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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 19 May 2012 15:33:08 -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/2012/May/19/t1337456001p5vlt3f9y3hmtlf.htm/, Retrieved Sun, 05 May 2024 19:40:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166763, Retrieved Sun, 05 May 2024 19:40:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-19 19:33:08] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
2,58
2,59
2,6
2,6
2,61
2,62
2,64
2,65
2,66
2,67
2,68
2,69
2,69
2,71
2,72
2,73
2,73
2,74
2,74
2,74
2,74
2,74
2,75
2,75
2,75
2,75
2,77
2,78
2,79
2,8
2,82
2,83
2,84
2,87
2,89
2,9
2,9
2,91
2,92
2,92
2,92
2,92
2,94
2,95
2,95
2,97
2,99
3
3
3,01
3,03
3,03
3,04
3,04
3,05
3,05
3,09
3,09
3,09
3,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166763&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166763&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999948929974004
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999948929974004 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166763&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]0.999948929974004[/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=166763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166763&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
alpha0.999948929974004
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22.592.580.00999999999999979
32.62.589999489299740.0100005107002601
42.62.599999489273665.10726341218515e-07
52.612.599999999973920.0100000000260825
62.622.609999489299740.0100005107002614
72.642.619999489273660.0200005107263412
82.652.63999897857340.0100010214266026
92.662.649999489247580.0100005107524246
102.672.659999489273660.0100005107263437
112.682.669999489273660.0100005107263428
122.692.679999489273660.0100005107263423
132.692.689999489273665.10726342550782e-07
142.712.689999999973920.0200000000260827
152.722.709998978599480.0100010214005213
162.732.719999489247580.0100005107524228
172.732.729999489273665.1072634388305e-07
182.742.729999999973920.0100000000260829
192.742.739999489299745.10700261191488e-07
202.742.739999999973922.60813592944942e-11
212.742.741.33226762955019e-15
222.742.740
232.752.740.00999999999999979
242.752.749999489299745.1070025985922e-07
252.752.749999999973922.60813592944942e-11
262.752.751.33226762955019e-15
272.772.750.02
282.782.769998978599480.0100010214005195
292.792.779999489247580.0100005107524233
302.82.789999489273660.0100005107263437
312.822.799999489273660.0200005107263426
322.832.81999897857340.0100010214266031
332.842.829999489247580.0100005107524241
342.872.839999489273660.0300005107263441
352.892.869998467873140.0200015321268627
362.92.889998978521230.0100010214787654
372.92.899999489247575.10752427018701e-07
382.912.899999999973920.0100000000260843
392.922.909999489299740.010000510700261
402.922.919999489273665.10726341218515e-07
412.922.919999999973922.60826915621237e-11
422.922.921.33226762955019e-15
432.942.920.02
442.952.939998978599480.0100010214005199
452.952.949999489247585.10752423021898e-07
462.972.949999999973920.020000000026084
472.992.969998978599480.0200010214005211
4832.989998978547320.0100010214526827
4932.999999489247575.10752425686434e-07
503.012.999999999973920.0100000000260838
513.033.009999489299740.0200005107002612
523.033.02999897857341.02142660152182e-06
533.043.029999999947840.0100000000521647
543.043.039999489299745.10700262523756e-07
553.053.039999999973920.0100000000260811
563.053.049999489299745.10700261191488e-07
573.093.049999999973920.0400000000260814
583.093.089997957198962.04280104121324e-06
593.093.089999999895671.04325881267187e-10
603.13.089999999999990.0100000000000056

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.59 & 2.58 & 0.00999999999999979 \tabularnewline
3 & 2.6 & 2.58999948929974 & 0.0100005107002601 \tabularnewline
4 & 2.6 & 2.59999948927366 & 5.10726341218515e-07 \tabularnewline
5 & 2.61 & 2.59999999997392 & 0.0100000000260825 \tabularnewline
6 & 2.62 & 2.60999948929974 & 0.0100005107002614 \tabularnewline
7 & 2.64 & 2.61999948927366 & 0.0200005107263412 \tabularnewline
8 & 2.65 & 2.6399989785734 & 0.0100010214266026 \tabularnewline
9 & 2.66 & 2.64999948924758 & 0.0100005107524246 \tabularnewline
10 & 2.67 & 2.65999948927366 & 0.0100005107263437 \tabularnewline
11 & 2.68 & 2.66999948927366 & 0.0100005107263428 \tabularnewline
12 & 2.69 & 2.67999948927366 & 0.0100005107263423 \tabularnewline
13 & 2.69 & 2.68999948927366 & 5.10726342550782e-07 \tabularnewline
14 & 2.71 & 2.68999999997392 & 0.0200000000260827 \tabularnewline
15 & 2.72 & 2.70999897859948 & 0.0100010214005213 \tabularnewline
16 & 2.73 & 2.71999948924758 & 0.0100005107524228 \tabularnewline
17 & 2.73 & 2.72999948927366 & 5.1072634388305e-07 \tabularnewline
18 & 2.74 & 2.72999999997392 & 0.0100000000260829 \tabularnewline
19 & 2.74 & 2.73999948929974 & 5.10700261191488e-07 \tabularnewline
20 & 2.74 & 2.73999999997392 & 2.60813592944942e-11 \tabularnewline
21 & 2.74 & 2.74 & 1.33226762955019e-15 \tabularnewline
22 & 2.74 & 2.74 & 0 \tabularnewline
23 & 2.75 & 2.74 & 0.00999999999999979 \tabularnewline
24 & 2.75 & 2.74999948929974 & 5.1070025985922e-07 \tabularnewline
25 & 2.75 & 2.74999999997392 & 2.60813592944942e-11 \tabularnewline
26 & 2.75 & 2.75 & 1.33226762955019e-15 \tabularnewline
27 & 2.77 & 2.75 & 0.02 \tabularnewline
28 & 2.78 & 2.76999897859948 & 0.0100010214005195 \tabularnewline
29 & 2.79 & 2.77999948924758 & 0.0100005107524233 \tabularnewline
30 & 2.8 & 2.78999948927366 & 0.0100005107263437 \tabularnewline
31 & 2.82 & 2.79999948927366 & 0.0200005107263426 \tabularnewline
32 & 2.83 & 2.8199989785734 & 0.0100010214266031 \tabularnewline
33 & 2.84 & 2.82999948924758 & 0.0100005107524241 \tabularnewline
34 & 2.87 & 2.83999948927366 & 0.0300005107263441 \tabularnewline
35 & 2.89 & 2.86999846787314 & 0.0200015321268627 \tabularnewline
36 & 2.9 & 2.88999897852123 & 0.0100010214787654 \tabularnewline
37 & 2.9 & 2.89999948924757 & 5.10752427018701e-07 \tabularnewline
38 & 2.91 & 2.89999999997392 & 0.0100000000260843 \tabularnewline
39 & 2.92 & 2.90999948929974 & 0.010000510700261 \tabularnewline
40 & 2.92 & 2.91999948927366 & 5.10726341218515e-07 \tabularnewline
41 & 2.92 & 2.91999999997392 & 2.60826915621237e-11 \tabularnewline
42 & 2.92 & 2.92 & 1.33226762955019e-15 \tabularnewline
43 & 2.94 & 2.92 & 0.02 \tabularnewline
44 & 2.95 & 2.93999897859948 & 0.0100010214005199 \tabularnewline
45 & 2.95 & 2.94999948924758 & 5.10752423021898e-07 \tabularnewline
46 & 2.97 & 2.94999999997392 & 0.020000000026084 \tabularnewline
47 & 2.99 & 2.96999897859948 & 0.0200010214005211 \tabularnewline
48 & 3 & 2.98999897854732 & 0.0100010214526827 \tabularnewline
49 & 3 & 2.99999948924757 & 5.10752425686434e-07 \tabularnewline
50 & 3.01 & 2.99999999997392 & 0.0100000000260838 \tabularnewline
51 & 3.03 & 3.00999948929974 & 0.0200005107002612 \tabularnewline
52 & 3.03 & 3.0299989785734 & 1.02142660152182e-06 \tabularnewline
53 & 3.04 & 3.02999999994784 & 0.0100000000521647 \tabularnewline
54 & 3.04 & 3.03999948929974 & 5.10700262523756e-07 \tabularnewline
55 & 3.05 & 3.03999999997392 & 0.0100000000260811 \tabularnewline
56 & 3.05 & 3.04999948929974 & 5.10700261191488e-07 \tabularnewline
57 & 3.09 & 3.04999999997392 & 0.0400000000260814 \tabularnewline
58 & 3.09 & 3.08999795719896 & 2.04280104121324e-06 \tabularnewline
59 & 3.09 & 3.08999999989567 & 1.04325881267187e-10 \tabularnewline
60 & 3.1 & 3.08999999999999 & 0.0100000000000056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166763&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]2.59[/C][C]2.58[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]3[/C][C]2.6[/C][C]2.58999948929974[/C][C]0.0100005107002601[/C][/ROW]
[ROW][C]4[/C][C]2.6[/C][C]2.59999948927366[/C][C]5.10726341218515e-07[/C][/ROW]
[ROW][C]5[/C][C]2.61[/C][C]2.59999999997392[/C][C]0.0100000000260825[/C][/ROW]
[ROW][C]6[/C][C]2.62[/C][C]2.60999948929974[/C][C]0.0100005107002614[/C][/ROW]
[ROW][C]7[/C][C]2.64[/C][C]2.61999948927366[/C][C]0.0200005107263412[/C][/ROW]
[ROW][C]8[/C][C]2.65[/C][C]2.6399989785734[/C][C]0.0100010214266026[/C][/ROW]
[ROW][C]9[/C][C]2.66[/C][C]2.64999948924758[/C][C]0.0100005107524246[/C][/ROW]
[ROW][C]10[/C][C]2.67[/C][C]2.65999948927366[/C][C]0.0100005107263437[/C][/ROW]
[ROW][C]11[/C][C]2.68[/C][C]2.66999948927366[/C][C]0.0100005107263428[/C][/ROW]
[ROW][C]12[/C][C]2.69[/C][C]2.67999948927366[/C][C]0.0100005107263423[/C][/ROW]
[ROW][C]13[/C][C]2.69[/C][C]2.68999948927366[/C][C]5.10726342550782e-07[/C][/ROW]
[ROW][C]14[/C][C]2.71[/C][C]2.68999999997392[/C][C]0.0200000000260827[/C][/ROW]
[ROW][C]15[/C][C]2.72[/C][C]2.70999897859948[/C][C]0.0100010214005213[/C][/ROW]
[ROW][C]16[/C][C]2.73[/C][C]2.71999948924758[/C][C]0.0100005107524228[/C][/ROW]
[ROW][C]17[/C][C]2.73[/C][C]2.72999948927366[/C][C]5.1072634388305e-07[/C][/ROW]
[ROW][C]18[/C][C]2.74[/C][C]2.72999999997392[/C][C]0.0100000000260829[/C][/ROW]
[ROW][C]19[/C][C]2.74[/C][C]2.73999948929974[/C][C]5.10700261191488e-07[/C][/ROW]
[ROW][C]20[/C][C]2.74[/C][C]2.73999999997392[/C][C]2.60813592944942e-11[/C][/ROW]
[ROW][C]21[/C][C]2.74[/C][C]2.74[/C][C]1.33226762955019e-15[/C][/ROW]
[ROW][C]22[/C][C]2.74[/C][C]2.74[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]2.75[/C][C]2.74[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]24[/C][C]2.75[/C][C]2.74999948929974[/C][C]5.1070025985922e-07[/C][/ROW]
[ROW][C]25[/C][C]2.75[/C][C]2.74999999997392[/C][C]2.60813592944942e-11[/C][/ROW]
[ROW][C]26[/C][C]2.75[/C][C]2.75[/C][C]1.33226762955019e-15[/C][/ROW]
[ROW][C]27[/C][C]2.77[/C][C]2.75[/C][C]0.02[/C][/ROW]
[ROW][C]28[/C][C]2.78[/C][C]2.76999897859948[/C][C]0.0100010214005195[/C][/ROW]
[ROW][C]29[/C][C]2.79[/C][C]2.77999948924758[/C][C]0.0100005107524233[/C][/ROW]
[ROW][C]30[/C][C]2.8[/C][C]2.78999948927366[/C][C]0.0100005107263437[/C][/ROW]
[ROW][C]31[/C][C]2.82[/C][C]2.79999948927366[/C][C]0.0200005107263426[/C][/ROW]
[ROW][C]32[/C][C]2.83[/C][C]2.8199989785734[/C][C]0.0100010214266031[/C][/ROW]
[ROW][C]33[/C][C]2.84[/C][C]2.82999948924758[/C][C]0.0100005107524241[/C][/ROW]
[ROW][C]34[/C][C]2.87[/C][C]2.83999948927366[/C][C]0.0300005107263441[/C][/ROW]
[ROW][C]35[/C][C]2.89[/C][C]2.86999846787314[/C][C]0.0200015321268627[/C][/ROW]
[ROW][C]36[/C][C]2.9[/C][C]2.88999897852123[/C][C]0.0100010214787654[/C][/ROW]
[ROW][C]37[/C][C]2.9[/C][C]2.89999948924757[/C][C]5.10752427018701e-07[/C][/ROW]
[ROW][C]38[/C][C]2.91[/C][C]2.89999999997392[/C][C]0.0100000000260843[/C][/ROW]
[ROW][C]39[/C][C]2.92[/C][C]2.90999948929974[/C][C]0.010000510700261[/C][/ROW]
[ROW][C]40[/C][C]2.92[/C][C]2.91999948927366[/C][C]5.10726341218515e-07[/C][/ROW]
[ROW][C]41[/C][C]2.92[/C][C]2.91999999997392[/C][C]2.60826915621237e-11[/C][/ROW]
[ROW][C]42[/C][C]2.92[/C][C]2.92[/C][C]1.33226762955019e-15[/C][/ROW]
[ROW][C]43[/C][C]2.94[/C][C]2.92[/C][C]0.02[/C][/ROW]
[ROW][C]44[/C][C]2.95[/C][C]2.93999897859948[/C][C]0.0100010214005199[/C][/ROW]
[ROW][C]45[/C][C]2.95[/C][C]2.94999948924758[/C][C]5.10752423021898e-07[/C][/ROW]
[ROW][C]46[/C][C]2.97[/C][C]2.94999999997392[/C][C]0.020000000026084[/C][/ROW]
[ROW][C]47[/C][C]2.99[/C][C]2.96999897859948[/C][C]0.0200010214005211[/C][/ROW]
[ROW][C]48[/C][C]3[/C][C]2.98999897854732[/C][C]0.0100010214526827[/C][/ROW]
[ROW][C]49[/C][C]3[/C][C]2.99999948924757[/C][C]5.10752425686434e-07[/C][/ROW]
[ROW][C]50[/C][C]3.01[/C][C]2.99999999997392[/C][C]0.0100000000260838[/C][/ROW]
[ROW][C]51[/C][C]3.03[/C][C]3.00999948929974[/C][C]0.0200005107002612[/C][/ROW]
[ROW][C]52[/C][C]3.03[/C][C]3.0299989785734[/C][C]1.02142660152182e-06[/C][/ROW]
[ROW][C]53[/C][C]3.04[/C][C]3.02999999994784[/C][C]0.0100000000521647[/C][/ROW]
[ROW][C]54[/C][C]3.04[/C][C]3.03999948929974[/C][C]5.10700262523756e-07[/C][/ROW]
[ROW][C]55[/C][C]3.05[/C][C]3.03999999997392[/C][C]0.0100000000260811[/C][/ROW]
[ROW][C]56[/C][C]3.05[/C][C]3.04999948929974[/C][C]5.10700261191488e-07[/C][/ROW]
[ROW][C]57[/C][C]3.09[/C][C]3.04999999997392[/C][C]0.0400000000260814[/C][/ROW]
[ROW][C]58[/C][C]3.09[/C][C]3.08999795719896[/C][C]2.04280104121324e-06[/C][/ROW]
[ROW][C]59[/C][C]3.09[/C][C]3.08999999989567[/C][C]1.04325881267187e-10[/C][/ROW]
[ROW][C]60[/C][C]3.1[/C][C]3.08999999999999[/C][C]0.0100000000000056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166763&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166763&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
22.592.580.00999999999999979
32.62.589999489299740.0100005107002601
42.62.599999489273665.10726341218515e-07
52.612.599999999973920.0100000000260825
62.622.609999489299740.0100005107002614
72.642.619999489273660.0200005107263412
82.652.63999897857340.0100010214266026
92.662.649999489247580.0100005107524246
102.672.659999489273660.0100005107263437
112.682.669999489273660.0100005107263428
122.692.679999489273660.0100005107263423
132.692.689999489273665.10726342550782e-07
142.712.689999999973920.0200000000260827
152.722.709998978599480.0100010214005213
162.732.719999489247580.0100005107524228
172.732.729999489273665.1072634388305e-07
182.742.729999999973920.0100000000260829
192.742.739999489299745.10700261191488e-07
202.742.739999999973922.60813592944942e-11
212.742.741.33226762955019e-15
222.742.740
232.752.740.00999999999999979
242.752.749999489299745.1070025985922e-07
252.752.749999999973922.60813592944942e-11
262.752.751.33226762955019e-15
272.772.750.02
282.782.769998978599480.0100010214005195
292.792.779999489247580.0100005107524233
302.82.789999489273660.0100005107263437
312.822.799999489273660.0200005107263426
322.832.81999897857340.0100010214266031
332.842.829999489247580.0100005107524241
342.872.839999489273660.0300005107263441
352.892.869998467873140.0200015321268627
362.92.889998978521230.0100010214787654
372.92.899999489247575.10752427018701e-07
382.912.899999999973920.0100000000260843
392.922.909999489299740.010000510700261
402.922.919999489273665.10726341218515e-07
412.922.919999999973922.60826915621237e-11
422.922.921.33226762955019e-15
432.942.920.02
442.952.939998978599480.0100010214005199
452.952.949999489247585.10752423021898e-07
462.972.949999999973920.020000000026084
472.992.969998978599480.0200010214005211
4832.989998978547320.0100010214526827
4932.999999489247575.10752425686434e-07
503.012.999999999973920.0100000000260838
513.033.009999489299740.0200005107002612
523.033.02999897857341.02142660152182e-06
533.043.029999999947840.0100000000521647
543.043.039999489299745.10700262523756e-07
553.053.039999999973920.0100000000260811
563.053.049999489299745.10700261191488e-07
573.093.049999999973920.0400000000260814
583.093.089997957198962.04280104121324e-06
593.093.089999999895671.04325881267187e-10
603.13.089999999999990.0100000000000056







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
613.099999489299743.083287321878063.11671165672142
623.099999489299743.07636551897683.12363345962268
633.099999489299743.071054151738723.12894482686076
643.099999489299743.066576434684453.13342254391503
653.099999489299743.062631473656523.13736750494296
663.099999489299743.05906494879413.14093402980538
673.099999489299743.055785185961313.14421379263817
683.099999489299743.052732453926253.14726652467323
693.099999489299743.049865263003783.1501337155957
703.099999489299743.047153404680453.15284557391903
713.099999489299743.044574073894123.15542490470536
723.099999489299743.042109553333463.15788942526603

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.09999948929974 & 3.08328732187806 & 3.11671165672142 \tabularnewline
62 & 3.09999948929974 & 3.0763655189768 & 3.12363345962268 \tabularnewline
63 & 3.09999948929974 & 3.07105415173872 & 3.12894482686076 \tabularnewline
64 & 3.09999948929974 & 3.06657643468445 & 3.13342254391503 \tabularnewline
65 & 3.09999948929974 & 3.06263147365652 & 3.13736750494296 \tabularnewline
66 & 3.09999948929974 & 3.0590649487941 & 3.14093402980538 \tabularnewline
67 & 3.09999948929974 & 3.05578518596131 & 3.14421379263817 \tabularnewline
68 & 3.09999948929974 & 3.05273245392625 & 3.14726652467323 \tabularnewline
69 & 3.09999948929974 & 3.04986526300378 & 3.1501337155957 \tabularnewline
70 & 3.09999948929974 & 3.04715340468045 & 3.15284557391903 \tabularnewline
71 & 3.09999948929974 & 3.04457407389412 & 3.15542490470536 \tabularnewline
72 & 3.09999948929974 & 3.04210955333346 & 3.15788942526603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166763&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]61[/C][C]3.09999948929974[/C][C]3.08328732187806[/C][C]3.11671165672142[/C][/ROW]
[ROW][C]62[/C][C]3.09999948929974[/C][C]3.0763655189768[/C][C]3.12363345962268[/C][/ROW]
[ROW][C]63[/C][C]3.09999948929974[/C][C]3.07105415173872[/C][C]3.12894482686076[/C][/ROW]
[ROW][C]64[/C][C]3.09999948929974[/C][C]3.06657643468445[/C][C]3.13342254391503[/C][/ROW]
[ROW][C]65[/C][C]3.09999948929974[/C][C]3.06263147365652[/C][C]3.13736750494296[/C][/ROW]
[ROW][C]66[/C][C]3.09999948929974[/C][C]3.0590649487941[/C][C]3.14093402980538[/C][/ROW]
[ROW][C]67[/C][C]3.09999948929974[/C][C]3.05578518596131[/C][C]3.14421379263817[/C][/ROW]
[ROW][C]68[/C][C]3.09999948929974[/C][C]3.05273245392625[/C][C]3.14726652467323[/C][/ROW]
[ROW][C]69[/C][C]3.09999948929974[/C][C]3.04986526300378[/C][C]3.1501337155957[/C][/ROW]
[ROW][C]70[/C][C]3.09999948929974[/C][C]3.04715340468045[/C][C]3.15284557391903[/C][/ROW]
[ROW][C]71[/C][C]3.09999948929974[/C][C]3.04457407389412[/C][C]3.15542490470536[/C][/ROW]
[ROW][C]72[/C][C]3.09999948929974[/C][C]3.04210955333346[/C][C]3.15788942526603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166763&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166763&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
613.099999489299743.083287321878063.11671165672142
623.099999489299743.07636551897683.12363345962268
633.099999489299743.071054151738723.12894482686076
643.099999489299743.066576434684453.13342254391503
653.099999489299743.062631473656523.13736750494296
663.099999489299743.05906494879413.14093402980538
673.099999489299743.055785185961313.14421379263817
683.099999489299743.052732453926253.14726652467323
693.099999489299743.049865263003783.1501337155957
703.099999489299743.047153404680453.15284557391903
713.099999489299743.044574073894123.15542490470536
723.099999489299743.042109553333463.15788942526603



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
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')