Location Income ($1,000) Urban 27 Rural 25 Suburban 25 Suburban 26 Rural 30 Urban 29 Rural 33 Urban 30 Suburban 32 Urban 34 Urban 35 Urban 40 Rural 30 Rural 33 Urban 42 Suburban 32 Urban 43 Urban 43 Rural 33 Urban 47 Suburban 35 Urban 54 Suburban 42 Rural 36 Urban 57 Suburban 44 Rural 38 Urban 54 Urban 54 Suburban 46 Rural 40 Urban 60 Urban 58 Urban 61 Urban 61 Urban 62 Suburban 49 Urban 68 Suburban 57 Rural 45 Urban 71 Suburban 57 Suburban 64 Rural 45 Urban 74 Suburban 65 Rural 47 Rural 53 Size 1 4 1 1 5 1 6 1 2 1 1 1 6 6 2 2 2 2 7 2 3 2 3 7 3 3 7 3 3 4 7 4 4 5 5 6 5 6 6 8 7 7 8 8 7 8 8 8 Years 2 2 1 2 5 3 10 4 4 6 8 9 9 11 10 4 10 10 13 10 5 11 5 13 11 6 15 8 10 6 15 11 10 13 13 14 8 14 8 16 15 9 9 17 19 10 18 18 Credit Balance($) 2,631 2,047 3,155 3,913 2,660 3,531 2,766 3,769 4,082 3,806 4,049 4,073 2,697 2,914 4,073 4,310 4,199 4,253 3,104 4,293 4,456 4,340 4,925 3,178 4,391 4,947 3,203 4,354 4,366 5,003 3,250 4,402 4,397 4,595 4,786 4,888 5,148 5,011 5,220 3,257 5,528 5,283 5,332 3,304 5,553 5,484 3,342 3,788 Suburban Suburban 66 69 8 8 10 10 5,756 5,861 Course Project: AJ DAVIS DEPARTMENT STORES Introduction AJ DAVIS is a department store chain, which has many credit customers and wants to find out more information about these customers. A sample of 50 credit customers is selected with data collected on the following five variables. 1. Location (rural, urban, suburban) 2. Income (in $1,000'sbe careful with this) 3. Size (household size, meaning number of people living in the household) 4. Years (the number of years that the customer has lived in the current location) 5. Credit balance (the customers current credit card balance on the store's credit card, in $). The data is available in Doc Sharing Course Project Data Set as an Excel file. You are to copy and paste the data set into a minitab worksheet. PROJECT PART A: Exploratory Data Analysis Open the file MATH533 Project Consumer.xls from the Course Project Data Set folder in Doc Sharing. For each of the five variables, process, organize, present, and summarize the data. Analyze each variable by itself using graphical and numerical techniques of summarization. Use minitab as much as possible, explaining what the printout tells you. You may wish to use some of the following graphs: stem-leaf diagram, frequency or relative frequency table, histogram, boxplot, dotplot, pie chart, bar graph. Caution: Not all of these are appropriate for each of these variables, nor are they all necessary. More is not necessarily better. In addition, be sure to find the appropriate measures of central tendency and measures of dispersion for the above data. Where appropriate use the five number summary (the Min, Q1, Median, Q3, Max). Once again, use minitab as appropriate, and explain what the results mean. Analyze the connections or relationships between the variables. There are 10 pairings here (location and income, location and size, location and years, location and credit balance, income and size, income and years, income and balance, size and years, size and credit balance, years and Credit Balance). Use graphical as well as numerical summary measures. Explain what you see. Be sure to consider all 10 pairings. Some variables show clear relationships, while others do not. Prepare your report in Microsoft Word (or some other word processing package), integrating your graphs and tables with text explanations and interpretations. Be sure that you have graphical and numerical back up for your explanations and interpretations. Be selective in what you include in the report. I'm not looking for a 20-page report on every variable and every possible relationship (that's 15 things to do). Rather, what I want you do is to highlight what you see for three individual variables (no more than one graph for each, one or two measures of central tendency and variability (as appropriate), and two or three sentences of interpretation). For the 10 pairings, identify and report only on three of the pairings, again using graphical and numerical summary (as appropriate), with interpretations. Please note that at least one of your pairings must include location and at least one of your pairings must not include location. All DeVry University policies are in effect, including the plagiarism policy. Project Part A report is due by the end of Week 2. Project Part A is worth 100 total points. See grading rubric below. Submission: The report from Part 4, including all relevant graphs and numerical analysis along with interpretations Format for report: A. Brief introduction B. Discuss your first individual variable, using graphical, numerical summary, and interpretation C. Discuss your second individual variable, using graphical, numerical summary, and interpretation D. Discuss your third individual variable, using graphical, numerical summary, and interpretation E. Discuss your first pairing of variables, using graphical, numerical summary, and interpretation F. Discuss your second pairing of variables, using graphical, numerical summary, and interpretation G. Discuss your third pairing of variables, using graphical, numerical summary, and interpretation H. Conclusion Project Part A: Grading Rubric Category Points % Description Three Individual graphical analysis, numerical analysis (when Variables 36 36 appropriate) and interpretation 12 points each Three Relationships 45 45 graphical analysis, numerical analysis (when Category 15 points each Communication Skills Points % Total 100 19 Description appropriate), and interpretation writing, grammar, clarity, logic, cohesiveness, 19 adherence to the above format A quality paper will meet or exceed all of the 100 above requirements. Project Part B: Hypothesis Testing and Confidence Intervals Your manager has speculated the following. a. The average (mean) annual income was greater than $45,000. b. The true population proportion of customers who live in a suburban area is less than 45%. c. The average (mean) number of years lived in the current home is greater than 8 years. d. The average (mean) credit balance for rural customers is less than $3,200. 1. Using the sample data, perform the hypothesis test for each of the above situations in order to see if there is evidence to support your manager's belief in each case A-D. In each case, use the Seven Elements of a Test of Hypothesis in Section 6.2 of your text book with = .05, and explain your conclusion in simple terms. Also, be sure to compute the p-value and interpret. 2. Follow this up with computing 95% confidence intervals for each of the variables described in A-D, and again interpreting these intervals. 3. Write a report to your manager about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical. 4. All DeVry University policies are in effect, including the plagiarism policy. 5. Project Part B report is due by the end of Week 6. 6. Project Part B is worth 100 total points. See the grading rubric below. Submission: The report from Part 3 and all of the relevant work done in the hypothesis testing (including minitab) in 1 and the confidence intervals (minitab) in Part 2 as an appendix Format for report: A. Summary report (about one paragraph on each of the speculations, A-D) B. Appendix with all of the steps in hypothesis testing (the format of the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book) for each speculation A-D, as well as the confidence intervals, including all minitab output Project Part B: Grading Rubric Category Points % Description Addressing each speculation hypothesis test, interpretation, 80 80 20 points each confidence interval, and interpretation one paragraph on each of the Summary report 20 20 speculations A quality paper will meet or exceed all Total 100 100 of the above requirements. Project Part C: Regression and Correlation Analysis Using MINITAB, perform the regression and correlation analysis for the data on income(Y), the dependent variable, and credit balance (X), the independent variable, by answering the following. 1. Generate a scatterplot for income ($1,000) versus credit balance($), including the graph of the best fit line. Interpret. 2. Determine the equation of the best fit line, which describes the relationship between income and credit balance. 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 credit balance to predict income? Explain. 7. Compute the 95% confidence interval for beta-1 (the population slope). Interpret this interval. 8. Using an interval, estimate the average income for customers that have credit balance of $4,000. Interpret this interval. 9. Using an interval, predict the income for a customer that has a credit balance of $4,000. Interpret this interval. 10. What can we say about the income for a customer that has a credit balance of $10,000? Explain your answer. In an attempt to improve the model, we attempt to do a multiple regression model predicting income based on credit balance, years, and size. 11. Using MINITAB, run the multiple regression analysis using the variables credit balance, years, and size to predict income. State the equation for this multiple regression model. 12. Perform the global test foruUtility (F-Test). Explain your conclusion. 13. Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, state which independent variables should we keep and which should be discarded. 14. Is this multiple regression model better than the linear model that we generated in parts 1-10? Explain. All DeVry University policies are in effect, including the plagiarism policy. 15. Project Part C report is due by the end of Week 7. 16. Project Part C is worth 100 total points. See the grading rubric below. Summarize your results from 1-14 in a report that is 3 pages or less in length and explains and interprets the results in ways that are understandable to someone who does not know statistics. Submission: The summary report + all of the work done in 1-14 (Minitab Output + interpretations) as an appendix Format: A. Summary Report B. Points 1-14 addressed with appropriate output, graphs, and interpretations. Be sure to number each point 1-14. Project Part C: Grading Rubric Category Questions 1-12 and 14 5 points each Points % Description 65 65 addressed with appropriate output, graphs, and interpretations Question 13 15 15 Summary 20 Total 100 addressed with appropriate output, graphs, and interpretations 20 writing, grammar, clarity, logic, and cohesiveness A quality paper will meet or exceed all of the 100 above requirements