Mathematics Homework Help

Competencies

In this project, you will demonstrate your mastery of the following competencies:

• Apply statistical techniques to address research problems
• Perform regression analysis to address an authentic problem

Overview

The purpose of this project is to have you complete all of the steps
of a real-world linear regression research project starting with
developing a research question, then completing a comprehensive
statistical analysis, and ending with summarizing your research
conclusions.

Scenario

You have been hired by the D. M. Pan National Real Estate Company to
develop a model to predict median housing prices for homes sold in 2019.
The CEO of D. M. Pan wants to use this information to help their real
estate agents better determine the use of square footage as a benchmark
for listing prices on homes. Your task is to provide a report predicting
the median housing prices based square footage. To complete this task,
use the provided real estate data set for all U.S. home sales as well as
national descriptive statistics and graphs provided.

Directions

Using the Project One Template located in the What to Submit section,
generate a report including your tables and graphs to determine if the
square footage of a house is a good indicator for what the listing price
should be. Reference the National Statistics and Graphs document for
national comparisons and the Real Estate County Data spreadsheet (both
found in the Supporting Materials section) for your statistical
analysis.

Note: Present your data in a clearly labeled table and using clearly labeled graphs.

Specifically, include the following in your report:

Introduction

1. Describe the report: Give a brief description of the purpose of your report.
   1. Define the question your report is trying to answer.
   2. Explain when using linear regression is most appropriate.
      1. When using linear regression, what would you expect the scatterplot to look like?
   3. Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.

Data Collection

1. Sampling the data: Select a random sample of 50 counties.
   1. Identify your response and predictor variables.
2. Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.

Data Analysis

1. Histogram: For your two variables, create histograms.
2. Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.
3. Interpret the graphs and statistics:
   1. Based on your graphs and sample statistics, interpret the center,
      spread, shape, and any unusual characteristic (outliers, gaps, etc.) for
      the two variables.
   2. Compare and contrast the shape, center, spread, and any unusual
      characteristic for your sample of house sales with the national
      population. Is your sample representative of national housing market
      sales?

Develop Your Regression Model

1. Scatterplot: Provide a graph of the scatterplot of the data with a line of best fit.
   1. Explain if a regression model is appropriate to develop based on your scatterplot.
2. Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
   1. Identify any possible outliers or influential points and discuss their effect on the correlation.
   2. Discuss keeping or removing outlier data points and what impact your decision would have on your model.
3. Find r: Find the correlation coefficient (r).
   1. Explain how the r value you calculated supports what you noticed in your scatterplot.

Determine the Line of Best Fit. Clearly define your variables. Find and interpret the regression equation. Assess the strength of the model.

1. Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.
2. Interpret regression equation: Interpret the slope and intercept in context.
3. Strength of the equation: Provide and interpret R-squared.
   1. Determine the strength of the linear regression equation you developed.
4. Use regression equation to make predictions: Use your regression equation to predict how much you should list your home for based on the square footage of your home.

Conclusions

1. Summarize findings: In one paragraph, summarize
   your findings in clear and concise plain language for the CEO to
   understand. Summarize your results.
   1. Did you see the results you expected, or was anything different from your expectations or experiences?
      1. What changes could support different results, or help to solve a different problem?
      2. Provide at least one question that would be interesting for follow-up research.

What to Submit

To complete this project, you must submit the following:

Project One Template: Use this template to structure your report, and submit the finished version as a Word document.

Supporting Materials

The following resources may help support your work on the project:

Document: National Statistics and Graphs
Use this data for input in your project report.

Spreadsheet: Real Estate County Data
Use this data for input in your project report.

Tutorial: Downloading Office 365 Programs
Use this tutorial for support with Office 365 programs.