Regression and Correlation Analysis Math533 Part C

Reliable Housewares is a local store that sells many household items and issues its own credit card to its customers. The store manager wants to study the purchasing behavior of its "credit" customers. To that end, he has come to DeVry and asked our MBA students for help. The manager has brought with him data on five variables of 55 randomly selected credit customers.

Ø LOCATION (Rural, Urban, Suburban – Household location of the credit customer)

Ø INCOME (in $1,000's – be careful with this)

Ø SIZE (Household Size - number of people living in the household of credit customer)

Ø YEARS (the number of years that the customer has lived in the current location)

Ø CREDIT BALANCE ($ balance on customer’s store credit card)

Regression and Correlation Analysis

Using Excel or MINITAB perform the regression and correlation analysis for the data on CREDIT BALANCE (Y) and SIZE (X) by answering the following.

1. Generate a scatterplot for CREDIT BALANCE vs. SIZE, including the graph of the "best fit" line. Interpret.
2. Determine the equation of the "best fit" line, which describes the relationship between CREDIT BALANCE and SIZE.
3. Determine the coefficient of correlation. Interpret.
4. Determine the coefficient of determination. Interpret.
5. Test the utility of this regression model (use a two tail test with ? =.05). Interpret your results, including the p-value.
6. Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE? Explain.
7. Compute the 95% confidence interval for ?1 (the population slope). Interpret this interval.
8. Using an interval, estimate the average credit balance for customers that have household size of 5. Interpret this interval.
9. Using an interval, predict the credit balance for a customer that has a household size of 5. Interpret this interval.
10. What can you say about the credit balance for a customer that has a household size of 10? Explain your answer.

In an attempt to improve the model, you have decided to develop a multiple regression model predicting CREDIT BALANCE based on INCOME, SIZE and YEARS.

1. Using Excel or MINITAB, run the multiple regression analysis with variables INCOME, SIZE and YEARS to predict CREDIT BALANCE. State the equation for this multiple regression model.
2. Perform the Global Test for Utility (F-Test) using critical-value or p-value approach. Explain and interpret your conclusion.
3. Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should you keep and which should you discard.
4. Develop a final multiple regression model including only the independent variables that you think it should be included in the model.
5. Is this new multiple regression model better than the simple linear model that you generated in bullets 1-10? Why? Explain.

• All DeVry University policies are in effect, including the plagiarism policy.
• Project Part C report is due by the end of Week 7.
• Project Part C is worth 100 total points. See grading rubric below.

Submission:A report in Microsoft Word containing an executive summary + all of the work done in 1-14 (Excel/Minitab Output + interpretations) as an appendix.

Report Format:

1. Executive Summary - Summarize your results from 1-14 in a report that is two pages or less in length. It will explains and interprets the results of your analysis in ways that are understandable to Management of Reliable Housewares who don't know statistics.
2. Appendix - Bullets 1-14 addressed with appropriate Minitab output, graphs and interpretations based on the context of the problem. Be sure to number each bullet 1-14.

Project Part C: Grading Rubric

Category	Points	Description
Executive Summary	20	Conclusion of your statistical analysis in a logical, lucid and cohesive way for Reliable Housewares Management
Questions 1-12, 14, and 15 - 5 pts. each	70	addressed with appropriate output, graphs and interpretations
Question 13	10	addressed with appropriate output, graphs and interpretations
Total	100	A quality paper will meet or exceed all of the above requirements. It will adhere to the format described and will be clear, concise, logical, with no spelling and grammatical errors