Wk 2 – Apply: Signature Assignment: Statistical Report
Assignment Content
Resources: Pastas R Us, Inc. Database & Microsoft Excel®, Wk 1: Descriptive Statistics Analysis Assignment
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:
o Median age between 25 – 45 years old
o Household median income above national average
o 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:
o Section 1: Scope and descriptive statistics
o Section 2: Analysis
o Section 3: Recommendations and Implementation
Section 1 – Scope and descriptive statistics
o State the report’s objective.
o Discuss the nature of the current database. What variables were analyzed?
o Summarize your descriptive statistics findings from Excel. Use a table and insert appropriate graphs.
Section 2 – Analysis
o Using Excel, create scatter plots and display the regression equations for the following pairs of variables:
o “BachDeg%” versus “Sales/SqFt”
o “MedIncome” versus “Sales/SqFt”
o “MedAge” versus “Sales/SqFt”
o “LoyaltyCard(%)” versus “SalesGrowth(%)”
o 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
o 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?
o 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?
o Based on your previous findings, recommend marketing positioning that targets a specific demographic. (Hint: Are younger people patronizing the restaurants more than older people?)
o 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?)
Cite references to support your assignment.
Format your citations according to APA guidelines. This includes an introduction, conclusion and reference page.
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36 10 1
18 24 22 29 33.9 28 35 40 35 39 35.9 30 33 17 30.9 22 29 32.1 29 30 34.8 18 38 19 49
37 34 25 0
36.4 30 4
21 32.2 30 34.8 30 28 857
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1.1921973902 1.2638662791 1.3426905457 1.4308738679 1.5318456091 1.6514108613 1.8007082352 904495556
2.0061237235 95939607
2.3669115357 66 18 31 41.2 20 24 29 30 35.1 14 34.9 28 34.8 29 32.2 23 32.4 17 30.4 36 35.6 26 37.9 26 40.9 34 26.4 16 29.6 36 37 34 36.4 30 34.2 16 36 23 -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 -78.5222407532 -66.833182556 -63.9367962151 -54.9666697606 -49.5089341383 -43.817663257 -30.5622414309 -29.7056802184 -28.8211160258 -21.3829190469 56692022
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>ChartDataSheet_
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36 10 1
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37 34 25 0
36.4 30 4
21 32.2 30 34.8 30 28 857
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HH Income (3 Miles)
Annual Sales Annual Sales
SqFt Sales/Person SalesGrowth% LoyaltyCard% Sales/SqFt MedIncome MedAge BachDeg% Annual sales 45177 34.4 31 FALSE 64864865
51888 41.2 20 FALSE FALSE 47303215
23708116
47453107
51379 40.3 24 FALSE FALSE 66081 35.4 29 FALSE FALSE 5 7.04 50999 31.5 18 FALSE FALSE 41562 36.3 30 FALSE FALSE -8.31 0.29 32929 24.7 14 44196 35.1 14 FALSE FALSE 5
75
5
50975 37.6 33 FALSE FALSE Median 2500 7 35 -0.25 72808 34.9 28 FALSE FALSE 75
2.34 79070 34.8 29 FALSE FALSE 114353 43.5 40 0.47 78497 36.2 39 FALSE FALSE 7.03 0.55 41245 32.2 23 FALSE FALSE 7.03 0.77 33003 30.9 22 FALSE FALSE 2.02 90988 37.7 37 FALSE FALSE 37950 34.3 24 FALSE FALSE 45206 32.4 17 FALSE FALSE 2.84 2.22 79312 32.1 37 FALSE FALSE 875
2.07 37345 31.4 22 FALSE FALSE 1.94 987.12 46226 30.4 36 FALSE 70024 33.9 34 FALSE FALSE 54982 35.6 26 FALSE FALSE 4.05 2.00 54932 35.9 20 FALSE FALSE 34097 33.6 20 FALSE FALSE 46593 37.9 26 FALSE FALSE 51893 40.6 21 FALSE FALSE 6.54 88162 37.7 37 FALSE FALSE 89016 36.4 34 FALSE FALSE 2.04 114353 40.9 34 FALSE FALSE 1.41 75366 30 FALSE FALSE 2.05 48163 26.4 16 FALSE FALSE 2.13 49956 37.1 28 FALSE FALSE 6.94 6.08 45990 30.3 36 FALSE FALSE 7.07 45723 31.3 18 FALSE FALSE 7.00 1.95 43800 29.6 36 FALSE FALSE 2.04 178.56 68711 32.9 18 FALSE FALSE 65150 40.7 24 FALSE FALSE 6.81 6.94 1.95 39329 29.3 22 FALSE FALSE 7.12 63657 37.3 29 FALSE FALSE 67099 39.8 25 FALSE FALSE 75151 33.9 28 FALSE FALSE 7.11 93876 35.0 40 FALSE FALSE 7.05 79701 35.0 39 FALSE FALSE 6.90 77115 35.9 30 FALSE FALSE 7.17 52766 17 FALSE FALSE 6.75 32929 30.9 22 FALSE FALSE 87863 38.5 29 FALSE FALSE 7.00 73752 40.5 19 FALSE FALSE 2.51 85366 32.1 29 FALSE FALSE 39180 34.8 18 FALSE FALSE 56077 19 FALSE FALSE 77449 37.0 34 FALSE FALSE 2.17 56822 34.7 25 FALSE FALSE 2.16 80470 36.4 30 FALSE FALSE 0.29 55584 36.8 21 FALSE FALSE 1.85 78001 32.2 30 FALSE FALSE Interpretation: 7.28 75307 34.8 30 FALSE FALSE to the right
2.19 76375 36.7 28 FALSE FALSE 61857 33.8 31 FALSE FALSE 2.16 61312 34.2 16 FALSE FALSE Outliers 72040 39.0 31 FALSE FALSE – 6.77 1.98 92414 34.9 40 FALSE FALSE – 92602 39.3 33 FALSE FALSE – 59599 35.6 28 FALSE FALSE 6.95 3.38 72453 36.0 23 FALSE FALSE 7.33 67925 41.1 16 FALSE FALSE 42631 24.7 25 FALSE FALSE The distribution is skewed 75652 40.5 25 FALSE FALSE 2.22 39650 32.9 18 FALSE FALSE 48033 30.3 15 FALSE FALSE 6.93 2.41 67403 36.2 19 FALSE FALSE 18.43 80597 32.4 27 FALSE FALSE 1.09 60928 43.5 21 FALSE FALSE 6.76 0.64 73762 41.6 29 FALSE FALSE 64225 31.4 15 FALSE FALSE Noodles Database – Page &P of &N Printed &D Doane/SewardData
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
70 28
44
96
35.1
14
84
50975
37.6
33
68
22
72
80
34.9
60
42
7
90
34.8
80 36
78
49
36.2
39
64
32
4
12
32.2
23
80 22
33003
30.9
88 78
90988
37.7
42 35
37950
34.3
68 32
4
52
32.4
80
48
79312
32.1
84 32
3
73
31.4
35
27
46
26
30.4
84 24
70024
33.9
78 16
54
82
35.6
80 39
54932
35.9
70 70
34097
33.6
76
4
65
37.9
56 12
51893
40.6
21
65 32
88162
62 0
89016
36.4
66
11
43
53
40.9
76 24
75366
92
481
63
26.4
112
49956
37.1
66
15
4
59
30.3
70 28
4
57
31.3
60 15
4
38
29.6
86
68
71
32.9
76 0
65150
40.7
68 16
39329
29.3
64 0
63657
37.3
52 36
67099
39.8
25
78 26
75151
64 28
93876
82 32
79701
86 30
77115
92 16
52766
72 10
32929
90 24
87863
38.5
64 20
73752
40.5
19
80 20
85366
102
39180
70 26
56077
62 26
7
74
68 20
56822
34.7
74 24
80
47
84 14
55
58
36.8
70 32
78001
96 32
75307
70 22
76375
36.7
76 32
61
33.8
62 28
6
13
34.2
92 23
72040
60 20
92414
54 15
92602
39.3
110
59599
78 0
7
2453
72 31
67925
41.1
74 29
42631
24.7
94
75652
80 16
39650
124
48033
46 20
67403
66 0
80597
63 28
60928
43.5
72 15
73762
41.6
76 24
64225
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–
1.5318456091
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–
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–
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2270
–
1.2638662791
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–
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–
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–
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–
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6.94
–
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–
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–
0.5490667518
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–
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–
0.47
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–
0.4348419815
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–
0.3980640685
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–
0.3618169976
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–
0.3260393031
-28.8211160258
–
0.29
-21.3829190469
–
0.2556692022
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0.220974732
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–
0.1865443062
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0.152333674
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–
0.1183004556
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0.64
–
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36.0
37
2.51
Residuals X data 3/19/2007 8:0
1.41
45177
34.4
69 16
51888
67 10
51379
40.3
70 4
66081
35.4
78 0 50999 31.5 18
62 28
41562
36.3
70 28
44196
84 29 50975 37.6 33
68 22
72808
60 42
79070
80 36 78497 36.2 39
64 32
41245
80 22 33003 30.9 22
88 78 90988 37.7 37
42 35 37950 34.3 24
68 32
45206
80 48 79312 32.1 37
84 32 37345 31.4 22
35 27
46226
84 24 70024 33.9 34
78 16
54982
80 39 54932 35.9 20
70 70 34097 33.6 20
76 33
46593
56 12 51893 40.6 21
65 32 88162 37.7 37
62 0 89016 36.4 34
66 20 114353
76 24 75366 35 30
92 36
48163
112 34 49956 37.1 28
66 15 45990 30.3 36
70 28 45723 31.3 18
60 15
43800
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
77449
68 20 56822 34.7 25
74 24 80470
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 61312
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 72453
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
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18.9663798116 0.2556692022
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19.5938287738 0.3260393031
19.7419844304 0.3618169976
23.7470781354 0.3980640685
25.1736217387 0.4348419815
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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
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336.0904495556 2.0061237235
372.5195939607 2.3669115357
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%
1
2354
6.81
-8.31
2.07
701.97
2
2604
7.57
-4.01
2.54
209.93
3 2453
6.89
-3.94
1.66
364.92
4
2340
7.13
-3.39
2.06
443.04
5
2500
7.04
-3.30
2.48
399.20
6
2806
6.93
–
1.94
2.96
264.64
7
2250
7.11
–
0.77
2.28
571.59
8
2400
-0.37
2.34
642.25
9 2709
6.58
2.20
461.45
10
1990
6.77
-0.17
638.82
11
2392
6.66
2.09
484.38
12
2408
7.03
0.55
2.47
58
1.09
13
2627
2.04
267.71
14 2500
7.00
1.92
2.02
57
2.84
15
1986
7.38
2.05
2.01
586.48
16 2500
7.18
2.12
2.64
368.73
17
2668
7.35
351.47
18
2517
6.95
2.88
458.24
19
1251
7.02
3.96
98
7.12
20
2998
6.85
4.04
2.17
35
7.45
21
2625
7.16
4.05
0.72
405.77
22
2300
6.99
680.80
23
2761
7.28
4.24
1.81
368.02
24
2764
7.07
4.58
2.13
303.95
25
2430
7.05
5.09
2.50
393.90
26
2154
6.54
5.14
2.63
562.12
27 2400
6.70
5.48
1.95
494.88
28 2430
6.91
5.86
310.07
29
2549
7.58
5.91
373.46
35.0
30 2500 7.03
5.98
235.81
31
3653
6.84
6.08
413.08
32
2440
2.08
625.22
33
2600
6.13
2.73
274.30
34
2160
6.27
542.62
35
2800
7.08
6.57
178.56
36
2757
6.75
6.90
1.62
375.33
37
2450
329.09
38 2400
7.64
1.64
29
7.37
39 2270
6.62
7.39
1.78
323.17
40 2800
6.76
7.67
2.23
468.84
41
2520
7.91
2.15
352.57
42
2487
8.08
2.83
380.34
43
2629
8.27
2.37
398.12
44
3200
7.17
8.54
3.07
312.15
33.0
45
2335
8.58
2.19
45
2.16
46 2500 7.45
8.72
1.28
698.64
47
2449
8.75
1.76
367.19
48 2625
6.96
8.79
431.93
49
3150
7.30
8.90
1.90
367.06
50 2625 6.96
9.12
1.98
400.53
38.0
51
2741
6.71
9.47
2.41
414.36
37.0
52 2500
6.82
10.17
481.11
53 2450 6.58
10.66
538.06
54
2986
7.56
10.97
330.48
55
2967
6.98
11.34
1.85
249.93
56
3000
11.45
1.88
291.87
57 2500 6.76
11.51
517.40
58 2600
6.92
11.73
2.56
551.58
59 2800
6.73
11.83
386.81
60 2986 6.91
11.95
2.10
427.50
39.0
61
2223
12.47
453.94
62 2300
7.33
12.80
0.87
512.46
63
3799
7.87
13.78
1.07
345.27
64
2700
14.09
3.38
234.04
65
2650
14.23
1.17
348.33
66 2500 6.95
14.60
2.14
348.47
67
2994
7.21
14.88
0.93
294.95
68
2718
7.25
15.42
361.14
69
3700
7.65
16.18
1.68
467.71
70
2000
17.23
403.78
71 2400
6.79
2.81
245.74
72 2450 7.37
20.76
339.94
73
2575
25.54
400.82
74 2400
7.97
28.81
1.77
326.54
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
70 28
44
96
35.1
14
84
50975
37.6
33
68
22
72
80
34.9
60
42
7
90
34.8
80 36
78
49
36.2
39
64
32
4
12
32.2
23
80 22
33003
30.9
88 78
90988
37.7
42 35
37950
34.3
68 32
4
52
32.4
80
48
79312
32.1
84 32
3
73
31.4
35
27
46
26
30.4
84 24
70024
33.9
78 16
54
82
35.6
80 39
54932
35.9
70 70
34097
33.6
76
4
65
37.9
56 12
51893
40.6
21
65 32
88162
62 0
89016
36.4
66
11
43
53
40.9
76 24
75366
92
481
63
26.4
112
49956
37.1
66
15
4
59
30.3
70 28
4
57
31.3
60 15
4
38
29.6
86
68
71
32.9
76 0
65150
40.7
68 16
39329
29.3
64 0
63657
37.3
52 36
67099
39.8
25
78 26
75151
64 28
93876
82 32
79701
86 30
77115
92 16
52766
72 10
32929
90 24
87863
38.5
64 20
73752
40.5
19
80 20
85366
102
39180
70 26
56077
62 26
7
74
68 20
56822
34.7
74 24
80
47
84 14
55
58
36.8
70 32
78001
96 32
75307
70 22
76375
36.7
76 32
61
33.8
62 28
6
13
34.2
92 23
72040
60 20
92414
54 15
92602
39.3
110
59599
78 0
7
2453
72 31
67925
41.1
74 29
42631
24.7
94
75652
80 16
39650
124
48033
46 20
67403
66 0
80597
63 28
60928
43.5
72 15
73762
41.6
76 24
64225
NormalPlot data 3/19/2007 7:49.03
–
–
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
69 16
51888
67 10
51379
40.3
70 4
66081
35.4
78 0 50999 31.5 18
62 28
41562
36.3
70 28
44196
84 29 50975 37.6 33
68 22
72808
60 42
79070
80 36 78497 36.2 39
64 32
41245
80 22 33003 30.9 22
88 78 90988 37.7 37
42 35 37950 34.3 24
68 32
45206
80 48 79312 32.1 37
84 32 37345 31.4 22
35 27
46226
84 24 70024 33.9 34
78 16
54982
80 39 54932 35.9 20
70 70 34097 33.6 20
76 33
46593
56 12 51893 40.6 21
65 32 88162 37.7 37
62 0 89016 36.4 34
66 20 114353
76 24 75366 35 30
92 36
48163
112 34 49956 37.1 28
66 15 45990 30.3 36
70 28 45723 31.3 18
60 15
43800
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
77449
68 20 56822 34.7 25
74 24 80470
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 61312
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 72453
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
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
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
Solutions
Pastas R Us, Inc. Database (n = 74 restaurants)
a)
Square Feet
Per Person Average Spending
Sales Growth Over Previous Year (%)
Loyalty Card % of Net Sales
Annual Sales
Median
Median Age (3 Miles)
% w/ Bachelor’s Degree (3 Miles)
b)
Obs
SqFt
Sales/Person
SalesGrowth%
LoyaltyCard%
Sales/SqFt
MedIncome
MedAge
BachDeg%
Annual sales
Outliers
Outliers Sales/Sqt.
1
2354
6.81
-8.31
2.07
701.97
1652437.4
FALSE
Mean
2580.472972973
7.04
7.4140540541
2.02
420.3054054054
62807.7027027027
35.2013513514
26.3108108108
1059381.31445946
2
2604
7.57
-4.01
2.54
209.93
546657.7
Standard dev
374.9190313674
0.2972610997
6.62
0.55
137.2395233139
17904.2729542418
3.6545521714
7.00
280423.448335629
3 2453
6.89
-3.94
1.66
364.92
895148.8
skew
0.5271708372
0.8852105267
0.4836821839
-0.7414615128
1.2107021855
0.2917664361
-0.1635915296
0.1376791324
0.3540457413
4
2340
7.13
-3.39
2.06
443.04
1036713.6
IQR
335.25
0.3525
7.4425
0.4675
150.7175
29241.25
10.5
351389.385
5
2500
-3.30
2.48
399.20
998000.0
5-Number Summary
6
2806
6.93
–
1.94
2.96
264.64
742579.8
Min
1251
6.54
178.56
499968
7
2250
7.11
–
0.77
2.28
571.59
1286077.5
1Q
2400
6.82
3.98
1.85
33
2.84
46953
32.525
20.25
877477.575
8 2400 7.13
-0.37
2.34
642.25
1541400.0
7.03
2.075
396.01
6
2757
26.5
1035749.205
9 2709
6.58
2.20
461.45
1250068.1
3rd Q
2735.25
7.17
11.4225
2.325
483.5625
76194.25
37.525
30.75
122886
6.96
10
1990
6.77
-0.17
638.82
1271251.8
Max
3799
7.97
28.81
3.38
98
7.12
1746600
11
2392
6.66
2.09
484.38
11586
37.0
12
2408
2.47
58
1.09
1399264.7
c)
Box-Plot
13
2627
2.04
267.71
703274.2
14 2500 7.00
1.92
572.84
1432100.0
annual sales
sales/sqft
15
1986
7.38
2.05
2.01
586.48
1164749.3
527084.0775
226.07625
16 2500
7.18
2.12
2.64
368.73
921825.0
17
2668
7.35
351.47
937722.0
350393.4975
10
6.76
18
2517
6.95
2.88
458.24
1153390.1
1755951.0375
709.63875
19 1251
7.02
3.96
1234887.1
TRUE
20
2998
6.85
4.04
2.17
35
7.45
1071635.1
21
2625
7.16
4.05
0.72
405.77
1065146.3
22
2300
6.99
680.80
1565840.0
23
2761
7.28
4.24
1.81
368.02
1016103.2
24
2764
7.07
4.58
2.13
303.95
840117.8
25
2430
7.05
5.09
2.50
393.90
957177.0
26
2154
5.14
2.63
562.12
1210806.5
27 2400
6.70
5.48
1.95
494.88
1187712.0
28 2430
6.91
5.86
310.07
753470.1
29
2549
7.58
5.91
373.46
35.0
951949.5
30 2500 7.03
5.98
235.81
589525.0
31
3653
6.84
6.08
413.08
1508981.2
Interpretation:
The box plot is not symmetric.
32
2440
2.08
625.22
1525536.8
Yes. I would prefer IQR to Standard deviation to describe Annual Sales dispersion as
33
2600
6.13
2.73
274.30
713180.0
the data is skewed
34
2160
6.27
542.62
1172059.2
35
2800
7.08
6.57
499968.0
36 2757
6.75
6.90
1.62
375.33
1034784.8
d)
Histogram
37
2450
329.09
806270.5
38 2400
7.64
1.64
29
7.37
713688.0
39 2270 6.62
7.39
1.78
323.17
733595.9
40 2800 6.76
7.67
2.23
468.84
1312752.0
41
2520
7.91
2.15
352.57
888476.4
42
2487
8.08
2.83
380.34
945905.6
43
2629
8.27
2.37
398.12
1046657.5
44
3200
8.54
3.07
312.15
33.0
998880.0
45
2335
8.58
2.19
45
2.16
1055793.6
46 2500 7.45
8.72
1.28
698.64
1746600.0
47
2449
8.75
1.76
367.19
899248.3
48 2625 6.96
8.79
431.93
1133816.3
49
3150
7.30
8.90
1.90
367.06
11562
39.0
50 2625 6.96
9.12
1.98
400.53
38.0
1051391.3
51
2741
6.71
9.47
2.41
414.36
1135760.8
52 2500 6.82
10.17
481.11
1202775.0
53 2450 6.58
10.66
538.06
1318247.0
54
2986
7.56
10.97
330.48
986813.3
55
2967
6.98
11.34
249.93
741542.3
No.the distribution is not symmetric
56
3000
11.45
1.88
291.87
875610.0
The distribution is skewed
57 2500 6.76
11.51
517.40
1293500.0
58 2600
6.92
11.73
2.56
551.58
1434108.0
59 2800
6.73
11.83
386.81
1083068.0
e)
60 2986 6.91
11.95
2.10
427.50
1276515.0
Yes. There is one outlier is Sales/ SqFt =987.12
61
2223
12.47
453.94
1009108.6
The SqFt area for the outlier is 1251 SqFt.
62 2300
7.33
12.80
0.87
512.46
1178658.0
The outlier is larger than the average sales/Sft of the restaurant. This may means that the sales for the restaurant had been overstated
63 3799
7.87
13.78
1.07
345.27
1311680.7
or the area of the restaurant had been understated
64
2700
14.09
234.04
631908.0
65
2650
14.23
1.17
348.33
923074.5
f)
IQR is the best measure of central tendency to describe Sales/SqFt.
66 2500 6.95
14.60
2.14
348.47
871175.0
Reason
67
2994
7.21
14.88
0.93
294.95
883080.3
68
2718
7.25
15.42
361.14
981578.5
69
3700
7.65
16.18
1.68
467.71
1730527.0
70
2000
17.23
403.78
807560.0
71 2400
6.79
2.81
245.74
589776.0
72 2450 7.37
20.76
339.94
832853.0
73
2575
25.54
400.82
1032111.5
74 2400 7.97 28.81
1.77
326.54
783696.0