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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 12:34:39 -0500
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/Dec/21/t1356111313vliyyh83tlgigah.htm/, Retrieved Thu, 25 Apr 2024 22:29:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204013, Retrieved Thu, 25 Apr 2024 22:29:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 17:34:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
96,24
95,56
95,56
95,56
95,96
95,96
95,96
95,96
95,61
95,30
95,68
97,94
97,32
97,32
97,45
98,08
98,25
98,25
97,95
97,81
97,68
98,03
98,03
98,03
98,11
98,11
98,11
97,95
97,95
97,95
97,95
97,95
97,95
97,89
97,16
97,16
97,16
97,18
97,18
96,47
97,47
97,47
97,47
97,47
96,63
96,78
96,25
96,25
96,28
95,62
95,62
96,85
96,85
96,85
96,85
96,85
96,85
96,85
96,75
97,15
98,28
98,28
98,28
98,51
98,51
98,51
96,03
96,03
96,77
96,92
96,92
96,92




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204013&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]3 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=204013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204013&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.945163820624744
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.945163820624744 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204013&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]0.945163820624744[/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=204013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204013&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
alpha0.945163820624744
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
295.5696.24-0.679999999999993
395.5695.5972886019752-0.0372886019751775
495.5695.5620447644666-0.00204476446656088
595.9695.56011212707110.399887872928929
695.9695.93807167687010.0219283231299272
795.9695.95879753453940.00120246546055114
895.9695.95993406138836.59386116836913e-05
995.6195.9599963841785-0.349996384178453
1095.395.6291924645035-0.329192464503507
1195.6895.31805165703250.361948342967509
1297.9495.66015213574052.27984786425954
1397.3297.8149818535672-0.494981853567168
1497.3297.3471429137097-0.0271429137097101
1597.4597.32148841368490.128511586315057
1698.0897.4429529156010.637047084398972
1798.2598.04506677180940.204933228190583
1898.2598.2387622447390.011237755261007
1997.9598.2493837644367-0.299383764436726
2097.8197.9664170618087-0.156417061808696
2197.6897.8185773140587-0.138577314058693
2298.0397.68759905045110.342400949548932
2398.0398.01122404011230.0187759598877193
2498.0398.02897039809570.00102960190434942
2598.1198.02994354056530.0800564594347151
2698.1198.10561000963030.00438999036971666
2798.1198.10975926970060.000240730299367442
2897.9598.1099867992701-0.159986799270115
2997.9597.9587730648225-0.00877306482244933
3097.9597.9504810813563-0.000481081356269897
3197.9597.9500263806635-2.63806635416586e-05
3297.9597.9500014466148-1.44661480305786e-06
3397.9597.9500000793268-7.93268242205158e-08
3497.8997.95000000435-0.0600000043499875
3597.1697.8932901710011-0.733290171001059
3697.1697.2002108313511-0.040210831351132
3797.1697.1622050083608-0.00220500836080362
3897.1897.1601209142340.0198790857660072
3997.1897.17890990688710.00109009311287878
4096.4797.1799402234585-0.709940223458531
4197.4796.50893040943930.961069590560712
4297.4797.41729861553990.052701384460093
4397.4797.46711005742840.00288994257158492
4497.4797.46984152659080.000158473409243243
4596.6397.4699913099237-0.839991309923704
4696.7896.67606191414460.103938085855376
4796.2596.7743004324801-0.524300432480118
4896.2596.278750632562-0.0287506325620086
4996.2896.25157657484430.0284234251556796
5095.6296.2784413679597-0.658441367959696
5195.6295.6561064089615-0.0361064089615297
5296.8595.62197993751841.22802006248158
5396.8596.78266007157730.0673399284226548
5496.8596.84630733560590.00369266439410865
5596.8596.84979750839290.000202491607083743
5696.8596.84998889613391.11038660861595e-05
5796.8596.84999939110646.08893586218073e-07
5896.8596.84999996661063.33893979131972e-08
5996.7596.8499999981691-0.0999999981690536
6097.1596.75548361783710.394516382162877
6198.2897.12836622890121.15163377109876
6298.2898.21684880395340.0631511960465758
6398.2898.27653702968580.00346297031417464
6498.5198.27981010393870.230189896061319
6598.5198.49737726556920.0126227344307921
6698.5198.50930781747060.00069218252944836
6796.0398.5099620433547-2.47996204335466
6896.0396.1659916434532-0.135991643453224
6996.7796.03745726215390.73254273784606
7096.9296.72983015502740.190169844972573
7196.9296.90957181226930.0104281877306818
7296.9296.9194281580270.000571841972956122

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 95.56 & 96.24 & -0.679999999999993 \tabularnewline
3 & 95.56 & 95.5972886019752 & -0.0372886019751775 \tabularnewline
4 & 95.56 & 95.5620447644666 & -0.00204476446656088 \tabularnewline
5 & 95.96 & 95.5601121270711 & 0.399887872928929 \tabularnewline
6 & 95.96 & 95.9380716768701 & 0.0219283231299272 \tabularnewline
7 & 95.96 & 95.9587975345394 & 0.00120246546055114 \tabularnewline
8 & 95.96 & 95.9599340613883 & 6.59386116836913e-05 \tabularnewline
9 & 95.61 & 95.9599963841785 & -0.349996384178453 \tabularnewline
10 & 95.3 & 95.6291924645035 & -0.329192464503507 \tabularnewline
11 & 95.68 & 95.3180516570325 & 0.361948342967509 \tabularnewline
12 & 97.94 & 95.6601521357405 & 2.27984786425954 \tabularnewline
13 & 97.32 & 97.8149818535672 & -0.494981853567168 \tabularnewline
14 & 97.32 & 97.3471429137097 & -0.0271429137097101 \tabularnewline
15 & 97.45 & 97.3214884136849 & 0.128511586315057 \tabularnewline
16 & 98.08 & 97.442952915601 & 0.637047084398972 \tabularnewline
17 & 98.25 & 98.0450667718094 & 0.204933228190583 \tabularnewline
18 & 98.25 & 98.238762244739 & 0.011237755261007 \tabularnewline
19 & 97.95 & 98.2493837644367 & -0.299383764436726 \tabularnewline
20 & 97.81 & 97.9664170618087 & -0.156417061808696 \tabularnewline
21 & 97.68 & 97.8185773140587 & -0.138577314058693 \tabularnewline
22 & 98.03 & 97.6875990504511 & 0.342400949548932 \tabularnewline
23 & 98.03 & 98.0112240401123 & 0.0187759598877193 \tabularnewline
24 & 98.03 & 98.0289703980957 & 0.00102960190434942 \tabularnewline
25 & 98.11 & 98.0299435405653 & 0.0800564594347151 \tabularnewline
26 & 98.11 & 98.1056100096303 & 0.00438999036971666 \tabularnewline
27 & 98.11 & 98.1097592697006 & 0.000240730299367442 \tabularnewline
28 & 97.95 & 98.1099867992701 & -0.159986799270115 \tabularnewline
29 & 97.95 & 97.9587730648225 & -0.00877306482244933 \tabularnewline
30 & 97.95 & 97.9504810813563 & -0.000481081356269897 \tabularnewline
31 & 97.95 & 97.9500263806635 & -2.63806635416586e-05 \tabularnewline
32 & 97.95 & 97.9500014466148 & -1.44661480305786e-06 \tabularnewline
33 & 97.95 & 97.9500000793268 & -7.93268242205158e-08 \tabularnewline
34 & 97.89 & 97.95000000435 & -0.0600000043499875 \tabularnewline
35 & 97.16 & 97.8932901710011 & -0.733290171001059 \tabularnewline
36 & 97.16 & 97.2002108313511 & -0.040210831351132 \tabularnewline
37 & 97.16 & 97.1622050083608 & -0.00220500836080362 \tabularnewline
38 & 97.18 & 97.160120914234 & 0.0198790857660072 \tabularnewline
39 & 97.18 & 97.1789099068871 & 0.00109009311287878 \tabularnewline
40 & 96.47 & 97.1799402234585 & -0.709940223458531 \tabularnewline
41 & 97.47 & 96.5089304094393 & 0.961069590560712 \tabularnewline
42 & 97.47 & 97.4172986155399 & 0.052701384460093 \tabularnewline
43 & 97.47 & 97.4671100574284 & 0.00288994257158492 \tabularnewline
44 & 97.47 & 97.4698415265908 & 0.000158473409243243 \tabularnewline
45 & 96.63 & 97.4699913099237 & -0.839991309923704 \tabularnewline
46 & 96.78 & 96.6760619141446 & 0.103938085855376 \tabularnewline
47 & 96.25 & 96.7743004324801 & -0.524300432480118 \tabularnewline
48 & 96.25 & 96.278750632562 & -0.0287506325620086 \tabularnewline
49 & 96.28 & 96.2515765748443 & 0.0284234251556796 \tabularnewline
50 & 95.62 & 96.2784413679597 & -0.658441367959696 \tabularnewline
51 & 95.62 & 95.6561064089615 & -0.0361064089615297 \tabularnewline
52 & 96.85 & 95.6219799375184 & 1.22802006248158 \tabularnewline
53 & 96.85 & 96.7826600715773 & 0.0673399284226548 \tabularnewline
54 & 96.85 & 96.8463073356059 & 0.00369266439410865 \tabularnewline
55 & 96.85 & 96.8497975083929 & 0.000202491607083743 \tabularnewline
56 & 96.85 & 96.8499888961339 & 1.11038660861595e-05 \tabularnewline
57 & 96.85 & 96.8499993911064 & 6.08893586218073e-07 \tabularnewline
58 & 96.85 & 96.8499999666106 & 3.33893979131972e-08 \tabularnewline
59 & 96.75 & 96.8499999981691 & -0.0999999981690536 \tabularnewline
60 & 97.15 & 96.7554836178371 & 0.394516382162877 \tabularnewline
61 & 98.28 & 97.1283662289012 & 1.15163377109876 \tabularnewline
62 & 98.28 & 98.2168488039534 & 0.0631511960465758 \tabularnewline
63 & 98.28 & 98.2765370296858 & 0.00346297031417464 \tabularnewline
64 & 98.51 & 98.2798101039387 & 0.230189896061319 \tabularnewline
65 & 98.51 & 98.4973772655692 & 0.0126227344307921 \tabularnewline
66 & 98.51 & 98.5093078174706 & 0.00069218252944836 \tabularnewline
67 & 96.03 & 98.5099620433547 & -2.47996204335466 \tabularnewline
68 & 96.03 & 96.1659916434532 & -0.135991643453224 \tabularnewline
69 & 96.77 & 96.0374572621539 & 0.73254273784606 \tabularnewline
70 & 96.92 & 96.7298301550274 & 0.190169844972573 \tabularnewline
71 & 96.92 & 96.9095718122693 & 0.0104281877306818 \tabularnewline
72 & 96.92 & 96.919428158027 & 0.000571841972956122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204013&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]95.56[/C][C]96.24[/C][C]-0.679999999999993[/C][/ROW]
[ROW][C]3[/C][C]95.56[/C][C]95.5972886019752[/C][C]-0.0372886019751775[/C][/ROW]
[ROW][C]4[/C][C]95.56[/C][C]95.5620447644666[/C][C]-0.00204476446656088[/C][/ROW]
[ROW][C]5[/C][C]95.96[/C][C]95.5601121270711[/C][C]0.399887872928929[/C][/ROW]
[ROW][C]6[/C][C]95.96[/C][C]95.9380716768701[/C][C]0.0219283231299272[/C][/ROW]
[ROW][C]7[/C][C]95.96[/C][C]95.9587975345394[/C][C]0.00120246546055114[/C][/ROW]
[ROW][C]8[/C][C]95.96[/C][C]95.9599340613883[/C][C]6.59386116836913e-05[/C][/ROW]
[ROW][C]9[/C][C]95.61[/C][C]95.9599963841785[/C][C]-0.349996384178453[/C][/ROW]
[ROW][C]10[/C][C]95.3[/C][C]95.6291924645035[/C][C]-0.329192464503507[/C][/ROW]
[ROW][C]11[/C][C]95.68[/C][C]95.3180516570325[/C][C]0.361948342967509[/C][/ROW]
[ROW][C]12[/C][C]97.94[/C][C]95.6601521357405[/C][C]2.27984786425954[/C][/ROW]
[ROW][C]13[/C][C]97.32[/C][C]97.8149818535672[/C][C]-0.494981853567168[/C][/ROW]
[ROW][C]14[/C][C]97.32[/C][C]97.3471429137097[/C][C]-0.0271429137097101[/C][/ROW]
[ROW][C]15[/C][C]97.45[/C][C]97.3214884136849[/C][C]0.128511586315057[/C][/ROW]
[ROW][C]16[/C][C]98.08[/C][C]97.442952915601[/C][C]0.637047084398972[/C][/ROW]
[ROW][C]17[/C][C]98.25[/C][C]98.0450667718094[/C][C]0.204933228190583[/C][/ROW]
[ROW][C]18[/C][C]98.25[/C][C]98.238762244739[/C][C]0.011237755261007[/C][/ROW]
[ROW][C]19[/C][C]97.95[/C][C]98.2493837644367[/C][C]-0.299383764436726[/C][/ROW]
[ROW][C]20[/C][C]97.81[/C][C]97.9664170618087[/C][C]-0.156417061808696[/C][/ROW]
[ROW][C]21[/C][C]97.68[/C][C]97.8185773140587[/C][C]-0.138577314058693[/C][/ROW]
[ROW][C]22[/C][C]98.03[/C][C]97.6875990504511[/C][C]0.342400949548932[/C][/ROW]
[ROW][C]23[/C][C]98.03[/C][C]98.0112240401123[/C][C]0.0187759598877193[/C][/ROW]
[ROW][C]24[/C][C]98.03[/C][C]98.0289703980957[/C][C]0.00102960190434942[/C][/ROW]
[ROW][C]25[/C][C]98.11[/C][C]98.0299435405653[/C][C]0.0800564594347151[/C][/ROW]
[ROW][C]26[/C][C]98.11[/C][C]98.1056100096303[/C][C]0.00438999036971666[/C][/ROW]
[ROW][C]27[/C][C]98.11[/C][C]98.1097592697006[/C][C]0.000240730299367442[/C][/ROW]
[ROW][C]28[/C][C]97.95[/C][C]98.1099867992701[/C][C]-0.159986799270115[/C][/ROW]
[ROW][C]29[/C][C]97.95[/C][C]97.9587730648225[/C][C]-0.00877306482244933[/C][/ROW]
[ROW][C]30[/C][C]97.95[/C][C]97.9504810813563[/C][C]-0.000481081356269897[/C][/ROW]
[ROW][C]31[/C][C]97.95[/C][C]97.9500263806635[/C][C]-2.63806635416586e-05[/C][/ROW]
[ROW][C]32[/C][C]97.95[/C][C]97.9500014466148[/C][C]-1.44661480305786e-06[/C][/ROW]
[ROW][C]33[/C][C]97.95[/C][C]97.9500000793268[/C][C]-7.93268242205158e-08[/C][/ROW]
[ROW][C]34[/C][C]97.89[/C][C]97.95000000435[/C][C]-0.0600000043499875[/C][/ROW]
[ROW][C]35[/C][C]97.16[/C][C]97.8932901710011[/C][C]-0.733290171001059[/C][/ROW]
[ROW][C]36[/C][C]97.16[/C][C]97.2002108313511[/C][C]-0.040210831351132[/C][/ROW]
[ROW][C]37[/C][C]97.16[/C][C]97.1622050083608[/C][C]-0.00220500836080362[/C][/ROW]
[ROW][C]38[/C][C]97.18[/C][C]97.160120914234[/C][C]0.0198790857660072[/C][/ROW]
[ROW][C]39[/C][C]97.18[/C][C]97.1789099068871[/C][C]0.00109009311287878[/C][/ROW]
[ROW][C]40[/C][C]96.47[/C][C]97.1799402234585[/C][C]-0.709940223458531[/C][/ROW]
[ROW][C]41[/C][C]97.47[/C][C]96.5089304094393[/C][C]0.961069590560712[/C][/ROW]
[ROW][C]42[/C][C]97.47[/C][C]97.4172986155399[/C][C]0.052701384460093[/C][/ROW]
[ROW][C]43[/C][C]97.47[/C][C]97.4671100574284[/C][C]0.00288994257158492[/C][/ROW]
[ROW][C]44[/C][C]97.47[/C][C]97.4698415265908[/C][C]0.000158473409243243[/C][/ROW]
[ROW][C]45[/C][C]96.63[/C][C]97.4699913099237[/C][C]-0.839991309923704[/C][/ROW]
[ROW][C]46[/C][C]96.78[/C][C]96.6760619141446[/C][C]0.103938085855376[/C][/ROW]
[ROW][C]47[/C][C]96.25[/C][C]96.7743004324801[/C][C]-0.524300432480118[/C][/ROW]
[ROW][C]48[/C][C]96.25[/C][C]96.278750632562[/C][C]-0.0287506325620086[/C][/ROW]
[ROW][C]49[/C][C]96.28[/C][C]96.2515765748443[/C][C]0.0284234251556796[/C][/ROW]
[ROW][C]50[/C][C]95.62[/C][C]96.2784413679597[/C][C]-0.658441367959696[/C][/ROW]
[ROW][C]51[/C][C]95.62[/C][C]95.6561064089615[/C][C]-0.0361064089615297[/C][/ROW]
[ROW][C]52[/C][C]96.85[/C][C]95.6219799375184[/C][C]1.22802006248158[/C][/ROW]
[ROW][C]53[/C][C]96.85[/C][C]96.7826600715773[/C][C]0.0673399284226548[/C][/ROW]
[ROW][C]54[/C][C]96.85[/C][C]96.8463073356059[/C][C]0.00369266439410865[/C][/ROW]
[ROW][C]55[/C][C]96.85[/C][C]96.8497975083929[/C][C]0.000202491607083743[/C][/ROW]
[ROW][C]56[/C][C]96.85[/C][C]96.8499888961339[/C][C]1.11038660861595e-05[/C][/ROW]
[ROW][C]57[/C][C]96.85[/C][C]96.8499993911064[/C][C]6.08893586218073e-07[/C][/ROW]
[ROW][C]58[/C][C]96.85[/C][C]96.8499999666106[/C][C]3.33893979131972e-08[/C][/ROW]
[ROW][C]59[/C][C]96.75[/C][C]96.8499999981691[/C][C]-0.0999999981690536[/C][/ROW]
[ROW][C]60[/C][C]97.15[/C][C]96.7554836178371[/C][C]0.394516382162877[/C][/ROW]
[ROW][C]61[/C][C]98.28[/C][C]97.1283662289012[/C][C]1.15163377109876[/C][/ROW]
[ROW][C]62[/C][C]98.28[/C][C]98.2168488039534[/C][C]0.0631511960465758[/C][/ROW]
[ROW][C]63[/C][C]98.28[/C][C]98.2765370296858[/C][C]0.00346297031417464[/C][/ROW]
[ROW][C]64[/C][C]98.51[/C][C]98.2798101039387[/C][C]0.230189896061319[/C][/ROW]
[ROW][C]65[/C][C]98.51[/C][C]98.4973772655692[/C][C]0.0126227344307921[/C][/ROW]
[ROW][C]66[/C][C]98.51[/C][C]98.5093078174706[/C][C]0.00069218252944836[/C][/ROW]
[ROW][C]67[/C][C]96.03[/C][C]98.5099620433547[/C][C]-2.47996204335466[/C][/ROW]
[ROW][C]68[/C][C]96.03[/C][C]96.1659916434532[/C][C]-0.135991643453224[/C][/ROW]
[ROW][C]69[/C][C]96.77[/C][C]96.0374572621539[/C][C]0.73254273784606[/C][/ROW]
[ROW][C]70[/C][C]96.92[/C][C]96.7298301550274[/C][C]0.190169844972573[/C][/ROW]
[ROW][C]71[/C][C]96.92[/C][C]96.9095718122693[/C][C]0.0104281877306818[/C][/ROW]
[ROW][C]72[/C][C]96.92[/C][C]96.919428158027[/C][C]0.000571841972956122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204013&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
295.5696.24-0.679999999999993
395.5695.5972886019752-0.0372886019751775
495.5695.5620447644666-0.00204476446656088
595.9695.56011212707110.399887872928929
695.9695.93807167687010.0219283231299272
795.9695.95879753453940.00120246546055114
895.9695.95993406138836.59386116836913e-05
995.6195.9599963841785-0.349996384178453
1095.395.6291924645035-0.329192464503507
1195.6895.31805165703250.361948342967509
1297.9495.66015213574052.27984786425954
1397.3297.8149818535672-0.494981853567168
1497.3297.3471429137097-0.0271429137097101
1597.4597.32148841368490.128511586315057
1698.0897.4429529156010.637047084398972
1798.2598.04506677180940.204933228190583
1898.2598.2387622447390.011237755261007
1997.9598.2493837644367-0.299383764436726
2097.8197.9664170618087-0.156417061808696
2197.6897.8185773140587-0.138577314058693
2298.0397.68759905045110.342400949548932
2398.0398.01122404011230.0187759598877193
2498.0398.02897039809570.00102960190434942
2598.1198.02994354056530.0800564594347151
2698.1198.10561000963030.00438999036971666
2798.1198.10975926970060.000240730299367442
2897.9598.1099867992701-0.159986799270115
2997.9597.9587730648225-0.00877306482244933
3097.9597.9504810813563-0.000481081356269897
3197.9597.9500263806635-2.63806635416586e-05
3297.9597.9500014466148-1.44661480305786e-06
3397.9597.9500000793268-7.93268242205158e-08
3497.8997.95000000435-0.0600000043499875
3597.1697.8932901710011-0.733290171001059
3697.1697.2002108313511-0.040210831351132
3797.1697.1622050083608-0.00220500836080362
3897.1897.1601209142340.0198790857660072
3997.1897.17890990688710.00109009311287878
4096.4797.1799402234585-0.709940223458531
4197.4796.50893040943930.961069590560712
4297.4797.41729861553990.052701384460093
4397.4797.46711005742840.00288994257158492
4497.4797.46984152659080.000158473409243243
4596.6397.4699913099237-0.839991309923704
4696.7896.67606191414460.103938085855376
4796.2596.7743004324801-0.524300432480118
4896.2596.278750632562-0.0287506325620086
4996.2896.25157657484430.0284234251556796
5095.6296.2784413679597-0.658441367959696
5195.6295.6561064089615-0.0361064089615297
5296.8595.62197993751841.22802006248158
5396.8596.78266007157730.0673399284226548
5496.8596.84630733560590.00369266439410865
5596.8596.84979750839290.000202491607083743
5696.8596.84998889613391.11038660861595e-05
5796.8596.84999939110646.08893586218073e-07
5896.8596.84999996661063.33893979131972e-08
5996.7596.8499999981691-0.0999999981690536
6097.1596.75548361783710.394516382162877
6198.2897.12836622890121.15163377109876
6298.2898.21684880395340.0631511960465758
6398.2898.27653702968580.00346297031417464
6498.5198.27981010393870.230189896061319
6598.5198.49737726556920.0126227344307921
6698.5198.50930781747060.00069218252944836
6796.0398.5099620433547-2.47996204335466
6896.0396.1659916434532-0.135991643453224
6996.7796.03745726215390.73254273784606
7096.9296.72983015502740.190169844972573
7196.9296.90957181226930.0104281877306818
7296.9296.9194281580270.000571841972956122







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7396.91996864237195.862561706078797.9773755786634
7496.91996864237195.464992586958298.3749446977838
7596.91996864237195.154805416283998.6851318684581
7696.91996864237194.891509348316698.9484279364254
7796.91996864237194.65866525703399.181272027709
7896.91996864237194.447654161273199.3922831234689
7996.91996864237194.253288161632599.5866491231096
8096.91996864237194.072157082724399.7677802020177
8196.91996864237193.901877097675499.9380601870666
8296.91996864237193.7407041889057100.099233095836
8396.91996864237193.5873167916711100.252620493071
8496.91996864237193.4406850593788100.399252225363

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 96.919968642371 & 95.8625617060787 & 97.9773755786634 \tabularnewline
74 & 96.919968642371 & 95.4649925869582 & 98.3749446977838 \tabularnewline
75 & 96.919968642371 & 95.1548054162839 & 98.6851318684581 \tabularnewline
76 & 96.919968642371 & 94.8915093483166 & 98.9484279364254 \tabularnewline
77 & 96.919968642371 & 94.658665257033 & 99.181272027709 \tabularnewline
78 & 96.919968642371 & 94.4476541612731 & 99.3922831234689 \tabularnewline
79 & 96.919968642371 & 94.2532881616325 & 99.5866491231096 \tabularnewline
80 & 96.919968642371 & 94.0721570827243 & 99.7677802020177 \tabularnewline
81 & 96.919968642371 & 93.9018770976754 & 99.9380601870666 \tabularnewline
82 & 96.919968642371 & 93.7407041889057 & 100.099233095836 \tabularnewline
83 & 96.919968642371 & 93.5873167916711 & 100.252620493071 \tabularnewline
84 & 96.919968642371 & 93.4406850593788 & 100.399252225363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204013&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]96.919968642371[/C][C]95.8625617060787[/C][C]97.9773755786634[/C][/ROW]
[ROW][C]74[/C][C]96.919968642371[/C][C]95.4649925869582[/C][C]98.3749446977838[/C][/ROW]
[ROW][C]75[/C][C]96.919968642371[/C][C]95.1548054162839[/C][C]98.6851318684581[/C][/ROW]
[ROW][C]76[/C][C]96.919968642371[/C][C]94.8915093483166[/C][C]98.9484279364254[/C][/ROW]
[ROW][C]77[/C][C]96.919968642371[/C][C]94.658665257033[/C][C]99.181272027709[/C][/ROW]
[ROW][C]78[/C][C]96.919968642371[/C][C]94.4476541612731[/C][C]99.3922831234689[/C][/ROW]
[ROW][C]79[/C][C]96.919968642371[/C][C]94.2532881616325[/C][C]99.5866491231096[/C][/ROW]
[ROW][C]80[/C][C]96.919968642371[/C][C]94.0721570827243[/C][C]99.7677802020177[/C][/ROW]
[ROW][C]81[/C][C]96.919968642371[/C][C]93.9018770976754[/C][C]99.9380601870666[/C][/ROW]
[ROW][C]82[/C][C]96.919968642371[/C][C]93.7407041889057[/C][C]100.099233095836[/C][/ROW]
[ROW][C]83[/C][C]96.919968642371[/C][C]93.5873167916711[/C][C]100.252620493071[/C][/ROW]
[ROW][C]84[/C][C]96.919968642371[/C][C]93.4406850593788[/C][C]100.399252225363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204013&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
7396.91996864237195.862561706078797.9773755786634
7496.91996864237195.464992586958298.3749446977838
7596.91996864237195.154805416283998.6851318684581
7696.91996864237194.891509348316698.9484279364254
7796.91996864237194.65866525703399.181272027709
7896.91996864237194.447654161273199.3922831234689
7996.91996864237194.253288161632599.5866491231096
8096.91996864237194.072157082724399.7677802020177
8196.91996864237193.901877097675499.9380601870666
8296.91996864237193.7407041889057100.099233095836
8396.91996864237193.5873167916711100.252620493071
8496.91996864237193.4406850593788100.399252225363



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')