Course Project: AJ DAVIS DEPARTMENT STORES Introduction

| October 22, 2018

Course Project: AJ DAVIS DEPARTMENT STORES
.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItem&#1″>Introduction|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItem&#2″>Project
Part A: Exploratory Data Analysis|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItem&#3″>Project
Part A: Grading Rubric|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItem&#4″>Project
Part B: Hypothesis Testing and Confidence Intervals|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItem&#5″>Project
Part B: Grading Rubric|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItem&#6″>Project
Part C: Regression and Correlation Analysis|.next.ecollege.com/(NEXT(c272f9a6ef))/Main/CourseMode/VizedHtmlView/RenderVizedHtmlView.ed?courseItemSubId=289453118&courseItemType=CourseContentItem&#7″>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
$1,000’s – 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 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

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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. 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 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 – 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

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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 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 α = .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

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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

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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
“best fit” line. Interpret.
Determine the
equation of the “best fit” 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 α =.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

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Category

Points

%

Description

Questions
1 – 12 and 14 – 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.

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