# When using linear regression, what would you expect the scatterplot to look like?

Learning Goal: I’m working on a applied mathematics project and need an explanation and answer to help me learn.CompetenciesIn 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

OverviewThe 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.ScenarioYou have been hired by the D. M. Pan National Real Estate Company to

develop a model to predict 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

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.DirectionsUsing 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 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:IntroductionDescribe the report: Give a brief description of the purpose of your report.

Define the question your report is trying to answer.

Explain when using linear regression is most appropriate.

When using linear regression, what would you expect the scatterplot to look like?

Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.

Data CollectionSampling the data: Select a random sample of 50 houses.

Identify your response and predictor variables.

Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.

Data AnalysisHistogram: For your two variables, create histograms.

Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.

Interpret the graphs and statistics:

Based on your graphs and sample statistics, interpret the center,

spread, shape, and any unusual characteristic (outliers, gaps, etc.) for

the two variables.

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 ModelScatterplot: Provide a graph of the scatterplot of the data with a line of best fit.

Explain if a regression model is appropriate to develop based on your scatterplot.

Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.

Identify any possible outliers or influential points and discuss their effect on the correlation.

Discuss keeping or removing outlier data points and what impact your decision would have on your model.

Find r: Find the correlation coefficient (r).

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.Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.

Interpret regression equation: Interpret the slope and intercept in context.

Strength of the equation: Provide and interpret R-squared.

Determine the strength of the linear regression equation you developed.

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.

ConclusionsSummarize findings: In one paragraph, summarize

your findings in clear and concise plain language for the CEO to

understand. Summarize your results.

Did you see the results you expected, or was anything different from your expectations or experiences?

What changes could support different results, or help to solve a different problem?

Provide at least one question that would be interesting for follow-up research.

You can use the following tutorial that is specifically about this

assignment. Make sure to check the assignment prompt for specific

numbers used for national statistics. The videos may use different

national statistics. You should use the national statistics posted with

this assignment.MAT-240 Module 4 Project One

What to SubmitTo 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.

Requirements: satisfactory to rubrics