reza hakimimofrad growthcurves
TRANSCRIPT
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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