Statistics Discussion and 2 responses

Initial Post – Instructions

Using your data from the Discussion from Week 2, go back and perform a linear regression.  Find the equation of the linear equation that best fits your data and calculate the correlation coefficient (R).  How does this compare to your analysis in week 2?

Response Post – Instructions

In your response posts, you will discuss the results and whether or not the results show a strong correlation or not.  Discuss the value of R and what it means?  What is ideal?  Is this a good fit?  Also, give examples in the real world where linear regression would make sense?  When is a linear model the ideal model?  In these cases what would you expect the value of R to be?

Data Set 01
Data Set 02
Data Set 03
Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
65.78
112.99
67.83
141.28
68.57
71.52
136.49
68.88
143.54
65.18
69.40
153.03
63.48
97.90
69.66
68.22
142.34
68.42
129.50
67.97
67.79
144.30
67.63
141.85
65.98
68.70
123.30
67.21
129.72
68.67
69.80
141.49
70.84
142.42
66.88
70.01
136.46
67.49
131.55
67.70
67.90
112.37
66.53
108.33
69.82
66.78
120.67
65.44
113.89
69.09
66.49
127.45
69.52
103.30
69.91
67.62
114.14
65.81
120.75
67.33
68.30
125.61
67.82
125.79
70.27
67.12
122.46
70.60
136.22
69.10
68.28
116.09
71.80
140.10
65.38
71.09
140.00
69.21
128.75
70.18
66.46
129.50
66.80
141.80
70.41
68.65
142.97
67.66
121.23
66.54
71.23
137.90
67.81
131.35
66.36
67.13
124.04
64.05
106.71
67.54
Chart Title
180.00
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
0
Series1
Series2
Series3
Series4
Series5
Series6
Series7
Series8
Series9
Series10
Series11
Series12
Series13
Series14
Series15
Series16
Series17
Series18
Series19
10
20
30
40
Series20
50
60
70
Expon. (Series20)
Data Set 04
Data Set 05
Data Set 06
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
124.36
66.50
128.73
68.64
134.63
64.87
124.86
69.00
137.55
66.78
121.90
67.09
139.67
68.30
129.76
70.05
155.38
68.35
137.37
67.01
128.82
66.28
128.94
65.61
106.45
70.81
135.32
69.20
129.10
67.76
128.76
68.22
109.61
69.13
139.47
68.02
145.68
69.06
142.47
67.36
140.89
67.66
116.82
67.73
132.75
70.09
131.59
66.31
143.62
67.22
103.53
70.18
121.12
69.44
134.93
67.37
124.73
68.23
131.51
63.84
147.02
65.27
129.31
68.13
136.55
67.72
126.33
70.84
134.02
70.24
141.49
70.05
125.48
69.92
140.40
71.49
140.61
70.19
115.71
64.29
102.84
69.20
112.14
65.95
123.49
68.25
128.52
70.06
133.46
70.01
147.89
66.36
120.30
70.56
131.80
68.61
155.90
68.36
138.60
66.29
120.03
68.81
128.07
65.48
132.96
63.43
123.10
69.76
119.37
69.72
115.62
66.77
128.14
65.46
133.81
67.73
122.52
68.89
115.48
68.83
Data Set 07
Data Set 08
Data Set 09
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
102.09
65.80
119.88
69.52
136.21
67.08
130.35
67.21
109.01
65.18
113.40
64.39
134.18
69.42
128.27
68.01
125.33
69.37
98.64
68.94
135.29
68.34
127.58
68.38
114.56
67.94
106.86
65.18
107.16
65.31
123.49
65.63
123.29
68.26
116.46
67.14
123.05
66.50
109.51
68.57
133.84
68.39
126.48
67.93
119.31
64.50
112.89
66.29
128.42
68.89
140.24
68.71
130.76
67.19
127.19
70.24
133.98
68.89
137.76
65.99
122.06
68.27
132.58
69.54
125.40
69.43
127.61
71.23
130.70
67.40
138.47
67.97
131.64
69.10
115.56
66.48
120.82
67.76
111.90
64.40
123.79
66.01
140.15
65.28
122.04
71.10
128.14
72.44
136.74
73.83
128.55
68.22
135.96
64.13
106.11
66.81
132.68
65.92
116.63
70.98
158.96
66.89
136.06
67.44
126.82
67.50
108.79
65.74
115.94
73.90
151.39
72.02
138.78
65.98
136.90
69.98
130.40
65.31
115.91
66.58
Data Set 10
Data Set 11
Data Set 12
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
146.29
67.11
135.02
65.73
121.50
65.84
109.88
65.87
116.23
66.43
112.71
65.77
139.05
66.78
109.17
70.01
135.00
71.14
119.90
68.74
124.22
69.48
128.68
67.83
128.31
66.23
141.16
68.63
124.41
65.07
127.24
65.96
129.15
68.36
140.03
69.71
115.23
68.58
127.87
68.39
117.52
69.93
124.80
66.59
120.92
68.77
143.87
66.12
126.95
66.97
127.65
69.92
141.17
68.61
111.27
68.08
101.47
71.56
155.94
69.00
122.61
70.19
144.99
68.45
134.01
66.79
124.21
65.52
110.95
66.71
130.10
68.02
124.65
67.46
132.86
66.68
106.23
69.67
119.52
67.41
146.34
67.94
112.05
71.82
139.30
69.66
145.59
68.90
136.19
72.75
104.83
65.80
120.84
67.29
131.24
67.28
123.04
66.11
115.78
69.57
131.32
67.41
118.89
68.24
128.30
67.67
119.53
68.53
121.49
68.02
127.47
69.04
117.00
68.47
119.25
71.39
127.88
67.97
138.53
68.52
Data Set 13
Data Set 14
Data Set 15
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
109.65
63.73
134.10
70.17
122.00
67.00
130.16
67.70
141.89
67.85
124.00
70.27
137.11
69.47
138.74
66.62
108.86
67.58
113.76
66.70
134.45
63.69
104.66
66.31
114.97
65.23
117.02
68.04
132.25
68.91
127.71
69.89
115.68
66.94
127.18
65.61
122.00
69.83
134.79
66.26
125.12
68.00
117.96
65.40
120.57
70.73
133.32
69.94
127.71
68.32
120.08
70.71
122.34
70.15
117.96
65.94
84.36
73.27
130.26
66.66
125.16
70.10
138.94
63.79
116.74
69.41
141.10
66.06
143.52
67.84
125.85
66.81
145.48
68.23
123.13
67.78
100.63
67.70
116.07
65.22
115.53
67.24
118.49
69.13
135.75
69.16
120.98
66.76
137.13
67.54
132.92
67.60
120.65
69.03
118.70
65.78
115.66
67.29
124.04
68.53
124.16
66.26
114.32
66.84
117.22
64.65
124.94
67.39
148.95
68.08
127.96
65.14
126.39
64.94
142.19
66.57
116.75
66.74
121.53
69.26
Data Set 16
Data Set 17
Data Set 18
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
133.30
69.08
138.73
67.98
130.64
68.74
127.41
69.64
130.95
66.62
122.39
69.52
125.08
69.08
124.30
67.30
133.87
70.31
102.81
68.01
135.37
65.96
134.83
67.30
134.22
68.86
124.20
66.54
137.84
67.61
100.98
63.19
111.24
68.08
112.68
67.86
145.89
65.58
129.40
65.83
121.20
66.47
155.30
69.12
127.74
69.24
114.93
68.92
138.72
69.79
121.33
64.69
110.38
68.47
116.26
67.48
118.22
69.21
126.03
69.52
120.61
69.09
123.34
67.17
118.70
70.24
114.41
68.55
151.91
67.85
119.31
67.86
133.34
68.21
115.31
69.27
150.74
68.00
92.75
67.10
122.38
67.91
121.11
67.14
131.78
71.24
129.23
67.08
118.41
68.10
118.39
69.12
138.28
70.02
142.76
68.99
131.15
65.50
144.06
70.05
145.63
69.33
130.20
66.59
120.85
70.87
127.34
70.09
129.18
68.00
113.30
66.06
115.97
68.74
143.14
72.58
149.32
65.24
104.44
64.19
Data Set 19
Data Set 20
Data Set 21
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
138.49
66.09
129.55
68.89
140.53
67.03
145.50
69.24
152.07
68.27
125.69
65.91
124.41
69.67
120.86
69.18
134.33
70.03
124.19
68.43
136.10
72.61
136.46
69.27
126.17
68.29
130.06
66.04
127.88
70.08
138.81
69.38
131.77
69.23
123.14
64.91
121.55
68.35
139.38
68.88
116.34
69.69
114.26
72.32
168.23
66.46
124.56
67.57
129.40
70.37
127.64
69.30
125.79
63.86
137.56
65.73
131.80
67.58
107.59
71.62
134.50
66.50
122.86
69.42
143.02
64.99
127.71
70.81
140.21
67.47
118.74
64.61
115.67
67.38
142.69
66.45
118.99
62.02
131.59
67.80
137.43
68.76
131.87
65.29
127.58
68.16
126.04
63.77
119.37
67.70
125.72
68.86
143.60
69.04
126.12
70.86
119.99
67.71
122.62
66.49
126.61
68.17
140.87
64.66
108.60
66.74
113.56
67.45
136.92
65.74
100.66
67.69
115.84
71.04
118.48
68.42
116.14
66.69
130.27
67.83
Data Set 22
Data Set 23
Data Set 24
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
125.45
67.15
108.75
68.04
121.50
65.57
117.17
68.30
134.40
68.12
119.28
68.30
137.32
65.41
131.21
71.24
126.55
71.03
149.44
68.67
130.83
66.92
129.25
70.77
151.07
70.07
127.08
71.10
134.78
67.51
117.00
69.13
119.41
69.41
146.07
69.51
138.18
67.02
105.56
69.17
162.41
66.45
127.62
65.52
134.47
68.58
130.19
68.57
120.75
70.20
132.69
69.60
132.19
67.01
144.25
67.67
126.06
69.05
127.46
68.70
105.79
69.73
126.35
68.29
125.35
68.23
120.16
67.62
142.36
69.25
134.76
70.41
109.08
70.80
124.59
68.24
121.94
65.70
125.97
69.66
122.36
67.69
125.67
65.70
110.23
66.73
123.23
68.84
145.96
68.48
134.47
67.58
131.40
69.52
119.92
66.63
115.51
65.25
124.30
66.98
111.51
66.84
125.11
70.71
128.38
72.01
138.68
69.90
116.41
71.27
136.85
67.44
135.02
67.65
133.39
66.56
118.06
66.06
116.51
68.31
Data Set 25
Data Set 26
Data Set 27
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
123.96
69.75
138.09
68.68
120.69
68.81
136.95
68.58
126.61
67.54
115.78
67.56
153.08
68.14
131.81
71.18
128.69
68.17
126.36
67.98
131.74
70.54
134.76
65.81
145.06
64.83
117.63
71.53
118.34
64.92
135.17
69.21
126.19
66.77
106.16
68.36
108.81
69.27
127.51
66.34
126.38
66.72
110.52
70.94
142.48
64.83
114.37
69.18
138.27
69.08
139.44
68.38
130.28
65.89
119.51
66.20
110.32
68.05
123.31
66.04
115.32
71.06
131.95
69.09
122.86
69.44
132.37
68.99
129.20
69.91
125.69
67.15
93.99
70.96
124.35
68.41
111.72
65.69
127.41
66.02
126.53
68.33
125.55
69.43
134.30
69.86
149.23
66.96
119.97
66.55
124.97
66.83
142.16
70.55
132.60
69.04
124.07
69.09
127.14
69.38
132.67
67.62
133.55
66.81
122.34
67.52
117.45
69.59
134.15
67.13
112.67
64.87
101.85
68.12
130.25
64.57
134.26
69.13
128.44
71.23
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
64.00
65.00
Data Set 28
Data Set 29
Data Set 30
Weight (lbs) Height (in) Weight (lbs) Height (in) Weight (lbs) Height (in)
134.04
66.43
130.37
70.43
129.59
69.04
127.75
66.32
122.89
67.68
134.11
67.36
127.62
68.03
107.87
67.88
106.13
70.36
139.40
68.29
118.59
68.07
127.06
69.89
113.94
66.92
125.65
66.99
121.92
65.15
147.52
71.78
148.60
71.58
150.74
69.41
132.65
66.05
150.28
64.37
116.01
68.51
132.81
69.01
127.07
67.93
125.47
65.72
105.09
68.71
128.71
69.92
131.61
63.98
127.52
65.01
118.42
69.94
129.07
70.08
130.73
66.06
125.39
66.80
129.11
68.43
128.58
71.16
149.27
70.11
148.16
68.24
122.57
67.55
107.35
68.95
105.39
67.83
157.30
68.83
133.70
68.03
110.54
66.31
121.11
68.12
124.85
69.36
118.64
69.75
147.51
67.91
112.70
68.45
122.82
65.71
117.49
67.64
127.84
65.70
124.89
66.88
132.45
69.78
134.16
69.56
135.77
67.28
118.18
68.00
138.60
65.85
116.46
70.63
123.73
69.41
126.04
68.80
125.36
69.94
Name Data 28
65.00
66.00
67.00
68.00
69.00
70.00
71.00
72.00
73.00
Weight (lbs)
133.12
138.33
124.50
136.72
115.02
132.64
143.13
134.74
122.62
153.56
126.29
134.72
134.60
118.39
121.30
132.28
139.06
110.70
154.11
124.16
Chart Title
180.00
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
0
10
Series1
Series2
Series3
Series4
Series5
Series6
Series7
Series8
Series9
Series10
Series11
Series12
Series13
Series14
Series15
Series16
Series17
Series18
Series19
20
30
40
Series20
50
60
70
Expon. (Series20)
Data Set 51
520.00
520.00
521.00
522.00
522.00
522.00
524.00
526.00
528.00
529.00
529.00
530.00
532.00
532.00
537.00
544.00
547.00
548.00
550.00
551.00
553.00
554.00
554.00
555.00
555.00
556.00
557.00
558.00
562.00
563.00
566.00
567.00
568.00
574.00
577.00
Bin
Frequency
520-539
14
535-549
4
550-564
12
565-579
7
580 & Above
13
28%
8%
24%
14%
26%
Mean
557.48
14 Median
555.50
Mode
522.00
Range
79.00
Variance
633.68
4 Standard Dev
25.17
12
578.00
579.00
581.00
586.00
587.00
587.00
587.00
588.00
588.00
588.00
590.00
591.00
594.00
598.00
599.00
50.00
7
13
Histogram
16
14
14
13
12
12
10
7
8
Frequency Bands
6
4
4
2
0
520-539
535-549
550-564
565-579
580 & Above
Pie Chart
26%
28%
520-539
535-549
550-564
8%
14%
565-579
580 & Above
24%
Compatibility Report for attachment_1.xls
Run on 12/19/2022 6:38
If the workbook is saved in an earlier file format or opened in
an earlier version of Microsoft Excel, the listed features will
not be available.
Minor loss of fidelity
Some cells or styles in this workbook contain formatting that
is not supported by the selected file format. These formats
will be converted to the closest format available.
# of
occurrences
Version
1
Excel 97-2003
Name Data 28
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
64.00
65.00
66.00
67.00
68.00
69.00
70.00
71.00
72.00
73.00
Compatibility Report for attachment_1.xls
Run on 12/19/2022 6:58
If the workbook is saved in an earlier file format or opened in
an earlier version of Microsoft Excel, the listed features will
not be available.
Minor loss of fidelity
Some cells or styles in this workbook contain formatting that
is not supported by the selected file format. These formats
will be converted to the closest format available.
# of
occurrences
Version
1
Excel 97-2003
Data Set 07
Height (in) Weight (lbs)
65.80
106.86
67.21
109.01
69.42
109.51
68.94
115.56
67.94
116.63
65.63
119.31
66.50
119.88
67.93
123.29
68.89
123.79
70.24
126.82
68.27
128.14
71.23
128.27
69.10
130.40
64.40
130.70
71.10
132.58
68.22
133.98
65.92
135.29
67.44
135.96
73.90
140.24
69.98
151.39
Chart Title
160.00
y = 1.8238x + 1.1303
R² = 0.1333
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
62.00
64.00
66.00
68.00
70.00
72.00
74.00
0.1333
126.84 VARIANCE
127.48 MEDIAN
125.88 MEAN
N/A MODE
74.00
76.00
0.37
Data Set 51
520.00
520.00
521.00
522.00
522.00
522.00
524.00
526.00
528.00
529.00
529.00
530.00
532.00
532.00
537.00
544.00
547.00
548.00
550.00
551.00
553.00
554.00
554.00
555.00
555.00
556.00
557.00
558.00
562.00
563.00
566.00
567.00
568.00
574.00
577.00
Bin
Frequency
520-539
14
535-549
4
550-564
12
565-579
7
580 & Above
13
28%
8%
24%
14%
26%
Mean
557.48
14 Median
555.50
Mode
522.00
Range
79.00
Variance
633.68
4 Standard Dev
25.17
12
578.00
579.00
581.00
586.00
587.00
587.00
587.00
588.00
588.00
588.00
590.00
591.00
594.00
598.00
599.00
50.00
7
13
Histogram
16
14
14
13
12
12
10
7
8
Frequency Bands
6
4
4
2
0
520-539
535-549
550-564
565-579
580 & Above
Pie Chart
26%
28%
520-539
535-549
550-564
8%
14%
565-579
580 & Above
24%
Number of Boys
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Height (in) Weight (lbs)
x
y
64.37
116.01
65.70
124.89
65.85
116.46
66.80
129.11
66.99
121.92
67.68
134.11
67.88
106.13
67.93
125.47
68.03
110.54
68.07
127.06
68.45
122.82
68.80
125.36
68.95
105.39
69.36
118.64
69.56
135.77
69.92
131.61
69.94
129.07
70.11
148.16
70.43
129.59
71.58
150.74
Data Set 29
Height Whole Number (ft)
x
5’3
5’4
5’4
5’5
5’5
5’5
5’5
5’5
5’6
5’6
5’6
5’6
5’6
5’7
5’7
5’7
5’7
5’8
5’8
5’9
Weight to Nearest Wole Number
y
105.00
106.00
110.00
116.00
116.00
118.00
121.00
122.00
124.00
125.00
125.00
127.00
129.00
129.00
129.00
131.00
134.00
135.00
148.00
150.00
y = 3.4364x
R² = 0.2681
Original Data Sheet 29
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
64.00
65.00
66.00
67.00
r=
0.517783739
Mean
133.37
Median
124.94
Mode
116,125,129,
68.00
69.00
70.00
y = 3.4364x – 109.33
R² = 0.2681
y = 1.9113x + 104.93
R² = 0.9181
Modified Data Sheet 29
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
70.00
71.00
72.00
0
5
10
15
Median Height (Inches)
5’6
Median Weight
125.00
Standard Deviation of Height
1.781302804
Standard Deviation of Weight
11.80098123
STDEV.P Height
1.73619921
STDEV.P Weight
11.52191567
STDEV.S Height
1.781302804
STDEV.S Weight
11.82123605
Correlation Coeffecient ®
0.51781762
Coeffecient of Determination (R^2)
R^2 = 0.9181
20
= 1.9113x + 104.93
R² = 0.9181
25