math assignment 5
TRANSCRIPT
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.995059
R Square 0.990142
Adjusted R 0.98891
Standard E 0.026886Observatio 10
ANOVA
df SS MS F ignificance F
Regression 1 0.5808 0.5808 803.5068 2.59E-09
Residual 8 0.005783 0.000723
Total 9 0.586583
Coefficientsandard Err t Stat P-value Lower 95% Upper 95% ower 95.0 pper 95.0
Intercept 4.384155 0.061252 71.57535 1.62E-12 4.242907 4.525403 4.242907 4.525403
X Variable -0.45319 0.015988 -28.3462 2.59E-09 -0.49006 -0.41632 -0.49006 -0.41632
RESIDUAL OUTPUT
bservationPredicted Y Residuals dard Residuals
1 3.113431 -0.02239 -0.88324
2 2.965953 0.029779 1.174811
3 2.854867 -0.02165 -0.85425
4 2.749817 0.022772 0.8983685 2.651827 -0.01277 -0.50379
6 2.581968 -0.01702 -0.6714
7 2.521453 0.043496 1.715967
8 2.468075 0.016831 0.664013
9 2.420327 -0.02243 -0.88496
10 2.319201 -0.01662 -0.65552
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-0.04
-0.02
0
0.02
0.04
0.06
0.000 1.000 2.000 3.000 4.000 5.000Residuals
X Variable 1
X Variable 1 Residual Plot
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.973155
R Square 0.947031
Adjusted R 0.94041
Standard E 0.06232Observatio 10
ANOVA
df SS MS F ignificance F
Regression 1 0.555512 0.555512 143.0316 2.2E-06
Residual 8 0.031071 0.003884
Total 9 0.586583
Coefficientsandard Err t Stat P-value Lower 95% Upper 95% ower 95.0 pper 95.0
Intercept 3.16414 0.046178 68.52077 2.29E-12 3.057653 3.270626 3.057653 3.270626
X Variable -0.00988 0.000826 -11.9596 2.2E-06 -0.01179 -0.00798 -0.01179 -0.00798
RESIDUAL OUTPUT
bservationPredicted Y Residuals dard Residuals
1 3.001004 0.090039 1.532413
2 2.938259 0.057473 0.978166
3 2.875514 -0.0423 -0.71994
4 2.800221 -0.02763 -0.470285 2.712378 -0.07332 -1.24788
6 2.637084 -0.07213 -1.2277
7 2.561791 0.003159 0.053759
8 2.486497 -0.00159 -0.02707
9 2.411203 -0.01331 -0.2265
10 2.222969 0.079616 1.355016
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-0.1
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0.05
0.1
0.000 20.000 40.000 60.000 80.000 100.000 120.000Residuals
X Variable 1
X Variable 1 Residual Plot
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Length(Inches) Length(cm) No. Of Swings
6.5 16.51 22
9 22.86 20
11.5 29.21 17
14.5 36.83 16
18 45.72 14
21 53.34 1324 60.96 13
27 68.58 12
30 76.2 11
37.5 95.25 10
a)
y = -0.1467x + 22.217
R = 0.8904
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NumberofSwings
Length (cm)
Graph of Number of Swings Against Length (cm)
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b)
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Length (cm)
X Variable 1 Residual Plot
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c) Power Relationship
Length(Inches) Length(cm) No. Of Swings Ln X Ln Y
6.500 16.510 22.000 2.804 3.091
9.000 22.860 20.000 3.129 2.996
11.500 29.210 17.000 3.375 2.833
14.500 36.830 16.000 3.606 2.773
18.000 45.720 14.000 3.823 2.63921.000 53.340 13.000 3.977 2.565
24.000 60.960 13.000 4.110 2.565
27.000 68.580 12.000 4.228 2.485
30.000 76.200 11.000 4.333 2.398
37.500 95.250 10.000 4.557 2.303
y = 80.17x-0.453
R = 0.9901
0
5
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15
20
25
0 20 40 60 80 100 120
NumberofSwings
Length (cm)
Graph of Number of Swings Against Length (cm)
y = -0.4532x + 4.3842
R = 0.9901
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500
0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000
Ln(NumberofSwings)
Ln(Length)
Graph of Ln(Number of Swings) Against Ln(Length)
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c) Exponential Relationship
Length(Inches) Length(cm) No. Of Swings X Ln Y
6.5 16.51 22 16.510 3.091
9 22.86 20 22.860 2.996
11.5 29.21 17 29.210 2.833
14.5 36.83 16 36.830 2.773
18 45.72 14 45.720 2.63921 53.34 13 53.340 2.565
24 60.96 13 60.960 2.565
27 68.58 12 68.580 2.485
30 76.2 11 76.200 2.398
37.5 95.25 10 95.250 2.303
y = 23.668e-0.01xR = 0.947
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0 20 40 60 80 100 120
NumberofSwings
Length (cm)
Graph of Number of Swings Against Length (cm)
y = -0.0099x + 3.1641
R = 0.947
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500
0.000 20.000 40.000 60.000 80.000 100.000 120.000
Ln(Num
berofSwings)
Length (cm)
Graph of Ln(Number of Swings) Against Length
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d)
Length(Inches) Length(cm) No. Of Swings Period, T
6.5 16.51 22 0.909
9 22.86 20 1.000
11.5 29.21 17 1.176
14.5 36.83 16 1.250
18 45.72 14 1.42921 53.34 13 1.538
24 60.96 13 1.538
27 68.58 12 1.667
30 76.2 11 1.818
37.5 95.25 10 2.000
y = 0.0138x + 0.7338
R = 0.9815
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0.5
1
1.5
2
2.5
0 20 40 60 80 100 120
Period(T)
Length (m)
Graph of Period (T) Against Length (m)
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Length(In.) Length(cm) Swing Period
6.5 16.51 22.50984266 0.888500213
9 22.86 19.42452257 1.029626336
11.5 29.21 17.38305436 1.150545789
14.5 36.83 15.65029416 1.277931251
18 45.72 14.19004475 1.409438825
21 53.34 13.23295603 1.51137810424 60.96 12.4562271 1.605622621
27 68.58 11.80903541 1.693618429
30 76.2 11.25864905 1.776412065
37.5 95.25 10.17620965 1.965368314
y = 0.0136x + 0.7442
R = 0.9825
0
0.5
1
1.5
2
2.5
0 20 40 60 80 100 120
Period(T)
Length (m)
Graph of Period (T) Against Length (m)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.943585
R Square 0.890352
Adjusted R 0.876646
Standard E 1.373299Observatio 10
ANOVA
df SS MS F ignificance F
Regression 1 122.5124 122.5124 64.9606 4.14E-05
Residual 8 15.08759 1.885949
Total 9 137.6
Coefficientsandard Err t Stat P-value Lower 95% Upper 95% ower 95.0 pper 95.0
Intercept 22.21709 1.017578 21.8333 2.04E-08 19.87055 24.56363 19.87055 24.56363
X Variable -0.14674 0.018206 -8.05981 4.14E-05 -0.18872 -0.10476 -0.18872 -0.10476
RESIDUAL OUTPUT
bservationPredicted Y Residuals dard Residuals
1 19.79442 2.205579 1.703467
2 18.86263 1.137374 0.878445
3 17.93083 -0.93083 -0.71892
4 16.81268 -0.81268 -0.627675 15.50816 -1.50816 -1.16482
6 14.39001 -1.39001 -1.07357
7 13.27186 -0.27186 -0.20997
8 12.1537 -0.1537 -0.11871
9 11.03555 -0.03555 -0.02746
10 8.240163 1.759837 1.359201
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-1.5
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0
0.5
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1.5
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2.5
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X Variable 1
X Variable 1 Residual Plot
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Length(In.) Length(cm)No. Of Swings
6.5 16.51 22
9 22.86 20
11.5 29.21 17
14.5 36.83 16
18 45.72 14
21 53.34 1324 60.96 13
27 68.58 12
30 76.2 11
37.5 95.25 10
y = 80.17x-0.453
R = 0.9901
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Series1
Power (Series1)
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Length(In.) Length(cm)No. Of Swings
6.5 16.51 22
9 22.86 20
11.5 29.21 17
14.5 36.83 16
18 45.72 14
21 53.34 1324 60.96 13
27 68.58 12
30 76.2 11
37.5 95.25 10
y = 23.668e-0.01x
R = 0.947
0
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Series1
Expon. (Series1)
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Length(In.) Length(cm)No. Of Swi Period, T
6.5 16.51 22 0.909091 Time Take 20
9 22.86 20 1
11.5 29.21 17 1.176471
14.5 36.83 16 1.25
18 45.72 14 1.428571
21 53.34 13 1.53846224 60.96 13 1.538462
27 68.58 12 1.666667
30 76.2 11 1.818182
37.5 95.25 10 2
y = 0.0138x + 0.7338
R = 0.9815
0
0.5
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1.5
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Series1
Linear (Series1)
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Length(In.) Length(cm) Swing Period
6.5 16.51 22.50984266 0.888500213
9 22.86 19.42452257 1.029626336
11.5 29.21 17.38305436 1.150545789
14.5 36.83 15.65029416 1.277931251
18 45.72 14.19004475 1.409438825
21 53.34 13.23295603 1.51137810424 60.96 12.4562271 1.605622621
27 68.58 11.80903541 1.693618429
30 76.2 11.25864905 1.776412065
37.5 95.25 10.17620965 1.965368314
y = 0.0136x + 0.7442
R = 0.9825
0
0.5
1
1.5
2
2.5
0 20 40 60 80 100 120
Series1
Linear (Series1)