math assignment 5

8/3/2019 Math Assignment 5

1/19

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


Multiple R 0.973155

R Square 0.947031

Adjusted R 0.94041


ANOVA


Regression 1 0.555512 0.555512 143.0316 2.2E-06

Residual 8 0.031071 0.003884

Total 9 0.586583


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


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

-0.05

0

0.05

0.1

0.000 20.000 40.000 60.000 80.000 100.000 120.000Residuals

X Variable 1



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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

0

5

10

15

20

25

0 20 40 60 80 100 120

NumberofSwings

Length (cm)

Graph of Number of Swings Against Length (cm)


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b)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120Residuals

Length (cm)



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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

10

15

20

25

0 20 40 60 80 100 120

NumberofSwings

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

0

5

10

15

20

25

0 20 40 60 80 100 120

NumberofSwings

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

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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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


Multiple R 0.943585

R Square 0.890352

Adjusted R 0.876646


ANOVA


Regression 1 122.5124 122.5124 64.9606 4.14E-05

Residual 8 15.08759 1.885949

Total 9 137.6


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


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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-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120Residuals

X Variable 1



13/19

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

0

5

10

15

20

25

0 20 40 60 80 1


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00 120

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

5

10

15

20

25

0 20 40 60 80 1


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00 120

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

1

1.5

2

2.5

0 20 40 60 80 1


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00 120

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)

math assignment 5

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