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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 May 2014 10:06:52 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/20/t14005948460740eh9pfih7g7v.htm/, Retrieved Wed, 15 May 2024 14:39:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234990, Retrieved Wed, 15 May 2024 14:39:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2014-04-28 15:57:15] [ccb4fa85fbb66dbee3adf4746bc114a3]
- RMPD    [Exponential Smoothing] [] [2014-05-20 14:06:52] [c97636ecf0aef6cf672ffb6fe15d6b60] [Current]
- R PD      [Exponential Smoothing] [] [2014-05-21 07:36:51] [ccb4fa85fbb66dbee3adf4746bc114a3]
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Dataseries X:
2,79
3,08
3,89
3,7
4,61
5,07
5,22
4,93
5,15
4,8
3,89
3,54
3,34
2,8
1,6
1,53
0,69
-0,11
-0,67
-0,2
-0,62
-0,58
-0,31
-0,25
-0,08
0,13
0,94
1,05
1,59
2,03
2,15
2,06
2,56
2,55
2,53
2,6
2,71
2,82
2,93
2,88
2,89
3,27
3,32
3,14
3,04
3,08
3,39
3,23
3,38
3,41
3,14
2,96
2,73
2,21
2,23
2,56
2,39
2,49
2,17
2,16
1,48
1,09
1,25
1,26
1,39
1,69
1,55
1,19
1,08
0,93
0,98
1,01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234990&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234990&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919534147806
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999919534147806 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234990&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999919534147806[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234990&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999919534147806
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23.082.790.29
33.893.079976664902860.810023335097136
43.73.88993482078204-0.189934820782044
54.613.700015283267220.909984716732784
65.074.609926777304280.460073222695716
75.225.069962979816060.150037020183936
84.935.21998792714331-0.289987927143311
95.154.930023334125680.219976665874317
104.85.14998229939012-0.349982299390118
113.894.80002816162397-0.910028161623973
123.543.89007322619155-0.350073226191546
133.343.54002816894048-0.200028168940476
142.83.34001609543708-0.540016095437077
151.62.80004345285532-1.20004345285532
161.531.6000965625191-0.0700965625191041
170.691.53000564037964-0.840005640379639
18-0.110.690067591769701-0.800067591769701
19-0.67-0.109935621879415-0.560064378120585
20-0.2-0.6699549339425310.469954933942531
21-0.62-0.200037815324253-0.419962184675747
22-0.58-0.6199662073849210.0399662073849208
23-0.31-0.5800032159149360.270003215914936
24-0.25-0.3100217260388640.0600217260388637
25-0.08-0.2500048296993360.170004829699336
260.13-0.08001367958349890.210013679583499
270.940.12998310107030.8100168989297
281.050.9399348212999360.110065178700064
291.591.04999114351160.540008856488401
302.031.589956547727170.440043452272829
312.152.029964591528610.12003540847139
322.062.14999034124856-0.0899903412485639
332.562.06000724114950.499992758850502
342.552.55995976765657-0.00995976765656836
352.532.55000080142119-0.0200008014211921
362.62.530001609381530.0699983906184696
372.712.599994367519850.110005632480153
382.822.709991148303040.110008851696964
392.932.8199911480440.110008851956001
402.882.92999114804398-0.0499911480439788
412.892.880004022580330.00999597741967051
423.272.889999195665160.380000804334841
433.323.269969422911440.0500305770885552
443.143.31999597424698-0.179995974246979
453.043.14001448352946-0.100014483529459
463.083.040008047750650.039991952249351
473.393.079996782013480.310003217986519
483.233.38997505532688-0.159975055326882
493.383.230012872529160.149987127470843
503.413.379987931157970.0300120688420304
513.143.4099975850533-0.269997585053305
522.963.14002172558577-0.180021725585772
532.732.96001448560156-0.230014485601563
542.212.7300185083116-0.520018508311601
552.232.210041843732430.0199581562675721
562.562.229998394049950.330001605950053
572.392.55997344613955-0.169973446139552
582.492.390013677058190.0999863229418061
592.172.48999195451532-0.319991954515317
602.162.17002574842532-0.0100257484253152
611.482.16000080673039-0.680000806730391
621.091.48005471684441-0.390054716844406
631.251.090031386085190.159968613914807
641.261.249987127989160.010012872010843
651.391.259999194305720.130000805694279
661.691.389989539374380.300010460625616
671.551.68997585940262-0.139975859402619
681.191.55001126327681-0.360011263276814
691.081.1900289686131-0.110028968613099
700.931.08000885357473-0.150008853574726
710.980.930012070590240.0499879294097604
721.010.9799959776786610.0300040223213394

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3.08 & 2.79 & 0.29 \tabularnewline
3 & 3.89 & 3.07997666490286 & 0.810023335097136 \tabularnewline
4 & 3.7 & 3.88993482078204 & -0.189934820782044 \tabularnewline
5 & 4.61 & 3.70001528326722 & 0.909984716732784 \tabularnewline
6 & 5.07 & 4.60992677730428 & 0.460073222695716 \tabularnewline
7 & 5.22 & 5.06996297981606 & 0.150037020183936 \tabularnewline
8 & 4.93 & 5.21998792714331 & -0.289987927143311 \tabularnewline
9 & 5.15 & 4.93002333412568 & 0.219976665874317 \tabularnewline
10 & 4.8 & 5.14998229939012 & -0.349982299390118 \tabularnewline
11 & 3.89 & 4.80002816162397 & -0.910028161623973 \tabularnewline
12 & 3.54 & 3.89007322619155 & -0.350073226191546 \tabularnewline
13 & 3.34 & 3.54002816894048 & -0.200028168940476 \tabularnewline
14 & 2.8 & 3.34001609543708 & -0.540016095437077 \tabularnewline
15 & 1.6 & 2.80004345285532 & -1.20004345285532 \tabularnewline
16 & 1.53 & 1.6000965625191 & -0.0700965625191041 \tabularnewline
17 & 0.69 & 1.53000564037964 & -0.840005640379639 \tabularnewline
18 & -0.11 & 0.690067591769701 & -0.800067591769701 \tabularnewline
19 & -0.67 & -0.109935621879415 & -0.560064378120585 \tabularnewline
20 & -0.2 & -0.669954933942531 & 0.469954933942531 \tabularnewline
21 & -0.62 & -0.200037815324253 & -0.419962184675747 \tabularnewline
22 & -0.58 & -0.619966207384921 & 0.0399662073849208 \tabularnewline
23 & -0.31 & -0.580003215914936 & 0.270003215914936 \tabularnewline
24 & -0.25 & -0.310021726038864 & 0.0600217260388637 \tabularnewline
25 & -0.08 & -0.250004829699336 & 0.170004829699336 \tabularnewline
26 & 0.13 & -0.0800136795834989 & 0.210013679583499 \tabularnewline
27 & 0.94 & 0.1299831010703 & 0.8100168989297 \tabularnewline
28 & 1.05 & 0.939934821299936 & 0.110065178700064 \tabularnewline
29 & 1.59 & 1.0499911435116 & 0.540008856488401 \tabularnewline
30 & 2.03 & 1.58995654772717 & 0.440043452272829 \tabularnewline
31 & 2.15 & 2.02996459152861 & 0.12003540847139 \tabularnewline
32 & 2.06 & 2.14999034124856 & -0.0899903412485639 \tabularnewline
33 & 2.56 & 2.0600072411495 & 0.499992758850502 \tabularnewline
34 & 2.55 & 2.55995976765657 & -0.00995976765656836 \tabularnewline
35 & 2.53 & 2.55000080142119 & -0.0200008014211921 \tabularnewline
36 & 2.6 & 2.53000160938153 & 0.0699983906184696 \tabularnewline
37 & 2.71 & 2.59999436751985 & 0.110005632480153 \tabularnewline
38 & 2.82 & 2.70999114830304 & 0.110008851696964 \tabularnewline
39 & 2.93 & 2.819991148044 & 0.110008851956001 \tabularnewline
40 & 2.88 & 2.92999114804398 & -0.0499911480439788 \tabularnewline
41 & 2.89 & 2.88000402258033 & 0.00999597741967051 \tabularnewline
42 & 3.27 & 2.88999919566516 & 0.380000804334841 \tabularnewline
43 & 3.32 & 3.26996942291144 & 0.0500305770885552 \tabularnewline
44 & 3.14 & 3.31999597424698 & -0.179995974246979 \tabularnewline
45 & 3.04 & 3.14001448352946 & -0.100014483529459 \tabularnewline
46 & 3.08 & 3.04000804775065 & 0.039991952249351 \tabularnewline
47 & 3.39 & 3.07999678201348 & 0.310003217986519 \tabularnewline
48 & 3.23 & 3.38997505532688 & -0.159975055326882 \tabularnewline
49 & 3.38 & 3.23001287252916 & 0.149987127470843 \tabularnewline
50 & 3.41 & 3.37998793115797 & 0.0300120688420304 \tabularnewline
51 & 3.14 & 3.4099975850533 & -0.269997585053305 \tabularnewline
52 & 2.96 & 3.14002172558577 & -0.180021725585772 \tabularnewline
53 & 2.73 & 2.96001448560156 & -0.230014485601563 \tabularnewline
54 & 2.21 & 2.7300185083116 & -0.520018508311601 \tabularnewline
55 & 2.23 & 2.21004184373243 & 0.0199581562675721 \tabularnewline
56 & 2.56 & 2.22999839404995 & 0.330001605950053 \tabularnewline
57 & 2.39 & 2.55997344613955 & -0.169973446139552 \tabularnewline
58 & 2.49 & 2.39001367705819 & 0.0999863229418061 \tabularnewline
59 & 2.17 & 2.48999195451532 & -0.319991954515317 \tabularnewline
60 & 2.16 & 2.17002574842532 & -0.0100257484253152 \tabularnewline
61 & 1.48 & 2.16000080673039 & -0.680000806730391 \tabularnewline
62 & 1.09 & 1.48005471684441 & -0.390054716844406 \tabularnewline
63 & 1.25 & 1.09003138608519 & 0.159968613914807 \tabularnewline
64 & 1.26 & 1.24998712798916 & 0.010012872010843 \tabularnewline
65 & 1.39 & 1.25999919430572 & 0.130000805694279 \tabularnewline
66 & 1.69 & 1.38998953937438 & 0.300010460625616 \tabularnewline
67 & 1.55 & 1.68997585940262 & -0.139975859402619 \tabularnewline
68 & 1.19 & 1.55001126327681 & -0.360011263276814 \tabularnewline
69 & 1.08 & 1.1900289686131 & -0.110028968613099 \tabularnewline
70 & 0.93 & 1.08000885357473 & -0.150008853574726 \tabularnewline
71 & 0.98 & 0.93001207059024 & 0.0499879294097604 \tabularnewline
72 & 1.01 & 0.979995977678661 & 0.0300040223213394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234990&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]3.08[/C][C]2.79[/C][C]0.29[/C][/ROW]
[ROW][C]3[/C][C]3.89[/C][C]3.07997666490286[/C][C]0.810023335097136[/C][/ROW]
[ROW][C]4[/C][C]3.7[/C][C]3.88993482078204[/C][C]-0.189934820782044[/C][/ROW]
[ROW][C]5[/C][C]4.61[/C][C]3.70001528326722[/C][C]0.909984716732784[/C][/ROW]
[ROW][C]6[/C][C]5.07[/C][C]4.60992677730428[/C][C]0.460073222695716[/C][/ROW]
[ROW][C]7[/C][C]5.22[/C][C]5.06996297981606[/C][C]0.150037020183936[/C][/ROW]
[ROW][C]8[/C][C]4.93[/C][C]5.21998792714331[/C][C]-0.289987927143311[/C][/ROW]
[ROW][C]9[/C][C]5.15[/C][C]4.93002333412568[/C][C]0.219976665874317[/C][/ROW]
[ROW][C]10[/C][C]4.8[/C][C]5.14998229939012[/C][C]-0.349982299390118[/C][/ROW]
[ROW][C]11[/C][C]3.89[/C][C]4.80002816162397[/C][C]-0.910028161623973[/C][/ROW]
[ROW][C]12[/C][C]3.54[/C][C]3.89007322619155[/C][C]-0.350073226191546[/C][/ROW]
[ROW][C]13[/C][C]3.34[/C][C]3.54002816894048[/C][C]-0.200028168940476[/C][/ROW]
[ROW][C]14[/C][C]2.8[/C][C]3.34001609543708[/C][C]-0.540016095437077[/C][/ROW]
[ROW][C]15[/C][C]1.6[/C][C]2.80004345285532[/C][C]-1.20004345285532[/C][/ROW]
[ROW][C]16[/C][C]1.53[/C][C]1.6000965625191[/C][C]-0.0700965625191041[/C][/ROW]
[ROW][C]17[/C][C]0.69[/C][C]1.53000564037964[/C][C]-0.840005640379639[/C][/ROW]
[ROW][C]18[/C][C]-0.11[/C][C]0.690067591769701[/C][C]-0.800067591769701[/C][/ROW]
[ROW][C]19[/C][C]-0.67[/C][C]-0.109935621879415[/C][C]-0.560064378120585[/C][/ROW]
[ROW][C]20[/C][C]-0.2[/C][C]-0.669954933942531[/C][C]0.469954933942531[/C][/ROW]
[ROW][C]21[/C][C]-0.62[/C][C]-0.200037815324253[/C][C]-0.419962184675747[/C][/ROW]
[ROW][C]22[/C][C]-0.58[/C][C]-0.619966207384921[/C][C]0.0399662073849208[/C][/ROW]
[ROW][C]23[/C][C]-0.31[/C][C]-0.580003215914936[/C][C]0.270003215914936[/C][/ROW]
[ROW][C]24[/C][C]-0.25[/C][C]-0.310021726038864[/C][C]0.0600217260388637[/C][/ROW]
[ROW][C]25[/C][C]-0.08[/C][C]-0.250004829699336[/C][C]0.170004829699336[/C][/ROW]
[ROW][C]26[/C][C]0.13[/C][C]-0.0800136795834989[/C][C]0.210013679583499[/C][/ROW]
[ROW][C]27[/C][C]0.94[/C][C]0.1299831010703[/C][C]0.8100168989297[/C][/ROW]
[ROW][C]28[/C][C]1.05[/C][C]0.939934821299936[/C][C]0.110065178700064[/C][/ROW]
[ROW][C]29[/C][C]1.59[/C][C]1.0499911435116[/C][C]0.540008856488401[/C][/ROW]
[ROW][C]30[/C][C]2.03[/C][C]1.58995654772717[/C][C]0.440043452272829[/C][/ROW]
[ROW][C]31[/C][C]2.15[/C][C]2.02996459152861[/C][C]0.12003540847139[/C][/ROW]
[ROW][C]32[/C][C]2.06[/C][C]2.14999034124856[/C][C]-0.0899903412485639[/C][/ROW]
[ROW][C]33[/C][C]2.56[/C][C]2.0600072411495[/C][C]0.499992758850502[/C][/ROW]
[ROW][C]34[/C][C]2.55[/C][C]2.55995976765657[/C][C]-0.00995976765656836[/C][/ROW]
[ROW][C]35[/C][C]2.53[/C][C]2.55000080142119[/C][C]-0.0200008014211921[/C][/ROW]
[ROW][C]36[/C][C]2.6[/C][C]2.53000160938153[/C][C]0.0699983906184696[/C][/ROW]
[ROW][C]37[/C][C]2.71[/C][C]2.59999436751985[/C][C]0.110005632480153[/C][/ROW]
[ROW][C]38[/C][C]2.82[/C][C]2.70999114830304[/C][C]0.110008851696964[/C][/ROW]
[ROW][C]39[/C][C]2.93[/C][C]2.819991148044[/C][C]0.110008851956001[/C][/ROW]
[ROW][C]40[/C][C]2.88[/C][C]2.92999114804398[/C][C]-0.0499911480439788[/C][/ROW]
[ROW][C]41[/C][C]2.89[/C][C]2.88000402258033[/C][C]0.00999597741967051[/C][/ROW]
[ROW][C]42[/C][C]3.27[/C][C]2.88999919566516[/C][C]0.380000804334841[/C][/ROW]
[ROW][C]43[/C][C]3.32[/C][C]3.26996942291144[/C][C]0.0500305770885552[/C][/ROW]
[ROW][C]44[/C][C]3.14[/C][C]3.31999597424698[/C][C]-0.179995974246979[/C][/ROW]
[ROW][C]45[/C][C]3.04[/C][C]3.14001448352946[/C][C]-0.100014483529459[/C][/ROW]
[ROW][C]46[/C][C]3.08[/C][C]3.04000804775065[/C][C]0.039991952249351[/C][/ROW]
[ROW][C]47[/C][C]3.39[/C][C]3.07999678201348[/C][C]0.310003217986519[/C][/ROW]
[ROW][C]48[/C][C]3.23[/C][C]3.38997505532688[/C][C]-0.159975055326882[/C][/ROW]
[ROW][C]49[/C][C]3.38[/C][C]3.23001287252916[/C][C]0.149987127470843[/C][/ROW]
[ROW][C]50[/C][C]3.41[/C][C]3.37998793115797[/C][C]0.0300120688420304[/C][/ROW]
[ROW][C]51[/C][C]3.14[/C][C]3.4099975850533[/C][C]-0.269997585053305[/C][/ROW]
[ROW][C]52[/C][C]2.96[/C][C]3.14002172558577[/C][C]-0.180021725585772[/C][/ROW]
[ROW][C]53[/C][C]2.73[/C][C]2.96001448560156[/C][C]-0.230014485601563[/C][/ROW]
[ROW][C]54[/C][C]2.21[/C][C]2.7300185083116[/C][C]-0.520018508311601[/C][/ROW]
[ROW][C]55[/C][C]2.23[/C][C]2.21004184373243[/C][C]0.0199581562675721[/C][/ROW]
[ROW][C]56[/C][C]2.56[/C][C]2.22999839404995[/C][C]0.330001605950053[/C][/ROW]
[ROW][C]57[/C][C]2.39[/C][C]2.55997344613955[/C][C]-0.169973446139552[/C][/ROW]
[ROW][C]58[/C][C]2.49[/C][C]2.39001367705819[/C][C]0.0999863229418061[/C][/ROW]
[ROW][C]59[/C][C]2.17[/C][C]2.48999195451532[/C][C]-0.319991954515317[/C][/ROW]
[ROW][C]60[/C][C]2.16[/C][C]2.17002574842532[/C][C]-0.0100257484253152[/C][/ROW]
[ROW][C]61[/C][C]1.48[/C][C]2.16000080673039[/C][C]-0.680000806730391[/C][/ROW]
[ROW][C]62[/C][C]1.09[/C][C]1.48005471684441[/C][C]-0.390054716844406[/C][/ROW]
[ROW][C]63[/C][C]1.25[/C][C]1.09003138608519[/C][C]0.159968613914807[/C][/ROW]
[ROW][C]64[/C][C]1.26[/C][C]1.24998712798916[/C][C]0.010012872010843[/C][/ROW]
[ROW][C]65[/C][C]1.39[/C][C]1.25999919430572[/C][C]0.130000805694279[/C][/ROW]
[ROW][C]66[/C][C]1.69[/C][C]1.38998953937438[/C][C]0.300010460625616[/C][/ROW]
[ROW][C]67[/C][C]1.55[/C][C]1.68997585940262[/C][C]-0.139975859402619[/C][/ROW]
[ROW][C]68[/C][C]1.19[/C][C]1.55001126327681[/C][C]-0.360011263276814[/C][/ROW]
[ROW][C]69[/C][C]1.08[/C][C]1.1900289686131[/C][C]-0.110028968613099[/C][/ROW]
[ROW][C]70[/C][C]0.93[/C][C]1.08000885357473[/C][C]-0.150008853574726[/C][/ROW]
[ROW][C]71[/C][C]0.98[/C][C]0.93001207059024[/C][C]0.0499879294097604[/C][/ROW]
[ROW][C]72[/C][C]1.01[/C][C]0.979995977678661[/C][C]0.0300040223213394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234990&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234990&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23.082.790.29
33.893.079976664902860.810023335097136
43.73.88993482078204-0.189934820782044
54.613.700015283267220.909984716732784
65.074.609926777304280.460073222695716
75.225.069962979816060.150037020183936
84.935.21998792714331-0.289987927143311
95.154.930023334125680.219976665874317
104.85.14998229939012-0.349982299390118
113.894.80002816162397-0.910028161623973
123.543.89007322619155-0.350073226191546
133.343.54002816894048-0.200028168940476
142.83.34001609543708-0.540016095437077
151.62.80004345285532-1.20004345285532
161.531.6000965625191-0.0700965625191041
170.691.53000564037964-0.840005640379639
18-0.110.690067591769701-0.800067591769701
19-0.67-0.109935621879415-0.560064378120585
20-0.2-0.6699549339425310.469954933942531
21-0.62-0.200037815324253-0.419962184675747
22-0.58-0.6199662073849210.0399662073849208
23-0.31-0.5800032159149360.270003215914936
24-0.25-0.3100217260388640.0600217260388637
25-0.08-0.2500048296993360.170004829699336
260.13-0.08001367958349890.210013679583499
270.940.12998310107030.8100168989297
281.050.9399348212999360.110065178700064
291.591.04999114351160.540008856488401
302.031.589956547727170.440043452272829
312.152.029964591528610.12003540847139
322.062.14999034124856-0.0899903412485639
332.562.06000724114950.499992758850502
342.552.55995976765657-0.00995976765656836
352.532.55000080142119-0.0200008014211921
362.62.530001609381530.0699983906184696
372.712.599994367519850.110005632480153
382.822.709991148303040.110008851696964
392.932.8199911480440.110008851956001
402.882.92999114804398-0.0499911480439788
412.892.880004022580330.00999597741967051
423.272.889999195665160.380000804334841
433.323.269969422911440.0500305770885552
443.143.31999597424698-0.179995974246979
453.043.14001448352946-0.100014483529459
463.083.040008047750650.039991952249351
473.393.079996782013480.310003217986519
483.233.38997505532688-0.159975055326882
493.383.230012872529160.149987127470843
503.413.379987931157970.0300120688420304
513.143.4099975850533-0.269997585053305
522.963.14002172558577-0.180021725585772
532.732.96001448560156-0.230014485601563
542.212.7300185083116-0.520018508311601
552.232.210041843732430.0199581562675721
562.562.229998394049950.330001605950053
572.392.55997344613955-0.169973446139552
582.492.390013677058190.0999863229418061
592.172.48999195451532-0.319991954515317
602.162.17002574842532-0.0100257484253152
611.482.16000080673039-0.680000806730391
621.091.48005471684441-0.390054716844406
631.251.090031386085190.159968613914807
641.261.249987127989160.010012872010843
651.391.259999194305720.130000805694279
661.691.389989539374380.300010460625616
671.551.68997585940262-0.139975859402619
681.191.55001126327681-0.360011263276814
691.081.1900289686131-0.110028968613099
700.931.08000885357473-0.150008853574726
710.980.930012070590240.0499879294097604
721.010.9799959776786610.0300040223213394







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.009997585700770.2543875142719781.76560765712957
741.00999758570077-0.05855343338056062.07854860478211
751.00999758570077-0.2986872429401362.31868241434168
761.00999758570077-0.5011313568617122.52112652826326
771.00999758570077-0.6794891355803212.69948430698187
781.00999758570077-0.8407374255097112.86073259691126
791.00999758570077-0.9890208689552613.00901604035681
801.00999758570077-1.127039962493113.14703513389466
811.00999758570077-1.25667049382163.27666566522315
821.00999758570077-1.37927822153893.39927339294045
831.00999758570077-1.495894188378053.5158893597796
841.00999758570077-1.607319415300643.62731458670219

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.00999758570077 & 0.254387514271978 & 1.76560765712957 \tabularnewline
74 & 1.00999758570077 & -0.0585534333805606 & 2.07854860478211 \tabularnewline
75 & 1.00999758570077 & -0.298687242940136 & 2.31868241434168 \tabularnewline
76 & 1.00999758570077 & -0.501131356861712 & 2.52112652826326 \tabularnewline
77 & 1.00999758570077 & -0.679489135580321 & 2.69948430698187 \tabularnewline
78 & 1.00999758570077 & -0.840737425509711 & 2.86073259691126 \tabularnewline
79 & 1.00999758570077 & -0.989020868955261 & 3.00901604035681 \tabularnewline
80 & 1.00999758570077 & -1.12703996249311 & 3.14703513389466 \tabularnewline
81 & 1.00999758570077 & -1.2566704938216 & 3.27666566522315 \tabularnewline
82 & 1.00999758570077 & -1.3792782215389 & 3.39927339294045 \tabularnewline
83 & 1.00999758570077 & -1.49589418837805 & 3.5158893597796 \tabularnewline
84 & 1.00999758570077 & -1.60731941530064 & 3.62731458670219 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234990&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]1.00999758570077[/C][C]0.254387514271978[/C][C]1.76560765712957[/C][/ROW]
[ROW][C]74[/C][C]1.00999758570077[/C][C]-0.0585534333805606[/C][C]2.07854860478211[/C][/ROW]
[ROW][C]75[/C][C]1.00999758570077[/C][C]-0.298687242940136[/C][C]2.31868241434168[/C][/ROW]
[ROW][C]76[/C][C]1.00999758570077[/C][C]-0.501131356861712[/C][C]2.52112652826326[/C][/ROW]
[ROW][C]77[/C][C]1.00999758570077[/C][C]-0.679489135580321[/C][C]2.69948430698187[/C][/ROW]
[ROW][C]78[/C][C]1.00999758570077[/C][C]-0.840737425509711[/C][C]2.86073259691126[/C][/ROW]
[ROW][C]79[/C][C]1.00999758570077[/C][C]-0.989020868955261[/C][C]3.00901604035681[/C][/ROW]
[ROW][C]80[/C][C]1.00999758570077[/C][C]-1.12703996249311[/C][C]3.14703513389466[/C][/ROW]
[ROW][C]81[/C][C]1.00999758570077[/C][C]-1.2566704938216[/C][C]3.27666566522315[/C][/ROW]
[ROW][C]82[/C][C]1.00999758570077[/C][C]-1.3792782215389[/C][C]3.39927339294045[/C][/ROW]
[ROW][C]83[/C][C]1.00999758570077[/C][C]-1.49589418837805[/C][C]3.5158893597796[/C][/ROW]
[ROW][C]84[/C][C]1.00999758570077[/C][C]-1.60731941530064[/C][C]3.62731458670219[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234990&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234990&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.009997585700770.2543875142719781.76560765712957
741.00999758570077-0.05855343338056062.07854860478211
751.00999758570077-0.2986872429401362.31868241434168
761.00999758570077-0.5011313568617122.52112652826326
771.00999758570077-0.6794891355803212.69948430698187
781.00999758570077-0.8407374255097112.86073259691126
791.00999758570077-0.9890208689552613.00901604035681
801.00999758570077-1.127039962493113.14703513389466
811.00999758570077-1.25667049382163.27666566522315
821.00999758570077-1.37927822153893.39927339294045
831.00999758570077-1.495894188378053.5158893597796
841.00999758570077-1.607319415300643.62731458670219



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')