Statistical Report

 

Purpose 

This assignment is intended to help you learn how to apply statistical methods when analyzing operational data, evaluating the performance of current marketing strategies, and recommending actionable business decisions. This is an opportunity to build critical-thinking and problem-solving skills within the context of data analysis and interpretation. You’ll gain a first-hand understanding of how data analytics supports decision-making and adds value to an organization.

Scenario: 

Pastas R Us, Inc. is a fast-casual restaurant chain specializing in noodle-based dishes, soups, and salads. Since its inception, the business development team has favored opening new restaurants in areas (within a 3-mile radius) that satisfy the following demographic conditions:

• Median age between 25 – 45 years old
• Household median income above national average
• At least 15% college educated adult population

Last year, the marketing department rolled out a Loyalty Card strategy to increase sales. Under this program, customers present their Loyalty Card when paying for their orders and receive some free food after making 10 purchases.

The company has collected data from its 74 restaurants to track important variables such as average sales per customer, year-on-year sales growth, sales per sq. ft., Loyalty Card usage as a percentage of sales, and others. A key metric of financial performance in the restaurant industry is annual sales per sq. ft. For example, if a 1200 sq. ft. restaurant recorded $2 million in sales last year, then it sold $1,667 per sq. ft.

Executive management wants to know whether the current expansion criteria can be improved. They want to evaluate the effectiveness of the Loyalty Card marketing strategy and identify feasible, actionable opportunities for improvement. As a member of the analytics department, you’ve been assigned the responsibility of conducting a thorough statistical analysis of the company’s available database to answer executive management’s questions.

Report: 

Write a 750-word statistical report that includes the following sections:

Section 1: Scope and descriptive statistics
Section 2: Analysis
Section 3: Recommendations and Implementation

Section 1 – Scope and descriptive statistics

• State the report’s objective.
• Discuss the nature of the current database. What variables were analyzed?
• Summarize your descriptive statistics findings from Excel. Use a table and insert appropriate graphs.

Section 2 – Analysis 

• Using Excel, create scatter plots and display the regression equations for the following pairs of variables:
• “BachDeg%” versus “Sales/SqFt”
• “MedIncome” versus “Sales/SqFt”
• “MedAge” versus “Sales/SqFt”
• “LoyaltyCard(%)” versus “SalesGrowth(%)”
• In your report, include the scatter plots. For each scatter plot, designate the type of relationship observed (increasing/positive, decreasing/negative, or no relationship) and determine what you can conclude from these relationships.

Section 3: Recommendations and implementation

• Based on your findings above, assess which expansion criteria seem to be more effective.Could any expansion criterion be changed or eliminated? If so, which one and why?
• Based on your findings above, does it appear as if the Loyalty Card is positively correlated with sales growth? Would you recommend changing this marketing strategy?
• Based on your previous findings, recommend marketing positioning that targets a specific demographic. (Hint: Are younger people patronizing the restaurants more than older people?)
• Indicate what information should be collected to track and evaluate the effectiveness of your recommendations. How can this data be collected? (Hint: Would you use survey/samples or census?)

2

>Chart

Data

Sheet_

/

/

0

7:

9.

6

7

.4

8

.2

9

.3

4

81

.4

0

999

2

.3

70 28

1

29

8

28

60

70

29

80 36

7

45

80 22

22

88 78

37

42 35

24

68 32

06

17

80

37

84 32

45

22

35

2

36

84 24

34

78 16

9

26

80 39

20

70 70

20

33

93

26

56 12

65 32

37.7 37

62 0

34

20

34

76 24

35 30

36

16

34

28

66

90

36

70 28

23

18

60 15

00

36

10

1

18

76 0

24

68 16

22

64 0

29

52 36

78 26

33.9 28

64 28

35 40

82 32

35 39

86 30

35.9 30

92 16

33 17

72 10

30.9 22

90 24

29

64 20

80 20

32.1 29

30

34.8 18

70 26

38 19

62 26

49

37 34

68 20

25

74 24

0

36.4 30

84 14

4

21

70 32

32.2 30

96 32

34.8 30

70 22

28

76 32

857

31

62 28

12

16

92 23

39 31

60 20

34.9 40

54 15

33

23

35.6 28

78 0

36 23

72 31

16

74 29

25

0

40.5 25

80 16

32.9 18

0

30.3 15

46 20

36.2 19

66 0

32.4 27

63 28

21

72 15

29

76 24

31.4 15

61237235

775

1306853

934

55399284

22178495

06742745

16197419

0.0168615273

0.0506037738

0.0844037498

0.1183004556

0.152333674

0.1865443062

0.220974732

0.2556692022

0.2906742745

0.3260393031

0.3618169976

0.3980640685

0.4348419815

0.4722178495

0.5102654979

0.5490667518

0.588713006

0.6293071641

0.6709660579

0.7138235056

0.7580342264

0.8037789242

0.8512709934

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0.952571595

1.0070695657

1.0647357757

1.1261791757

33804168

1.1921973902

1.2638662791

1.3426905457

1.4308738679

1.5318456091

1.6514108613

1.8007082352

904495556

2.0061237235

95939607

2.3669115357

66 18

31
69 16

41.2 20
67 10

24
70 4

29
78 0 50999 31.5 18
62 28

30
70 28

35.1 14
84 29 50975 37.6 33
68 22

34.9 28
60 42

34.8 29
80 36 78497 36.2 39
64 32

32.2 23
80 22 33003 30.9 22
88 78 90988 37.7 37
42 35 37950 34.3 24
68 32

32.4 17
80 48 79312 32.1 37
84 32 37345 31.4 22
35 27

30.4 36
84 24 70024 33.9 34
78 16

35.6 26
80 39 54932 35.9 20
70 70 34097 33.6 20
76 33

37.9 26
56 12 51893 40.6 21
65 32 88162 37.7 37
62 0 89016 36.4 34
66 20

40.9 34
76 24 75366 35 30
92 36

26.4 16
112 34 49956 37.1 28
66 15 45990 30.3 36
70 28 45723 31.3 18
60 15

29.6 36
86 10 68711 32.9 18
76 0 65150 40.7 24
68 16 39329 29.3 22
64 0 63657 37.3 29
52 36 67099 39.8 25
78 26 75151 33.9 28
64 28 93876 35 40
82 32 79701 35 39
86 30 77115 35.9 30
92 16 52766 33 17
72 10 32929 30.9 22
90 24 87863 38.5 29
64 20 73752 40.5 19
80 20 85366 32.1 29
102 30 39180 34.8 18
70 26 56077 38 19
62 26

37 34
68 20 56822 34.7 25
74 24

36.4 30
84 14 55584 36.8 21
70 32 78001 32.2 30
96 32 75307 34.8 30
70 22 76375 36.7 28
76 32 61857 33.8 31
62 28

34.2 16
92 23 72040 39 31
60 20 92414 34.9 40
54 15 92602 39.3 33
110 23 59599 35.6 28
78 0

36 23
72 31 67925 41.1 16
74 29 42631 24.7 25
94 0 75652 40.5 25
80 16 39650 32.9 18
124 0 48033 30.3 15
46 20 67403 36.2 19
66 0 80597 32.4 27
63 28 60928 43.5 21
72 15 73762 41.6 29
76 24 64225 31.4 15

-259.9497306439

-188.5900144767

-178.1863109741

-165.2888689211

-156.2930386781

-147.1995334043

-145.0204151759

-132.7962270775

-132.5838765031

-127.8657575015

-124.4916500844

-123.016384493

-118.431306853

-110.8440652315

-110.1477551652

-109.3430277914

-105.1097263145

-104.7616892077

-100.1917272772

-96.9455399284

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-30.5622414309

-29.7056802184

-28.8211160258

-21.3829190469

56692022

-20.8096302471

-18.0336858908

-16.4732294274

-15.5268611118

-12.5832024808

-11.5991899485

-10.6416197419

-6.4663288735 0.0168615273
6.6082090726 0.0506037738
10.1026389027 0.0844037498
10.1556691582 0.1183004556
11.5424324103 0.152333674
13.4792557233 0.1865443062
15.0213966843 0.220974732
18.9663798116 0.2556692022
19.2122025279 0.2906742745
19.5938287738 0.3260393031
19.7419844304 0.3618169976
23.7470781354 0.3980640685
25.1736217387 0.4348419815
28.9194386872 0.4722178495
38.4697564504 0.5102654979
50.9831788417 0.5490667518
53.0357068283 0.588713006
61.102903906 0.6293071641
63.1204953548 0.6709660579
63.8380153718 0.7138235056
71.0833539728 0.7580342264
71.3281648375 0.8037789242
75.1828858929 0.8512709934
75.2802525469 0.9007655189
81.3206554357 0.952571595
81.6351025536 1.0070695657
105.576464442 1.0647357757
115.0253844293 1.1261791757
122.2233804168 1.1921973902
150.1178490106 1.2638662791
180.3934285167 1.3426905457
196.2671375845 1.4308738679
205.7993140008 1.5318456091
234.8563337617 1.6514108613
289.7338930992 1.8007082352
336.0904495556 2.0061237235
372.5195939607 2.3669115357

		This worksheet contains values required for MegaStat charts.
Residuals X data	3							1	9	2																0	7			4								2	5
								6													1	8		45							17																34												31
		69																				16		51		88				41																					20
		67							10	51												37								40																				24
																70	6							60												35																							29
									78				50			31.5					18
								62																												28	41			56																			36																							30
	44		96			35.1						14
							84			50975			37.6											33
								68																			22								72												80						34.9
				42	7		90									34.8
		78	49						36.2											39
								64																	32	4			12						32.2											23
		33003						30.9
		90988						37.7
		37950			34.3
4			52						32.4
		48			79312						32.1
		3	73						31.4
					27				46													26			30.4
		70024						33.9
			54		82						35.6
		54932						35.9
		34097			33.6
									76	4			65			37.9
		51893			40.6										21
		88162
		89016						36.4
66			11	43	53			40.9
		75366
					92	481			63			26.4
	112			49956			37.1
														15			4	59						30.3
		4	57			31.3
4			38			29.6
			86			68	71						32.9
		65150			40.7
		39329			29.3
		63657			37.3
		67099			39.8					25
		75151
		93876
		79701
		77115
		52766
		32929
		87863			38.5
		73752						40.5				19
		85366
	102			39180
		56077
7					74
		56822			34.7
	80	47
			55	58			36.8
		78001
		75307
		76375			36.7
			61			33.8
	6	13			34.2
		72040
		92414
		92602			39.3
	110			59599
	7	2453
		67925			41.1
		42631			24.7
	94			75652
		39650
	124			48033
		67403
		80597
		60928			43.5
		73762			41.6
		64225
NormalPlot data 3/19/2007 7:49.03
	-259.9497306439	–		2.3669115357
	-188.5900144767	–			2.00
	-178.1863109741	–		1.8007082352
	-165.2888689211	–		1.6514108613
	-156.2930386781	–		1.5318456091
	-147.1995334043	–		1.4308738679
	-145.0204151759	–		1.3426905457
	-132.796	2270	–		1.2638662791
	-132.5838765031	–		1.1921973902
	-127.8657575015	–		1.1261791757
	-124.4916500844	–		1.0647357757
	-123.016384493	–		1.0070695657
	-1	18.43	–		0.952571595
	-110.8440652315	–		0.9007655189
	-110.1477551652	–		0.851	2709
	-109.3430277914	–		0.8037789242
	-105.1097263145	–		0.7580342264
	-104.7616892077	–		0.7138235056
	-100.1917272772	–		0.6709660579
	-9		6.94	–		0.6293071641
	-78.5222407532	–		0.588713006
	-66.833182556	–		0.5490667518
	-63.9367962151	–		0.5102654979
	-54.9666697606	–			0.47
	-49.5089341383	–		0.4348419815
	-43.817663257	–		0.3980640685
	-30.5622414309	–		0.3618169976
	-29.7056802184	–		0.3260393031
	-28.8211160258	–			0.29
	-21.3829190469	–		0.2556692022
	-20.8096302471	–		0.220974732
	-18.0336858908	–		0.1865443062
	-16.4732294274	–		0.152333674
	-15.5268611118	–		0.1183004556
	-12.5832024808	–		0.0844037498
	-11.5991899485	–		0.0506037738
	-1	0.64	–		0.0168615273
	-6.4663288735
	6.6082090726
	10.1026389027
	10.1556691582
	11.5424324103
	13.4792557233
	15.0213966843
	18.9663798116
	19.2122025279
	19.5938287738
	19.7419844304
	23.7470781354
	25.1736217387
	28.9194386872
	38.4697564504
	50.9831788417
	53.0357068283
	61.102903906
	63.1204953548
	63.8380153718
	71.0833539728
	71.3281648375
	75.1828858929
	75.2802525469
	81.3206554357
	81.6351025536
	105.576464442
	115.0253844293
	12		2.22
	150.1178490106
	180.3934285167
	196.2671375845
	205.7993140008
	234.8563337617
	289.7338930992
	3	36.0
	37	2.51
Residuals X data 3/19/2007 8:0	1.41
	45177		34.4		51888		51379		40.3		66081		35.4		41562		36.3		44196		72808		79070		41245		45206		46226		54982		46593	114353		48163		43800		77449	80470	61312	72453
NormalPlot data 3/19/2007 8:01.03
-2.3669115357	-2.0061237235	-1.8007082352	-1.6514108613	-1.5318456091	-1.4308738679	-1.3426905457	-1.2638662791	-1.1921973902	-1.1261791757	-1.0647357757	-1.0070695657	-0.952571595	-0.9007655189	-0.8512709934	-0.8037789242	-0.7580342264	-0.7138235056	-0.6709660579	-0.6293071641	-0.588713006	-0.5490667518	-0.5102654979	-0.4722178495	-0.4348419815	-0.3980640685	-0.3618169976	-0.3260393031	-0.2906742745		-0.25	-0.220974732	-0.1865443062	-0.152333674	-0.1183004556	-0.0844037498	-0.0506037738	-0.0168615273

Data

1

45177 34.4 31

2

51888 41.2 20

3 2453

51379 40.3 24

4

66081 35.4 29

5

50999 31.5 18

6

41562 36.3 30

7

44196 35.1 14

8

7.13

50975 37.6 33

9 2709

-0.25

72808 34.9 28

10

2.34

79070 34.8 29

11

0.47

78497 36.2 39

12

41245 32.2 23

13

7.03 0.77

33003 30.9 22

14 2500

90988 37.7 37

15

37950 34.3 24

16 2500

45206 32.4 17

17

2.84 2.22

79312 32.1 37

18

2.07

37345 31.4 22

19

1.94

46226 30.4 36

20

70024 33.9 34

21

54982 35.6 26

22

4.05 2.00

54932 35.9 20

23

34097 33.6 20

24

46593 37.9 26

25

51893 40.6 21

26

88162 37.7 37

27 2400

89016 36.4 34

28 2430

2.04

114353 40.9 34

29

1.41

75366

30

30 2500 7.03

2.05

48163 26.4 16

31

2.13

49956 37.1 28

32

6.94 6.08

45990 30.3 36

33

7.07

45723 31.3 18

34

7.00

1.95

43800 29.6 36

35

2.04

68711 32.9 18

36

65150 40.7 24

37

6.81 6.94 1.95

39329 29.3 22

38 2400

7.12

63657 37.3 29

39 2270

67099 39.8 25

40 2800

75151 33.9 28

41

7.11

93876 35.0 40

42

7.05

79701 35.0 39

43

6.90

77115 35.9 30

44

52766

17

45

6.75

32929 30.9 22

46 2500 7.45

87863 38.5 29

47

7.00

73752 40.5 19

48 2625

2.51

85366 32.1 29

49

39180 34.8 18

50 2625 6.96

56077

19

51

77449

34

52 2500

2.17

56822 34.7 25

53 2450 6.58

2.16

80470 36.4 30

54

0.29

55584 36.8 21

55

78001 32.2 30

56

7.28

75307 34.8 30

57 2500 6.76

2.19

76375 36.7 28

58 2600

61857 33.8 31

59 2800

2.16

61312 34.2 16

60 2986 6.91

72040

31

61

6.77

1.98

92414 34.9 40

62 2300

92602 39.3 33

63

59599 35.6 28

64

6.95

72453 36.0 23

65

7.33

67925 41.1 16

66 2500 6.95

42631 24.7 25

67

75652 40.5 25

68

2.22

39650 32.9 18

69

48033 30.3 15

70

6.93

2.41

67403 36.2 19

71 2400

18.43

80597 32.4 27

72 2450 7.37

1.09

60928 43.5 21

73

6.76

0.64

73762 41.6 29

74 2400

64225 31.4 15

Pastas R Us, Inc. Database (n = 74 restaurants)
Square Feet	Per Person Average Spending	Sales Growth Over Previous Year (%)	Loyalty Card % of Net Sales	Annual Sales Per Sq Ft	Median HH Income (3 Miles)	Median Age (3 Miles)	% w/ Bachelor’s Degree (3 Miles)
Obs	SqFt	Sales/Person	SalesGrowth%	LoyaltyCard%	Sales/SqFt	MedIncome	MedAge	BachDeg%
2354		6.81	-8.31		2.07	701.97
2604	7.57	-4.01	2.54	209.93
6.89	-3.94	1.66	364.92
2340		7.13	-3.39	2.06	443.04
							2500	7.04	-3.30	2.48	399.20
2806		6.93	–	1.94	2.96	264.64
2250		7.11	–	0.77	2.28	571.59
				2400	-0.37		2.34	642.25
	6.58	2.20	461.45
1990		6.77	-0.17	638.82
2392	6.66	2.09	484.38
2408			7.03	0.55	2.47	58	1.09
2627			2.04	267.71
		7.00	1.92	2.02	57	2.84
1986	7.38		2.05	2.01	586.48
7.18	2.12	2.64	368.73
2668	7.35	351.47
2517			6.95	2.88	458.24
1251	7.02	3.96	98	7.12
2998	6.85	4.04		2.17	35	7.45
		2625	7.16		4.05	0.72	405.77
	2300	6.99	680.80
2761		7.28	4.24	1.81	368.02
2764		7.07	4.58		2.13	303.95
	2430		7.05	5.09	2.50	393.90
2154	6.54	5.14	2.63	562.12
6.70	5.48			1.95	494.88
	6.91	5.86	310.07
2549	7.58	5.91	373.46			35.0
5.98	235.81
3653	6.84		6.08	413.08
2440	2.08	625.22
	2600	6.13	2.73	274.30
2160	6.27	542.62
		2800	7.08	6.57	178.56
2757		6.75		6.90	1.62	375.33
		2450	329.09
7.64	1.64	29	7.37
6.62	7.39	1.78	323.17
		6.76	7.67	2.23	468.84
2520	7.91	2.15	352.57
2487	8.08	2.83	380.34
2629	8.27	2.37	398.12
3200	7.17	8.54	3.07	312.15	33.0
2335	8.58		2.19	45		2.16
8.72	1.28	698.64
2449	8.75	1.76	367.19
	6.96	8.79	431.93
3150	7.30	8.90	1.90	367.06
9.12		1.98	400.53	38.0
2741	6.71	9.47		2.41	414.36	37.0
6.82	10.17	481.11
10.66	538.06
	2986	7.56	10.97	330.48
2967	6.98	11.34	1.85	249.93
3000	11.45	1.88	291.87
11.51	517.40
6.92	11.73	2.56	551.58
6.73	11.83	386.81
11.95	2.10	427.50	39.0
2223	12.47	453.94
	7.33	12.80	0.87	512.46
3799	7.87	13.78	1.07	345.27
2700	14.09	3.38	234.04
2650	14.23	1.17	348.33
14.60	2.14	348.47
2994	7.21	14.88	0.93	294.95
2718	7.25	15.42	361.14
3700	7.65	16.18	1.68	467.71
2000	17.23	403.78
6.79	2.81	245.74
20.76	339.94
2575	25.54	400.82
7.97	28.81	1.77	326.54

Noodles Database – Page &P of &N Printed &D Doane/Seward