Median Housing Price Prediction Model Using Square Footage Data

Median Housing Price Model for D. M. Pan National Real Estate Company Report: Housing Price Prediction Model for D.M. Pan National Real Estate Company Darnell Harper Department of Mathematics, SNHU MAT 240: Applied Statistics Vincent Frazier Feb 02, 2024

Median Housing Price Model for D. M. Pan National Real Estate Company Introduction Describe the report: The purpose of this report is to determine if the square footage is a good indicator for what the listing price should be for the properties. Describe the report: Using linear regression is most appropriate when making a prediction or forecasting the value of a dependent variable based on the known value of the independent variable. Describe the report: When using a linear regression, one should expect the scatterplot to be represented as data points scattered around a straight line. Describe the report: The response (y) variable is a random variable while the predictor (x) variable is assumed as non-random or fixed and measured without error. Data Collection Sampling the data: I selected random five properties from ten different regions, I then sorted them randomly throughout the spreadsheet and used the excel formula fx=rand(). Sampling the data: The predictor variable is square footage of the property and the response variable is the listing price of the property.

Median Housing Price Model for D. M. Pan National Real Estate Company Scatterplot: 1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 2,800 - 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 450,000 500,000 f(x) = 87.19 x + 134221.18 R² = 0.18 Housing Price Prediction Square Footage Listing Price Data Analysis

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

Median Housing Price Model for D. M. Pan National Real Estate Company Histogram Summary statistics: Listing Price Square Feet Area Mean 297,050 1,868 Median 307,150 1,834 Std Dev 71,644.33 $ 344.9920531 Interpret the graphs and statistics: After reviewing the information on the graphs and statistics, the center is as follows:

Median Housing Price Model for D. M. Pan National Real Estate Company Listing Price Square Feet Area Mean 297,050 1,868 Median 307,150 1,834 Mode 331100 2005 Midrange 372900 2501 I do not see any unusual characteristics within this scatterplot. Interpret the graphs and statistics: After comparing my sample to the National Summary Statistics and Graphs Real Estate Data PDF, I noticed that my sample follows the same trend as the national data. The national data displays a noticeably more frequent listing price between $200,000 and $400,000 the same pattern in which my sample does. Develop Regression Model

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Median Housing Price Model for D. M. Pan National Real Estate Company Scatterplot: 1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 2,800 - 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 450,000 500,000 f(x) = 87.19 x + 134221.18 R² = 0.18 Housing Price Prediction Square Footage Listing Price The regression model is appropriate based on the trendline as well as the data points showing no outliers when it comes to the relationship between the square footage and listing price of the property. Discuss associations: Discuss the associations in the scatterplot, including the direction, strength, and form, in the context of your model.] The direction of the scatterplot is a positive direction with a linear form that has a moderate strength due to the correlation coefficient being 0.42.

Median Housing Price Model for D. M. Pan National Real Estate Company [ Discuss associations: One possible outlier could be a property in Etowah County in Alabama that has a listing price of $167,000 with a square footage of 2,372 Sq Ft. This outlier has no effect on the correlation coefficient in this sample. Discuss associations: If I were to remove the outlier, it would not have a significant impact on the model. The correlation would still have a moderate strength with no significant difference. Calculate r : The correlation coefficient calculated is 0.4198 and supports my scatterplot based on the strength and direction of the datapoints in the model. Determine the Line of Best Fit Regression equation: The regression equation is y = 87.188x + 134221 where the dependent variable is the listing price and the independent variable is the square feet. Interpret regression equation: The slope represents the change in listing price when there is a unit change in square footage. The intercept represents if there is 0 square footage then the listing price would be $134,221. Strength of the equation: R-squared is listed as 0.1763 and based on R-squared, the linear equation would have a weak correlation due to there being relatively no change in the listing price. Use regression equation to make predictions: Based on the regression equation, the listing price should be $265,003 if the square feet is 1500. Conclusions Summarize findings: In conclusion, what was found in this report is roughly what is the national average when it comes to housing prices based on square feet. Other than the one outlier

Median Housing Price Model for D. M. Pan National Real Estate Company in the model, the forgone conclusion is the listing price will be based on the square feet. So the larger the property is in size, the higher the listing price is. Summarize findings: The results I yielded in the report is what I expected. Summarize findings: I believe if we were to us worldwide housing information or housing information based on North America instead of just America, it would yield different results. Summarize findings: One question I would like to ask is, why is it that certain regions have higher listing prices for the same square feet as a house in another region? What is the determining factor in creating these prices based just on the region if there is no difference in size?

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