Course Project: AJ DAVIS DEPARTMENT STORES

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Part A: Exploratory Data Analysis|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItemâ€³>Project

Part A: Grading Rubric|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItemâ€³>Project

Part B: Hypothesis Testing and Confidence Intervals|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItemâ€³>Project

Part B: Grading Rubric|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItemâ€³>Project

Part C: Regression and Correlation Analysis|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItemâ€³>Project

Part C: Grading Rubric

Introduction

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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:

LOCATION (Rural,

Urban, Suburban)

INCOME (in

$1,000â€™s Ã¢â‚¬â€œ be careful with this)

SIZE (Household

Size, meaning number of people living in the household)

YEARS (the number

of years that the customer has lived in the current location)

CREDIT BALANCE

(the customers current credit card balance on the storeâ€™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

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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. Iâ€™m not looking for a 20 page

report on every variable and every possible relationship (thatâ€™s 15 things

to do). Rather what I want you do is to highlight what you see forthree 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 onthree 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.

.

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:

Brief

Introduction

Discuss your 1st

individual variable, using graphical, numerical summary and interpretation

Discuss your 2nd

individual variable, using graphical, numerical summary and interpretation

Discuss your 3rd

individual variable, using graphical, numerical summary and interpretation

Discuss your 1st

pairing of variables, using graphical, numerical summary and

interpretation

Discuss your 2nd

pairing of variables, using graphical, numerical summary and

interpretation

Discuss your 3rd

pairing of variables, using graphical, numerical summary and

interpretation

Conclusion

Project Part A: Grading Rubric

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Category

Points

%

Description

Three

Individual Variables â€“ 12pts. each

36

36

graphical

analysis, numerical analysis (when appropriate) and interpretation

Three

Relationships â€“ 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:

the average

(mean) annual income was less than $50,000,

the true

population proportion of customers who live in an urban area exceeds 40%,

the average

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

the average

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

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 managerÃ¢â‚¬â„¢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 Î± = .05, and explain

your conclusion in simple terms. Also be sure to compute the p-value

and interpret.

Follow this up

with computing 95% confidence intervals for each of the variables

described in a.-d., and again interpreting these intervals.

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.

All DeVry

University policies are in effect, including the plagiarism policy.

Project Part B

report is due by the end of Week 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:

Summary Report

(about 1 paragraph on each of the speculations a.-d.)

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 â€“ 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.

Generate a

scatterplot for CREDIT BALANCE vs. SIZE, including the graph of the

â€œbest fitâ€ line. Interpret.

Determine the

equation of the â€œbest fitâ€ line, which describes the

relationship between CREDIT BALANCE and SIZE.

Determine the

coefficient of correlation. Interpret.

Determine the

coefficient of determination. Interpret.

Test the utility

of this regression model (use a two tail test with Î± =.05). Interpret your

results, including the p-value.

Based on your

findings in 1-5, what is your opinion about using SIZE to predict CREDIT

BALANCE? Explain.

Compute the 95%

confidence interval for beta-1 (the population slope). Interpret

this interval.

Using an

interval, estimate the average credit balance for customers that have

household size of 5. Interpret this interval.

Using an

interval, predict the credit balance for a customer that has a household

size of 5. Interpret this interval.

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.

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.

Perform the

Global Test for Utility (F-Test). Explain your conclusion.

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.

Is this multiple

regression model better than the linear model that we generated in parts

1-10? Explain.

All

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:

Summary Report

Points 1-14

addressed with appropriate output, graphs and interpretations. Be sure to

number each point 1-14.

Project Part C: Grading Rubric

Category

Points

%

Description

Questions

1 â€“ 12 and 14 â€“ 5 pts. each

65

65

addressed

with appropriate output, graphs and interpretations

Question

13

15

15

addressed

with appropriate output, graphs and interpretations

Summary

20

20

writing,

grammar, clarity, logic, and cohesiveness

Total

100

100

A

quality paper will meet or exceed all of the above requirements.