (Final Edit)

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Feb 20, 2024

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Median Housing Price Prediction Model for D. M. Pan National Real Estate Company 1 Report: Housing Price Prediction Model for D. M. Pan National Real Estate Company Mike Leal Jr Southern New Hampshire University

Median Housing Price Model for D. M. Pan National Real Estate Company 2 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 the square footage of a home is a good indicator of what the listing price should be. Using a linear regression is generally appropriate when predicting the 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 two variables. This means that as the square footage of the home increases the listing price also increases. The response (dependent variable “y-axis”) is the variable being modeled or predicted. In this case, the y-axis is the median listing price. The predictor (independent variable “x-axis”) is the variable used to predict the response. For this report, the x-axis is the square footage. Data Collection For this analysis, I used Real Estate County Data to collect records on the listing prices and square footage of homes in 2019 and transferred them to Microsoft Excel. 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 genuinely random sample. The predictor variable is the square footage 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 3 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 - 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 f(x) = 105.74 x + 119460.75 Scatterplot of Y vs X Data Analysis There are certain assumptions or conditions that must be met before creating a linear regression model. 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 property and the response variable is what the median listing price should be based on the square footage.

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Median Housing Price Model for D. M. Pan National Real Estate Company 4 Median Listing PriceMedian Square Foot Mean 343,221 2,116 Median 318,300 1,918 Standard Deviation 114805.684 944.4000607

Median Housing Price Model for D. M. Pan National Real Estate Company 5 The first histogram, which shows the median square feet, is skewed right. This shows that most homes in this sample are less than 2,757 square feet. There are a few outliers in this dataset ranging from 2,757-5,957. The listing price histogram is the same as the first being skewed right. There are a few outliers in this set as well ranging from 403,400-763,400. The median price per square foot in this sample is around 105.74$ per square foot, which compared to the national average is a bit lower. Develop Regression Model 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 - 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 f(x) = 105.74 x + 119460.75 Scatterplot of y vs x A regression model can be developed because we have a positive linear trend in this scatterplot. Because the r value is .869, the correlation is moderately strong. On top of this, the outliers make it so that the y-intercept is a positive number, which in this situation wouldn’t make sense.

Median Housing Price Model for D. M. Pan National Real Estate Company 6 Determine the Line of Best Fit Y = 105.74x + 119461 The slope shows that for every additional square foot is an increase of $105.74 to the listing price. The y-intercept is 119461. R-Squared is .869. Because of this, given the data sample, the correlation is moderately strong. For a home with a square footage of 1,500, I would set the listing price at $278,071. We can interpret this listing price by plugging 1,500 into the equation as (x). Conclusions By using the data selected, I was able to calculate the average price per square footage and how it affects the overall listing price. By creating histograms, we were able to look more in-depth at data of both listing price and square footage. Everything seemed to fit my expectations, and nothing was different from what I assumed I would find. However, changing the sample group would result in different outcomes. Something interesting would be finding the averages for each individual section in the United States and seeing how they compare to one another.

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