Final Project – graduate researcher

Math 302 Final Project will be available on Friday morning of Week 6 in the course. You have 3 full weekends to review and work on the Final Project.

Scenario Background

Martha is considering opening a new fitness club in New Orleans. While doing some research she found data on the average price of fitness club monthly memberships for 16 cities in the US (source: https://www.numbeo.com/cost-of-living/prices_by_city.jsp). While she was very excited about this data, unfortunately New Orleans was not included. Regardless, Martha knows that she can use this data to give herself and her investors a good idea for a reasonable fee to charge in New Orleans. Of course, the gym membership fee in a big city like New York will be expensive because everything is expense in New York. The “Cost of Living Index” is useful to compare prices in different locations (For more information about the “Cost of Living Index” please see this website: https://www.numbeo.com/cost-of-living/cpi_explained.jsp). Martha decided to use the “Cost of Living Index” to explain the variability in fitness membership fees using a simple linear regression (see results in the first tab of Excel attachment).

While the “Cost of Living Index” is very helpful because it summarizes a lot of different costs in each city, Martha is also interested in looking more into particular costs which she believes may affect her business. First, with the rising cost of gas, she is concerned that people may go to the gym less in locations where gas costs more. Next, she knows Apartment rent is less expensive in New Orleans than a lot of other big cities, and therefore is interested in knowing if the money that people save on rent may translate to their willingness to pay more for a fitness membership. Lastly, she wants to explore whether fitness membership prices are higher where the average monthly salaries are higher. Martha used these three variables (gas price, apartment price, salary) to explain the variability in fitness membership fees using a multiple linear regression (see results in the second tab of Excel attachment).

Assignment Guidance

Martha has completed a lot of calculations, though now it is time for her to meet with her investors and share her findings. Help Martha interpret her calculations. There are two datasets and analyses in the attachment. On the first tab you will find the data, summary statistics, and simple linear regression for fitness membership fees and “Cost of Living Index”. On the second tab you will find the data, summary statistics, and multiple linear regression for fitness membership fees and gas price, apartment price, and salary.

Address the following questions in your report:

1. Looking at the data for “Fitness Club Membership fees”, are there any outliers? If so, which cities? *Use the Lower and Upper Bounds to find outliers (Hint: Review about outliers in our textbook: Measures of the Location of the Data)
2. Looking at the data for “Cost of Living Index”, are there any outliers? If so, which cities? *Again, make sure that you are using the lower and upper bounds to identify outliers.
3. The “Cost of Living Index” for New Orleans is 74.98. How does this compare to the other cities in this dataset? *Use the provided statistics on Mean, Median, Min, Q1, Q3, and/or Max to write this comparison.
4. Looking at the simple linear regression, is there a significant linear relationship between “Cost of Living Index” and Fitness Club Monthly Fee at significance level α = 0.05? (HINT: Excel uses scientific notation for small numbers. For example, 1.1623E-6 is the method Excel uses to write 0.0000011623). If significant, interpret the relationship between the “Cost of Living Index” and fitness membership fees (i.e., is there a positive relationship, or a negative relationship?)
5. The “Cost of Living Index” for New Orleans is 74.98. Predict the Fitness Club Monthly Fee for New Orleans. Provide a 95% prediction interval for your prediction. *This is the ONLY calculation you are asked to do for this project. ALL other calculations are already provided for you in Martha’s Excel attachment.
6. Looking at the multiple linear regression, are there any significant predictors at significance level α = 0.05? If significant, interpret the relationship between the significant predictor and fitness membership fees (i.e., is there a positive relationship, or a negative relationship?)
7. The average price of gas for New Orleans is $4.11, the price of a one bedroom apartment is $1,634, and the average monthly salary is $5,107. How do these compare to the other cities in this dataset? *Use the provided statistics on Mean, Median, Min, Q1, Q3, and/or Max to write this comparison.

Final Project Overview

The final project is worth 100 points and no calculations are needed other than the 95% prediction interval. All bullets under the “Assignment Guidance” should be included in your report. Your report will be an “Executive Summary” for Martha, where you will make a suggestion for her Fitness Club Membership Fee and justify your results. Please review how to write an Executive Summary on this website: https://www.alchemer.com/resources/blog/how-to-write-executive-summary/. Additionally, please make sure that you carefully review the grading rubric for this project.

You will be writing your own Executive Summary and submitting it through Turnitin. From Turnitin, an originality report will be generated. No Turnitin report should exceed 20% of originality because you are writing this up in your own words. If your originality report is over 20%, further action will need to be required from your instructor. This can include an automatic failure and 0 for plagiarism. If you have questions about Academic Plagiarism, please contact your instructor.