Instructions

Progress Check

Use this activity to assess whether you can:

• Use StatCrunch to graph a scatterplot with its least squares regression line and to simultaneously produce the equation of the regression line along with its correlation coefficient, r.
• Identify the x with the largest absolute prediction error.
• Explain why a given data point is an outlier.

In this activity you will use StatCrunch and embed your results in an essay question. The essay questions are not automatically graded; your instructor will enter the points for these questions later. WARNING: you will need to enter your response to each essay question with every attempt. Your instructor will only grade the essay for your attempt with the highest total score for the automatically graded questions.

Discussion Board

Use the Module 27 discussion board (opens in a new tab) to ask questions or provide feedback about the problems in any Module 27 activity – including this lab.

Attempt History

	Attempt	Time	Score
LATEST	Attempt 1	25 minutes	4 out of 10 *

* Some questions not yet graded

Correct answers are hidden.

Score for this attempt: 4 out of 10 *

Submitted May 2 at 10:36am

This attempt took 25 minutes.

Learn by Doing

Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.

A list of StatCrunch directions is provided at the bottom of this text-box.

Context

The modern Olympic Games have changed dramatically since their inception in 1896. Are athletes getting better? We will use regression to investigate the change in winning times for one event—the men’s 1,500 meter race.

Variables

Year: the year of the Olympic Games, from 1896 to 2000.
Time: the winning time for the 1,500 meter race, in seconds.

Since the winning time depends on the year, the Year since 1896 is the explanatory variable, and the Winning time is the response variable.

Data

Download the olympics (Links to an external site.) datafile for the men’s 1,500 meter race. Then upload the datafile in StatCrunch. If you need a reminder about how to do this, review the list of StatCrunch directions below.

Prompt

In the first two questions below, you will use StatCrunch to produce and examine the scatterplot for the olympics datafile. You will also use StatCrunch to find the regression equation and correlation coefficient.

List of StatCrunch Directions

As you work through numbers 1) and 2) below, refer back to these StatCrunch directions when you need a quick reminder.

• Purchase StatCrunch (You only need to do this once.)
• Open StatCrunch
• Download Excel Data File
• Upload Excel Data File to StatCrunch
• Download StatCrunch Output Window (do not take screenshots; please use these directions)
• Upload Files to Your Stat-Class Folder in Canvas
• Embed Pictures in a Discussion Post (do not post attachments; please use these directions)
• Copy and Paste StatCrunch Text Output
• Produce Scatterplot, LSR Line, Regression Equation, & R (All at the same time!)

UnansweredQuestion 1Not yet graded / 3 pts

These directions assume that you have uploaded the olympics datafile in StatCrunch, and the StatCrunch worksheet with the data is open. If not, please see the Data section above.

1. Using the year since 1896 as the explanatory variable and the winning time as the response variable: graph the scatterplot with the regression line and produce the regression equation with the correlation coefficient – all at the same time (directions)
2. Toggle to the output page with the scatterplot and regression line. Notice that the data has a strong linear association, so it makes sense to use linear regression. (Always check the form of the scatterplot before using linear regression.)
3. Download the StatCrunch output page with your scatterplot and regression line graphed together. (directions)
4. Save the .png file (the graph of your scatterplot and regression line) to your Stats-Class folder. (directions)
5. Embed the .png file for your scatterplot and regression line in the text-box below. (directions)

UnansweredQuestion 2Not yet graded / 3 pts

These directions assume you have produced the Simple linear regression results in a multipage StatCrunch output window. If not please see the previous question.

• Toggle to the StatCrunch output page with the regression equation, correlation coefficient, and other statistics.
• Under the heading Simple linear regression results, copy and paste the first five lines (dependent variable, independent variable, linear equation, sample size, and R) into the text-box below. (directions)

Simple linear regression results:

Dependent Variable: Time
Independent Variable: Year
Time = 994.19341 – 0.39304496 Year
Sample size: 24
R (correlation coefficient) = -0.89075356

Question 32 / 2 pts

For which of the years 1900, 1940, or 2000 is the absolute prediction error the largest?

1900 1940

undefinedundefined2000undefined

Correct. Vertical distance from the regression line is the prediction error. The data point for 2000 is father from the regression line than the other options, so the prediction error is largest.

Question 42 / 2 pts

For the year 1896, the winning time for the men’s 1500-meter race is an outlier. In what ways is this data point an outlier? Check all that apply

undefinedan outlier with respect to Y=Time

Correct. The winning time in 1896 is much larger than the other winning times.

undefinedan outlier with respect to X=Yearundefinedundefinedan outlier with respect to the form of the relationship between X and Y

Correct. The data point (1896, 273) deviates from the pattern in the rest of the data. It does not follow the strong, negative association or the linear pattern.

Score: 4 out of 10

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 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.

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 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 houses.
   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 Data
Use this data for input in your project report.

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

I’m studying and need help with a Statistics question to help me learn.

Using the topic Gun Control and the Gun Control codebook complete the following tasks:

• Develop a theory.
• Develop a corresponding hypothesis
• Identify the independent (IV) and dependent (DV) variables in your hypothesis
• Operationalize your independent and dependent variables.
  • Hint: What are the attributes (categories) of your variable?
• Identify the level of measurement (LOM) of the independent and dependent variables in your hypothesis.

Part 2: Using the Gun Control dataset complete the following tasks:

• Run frequencies on the variables:
  • Religion.
  • Education.
  • OwnGun.
  • CauseViolence.
  • AmericanOwn.
  • ConcealedWeapons.
• Summarize your findings.

Part 3: Using the Gun Control dataset complete the following tasks:

• Run the measures of central tendency (MOCT) that correspond with each of the following variables’ levels of measurement (LOM):
  • Religion.
  • Education.
  • OwnGun.
  • CauseViolence.
  • AmericanOwn.
  • ConcealedWeapons.
• Summarize your findings.

Part 4: Using the Gun Control dataset complete the following tasks:

• Run the measures of variability (MOV) that correspond with each of the following variables’ LOM:
  • Religion.
  • Education.
  • OwnGun.
  • CauseViolence.
  • AmericanOwn.
  • ConcealedWeapons.
• Summarize your findings.

Whether in a scholarly or practitioner setting, good research and data analysis should have the benefit of peer feedback. For this Discussion, you will post your response to the hypothesis test, along with the results. Be sure and remember that the goal is to obtain constructive feedback to improve the research and its interpretation, so please view this as an opportunity to learn from one another.

To prepare for this Discussion:

• Review this week’s Learning Resources and media program related to multiple regression.
• Create a research question using the Afrobarometer Dataset or the HS Long Survey Dataset, that can be answered by multiple regression.

Use SPSS to answer the research questions.

1. If you are using the Afrobarometer Dataset, report the mean of Q1 (Age). If you are using the HS Long Survey Dataset, report the mean of X1SES.
2. What is your research question?
3. What is the null hypothesis for your question?
4. What research design would align with this question?
5. What dependent variable was used and how is it measured?
6. What independent variables are used and how are they measured? What is the justification for including these predictor variables?
7. If you found significance, what is the strength of the effect?
8. Explain your results for a lay audience, explain what the answer to your research question.

Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.

Learning Resources

Required Readings

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 12, “Regression and Correlation” (pp. 401-457) (previously read in Week 8)

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 8, “Correlation and Regression Analysis”
• Chapter 11, “Editing Output” (previously read in Week 2, 3, 4, 5. 6, 7, and 8)

Walden University Library. (n.d.). Course Guide and Assignment Help for RSCH 8210. Retrieved from http://academicguides.waldenu.edu/rsch8210

For help with this week’s research, see this Course Guide and related weekly assignment resources.

Document: Walden University: Research Design Alignment Table

Required Media

Laureate Education (Producer). (2016g). Multiple regression [Video file]. Baltimore, MD: Author.

Note: The approximate length of this media piece is 7 minutes.

In this media program, Dr. Matt Jones demonstrates multiple regression using the SPSS software.

Accessible player –Downloads– Download Video w/CC Download Audio Download Transcript

Optional Resources

Skill Builder: Interpreting the Results from Regression Models

To access these Skill Builders, navigate back to your Blackboard Course Home page, and locate “Skill Builders” in the left navigation pane. From there, click on the relevant Skill Builder link for this week.

You are encouraged to click through these and all Skill Builders to gain additional practice with these concepts. Doing so will bolster your knowledge of the concepts you’re learning this week and throughout the course.

• Why did the authors use multiple regression?
• Do you think it’s the most appropriate choice? Why or      why not?
• Did the authors display the data?
• Do the results stand alone? Why or why not?
• Did the authors report effect size? If yes, is this      meaningful?

Use proper APA format, citations, and referencing.

Learning Resources

Required Readings

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 12, “Regression and Correlation” (pp. 401-457) (previously read in Week 8)

Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 8, “Correlation and Regression Analysis”
• Chapter 11, “Editing Output” (previously read in Week 2, 3, 4, 5. 6, 7, and 8)

Walden University Library. (n.d.). Course Guide and Assignment Help for RSCH 8210. Retrieved from http://academicguides.waldenu.edu/rsch8210

For help with this week’s research, see this Course Guide and related weekly assignment resources.

Document: Walden University: Research Design Alignment Table

Required Media

Laureate Education (Producer). (2016g). Multiple regression [Video file]. Baltimore, MD: Author.

Note: The approximate length of this media piece is 7 minutes.

In this media program, Dr. Matt Jones demonstrates multiple regression using the SPSS software.

Accessible player  –Downloads– Download Video w/CC Download Audio Download Transcript 

Optional Resources

Skill Builder: Interpreting the Results from Regression Models

To access these Skill Builders, navigate back to your Blackboard Course Home page, and locate “Skill Builders” in the left navigation pane. From there, click on the relevant Skill Builder link for this week.

You are encouraged to click through these and all Skill Builders to gain additional practice with these concepts. Doing so will bolster your knowledge of the concepts you’re learning this week and throughout the course.

I have attached the questions, and I marked them with yellow. please make sure to go through the questions before bidding. I will provide more information if needed later. Thank you.

Week 5: Consumer Mathematics

Everyone benefits from effective money management. Money is earned, bills are paid, and savings accounts are created. But what happens when the money you earn is not enough to cover your immediate needs or wants? This is where a loan comes in.

No matter how much money you make in your lifetime, it is likely that at some point you will take out a loan. This could be for education, a home, a car, or a hobby, such as a boat. If you have taken out a loan, you already know there is a cost for taking that loan. How much of that loan is interest, or money paid to the financial institution for lending you the cash? How much of your monthly payment is paying down the debt, and how much is paying interest on that amount? If you haven’t taken out a loan before, you will be glad to work through this math now so that you are prepared for the true costs involved.

This week, you will explore the math behind finances, loans, and interest payments. You also re-examine your own personal financial management techniques.

Discussion: Repaying Loans

Before taking out a loan, it is important to know the repayment terms and how your interest rate and the time of the loan affect the total loan balance.

For this Discussion, you examine the effect of simple and compound interest, as well as time on the principal balance of a loan. You also explore how these variables affect loan repayment.

To prepare for this Discussion:

• Think of a big-ticket item you might need to take out a loan to purchase. Dream big. What have you always wanted? This could be a boat, car, motorcycle, a trip around the world, etc. Research the cost of this item.
• Select a reasonable interest rate for your item (between 2% and 10% is standard).
• Select a time period to pay off your loan (between 3 and 10 years is common

• Post at least 2 paragraphs in response to the following:
  • Paragraph 1:
    • Describe the item you are taking a loan out for and the purchase price.
    • Include your chosen interest rate and amount of time for your loan.
    • Determine the amount of interest you will pay throughout the term of the loan and the final cost of the item when the loan is paid in full. Note: Assume your bank uses the simple interest formula: Interest = Principal * Rate * Time.
    • Show the work needed to find the amount of interest and total cost.
    • Determine the monthly payment for this loan.
  • Paragraph 2:
    • Repeat the interest computation however lower the time frame by one year. Show your work.
    • Determine the total amount of the loan when paid in full.
    • Compute the new monthly payment.
    • Explain if you are surprised by the results. Why, or why not?
    • Discuss one change you could make in your life to make the new monthly payment possible.

Competency

Describe the data using the measures of central tendency and measures of variability.

 

Instructions

Scenario (information repeated for deliverable 01, 03, and 04)

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

• A listing of the jobs by title
• The salary (in dollars) for each job
• The client needs the preliminary findings by the end of the day. Your boss asks you to first compute some basic statistics and then analyze the results in the four questions given in the Excel spreadsheet.
• Background information on the DataThe data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.
   

Competency

Apply the normal distribution, standard normal distribution, and central limit theorem.

 

Scenario

Frank has only had a brief introduction to statistics when he was in high school 12 years ago, and that did not cover inferential statistics. He is not confident in his ability to answer some of the problems posed in the course.

As Frank’s tutor, you need to provide Frank with guidance and instruction on a spreadsheet he has partially filled out. Your job is to help him understand and comprehend the material. You should not simply be providing him with an answer as this will not help when it comes time to take the test. Instead, you will be providing a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology.

 

To complete this assignment, you must first download the spreadsheet, and then complete it by including the following items on the spreadsheet:

Incorrect Answers – Correct any wrong answers. You must also explain the error performed in the problem in your own words.

Partially Finished Work – Complete any partially completed work. Make sure to provide step-by-step instructions including explanations.

Blank Questions – Show how to complete any blank questions by providing step-by-step instructions including explanations.

Your step-by-step breakdown of the problems, including explanations and calculations performed, should be present within the Excel spreadsheet provided.