# MATH 433 DeVry Course Project

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MATH 433 DeVry Course Project

MATH433

MATH 433 DeVry Course Project

MATH 433 DeVry Course Project

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’s – be 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/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 ten 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 1 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.

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 1st individual variable, using graphical, numerical summary and interpretation

C.        Discuss your 2nd individual variable, using graphical, numerical summary and interpretation

D.        Discuss your 3rd individual variable, using graphical, numerical summary and interpretation

E.         Discuss your 1st pairing of variables, using graphical, numerical summary and interpretation

F.         Discuss your 2nd pairing of variables, using graphical, numerical summary and interpretation

G.        Discuss your 3rd pairing of variables, using graphical, numerical summary and interpretation

H.        Conclusion

 Category Points % Description Three Individual Variables -12pts each 36 36 graphical analysis, numerical analysis (when appropriate) and interpretation Three Relationships – 15 pts. each 45 45 graphical analysis, numerical analysis (when appropriate) and interpretation Communication Skills 19 19 writing, grammar, clarity, logic, cohesiveness, adherence to the above format Total 100 100 A quality paper will meet or exceed all of the 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 \$3200.

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 grading rubric below. Submission: The report from part 3 + all of the relevant work done in the hypothesis testing (including Minitab) in 1., and the confidence intervals (Minitab) in 2 as an appendix. Format for report:

A.        Summary Report (about 1 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, and including all Minitab output

 Category Points % Description Addressing each speculation – 20 pts. each 80 80 hypothesis test, interpretation, confidence interval and interpretation Summary report 20 20 1 paragraph on each of the speculations Total 100 100 A quality paper will meet or exceed all 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) and CREDIT BALANCE (X) by answering the following.

1. Generate a scatterplot for INCOME (\$1000) vs. 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 for Utility (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, 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 grading rubric below. Summarize your results from 1-14 in a report that is three 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.

Other Requirements:

 Location Income (\$1000) Size Years Credit Balance(\$) Urban 27 1 2 2631 Rural 25 4 2 2047 Suburban 25 1 1 3155 Suburban 26 1 2 3913 Rural 30 5 5 2660 Urban 29 1 3 3531 Rural 33 6 10 2766 Urban 30 1 4 3769 Suburban 32 2 4 4082 Urban 34 1 6 3806 Urban 35 1 8 4049 Urban 40 1 9 4073 Rural 30 6 9 2697 Rural 33 6 11 2914 Urban 42 2 10 4073 Suburban 32 2 4 4310 Urban 43 2 10 4199 Urban 43 2 10 4253 Rural 33 7 13 3104 Urban 47 2 10 4293 Suburban 35 3 5 4456 Urban 54 2 11 4340 Suburban 42 3 5 4925 Rural 36 7 13 3178 Urban 57 3 11 4391 Suburban 44 3 6 4947 Rural 38 7 15 3203 Urban 54 3 8 4354 Urban 54 3 10 4366 Suburban 46 4 6 5003 Rural 40 7 15 3250 Urban 60 4 11 4402 Urban 58 4 10 4397 Urban 61 5 13 4595 Urban 61 5 13 4786 Urban 62 6 14 4888 Suburban 49 5 8 5148 Urban 68 6 14 5011 Suburban 57 6 8 5220 Rural 45 8 16 3257 Urban 71 7 15 5528 Suburban 57 7 9 5283 Suburban 64 8 9 5332 Rural 45 8 17 3304 Urban 74 7 19 5553 Suburban 65 8 10 5484 Rural 47 8 18 3342 Rural 53 8 18 3788 Suburban 66 8 10 5756 Suburban 69 8 10 5861