## MATH533 week 7 Project Part C: Regression and Correlation Analysis

MATH533 week 7 Project Part C: Regression and Correlation Analysis

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 appears below, and is available in Doc Sharing Course Project Data Set as an EXCEL file:

LOCATION INCOME($1000) SIZE YEARS CREDIT BALANCE($)

Urban 54 3 12 4016

Rural 30 2 12 3159

Suburban 32 4 17 5100

Suburban 50 5 14 4742

Rural 31 2 4 1864

Urban 55 2 9 4070

Rural 37 1 20 2731

Urban 40 2 7 3348

Suburban 66 4 10 4764

Urban 51 3 16 4110

Urban 25 3 11 4208

Urban 48 4 16 4219

Rural 27 1 19 2477

Rural 33 2 12 2514

Urban 65 3 12 4214

Suburban 63 4 13 4965

Urban 42 6 15 4412

Urban 21 2 18 2448

Rural 44 1 7 2995

Urban 37 5 5 4171

Suburban 62 6 13 5678

Urban 21 3 16 3623

Suburban 55 7 15 5301

Rural 42 2 19 3020

Urban 41 7 18 4828

Suburban 54 6 14 5573

Rural 30 1 14 2583

Rural 48 2 8 3866

Urban 34 5 5 3586

Suburban 67 4 13 5037

Rural 50 2 11 3605

Urban 67 5 1 5345

Urban 55 6 16 5370

Urban 52 2 11 3890

Urban 62 3 2 4705

Urban 64 2 6 4157

Suburban 22 3 18 3579

Urban 29 4 4 3890

Suburban 39 2 18 2972

Rural 35 1 11 3121

Urban 39 4 15 4183

Suburban 54 3 9 3730

Suburban 23 6 18 4127

Rural 27 2 1 2921

Urban 26 7 17 4603

Suburban 61 2 14 4273

Rural 30 2 14 3067

Rural 22 4 16 3074

Suburban 46 5 13 4820

Suburban 66 4 20 5149

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. 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 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

Project Part A: Grading Rubric

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 less than $50,000,

b. the true population proportion of customers who live in an urban area exceeds 40%,

c. the average (mean) number of years lived in the current home is less than 13 years,

d. the average (mean) credit balance for suburban customers is more than $4300.

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

Project Part B: Grading Rubric

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 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 . 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 we 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, we attempt to do a multiple regression model predicting CREDIT BALANCE based on INCOME, SIZE and YEARS.

11. Using MINITAB run the multiple regression analysis using the variables INCOME, SIZE and YEARS to predict CREDIT BALANCE. 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.

15. All DeVry University policies are in effect, including the plagiarism policy.

16. Project Part C report is due by the end of Week 7.

17. 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.