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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 11 Jan 2016 13:57:09 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/11/t1452520679pzat28jgebx7kpd.htm/, Retrieved Tue, 07 May 2024 09:59:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289660, Retrieved Tue, 07 May 2024 09:59:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Exponential Smoot...] [2015-11-29 14:33:48] [b78554c675fd79077ee7678381a14583]
- R P     [Exponential Smoothing] [Double exponentia...] [2016-01-11 13:57:09] [3f1a7081c5450f075552d8bc3f139f2c] [Current]
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Dataseries X:
26.133
25.979
25.541
25.308
25.663
25.78
25.328
24.806
24.651
24.531
24.633
25.174
24.449
24.277
24.393
24.301
24.381
24.286
24.335
24.273
24.556
24.841
25.464
25.514
25.531
25.042
24.676
24.809
25.313
25.64
25.447
25.021
24.752
24.939
25.365
25.214
25.563
25.475
25.659
25.841
25.888
25.759
25.944
25.818
25.789
25.662
26.927
27.521
27.485
27.444
27.395
27.45
27.437
27.45
27.458
27.816
27.599
27.588
27.667
27.64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289660&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289660&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0710311049597833
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0710311049597833 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289660&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0710311049597833[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289660&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
alpha1
beta0.0710311049597833
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
325.54125.825-0.283999999999999
425.30825.3668271661914-0.0588271661914206
525.66325.12964860757520.533351392424809
625.7825.5225331463110.257466853689035
725.32825.657821301419-0.329821301419017
824.80625.1823937299399-0.376393729939949
924.65124.63365806740240.017341932597617
1024.53124.47988988403690.0511101159630698
1124.63324.36352029204840.269479707951593
1225.17424.48466173346840.68933826653155
1324.44925.0746261922312-0.625626192231245
1424.27724.3051872725053-0.0281872725052814
1524.39324.13118509939340.261814900606574
1624.30124.26578210107840.0352178989215517
1724.38124.17628366735320.204716332646793
1824.28624.27082489466440.015175105335576
1924.33524.17690279916430.158097200835709
2024.27324.23713261803070.0358673819693003
2124.55624.1776803178040.378319682196008
2224.84124.48755278285840.353447217141589
2325.46424.79765852923690.666341470763058
2425.51425.46798950018580.046010499814237
2525.53125.52125767682730.0097423231726772
2625.04225.5389496848072-0.496949684807149
2724.67625.0146507995859-0.338650799585889
2824.80924.62459605909580.184403940904218
2925.31324.77069447477720.542305525222847
3025.6425.31321503545950.326784964540476
3125.44725.6634269325751-0.216426932575079
3225.02125.4550538884112-0.434053888411214
3324.75224.9982225611053-0.246222561105277
3424.93924.71173310052390.22726689947606
3525.36524.91487611951450.450123880485489
3625.21425.3728489161142-0.158848916114177
3725.56325.21056570208090.352434297919075
3825.47525.5845994996878-0.109599499687839
3925.65925.4888145261220.170185473878021
4025.84125.68490298837960.156097011620368
4125.88825.8779907315960.0100092684040511
4225.75925.9257017009905-0.166701700990529
4325.94425.78486069497050.159139305029502
4425.81825.9811645356493-0.163164535649273
4525.78925.8435747783919-0.0545747783918564
4625.66225.8106982715797-0.14869827157975
4726.92725.67313606904381.25386393095617
4827.52127.02719940952890.493800590471139
4927.48527.6562746110998-0.171274611099822
5027.44427.6081087862218-0.164108786221842
5127.39527.5554519578029-0.160451957802895
5227.4527.4950548779472-0.045054877947198
5327.43727.5468545801828-0.109854580182777
5427.4527.5260514879675-0.0760514879675043
5527.45827.5336494667433-0.0756494667433358
5627.81627.53627600153090.279723998469063
5727.59927.914145106226-0.315145106225962
5827.58827.6747600011081-0.0867600011080647
5927.66727.6575973423630.00940265763695436
6027.6427.7372652235246-0.097265223524559

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 25.541 & 25.825 & -0.283999999999999 \tabularnewline
4 & 25.308 & 25.3668271661914 & -0.0588271661914206 \tabularnewline
5 & 25.663 & 25.1296486075752 & 0.533351392424809 \tabularnewline
6 & 25.78 & 25.522533146311 & 0.257466853689035 \tabularnewline
7 & 25.328 & 25.657821301419 & -0.329821301419017 \tabularnewline
8 & 24.806 & 25.1823937299399 & -0.376393729939949 \tabularnewline
9 & 24.651 & 24.6336580674024 & 0.017341932597617 \tabularnewline
10 & 24.531 & 24.4798898840369 & 0.0511101159630698 \tabularnewline
11 & 24.633 & 24.3635202920484 & 0.269479707951593 \tabularnewline
12 & 25.174 & 24.4846617334684 & 0.68933826653155 \tabularnewline
13 & 24.449 & 25.0746261922312 & -0.625626192231245 \tabularnewline
14 & 24.277 & 24.3051872725053 & -0.0281872725052814 \tabularnewline
15 & 24.393 & 24.1311850993934 & 0.261814900606574 \tabularnewline
16 & 24.301 & 24.2657821010784 & 0.0352178989215517 \tabularnewline
17 & 24.381 & 24.1762836673532 & 0.204716332646793 \tabularnewline
18 & 24.286 & 24.2708248946644 & 0.015175105335576 \tabularnewline
19 & 24.335 & 24.1769027991643 & 0.158097200835709 \tabularnewline
20 & 24.273 & 24.2371326180307 & 0.0358673819693003 \tabularnewline
21 & 24.556 & 24.177680317804 & 0.378319682196008 \tabularnewline
22 & 24.841 & 24.4875527828584 & 0.353447217141589 \tabularnewline
23 & 25.464 & 24.7976585292369 & 0.666341470763058 \tabularnewline
24 & 25.514 & 25.4679895001858 & 0.046010499814237 \tabularnewline
25 & 25.531 & 25.5212576768273 & 0.0097423231726772 \tabularnewline
26 & 25.042 & 25.5389496848072 & -0.496949684807149 \tabularnewline
27 & 24.676 & 25.0146507995859 & -0.338650799585889 \tabularnewline
28 & 24.809 & 24.6245960590958 & 0.184403940904218 \tabularnewline
29 & 25.313 & 24.7706944747772 & 0.542305525222847 \tabularnewline
30 & 25.64 & 25.3132150354595 & 0.326784964540476 \tabularnewline
31 & 25.447 & 25.6634269325751 & -0.216426932575079 \tabularnewline
32 & 25.021 & 25.4550538884112 & -0.434053888411214 \tabularnewline
33 & 24.752 & 24.9982225611053 & -0.246222561105277 \tabularnewline
34 & 24.939 & 24.7117331005239 & 0.22726689947606 \tabularnewline
35 & 25.365 & 24.9148761195145 & 0.450123880485489 \tabularnewline
36 & 25.214 & 25.3728489161142 & -0.158848916114177 \tabularnewline
37 & 25.563 & 25.2105657020809 & 0.352434297919075 \tabularnewline
38 & 25.475 & 25.5845994996878 & -0.109599499687839 \tabularnewline
39 & 25.659 & 25.488814526122 & 0.170185473878021 \tabularnewline
40 & 25.841 & 25.6849029883796 & 0.156097011620368 \tabularnewline
41 & 25.888 & 25.877990731596 & 0.0100092684040511 \tabularnewline
42 & 25.759 & 25.9257017009905 & -0.166701700990529 \tabularnewline
43 & 25.944 & 25.7848606949705 & 0.159139305029502 \tabularnewline
44 & 25.818 & 25.9811645356493 & -0.163164535649273 \tabularnewline
45 & 25.789 & 25.8435747783919 & -0.0545747783918564 \tabularnewline
46 & 25.662 & 25.8106982715797 & -0.14869827157975 \tabularnewline
47 & 26.927 & 25.6731360690438 & 1.25386393095617 \tabularnewline
48 & 27.521 & 27.0271994095289 & 0.493800590471139 \tabularnewline
49 & 27.485 & 27.6562746110998 & -0.171274611099822 \tabularnewline
50 & 27.444 & 27.6081087862218 & -0.164108786221842 \tabularnewline
51 & 27.395 & 27.5554519578029 & -0.160451957802895 \tabularnewline
52 & 27.45 & 27.4950548779472 & -0.045054877947198 \tabularnewline
53 & 27.437 & 27.5468545801828 & -0.109854580182777 \tabularnewline
54 & 27.45 & 27.5260514879675 & -0.0760514879675043 \tabularnewline
55 & 27.458 & 27.5336494667433 & -0.0756494667433358 \tabularnewline
56 & 27.816 & 27.5362760015309 & 0.279723998469063 \tabularnewline
57 & 27.599 & 27.914145106226 & -0.315145106225962 \tabularnewline
58 & 27.588 & 27.6747600011081 & -0.0867600011080647 \tabularnewline
59 & 27.667 & 27.657597342363 & 0.00940265763695436 \tabularnewline
60 & 27.64 & 27.7372652235246 & -0.097265223524559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289660&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]3[/C][C]25.541[/C][C]25.825[/C][C]-0.283999999999999[/C][/ROW]
[ROW][C]4[/C][C]25.308[/C][C]25.3668271661914[/C][C]-0.0588271661914206[/C][/ROW]
[ROW][C]5[/C][C]25.663[/C][C]25.1296486075752[/C][C]0.533351392424809[/C][/ROW]
[ROW][C]6[/C][C]25.78[/C][C]25.522533146311[/C][C]0.257466853689035[/C][/ROW]
[ROW][C]7[/C][C]25.328[/C][C]25.657821301419[/C][C]-0.329821301419017[/C][/ROW]
[ROW][C]8[/C][C]24.806[/C][C]25.1823937299399[/C][C]-0.376393729939949[/C][/ROW]
[ROW][C]9[/C][C]24.651[/C][C]24.6336580674024[/C][C]0.017341932597617[/C][/ROW]
[ROW][C]10[/C][C]24.531[/C][C]24.4798898840369[/C][C]0.0511101159630698[/C][/ROW]
[ROW][C]11[/C][C]24.633[/C][C]24.3635202920484[/C][C]0.269479707951593[/C][/ROW]
[ROW][C]12[/C][C]25.174[/C][C]24.4846617334684[/C][C]0.68933826653155[/C][/ROW]
[ROW][C]13[/C][C]24.449[/C][C]25.0746261922312[/C][C]-0.625626192231245[/C][/ROW]
[ROW][C]14[/C][C]24.277[/C][C]24.3051872725053[/C][C]-0.0281872725052814[/C][/ROW]
[ROW][C]15[/C][C]24.393[/C][C]24.1311850993934[/C][C]0.261814900606574[/C][/ROW]
[ROW][C]16[/C][C]24.301[/C][C]24.2657821010784[/C][C]0.0352178989215517[/C][/ROW]
[ROW][C]17[/C][C]24.381[/C][C]24.1762836673532[/C][C]0.204716332646793[/C][/ROW]
[ROW][C]18[/C][C]24.286[/C][C]24.2708248946644[/C][C]0.015175105335576[/C][/ROW]
[ROW][C]19[/C][C]24.335[/C][C]24.1769027991643[/C][C]0.158097200835709[/C][/ROW]
[ROW][C]20[/C][C]24.273[/C][C]24.2371326180307[/C][C]0.0358673819693003[/C][/ROW]
[ROW][C]21[/C][C]24.556[/C][C]24.177680317804[/C][C]0.378319682196008[/C][/ROW]
[ROW][C]22[/C][C]24.841[/C][C]24.4875527828584[/C][C]0.353447217141589[/C][/ROW]
[ROW][C]23[/C][C]25.464[/C][C]24.7976585292369[/C][C]0.666341470763058[/C][/ROW]
[ROW][C]24[/C][C]25.514[/C][C]25.4679895001858[/C][C]0.046010499814237[/C][/ROW]
[ROW][C]25[/C][C]25.531[/C][C]25.5212576768273[/C][C]0.0097423231726772[/C][/ROW]
[ROW][C]26[/C][C]25.042[/C][C]25.5389496848072[/C][C]-0.496949684807149[/C][/ROW]
[ROW][C]27[/C][C]24.676[/C][C]25.0146507995859[/C][C]-0.338650799585889[/C][/ROW]
[ROW][C]28[/C][C]24.809[/C][C]24.6245960590958[/C][C]0.184403940904218[/C][/ROW]
[ROW][C]29[/C][C]25.313[/C][C]24.7706944747772[/C][C]0.542305525222847[/C][/ROW]
[ROW][C]30[/C][C]25.64[/C][C]25.3132150354595[/C][C]0.326784964540476[/C][/ROW]
[ROW][C]31[/C][C]25.447[/C][C]25.6634269325751[/C][C]-0.216426932575079[/C][/ROW]
[ROW][C]32[/C][C]25.021[/C][C]25.4550538884112[/C][C]-0.434053888411214[/C][/ROW]
[ROW][C]33[/C][C]24.752[/C][C]24.9982225611053[/C][C]-0.246222561105277[/C][/ROW]
[ROW][C]34[/C][C]24.939[/C][C]24.7117331005239[/C][C]0.22726689947606[/C][/ROW]
[ROW][C]35[/C][C]25.365[/C][C]24.9148761195145[/C][C]0.450123880485489[/C][/ROW]
[ROW][C]36[/C][C]25.214[/C][C]25.3728489161142[/C][C]-0.158848916114177[/C][/ROW]
[ROW][C]37[/C][C]25.563[/C][C]25.2105657020809[/C][C]0.352434297919075[/C][/ROW]
[ROW][C]38[/C][C]25.475[/C][C]25.5845994996878[/C][C]-0.109599499687839[/C][/ROW]
[ROW][C]39[/C][C]25.659[/C][C]25.488814526122[/C][C]0.170185473878021[/C][/ROW]
[ROW][C]40[/C][C]25.841[/C][C]25.6849029883796[/C][C]0.156097011620368[/C][/ROW]
[ROW][C]41[/C][C]25.888[/C][C]25.877990731596[/C][C]0.0100092684040511[/C][/ROW]
[ROW][C]42[/C][C]25.759[/C][C]25.9257017009905[/C][C]-0.166701700990529[/C][/ROW]
[ROW][C]43[/C][C]25.944[/C][C]25.7848606949705[/C][C]0.159139305029502[/C][/ROW]
[ROW][C]44[/C][C]25.818[/C][C]25.9811645356493[/C][C]-0.163164535649273[/C][/ROW]
[ROW][C]45[/C][C]25.789[/C][C]25.8435747783919[/C][C]-0.0545747783918564[/C][/ROW]
[ROW][C]46[/C][C]25.662[/C][C]25.8106982715797[/C][C]-0.14869827157975[/C][/ROW]
[ROW][C]47[/C][C]26.927[/C][C]25.6731360690438[/C][C]1.25386393095617[/C][/ROW]
[ROW][C]48[/C][C]27.521[/C][C]27.0271994095289[/C][C]0.493800590471139[/C][/ROW]
[ROW][C]49[/C][C]27.485[/C][C]27.6562746110998[/C][C]-0.171274611099822[/C][/ROW]
[ROW][C]50[/C][C]27.444[/C][C]27.6081087862218[/C][C]-0.164108786221842[/C][/ROW]
[ROW][C]51[/C][C]27.395[/C][C]27.5554519578029[/C][C]-0.160451957802895[/C][/ROW]
[ROW][C]52[/C][C]27.45[/C][C]27.4950548779472[/C][C]-0.045054877947198[/C][/ROW]
[ROW][C]53[/C][C]27.437[/C][C]27.5468545801828[/C][C]-0.109854580182777[/C][/ROW]
[ROW][C]54[/C][C]27.45[/C][C]27.5260514879675[/C][C]-0.0760514879675043[/C][/ROW]
[ROW][C]55[/C][C]27.458[/C][C]27.5336494667433[/C][C]-0.0756494667433358[/C][/ROW]
[ROW][C]56[/C][C]27.816[/C][C]27.5362760015309[/C][C]0.279723998469063[/C][/ROW]
[ROW][C]57[/C][C]27.599[/C][C]27.914145106226[/C][C]-0.315145106225962[/C][/ROW]
[ROW][C]58[/C][C]27.588[/C][C]27.6747600011081[/C][C]-0.0867600011080647[/C][/ROW]
[ROW][C]59[/C][C]27.667[/C][C]27.657597342363[/C][C]0.00940265763695436[/C][/ROW]
[ROW][C]60[/C][C]27.64[/C][C]27.7372652235246[/C][C]-0.097265223524559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289660&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
325.54125.825-0.283999999999999
425.30825.3668271661914-0.0588271661914206
525.66325.12964860757520.533351392424809
625.7825.5225331463110.257466853689035
725.32825.657821301419-0.329821301419017
824.80625.1823937299399-0.376393729939949
924.65124.63365806740240.017341932597617
1024.53124.47988988403690.0511101159630698
1124.63324.36352029204840.269479707951593
1225.17424.48466173346840.68933826653155
1324.44925.0746261922312-0.625626192231245
1424.27724.3051872725053-0.0281872725052814
1524.39324.13118509939340.261814900606574
1624.30124.26578210107840.0352178989215517
1724.38124.17628366735320.204716332646793
1824.28624.27082489466440.015175105335576
1924.33524.17690279916430.158097200835709
2024.27324.23713261803070.0358673819693003
2124.55624.1776803178040.378319682196008
2224.84124.48755278285840.353447217141589
2325.46424.79765852923690.666341470763058
2425.51425.46798950018580.046010499814237
2525.53125.52125767682730.0097423231726772
2625.04225.5389496848072-0.496949684807149
2724.67625.0146507995859-0.338650799585889
2824.80924.62459605909580.184403940904218
2925.31324.77069447477720.542305525222847
3025.6425.31321503545950.326784964540476
3125.44725.6634269325751-0.216426932575079
3225.02125.4550538884112-0.434053888411214
3324.75224.9982225611053-0.246222561105277
3424.93924.71173310052390.22726689947606
3525.36524.91487611951450.450123880485489
3625.21425.3728489161142-0.158848916114177
3725.56325.21056570208090.352434297919075
3825.47525.5845994996878-0.109599499687839
3925.65925.4888145261220.170185473878021
4025.84125.68490298837960.156097011620368
4125.88825.8779907315960.0100092684040511
4225.75925.9257017009905-0.166701700990529
4325.94425.78486069497050.159139305029502
4425.81825.9811645356493-0.163164535649273
4525.78925.8435747783919-0.0545747783918564
4625.66225.8106982715797-0.14869827157975
4726.92725.67313606904381.25386393095617
4827.52127.02719940952890.493800590471139
4927.48527.6562746110998-0.171274611099822
5027.44427.6081087862218-0.164108786221842
5127.39527.5554519578029-0.160451957802895
5227.4527.4950548779472-0.045054877947198
5327.43727.5468545801828-0.109854580182777
5427.4527.5260514879675-0.0760514879675043
5527.45827.5336494667433-0.0756494667433358
5627.81627.53627600153090.279723998469063
5727.59927.914145106226-0.315145106225962
5827.58827.6747600011081-0.0867600011080647
5927.66727.6575973423630.00940265763695436
6027.6427.7372652235246-0.097265223524559







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6127.703356367223427.061976529500628.3447362049463
6227.766712734446926.826898083964628.7065273849292
6327.830069101670326.638514868342729.021623334998
6427.893425468893826.470341182835629.316509754952
6527.956781836117226.312548030375229.6010156418593
6628.020138203340726.160310171772229.8799662349092
6728.083494570564126.010890790218330.15609835091
6828.146850937787625.862593022025430.4311088535498
6928.21020730501125.714299706330330.7061149036918
7028.273563672234525.565243339540730.9818840049283
7128.336920039457925.414879977514331.2589601014016
7228.400276406681425.262815158091331.5377376552714

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 27.7033563672234 & 27.0619765295006 & 28.3447362049463 \tabularnewline
62 & 27.7667127344469 & 26.8268980839646 & 28.7065273849292 \tabularnewline
63 & 27.8300691016703 & 26.6385148683427 & 29.021623334998 \tabularnewline
64 & 27.8934254688938 & 26.4703411828356 & 29.316509754952 \tabularnewline
65 & 27.9567818361172 & 26.3125480303752 & 29.6010156418593 \tabularnewline
66 & 28.0201382033407 & 26.1603101717722 & 29.8799662349092 \tabularnewline
67 & 28.0834945705641 & 26.0108907902183 & 30.15609835091 \tabularnewline
68 & 28.1468509377876 & 25.8625930220254 & 30.4311088535498 \tabularnewline
69 & 28.210207305011 & 25.7142997063303 & 30.7061149036918 \tabularnewline
70 & 28.2735636722345 & 25.5652433395407 & 30.9818840049283 \tabularnewline
71 & 28.3369200394579 & 25.4148799775143 & 31.2589601014016 \tabularnewline
72 & 28.4002764066814 & 25.2628151580913 & 31.5377376552714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289660&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]27.7033563672234[/C][C]27.0619765295006[/C][C]28.3447362049463[/C][/ROW]
[ROW][C]62[/C][C]27.7667127344469[/C][C]26.8268980839646[/C][C]28.7065273849292[/C][/ROW]
[ROW][C]63[/C][C]27.8300691016703[/C][C]26.6385148683427[/C][C]29.021623334998[/C][/ROW]
[ROW][C]64[/C][C]27.8934254688938[/C][C]26.4703411828356[/C][C]29.316509754952[/C][/ROW]
[ROW][C]65[/C][C]27.9567818361172[/C][C]26.3125480303752[/C][C]29.6010156418593[/C][/ROW]
[ROW][C]66[/C][C]28.0201382033407[/C][C]26.1603101717722[/C][C]29.8799662349092[/C][/ROW]
[ROW][C]67[/C][C]28.0834945705641[/C][C]26.0108907902183[/C][C]30.15609835091[/C][/ROW]
[ROW][C]68[/C][C]28.1468509377876[/C][C]25.8625930220254[/C][C]30.4311088535498[/C][/ROW]
[ROW][C]69[/C][C]28.210207305011[/C][C]25.7142997063303[/C][C]30.7061149036918[/C][/ROW]
[ROW][C]70[/C][C]28.2735636722345[/C][C]25.5652433395407[/C][C]30.9818840049283[/C][/ROW]
[ROW][C]71[/C][C]28.3369200394579[/C][C]25.4148799775143[/C][C]31.2589601014016[/C][/ROW]
[ROW][C]72[/C][C]28.4002764066814[/C][C]25.2628151580913[/C][C]31.5377376552714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289660&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289660&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
6127.703356367223427.061976529500628.3447362049463
6227.766712734446926.826898083964628.7065273849292
6327.830069101670326.638514868342729.021623334998
6427.893425468893826.470341182835629.316509754952
6527.956781836117226.312548030375229.6010156418593
6628.020138203340726.160310171772229.8799662349092
6728.083494570564126.010890790218330.15609835091
6828.146850937787625.862593022025430.4311088535498
6928.21020730501125.714299706330330.7061149036918
7028.273563672234525.565243339540730.9818840049283
7128.336920039457925.414879977514331.2589601014016
7228.400276406681425.262815158091331.5377376552714



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')