MAT 240 Module Two Assignment
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Southern New Hampshire University *
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240
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Mathematics
Date
Feb 20, 2024
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Selling Price and Area Analysis for D.M. Pan National Real Estate Company
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Report: Selling Price and Area Analysis for D.M. Pan National Real Estate Company
Pamela G. Ware
Department of Mathematics, SNHU
MAT 240: Applied Statistics
Professor Patterson
Jan. 22, 2024
Selling Price and Area Analysis for D.M. Pan National Real Estate Company
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Report: Selling Price and Area Analysis for D.M. Pan National Real Estate Company
Introduction
The purpose of this report is to make predictions for D.M. Pan National Real Estate Company on median house prices for which homes sold in the year 2019. The purpose of this report would be to demonstrate whether the square footage of a home is a good indication of what the listing price should be. When trying to predict what the values of a variable are based on the values of another variable, linear regression will be the most appropriate method to choose
from. In this report, we will attempt to predict median listing price of homes based on the variable’s square footage. Our expectation of a scatterplot based on these variables is that the scatterplot would demonstrate a positive correlation between the two variables. This means that as the amount of square footage of the home gets larger, so does the listing price. The response or dependent variable is the variable you will model or predict. In this report, the dependent variable is the median listing prices. The predictor or independent variable is the variable you will use to predict the response. In this report, the independent variable is the square footage.
Generate a Representative Sample of the Data
From the Real Estate County Data in the spreadsheet, I selected the West South Central regional column. I selected all the properties in the West South Central region and copied them to a new spreadsheet. I then added a column to the right where each field has a random number assigned to it, using the =RAND() formula and sorted those fields from smallest to largest. I then selected the first 30 properties listed. This will become my random sample, since they were selected at random. The predictor variables are the square footage, and the response variables would be what the median listing price would need to be for the square footage.
Analyze Your Sample
The following steps were required for me to analyze my sample. I had to clean and process the data. This step involves organizing the data, removing any missing or inconsistent data points, and transforming data as needed to fit the format of my analysis tool. Second, I had to determine the appropriate statistical tests. This step involves deciding which statistical tests will be used given the type of data and research question. For example, if I have a continuous variable, I can use regression analysis.
Selling Price and Area Analysis for D.M. Pan National Real Estate Company
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Third, I applied the chosen analysis technique. This step involves running the chosen statistical test on the sample data to determine whether the results are statistically significant and can be generalized to the population. Next, I evaluated the results, interpreting the results of the analysis in relation to the research question and drawing conclusions about the population from the sample data. Finally, I report the findings, presenting the results of the analysis in a clear manner and discussing the limitations of the study.
I selected the data for the West South Central Region (Arkansas, Louisiana, Oklahoma, and Texas) that I wanted to analyze, making sure that I had both the dependent variable and independent variable in my data selection. For example, the dependent variable is the “listing price” and the independent variable is
the “median square footage”. I selected “Insert” in the menu bar at the top of the screen and clicked on “Scatter” in the “Charts” section. I then selected a scatterplot with the dependent variable on the y-axis and the independent variable on the x-axis. I right clicked on the y-axis and selected “Format Axis.” In the ”Format Axis” dialog box, I selected the “Number” tab and chose “Currency” in the “Category” section, set the decimal places to zero (0) and clicked “Ok.” Then I added a trendline by right-clicking on a data point in the scatterplot and selecting “Add Trendline.” I selected a linear regression trendline and displayed the equation and R-squared value on the chart.
I had to interpret the results, the trendline equation shows the relationship between the dependent variable and independent variable, which is y=110.06x+28562. It suggests that the model explains the data well. I also checked the statistical significance of the relationship between the two variables by conducting a hypothesis test. I calculated the regression coefficient, standard error, t-statistic, and p-
value, and used the Data Analysis Toolpak in Excel. I had to make sure my sample size was large enough to be representative and considered the limitations of my analysis.
Mean
$259,270.97
$342,365.00
Median
$254,100.00
$318,000.00
Std. Dev.
$85,068.43
$125,914
$1,997.36
$1,884.50
$465.78
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Selling Price and Area Analysis for D.M. Pan National Real Estate Company
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Generate Scatterplot
Observe Patterns
In a scatterplot, x and y represent two different variables that are being analyzed for a possible relationship or correlation. The variable on the x-axis is the independent variable, while the variable on the y-axis is the dependent variable. This means that the values on the y-axis (Listing Price) depend on the values on the x-axis (Square Foot).
The regression equation for the scatterplot is y=110.06x+28562, where x represents the median square feet of the houses and y represents the median listing price in dollars.
I see the shape as linear.
If I had an 1,800 square foot house, I could substitute x=1800 into the regression equation
and estimate the median listing price to be approximately $209,698.
I see two potential outliers in the scatterplot. One for Nacogdoches County for a house with 5,107 square feet for $630.800 and the second in McLennan County with 3,920 square feet for $407,300. Both were selected in a random sample, neither are anywhere near the other data points in that region and both are the only houses in the sample with more than 3,900 square feet.
Selling Price and Area Analysis for D.M. Pan National Real Estate Company
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I think the two outliers appeared in the scatterplot because they were randomly generated with the region that I chose. The prices for these two homes were significantly higher than the rest of the homes from the sample.