Reza Hakimimofrad GrowthCurves

7/31/2019 Reza Hakimimofrad GrowthCurves

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Linear

Simple Growth

20.00%

Time Amount 1st Diff

0 1.001 1.20 0.20

2 1.40 0.20

3 1.60 0.20

4 1.80 0.20

5 2.00 0.20

6 2.20 0.20

7 2.40 0.20

8 2.60 0.20

9 2.80 0.20

10 3.00 0.20

Fitting the "Curve"

Slope 0.200

Std Error 0.000

R^2 1.000

F Value 1.52E+32

Linear Fitting SSR 4.400

SUMMARY OUTPUT

Regression Statistics

Multiple R 1R Square 1

Adjusted R Square 1

Standard Error 5.1942E-16

Observations 11

ANOVA

df SS MS F nificance F

Using L

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0

Amount

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Linear

Regression 1 4.4 4.4 1.6E+31 2E-137

Residual 9 2.4E-30 3E-31

Total 10 4.4

Coefficients ndard E t Stat P-value ower 95 Upper 95%

Intercept 1 2.9E-16 3E+15 8E-137 1 1

X Variable 1 0.2 5E-17 4E+15 2E-137 0.2 0.2

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Linear

The array function returns the following values:

1.000 Intercept

0.000 Std Error

0.000 Std Error of Est

9.000 df

0.000 SSE

Highlight 5 rows plus number of

colums equal to the total number ofnest

(Note: for multiple regression the values are in the order reading right

to left starting with the intercept)

2 4 6 8 10 12

Time

Simple Growth20.00%

Amount 1st Diff

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Quadratic

Quadratic Growth

10%

Time Amount 1st Diff 2nd Diff

0 1.001 1.20 0.20

2 1.60 0.40 0.20

3 2.20 0.60 0.20

4 3.00 0.80 0.20

5 4.00 1.00 0.20

6 5.20 1.20 0.20

7 6.60 1.40 0.20

8 8.20 1.60 0.20

9 10.00 1.80 0.20

10 12.00 2.00 0.20

10%

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

0 2 4

Amount

Quadra

Amount

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Quadratic

0%

2%

4%

6%

8%

10%

12%

6 8 10 12

Time

tic Growth

1st Diff 2nd Diff

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Cubic

Cubic Growth

20%

Time Amount 1st Diff 2nd Diff 3rd Diff

0 1.001 1.60 0.60

2 3.80 2.20 1.60

3 8.80 5.00 2.80 1.20

4 17.80 9.00 4.00 1.20

5 32.00 14.20 5.20 1.20

6 52.60 20.60 6.40 1.20

7 80.80 28.20 7.60 1.20

8 117.80 37.00 8.80 1.20

9 164.80 47.00 10.00 1.20

10 223.00 58.20 11.20 1.20

20%

0.00

50.00

100.00

150.00

200.00

250.00

0 2

Amount

Cu

Amount 1

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Cubic

0.00

50.00

100.00

150.00

200.00

250.00

0 5

Amount

Cubic20.

A

0%

5%

10%

15%

20%

25%

4 6 8 10 12

Time

ic Growth

st Diff 2nd Diff 3rd Diff

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Cubic

10 15

Time

Growth.00%

ount Series2

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Compound

Compound Growth

y=a(1+I)(^t)

0.30 30%

Time Amount 1st Diff 2nd Diff 3rd Diff @LN(Amount)0 1.00 0

1 1.30 0.30 0.2624

2 1.69 0.39 0.09 0.5247

3 2.20 0.51 0.12 0.03 0.7871

4 2.86 0.66 0.15 0.04 1.0495

5 3.71 0.86 0.20 0.05 1.3118

6 4.83 1.11 0.26 0.06 1.5742

7 6.27 1.45 0.33 0.08 1.8365

8 8.16 1.88 0.43 0.10 2.0989

9 10.60 2.45 0.56 0.13 2.3613

10 13.79 3.18 0.73 0.17 2.6236

30

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0

Amount

Amount

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Compound

0%

5%

10%

15%

20%

25%

30%

35%

2 4 6 8 10 12

Time

Compound Growth

1st Difference 2nd Diff 3rd Diff Series4

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Compound Fit

Compound Growth (Semi Log)

y=a(b)(^t) Ln(Est) = e0.172+0.281T Alternativ

Time Value ln(Value) ln(Estimated) Exp (Est) Error

0 1.00000 0.00000 0.17221 1.18792 -0.1879

1 1.76518 0.56825 0.45337 1.57361 0.19162 2.59258 0.95265 0.73453 2.08451 0.5081

3 2.83009 1.04031 1.01570 2.76129 0.0688

4 2.94917 1.08152 1.29686 3.65780 -0.7086

5 5.70597 1.74151 1.57803 4.84538 0.8606

6 5.81607 1.76063 1.85919 6.41854 -0.6025

7 8.58926 2.15051 2.14035 8.50245 0.0868

8 8.87155 2.18285 2.42152 11.26294 -2.3914

9 16.26919 2.78927 2.70268 14.91969 1.3495

10 21.99407 3.09077 2.98385 19.76368 2.2304

Used the regression feature to do the following

Regression Statistics

Multiple R 0.9859

R Square 0.9721

Adjusted R Square 0.9690

Standard Error 0.1666

Observations 11

ANOVA

df SS MS F Significance F

Regression 1.0000 8.6959 8.6959 313.2437 0.0000

Residual 9.0000 0.2498 0.0278

Total 10.0000 8.9457

Coefficien Standard Error t Statistic P-value Lower 95. Upper 95.

Intercept 0.1722 0.0940 1.8323 0.0968 -0.0404 0.3848

x1 0.2812 0.0159 17.6987 0.0000 0.2452 0.3171

1

1

2

2

Values

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Compound Fit

exp(x1) = 1.32467

xp(Intercept) = 1.18792

e:

Estimate = 1.188(1.325)^t

1.18792

1.573612.08451

2.76129

3.65780

4.84538

6.41854

8.50245

11.26294

14.91969

19.76368

00

.0

.0

.0

.0

.0

.0

0 5 10 15

Time

Data

Actual Est

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Log

Log

y=a + exp(bt)

1 0.20 2

1 2.221403

2 2.491825

3 2.822119

4 3.225541

5 3.718282

6 4.320117

7 5.0552

8 5.953032

9 7.049647

10 8.389056

11 10.02501

12 12.0231813 14.46374

14 17.44465

15 21.08554

16 25.53253

17 30.9641

18 37.59823

19 45.70118

20 55.59815

21 67.68633

22 82.45087

23 100.4843

24 122.510425 149.4132

0

20

40

60

80

100

120

140

0 5 10 15

Amount

Time

Log Growth

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Log

20 25 30

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ModLog

Modified Log

y=a - b exp(-gt)

20 5 0.20 15

1 15.90635

2 16.6484

3 17.25594

4 17.75336

5 18.1606

6 18.49403

7 18.76702

8 18.99052

9 19.17351

10 19.32332

11 19.44598

12 19.5464113 19.62863

14 19.69595

15 19.75106

16 19.79619

17 19.83313

18 19.86338

19 19.88815

20 19.90842

21 19.92502

22 19.93861

23 19.94974

24 19.9588525 19.96631

0

5

10

15

20

25

0 5 10

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ModLog

15 20 25 30

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Logistic

Logistic

y=a /(1 + b exp(-gt))

400 15 0.350 25

1 34.57121

2 47.34412

3 64.00956

4 85.12532

5 110.9075

6 141.0016

7 174.3372

8 209.1885

9 243.4894

10 275.2999

11 303.215

12 326.548313 345.2717

14 359.8097

15 370.8123

16 378.9788

17 384.9531

18 389.2775

19 392.3837

20 394.6025

21 396.1813

22 397.3014

23 398.0945

24 398.655325 399.0515

0

50

100

150

200

250

300

350

400

450

0 10 20

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Logistic

30

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Gompertz

Gompertz

y=a*exp( - b exp(-gt))

40 8 0.20 0.013419

1 0.057213

2 0.187555

3 0.495785

4 1.098832

5 2.10822

6 3.594216

7 5.562812

8 7.954257

9 10.65989

10 13.54743

11 16.48505

12 19.3585813 22.08041

14 24.59145

15 26.85852

16 28.86939

17 30.62735

18 32.14605

19 33.44537

20 34.54816

21 35.47807

22 36.25802

23 36.90934

24 37.451325 37.90094

0

5

10

15

20

25

30

35

40

0 10 20

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Gompertz

30

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Fitting

Gompertz

y=a*exp( - b exp(-gt)Constraints => 0.00 0.00 0.00 ===================>

Parameters--------> 0.00 0.00 0.00Time Actual Estimated Errors Error Squared:

0 0.0134 0.0000 0.00 From Cell E33

1 0.8578 0.0000 0.74 27624.02

2 2.1144 0.0000 4.47

3 0.7045 0.0000 0.50

4 1.4474 0.0000 2.09

5 3.7459 0.0000 14.03

6 7.7099 0.0000 59.44

7 8.4362 0.0000 71.17

8 12.6409 0.0000 159.799 15.8914 0.0000 252.54

10 20.6619 0.0000 426.92

11 23.6281 0.0000 558.29

12 24.9492 0.0000 622.46

13 24.2994 0.0000 590.46

14 38.3605 0.0000 1471.53 To try the fit choose the so

15 31.0265 0.0000 962.64 minimize the error sum of

16 29.4591 0.0000 867.84 while choosing the values

17 45.0139 0.0000 2026.25 d5..f5. These parameters a

18 46.6111 0.0000 2172.59 values in d3..f3.19 43.0402 0.0000 1852.46

20 50.6268 0.0000 2563.07

21 54.2022 0.0000 2937.88

22 53.6476 0.0000 2878.07

23 47.5499 0.0000 2261.00

24 47.0321 0.0000 2212.01

25 51.5343 0.0000 2655.78

Sum Error ^2 = 27624.02

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0

Values

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Fitting

Try These

0.00 5.00 0.10

lver function and

quares in cell E33,

or the parameters in

e constrained by the

5 10 15 20 25 30

Time

Data

Actual Fitted

Documents

Reza Hakimimofrad GrowthCurves