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Regression and Scatter plots

3 min read
Posted on 
December 15th, 2022
Home Uncategorized Regression and Scatter plots

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.

Please use my Supplied Excel Sheet with prior Data. 

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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

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

752

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

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

0674

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

0.9007655189

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

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

-78.5222407532

-66.833182556

-63.9367962151

-54.9666697606

-49.5089341383

-43.817663257

-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
37

 345 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
73 4

 0.5 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 40.5
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 2745
-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 37345 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

Pastas R Us, Inc. Database (n = 74 restaurants) a) b) 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) Total Sales MEAN SD SKEW 5-NUMBER SUMMARY IQR SqFt 2580.472972973 374.9190313674 0.5271708372 2400

,

2500

,2500,2580.47,2745

345
Obs

SqFt

Sales/Person SalesGrowth% LoyaltyCard% Sales/SqFt MedIncome MedAge BachDeg%

Annual Sales Sales/Person

7.04

40540541 0.2972610997 0.9036

3150

33 6.81

,7,

7.03

,7.04,

7.18 0.37 1

2354

6.81

-8.31 2.07 701.97

45177 34.4 31

1652437.4

SalesGrowth%

7.4140540541 6.62

47303215 0.4937474711 3.69

,

4.05

,7.03,7.41,11.47 7.775 2

2604 7.57 -4.01 2.54 209.93

51888 41.2 20

546657.7

LoyaltyCard%

2.02

64864865 0.55

23708116 -0.7568911137 1.84

,2.03,

2.04

,

2.08

,

2.34

0.5
3 2453

6.89 -3.94 1.66 364.92

51379 40.3 24

895148.8

Sales/SqFt

420.3054054054 137.2395233139 1.23589655 330.13,

396.01

,420.31,48

7.00

,n/a 156.8725 4

2340 7.13 -3.39 2.06 443.04

66081 35.4 29

1036713.6

MedIncome

62807.7027027027 17904.2729542418 0.2978380118 46501.25

,6

2757

,62807.70,

76560

,n/a 3005

8.75 5 2500 7.04

-3.30 2.48 399.20

50999 31.5 18

998000.0

MedAge

35.2013513514 3.6545521714 -0.1669958223 32.4,34.8,35,35.20,37 5.225 6

2806 6.93 –

1.94 2.96 264.64

41562 36.3 30

742579.8

BachDeg%

26.3108108108 7.0047453107 0.1405441956 20,26.31,

26.5

,29,31

11
7

2250 7.11 –

0.77 2.28 571.59

44196 35.1 14

1286077.5

Annual Sales

1059381.31445946 280423.448335629 0.3614133314 874501.3,1035749,1059381,1238682,n/a 364181.1025 8 2400 7.13

-0.37

2.34

642.25

50975 37.6 33

1541400.0 9 2709

6.58

-0.25

2.20 461.45

72808 34.9 28

1250068.1 c) Minimum Lower Quartile Upper Quartile Maximum 10

1990 6.77 -0.17

2.34

638.82

79070 34.8 29

127

1251

.8 499968 11

2392 6.66

0.47

2.09 484.38

78497 36.2 39

11586

37.0 12

2408

7.03 0.55

2.47 58

1.09

41245 32.2 23

1399264.7 13

2627

7.03 0.77 2.04

267.71

33003 30.9 22

703274.2 14 2500 7.00

1.92

2.02

57

2.84

90988 37.7 37

1432100.0 15

1986 7.38 2.05 2.01 586.48

37950 34.3 24

1164749.3 16 2500 7.18

2.12 2.64 368.73

45206 32.4 17

921825.0 17

2668 7.35

2.84 2.22

351.47

79312 32.1 37

937722.0 18

2517 6.95 2.88

2.07

458.24

37345 31.4 22

1153390.1 19 1251

7.02 3.96

1.94

98

7.12

46226 30.4 36

1234887.1 20

2998 6.85 4.04 2.17 35

7.45

70024 33.9 34

1071635.1 21

2625 7.16

4.05

0.72 405.77

54982 35.6 26

1065146.3 22

2300 6.99

4.05 2.00

680.80

54932 35.9 20

1565840.0 23

2761 7.28 4.24 1.81 368.02

34097 33.6 20

1016103.2 24

2764 7.07 4.58 2.13 303.95

46593 37.9 26

840117.8 25

2430 7.05 5.09 2.50 393.90

51893 40.6 21

957177.0 26

2154 6.54 5.14 2.63 562.12

88162 37.7 37

1210806.5 27 2400

6.70 5.48 1.95 494.88

89016 36.4 34

1187712.0 explanation 28 2430

6.91 5.86

2.04

310.07

114353 40.9 34

753470.1 The above boxplot illustration of annual sales is symmetric 29

2549 7.58 5.91

1.41

373.46

75366

35.0

30

951949.5 No,because the variable measures can contain outliers which may exergerrate the threashold upon which the IQR lies.Standard deviation is most suitable in measuring dispersion in this case. 30 2500 7.03

5.98

2.05

235.81

48163 26.4 16

589525.0 31

3653 6.84 6.08

2.13

413.08

49956 37.1 28

1508981.2 d) 32

2440

6.94 6.08 2.08

625.22

45990 30.3 36

1525536.8 33

2600

7.07

6.13 2.73 274.30

45723 31.3 18

713180.0 34

2160

7.00

6.27

1.95

542.62

43800 29.6 36

1172059.2 35

2800 7.08 6.57

2.04

178.56

68711 32.9 18

499968.0 36 2757

6.75 6.90 1.62 375.33

65150 40.7 24

1034784.8 37

2450

6.81 6.94 1.95

329.09

39329 29.3 22

806270.5 38 2400

7.64

7.12

1.64 29

7.37

63657 37.3 29

713688.0 39 2270 6.62

7.39 1.78 323.17

67099 39.8 25

733595.9 40 2800

6.76 7.67 2.23 468.84

75151 33.9 28

1312752.0 41

2520

7.11

7.91 2.15 352.57

93876 35.0 40

888476.4 42

2487

7.05

8.08 2.83 380.34

79701 35.0 39

945905.6 43

2629

6.90

8.27 2.37 398.12

77115 35.9 30

1046657.5 44

3200 7.17 8.54 3.07 312.15

52766

33.0

17

998880.0 45

2335

6.75

8.58 2.19 45

2.16

32929 30.9 22

1055793.6 46 2500 7.45

8.72 1.28 698.64

87863 38.5 29

1746600.0 47

2449

7.00 8.75

1.76 367.19

73752 40.5 19

899248.3 48 2625

6.96 8.79

2.51

431.93

85366 32.1 29

1133816.3 49 3150

7.30 8.90 1.90 367.06

39180 34.8 18

11562

39.0

explanation
50 2625 6.96

9.12 1.98 400.53

56077

38.0

19

1051391.3 The distribution is not symmetric as most observation are

skew

ed to the left. 51

2741 6.71 9.47 2.41 414.36

77449 37.0 34

1135760.8 52 2500

6.82 10.17

2.17

481.11

56822 34.7 25

1202775.0 53 2450 6.58

10.66

2.16

538.06

80470 36.4 30

1318247.0 54

2986 7.56 10.97

0.29

330.48

55584 36.8 21

986813.3 55

2967 6.98 11.34 1.85 249.93

78001 32.2 30

741542.3 56

3000

7.28

11.45 1.88 291.87

75307 34.8 30

875610.0 57 2500 6.76

11.51

2.19

517.40

76375 36.7 28

1293500.0 58 2600

6.92 11.73 2.56 551.58

61857 33.8 31

1434108.0 59 2800

6.73 11.83

2.16

386.81

61312 34.2 16

1083068.0 60 2986 6.91

11.95 2.10 427.50

72040 39.0 31

1276515.0 61

2223

6.77

12.47

1.98

453.94

92414 34.9 40

1009108.6 62 2300

7.33 12.80 0.87 512.46

92602 39.3 33

1178658.0 63

3799 7.87 13.78 1.07 345.27

59599 35.6 28

1311680.7 64

2700

6.95

14.09 3.38 234.04

72453 36.0 23

631908.0 65

2650

7.33

14.23 1.17 348.33

67925 41.1 16

923074.5 66 2500 6.95

14.60 2.14 348.47

42631 24.7 25

871175.0 67

2994 7.21 14.88 0.93 294.95

75652 40.5 25

883080.3 68

2718 7.25 15.42

2.22

361.14

39650 32.9 18

981578.5 69

3700 7.65 16.18 1.68 467.71

48033 30.3 15

1730527.0 70

2000

6.93

17.23

2.41

403.78

67403 36.2 19

807560.0

explanation

71 2400

6.79

18.43

2.81 245.74

80597 32.4 27

589776.0

there exist an outlier in the variable measurements as shown in the above

scatter plot

.The outlier is 987.12 sales/ft.

72 2450 7.37

20.76

1.09

339.94

60928 43.5 21

832853.0 73

2575

6.76

25.54

0.64

400.82

73762 41.6 29

1032111.5 there were excess sales on that day or a customer may have made a prepayment on a certain sale of that day resulting to an excess amount. 74 2400

7.97 28.81 1.77 326.54

64225 31.4 15

783696.0 average 2580.472972973

7.0440540541 sd 372.3771781179

0.2972610997 7.4140540541

2.0264864865

420.3054054054 62807.7027027027 35.2013513514 26.3108108108 1059381.31445946

e) Mean is the best measure of cental tendency to describe sales/sqr ft.Reason is it serves as a pivot upon which the measurements are distributed from. skew 0.5271708372

0.9036315033 6.6247303215 0.5523708116

137.2395233139 17904.2729542418 3.6545521714 7.0047453107 280423.448335629
mode

2500 7.03 0.4937474711 -0.7568911137 1.23589655 0.2978380118 -0.1669958223 0.1405441956 0.3614133314
median 2500 7 4.05 2.04

ERROR:#N/A

ERROR:#N/A 34.8 29 ERROR:#N/A
q1 2400

6.8175

7.03

2.075

396.01

62757

35 26.5

1035749.205 q3 2745

7.1875

3.69 1.84

330.1325

46501.25 32.4 20

874501.25 IQR 345 0.37

11.465

2.34

487.005

76560

37.625

31

1238682.3525 7.775 0.5 156.8725

30058.75

5.225 11 364181.1025

2580.472972973 7.0440540541

2500 7.03 7.4140540541 2.0264864865 420.3054054054 62807.7027027027 35.2013513514 26.3108108108 1059381.31445946

2500 7 4.05 2.04 ERROR:#N/A ERROR:#N/A 34.8 29 ERROR:#N/A
2400 6.8175 7.03 2.075 396.01 62757 35 26.5 1035749.205
2745 7.1875 3.69 1.84 330.1325 46501.25 32.4 20 874501.25
11.465 2.34 487.005 76560 37.625 31 1238682.3525

2400 6.8175
2500 7 3.69 1.84 420.3054054054 62807.7027027027 32.4 20 1059381.31445946
2500 7.03 4.05 2.0264864865 330.1325 46501.25 34.8 26.3108108108 874501.25
2580.472972973 7.0440540541 7.03 2.04 396.01 62757 35 26.5 1035749.205
2745 7.1875 7.4140540541 2.075 487.005 76560 35.2013513514 29 1238682.3525
11.465 2.34 ERROR:#N/A ERROR:#N/A 37.625 31 ERROR:#N/A
2400,2500,2500,2580.47,2745 6.81,7,7.03,7.04,7.18

874501.3,1035749,1059381,1238682,n/a
3.69,4.05,7.03,7.41,11.47 1.84,2.03,2.04,2.08,2.34 330.13,396.01,420.31,487.00,n/a 46501.25,62757,62807.70,76560,n/a

32.4,34.8,35,35.20,37

20,26.31,26.5,29,31

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

scatter plot

701.97 209.93 364.92 443.04 399.2 264.64 571.59 642.25 461.45 638.82000000000005 484.38 581.09 267.70999999999998 572.84 586.48 368.73 351.47 458.24 987.12 357.45 405.77 680.8 368.02 303.95 393.9 562.12 494.88 310.07 373.46 235.81 413.08 625.22 274.3 542.62 178.56 375.33 329.09 297.37 323.17 468.84 352.57 380.34 398.12 312.14999999999998 452.16 698.64 367.19 431.93 367.06 400.53 414.36 481.11 538.05999999999995 330.48 249.93 291.87 517.4 551.58000000000004 386.81 427.5 453.94 512.46 345.27 234.04 348.33 348.47 294.95 361.14 467.71 403.78 245.74 339.94 400.82 326.54000000000002

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