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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 21:22:21 +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/2014/Nov/30/t14173825846yqogam3cabzthg.htm/, Retrieved Sun, 19 May 2024 14:36:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261673, Retrieved Sun, 19 May 2024 14:36:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 21:22:21] [10cb439e718ee6ebb3ca27a8e32cf1a7] [Current]
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Dataseries X:
27.88
28.06
28.08
28.12
28.11
28.18
28.2
28.37
28.64
28.75
28.97
29.08
29.16
29.24
29.36
29.35
29.43
29.49
29.61
29.66
29.75
29.74
29.97
30.02
30.09
30.16
30.33
30.41
30.44
30.45
30.46
30.51
30.54
30.82
30.88
30.89
31.13
31.41
31.47
31.56
31.62
31.65
31.79
31.98
32.14
32.32
32.5
32.55
32.66
32.68
32.72
32.8
32.93
32.96
32.98
33.09
33.46
33.65
33.82
33.83
33.92
33.87
34.03
34.11
34.29
34.44
34.64
34.77
35.01
35.19
35.32
35.35




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261673&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261673&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261673&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.109212986776831
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.109212986776831 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261673&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]0.109212986776831[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261673&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261673&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
beta0.109212986776831
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
328.0828.24-0.16
428.1228.2425259221157-0.122525922115702
528.1128.2691445002039-0.159144500203865
628.1828.2417638540075-0.061763854007495
728.228.3050184390365-0.105018439036488
828.3728.31354906164270.0564509383573295
928.6428.4897142372270.150285762772967
1028.7528.7761273942495-0.0261273942495031
1128.9728.88327394348680.0867260565131822
1229.0829.11274555515-0.0327455551499973
1329.1629.2191693152684-0.0591693152683987
1429.2429.2927072576224-0.0527072576224015
1529.3629.3669509405926-0.00695094059264179
1629.3529.4861918076096-0.13619180760961
1729.4329.461317893526-0.0313178935260332
1829.4929.5378975728345-0.0478975728344935
1929.6129.59266653584590.0173334641541238
2029.6629.7145595752373-0.054559575237338
2129.7529.7586009610684-0.00860096106839237
2229.7429.847661624421-0.107661624420963
2329.9729.82590357685670.144096423143296
2430.0230.071640777612-0.0516407776120396
2530.0930.1160009340496-0.0260009340495522
2630.1630.183161294383-0.0231612943830122
2730.3330.25063178024580.0793682197541727
2830.4130.4292998205803-0.0192998205803399
2930.4430.5071920295305-0.0671920295305029
3030.4530.5298537872979-0.079853787297882
3130.4630.5311327166816-0.0711327166816353
3230.5130.5333641002353-0.023364100235284
3330.5430.5808124370652-0.0408124370652381
3430.8230.60635518891570.213644811084301
3530.8830.9096879768436-0.02968797684359
3630.8930.9664456642211-0.0764456642211364
3731.1330.96809680490540.161903195094588
3831.4131.22577873641040.184221263589599
3931.4731.5258980908348-0.0558980908348268
4031.5631.5797932933796-0.0197932933796316
4131.6231.6676316086915-0.0476316086914892
4231.6531.7224296184413-0.072429618441312
4331.7931.74451936348020.0454806365197733
4431.9831.88948643963510.0905135603649398
4532.1432.08937169590630.0506283040936779
4632.3232.25490096421180.0650990357881582
4732.532.44201062434660.0579893756534418
4832.5532.628343817263-0.0783438172629971
4932.6632.6697876549842-0.00978765498420131
5032.6832.7787187159498-0.0987187159498362
5132.7232.7879373501302-0.0679373501301797
5232.832.8205177092088-0.0205177092087609
5332.9332.89827690890430.0317230910957491
5432.9633.0317414824326-0.0717414824326141
5532.9833.0539063808604-0.0739063808603575
5633.0933.06583484426470.0241651557352824
5733.4633.17847399309850.281526006901494
5833.6533.57922028916760.0707797108324257
5933.8233.77695035279080.043049647209223
6033.8333.9516519333422-0.121651933342186
6133.9233.9483659623547-0.0283659623547052
6233.8734.0352680308832-0.165268030883155
6334.0333.96721861561170.0627813843883231
6434.1134.1340751581147-0.0240751581147123
6534.2934.21144583818990.0785541618101178
6634.4434.40002497282490.0399750271750818
6734.6434.55439076493920.0856092350608151
6834.7734.76374040519590.00625959480414195
6935.0134.89442403424040.115575965759561
7035.1935.14704643066070.0429535693393461
7135.3235.3317375182609-0.0117375182609223
7235.3535.4604556288343-0.110455628834302

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 28.08 & 28.24 & -0.16 \tabularnewline
4 & 28.12 & 28.2425259221157 & -0.122525922115702 \tabularnewline
5 & 28.11 & 28.2691445002039 & -0.159144500203865 \tabularnewline
6 & 28.18 & 28.2417638540075 & -0.061763854007495 \tabularnewline
7 & 28.2 & 28.3050184390365 & -0.105018439036488 \tabularnewline
8 & 28.37 & 28.3135490616427 & 0.0564509383573295 \tabularnewline
9 & 28.64 & 28.489714237227 & 0.150285762772967 \tabularnewline
10 & 28.75 & 28.7761273942495 & -0.0261273942495031 \tabularnewline
11 & 28.97 & 28.8832739434868 & 0.0867260565131822 \tabularnewline
12 & 29.08 & 29.11274555515 & -0.0327455551499973 \tabularnewline
13 & 29.16 & 29.2191693152684 & -0.0591693152683987 \tabularnewline
14 & 29.24 & 29.2927072576224 & -0.0527072576224015 \tabularnewline
15 & 29.36 & 29.3669509405926 & -0.00695094059264179 \tabularnewline
16 & 29.35 & 29.4861918076096 & -0.13619180760961 \tabularnewline
17 & 29.43 & 29.461317893526 & -0.0313178935260332 \tabularnewline
18 & 29.49 & 29.5378975728345 & -0.0478975728344935 \tabularnewline
19 & 29.61 & 29.5926665358459 & 0.0173334641541238 \tabularnewline
20 & 29.66 & 29.7145595752373 & -0.054559575237338 \tabularnewline
21 & 29.75 & 29.7586009610684 & -0.00860096106839237 \tabularnewline
22 & 29.74 & 29.847661624421 & -0.107661624420963 \tabularnewline
23 & 29.97 & 29.8259035768567 & 0.144096423143296 \tabularnewline
24 & 30.02 & 30.071640777612 & -0.0516407776120396 \tabularnewline
25 & 30.09 & 30.1160009340496 & -0.0260009340495522 \tabularnewline
26 & 30.16 & 30.183161294383 & -0.0231612943830122 \tabularnewline
27 & 30.33 & 30.2506317802458 & 0.0793682197541727 \tabularnewline
28 & 30.41 & 30.4292998205803 & -0.0192998205803399 \tabularnewline
29 & 30.44 & 30.5071920295305 & -0.0671920295305029 \tabularnewline
30 & 30.45 & 30.5298537872979 & -0.079853787297882 \tabularnewline
31 & 30.46 & 30.5311327166816 & -0.0711327166816353 \tabularnewline
32 & 30.51 & 30.5333641002353 & -0.023364100235284 \tabularnewline
33 & 30.54 & 30.5808124370652 & -0.0408124370652381 \tabularnewline
34 & 30.82 & 30.6063551889157 & 0.213644811084301 \tabularnewline
35 & 30.88 & 30.9096879768436 & -0.02968797684359 \tabularnewline
36 & 30.89 & 30.9664456642211 & -0.0764456642211364 \tabularnewline
37 & 31.13 & 30.9680968049054 & 0.161903195094588 \tabularnewline
38 & 31.41 & 31.2257787364104 & 0.184221263589599 \tabularnewline
39 & 31.47 & 31.5258980908348 & -0.0558980908348268 \tabularnewline
40 & 31.56 & 31.5797932933796 & -0.0197932933796316 \tabularnewline
41 & 31.62 & 31.6676316086915 & -0.0476316086914892 \tabularnewline
42 & 31.65 & 31.7224296184413 & -0.072429618441312 \tabularnewline
43 & 31.79 & 31.7445193634802 & 0.0454806365197733 \tabularnewline
44 & 31.98 & 31.8894864396351 & 0.0905135603649398 \tabularnewline
45 & 32.14 & 32.0893716959063 & 0.0506283040936779 \tabularnewline
46 & 32.32 & 32.2549009642118 & 0.0650990357881582 \tabularnewline
47 & 32.5 & 32.4420106243466 & 0.0579893756534418 \tabularnewline
48 & 32.55 & 32.628343817263 & -0.0783438172629971 \tabularnewline
49 & 32.66 & 32.6697876549842 & -0.00978765498420131 \tabularnewline
50 & 32.68 & 32.7787187159498 & -0.0987187159498362 \tabularnewline
51 & 32.72 & 32.7879373501302 & -0.0679373501301797 \tabularnewline
52 & 32.8 & 32.8205177092088 & -0.0205177092087609 \tabularnewline
53 & 32.93 & 32.8982769089043 & 0.0317230910957491 \tabularnewline
54 & 32.96 & 33.0317414824326 & -0.0717414824326141 \tabularnewline
55 & 32.98 & 33.0539063808604 & -0.0739063808603575 \tabularnewline
56 & 33.09 & 33.0658348442647 & 0.0241651557352824 \tabularnewline
57 & 33.46 & 33.1784739930985 & 0.281526006901494 \tabularnewline
58 & 33.65 & 33.5792202891676 & 0.0707797108324257 \tabularnewline
59 & 33.82 & 33.7769503527908 & 0.043049647209223 \tabularnewline
60 & 33.83 & 33.9516519333422 & -0.121651933342186 \tabularnewline
61 & 33.92 & 33.9483659623547 & -0.0283659623547052 \tabularnewline
62 & 33.87 & 34.0352680308832 & -0.165268030883155 \tabularnewline
63 & 34.03 & 33.9672186156117 & 0.0627813843883231 \tabularnewline
64 & 34.11 & 34.1340751581147 & -0.0240751581147123 \tabularnewline
65 & 34.29 & 34.2114458381899 & 0.0785541618101178 \tabularnewline
66 & 34.44 & 34.4000249728249 & 0.0399750271750818 \tabularnewline
67 & 34.64 & 34.5543907649392 & 0.0856092350608151 \tabularnewline
68 & 34.77 & 34.7637404051959 & 0.00625959480414195 \tabularnewline
69 & 35.01 & 34.8944240342404 & 0.115575965759561 \tabularnewline
70 & 35.19 & 35.1470464306607 & 0.0429535693393461 \tabularnewline
71 & 35.32 & 35.3317375182609 & -0.0117375182609223 \tabularnewline
72 & 35.35 & 35.4604556288343 & -0.110455628834302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261673&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]28.08[/C][C]28.24[/C][C]-0.16[/C][/ROW]
[ROW][C]4[/C][C]28.12[/C][C]28.2425259221157[/C][C]-0.122525922115702[/C][/ROW]
[ROW][C]5[/C][C]28.11[/C][C]28.2691445002039[/C][C]-0.159144500203865[/C][/ROW]
[ROW][C]6[/C][C]28.18[/C][C]28.2417638540075[/C][C]-0.061763854007495[/C][/ROW]
[ROW][C]7[/C][C]28.2[/C][C]28.3050184390365[/C][C]-0.105018439036488[/C][/ROW]
[ROW][C]8[/C][C]28.37[/C][C]28.3135490616427[/C][C]0.0564509383573295[/C][/ROW]
[ROW][C]9[/C][C]28.64[/C][C]28.489714237227[/C][C]0.150285762772967[/C][/ROW]
[ROW][C]10[/C][C]28.75[/C][C]28.7761273942495[/C][C]-0.0261273942495031[/C][/ROW]
[ROW][C]11[/C][C]28.97[/C][C]28.8832739434868[/C][C]0.0867260565131822[/C][/ROW]
[ROW][C]12[/C][C]29.08[/C][C]29.11274555515[/C][C]-0.0327455551499973[/C][/ROW]
[ROW][C]13[/C][C]29.16[/C][C]29.2191693152684[/C][C]-0.0591693152683987[/C][/ROW]
[ROW][C]14[/C][C]29.24[/C][C]29.2927072576224[/C][C]-0.0527072576224015[/C][/ROW]
[ROW][C]15[/C][C]29.36[/C][C]29.3669509405926[/C][C]-0.00695094059264179[/C][/ROW]
[ROW][C]16[/C][C]29.35[/C][C]29.4861918076096[/C][C]-0.13619180760961[/C][/ROW]
[ROW][C]17[/C][C]29.43[/C][C]29.461317893526[/C][C]-0.0313178935260332[/C][/ROW]
[ROW][C]18[/C][C]29.49[/C][C]29.5378975728345[/C][C]-0.0478975728344935[/C][/ROW]
[ROW][C]19[/C][C]29.61[/C][C]29.5926665358459[/C][C]0.0173334641541238[/C][/ROW]
[ROW][C]20[/C][C]29.66[/C][C]29.7145595752373[/C][C]-0.054559575237338[/C][/ROW]
[ROW][C]21[/C][C]29.75[/C][C]29.7586009610684[/C][C]-0.00860096106839237[/C][/ROW]
[ROW][C]22[/C][C]29.74[/C][C]29.847661624421[/C][C]-0.107661624420963[/C][/ROW]
[ROW][C]23[/C][C]29.97[/C][C]29.8259035768567[/C][C]0.144096423143296[/C][/ROW]
[ROW][C]24[/C][C]30.02[/C][C]30.071640777612[/C][C]-0.0516407776120396[/C][/ROW]
[ROW][C]25[/C][C]30.09[/C][C]30.1160009340496[/C][C]-0.0260009340495522[/C][/ROW]
[ROW][C]26[/C][C]30.16[/C][C]30.183161294383[/C][C]-0.0231612943830122[/C][/ROW]
[ROW][C]27[/C][C]30.33[/C][C]30.2506317802458[/C][C]0.0793682197541727[/C][/ROW]
[ROW][C]28[/C][C]30.41[/C][C]30.4292998205803[/C][C]-0.0192998205803399[/C][/ROW]
[ROW][C]29[/C][C]30.44[/C][C]30.5071920295305[/C][C]-0.0671920295305029[/C][/ROW]
[ROW][C]30[/C][C]30.45[/C][C]30.5298537872979[/C][C]-0.079853787297882[/C][/ROW]
[ROW][C]31[/C][C]30.46[/C][C]30.5311327166816[/C][C]-0.0711327166816353[/C][/ROW]
[ROW][C]32[/C][C]30.51[/C][C]30.5333641002353[/C][C]-0.023364100235284[/C][/ROW]
[ROW][C]33[/C][C]30.54[/C][C]30.5808124370652[/C][C]-0.0408124370652381[/C][/ROW]
[ROW][C]34[/C][C]30.82[/C][C]30.6063551889157[/C][C]0.213644811084301[/C][/ROW]
[ROW][C]35[/C][C]30.88[/C][C]30.9096879768436[/C][C]-0.02968797684359[/C][/ROW]
[ROW][C]36[/C][C]30.89[/C][C]30.9664456642211[/C][C]-0.0764456642211364[/C][/ROW]
[ROW][C]37[/C][C]31.13[/C][C]30.9680968049054[/C][C]0.161903195094588[/C][/ROW]
[ROW][C]38[/C][C]31.41[/C][C]31.2257787364104[/C][C]0.184221263589599[/C][/ROW]
[ROW][C]39[/C][C]31.47[/C][C]31.5258980908348[/C][C]-0.0558980908348268[/C][/ROW]
[ROW][C]40[/C][C]31.56[/C][C]31.5797932933796[/C][C]-0.0197932933796316[/C][/ROW]
[ROW][C]41[/C][C]31.62[/C][C]31.6676316086915[/C][C]-0.0476316086914892[/C][/ROW]
[ROW][C]42[/C][C]31.65[/C][C]31.7224296184413[/C][C]-0.072429618441312[/C][/ROW]
[ROW][C]43[/C][C]31.79[/C][C]31.7445193634802[/C][C]0.0454806365197733[/C][/ROW]
[ROW][C]44[/C][C]31.98[/C][C]31.8894864396351[/C][C]0.0905135603649398[/C][/ROW]
[ROW][C]45[/C][C]32.14[/C][C]32.0893716959063[/C][C]0.0506283040936779[/C][/ROW]
[ROW][C]46[/C][C]32.32[/C][C]32.2549009642118[/C][C]0.0650990357881582[/C][/ROW]
[ROW][C]47[/C][C]32.5[/C][C]32.4420106243466[/C][C]0.0579893756534418[/C][/ROW]
[ROW][C]48[/C][C]32.55[/C][C]32.628343817263[/C][C]-0.0783438172629971[/C][/ROW]
[ROW][C]49[/C][C]32.66[/C][C]32.6697876549842[/C][C]-0.00978765498420131[/C][/ROW]
[ROW][C]50[/C][C]32.68[/C][C]32.7787187159498[/C][C]-0.0987187159498362[/C][/ROW]
[ROW][C]51[/C][C]32.72[/C][C]32.7879373501302[/C][C]-0.0679373501301797[/C][/ROW]
[ROW][C]52[/C][C]32.8[/C][C]32.8205177092088[/C][C]-0.0205177092087609[/C][/ROW]
[ROW][C]53[/C][C]32.93[/C][C]32.8982769089043[/C][C]0.0317230910957491[/C][/ROW]
[ROW][C]54[/C][C]32.96[/C][C]33.0317414824326[/C][C]-0.0717414824326141[/C][/ROW]
[ROW][C]55[/C][C]32.98[/C][C]33.0539063808604[/C][C]-0.0739063808603575[/C][/ROW]
[ROW][C]56[/C][C]33.09[/C][C]33.0658348442647[/C][C]0.0241651557352824[/C][/ROW]
[ROW][C]57[/C][C]33.46[/C][C]33.1784739930985[/C][C]0.281526006901494[/C][/ROW]
[ROW][C]58[/C][C]33.65[/C][C]33.5792202891676[/C][C]0.0707797108324257[/C][/ROW]
[ROW][C]59[/C][C]33.82[/C][C]33.7769503527908[/C][C]0.043049647209223[/C][/ROW]
[ROW][C]60[/C][C]33.83[/C][C]33.9516519333422[/C][C]-0.121651933342186[/C][/ROW]
[ROW][C]61[/C][C]33.92[/C][C]33.9483659623547[/C][C]-0.0283659623547052[/C][/ROW]
[ROW][C]62[/C][C]33.87[/C][C]34.0352680308832[/C][C]-0.165268030883155[/C][/ROW]
[ROW][C]63[/C][C]34.03[/C][C]33.9672186156117[/C][C]0.0627813843883231[/C][/ROW]
[ROW][C]64[/C][C]34.11[/C][C]34.1340751581147[/C][C]-0.0240751581147123[/C][/ROW]
[ROW][C]65[/C][C]34.29[/C][C]34.2114458381899[/C][C]0.0785541618101178[/C][/ROW]
[ROW][C]66[/C][C]34.44[/C][C]34.4000249728249[/C][C]0.0399750271750818[/C][/ROW]
[ROW][C]67[/C][C]34.64[/C][C]34.5543907649392[/C][C]0.0856092350608151[/C][/ROW]
[ROW][C]68[/C][C]34.77[/C][C]34.7637404051959[/C][C]0.00625959480414195[/C][/ROW]
[ROW][C]69[/C][C]35.01[/C][C]34.8944240342404[/C][C]0.115575965759561[/C][/ROW]
[ROW][C]70[/C][C]35.19[/C][C]35.1470464306607[/C][C]0.0429535693393461[/C][/ROW]
[ROW][C]71[/C][C]35.32[/C][C]35.3317375182609[/C][C]-0.0117375182609223[/C][/ROW]
[ROW][C]72[/C][C]35.35[/C][C]35.4604556288343[/C][C]-0.110455628834302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261673&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261673&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
328.0828.24-0.16
428.1228.2425259221157-0.122525922115702
528.1128.2691445002039-0.159144500203865
628.1828.2417638540075-0.061763854007495
728.228.3050184390365-0.105018439036488
828.3728.31354906164270.0564509383573295
928.6428.4897142372270.150285762772967
1028.7528.7761273942495-0.0261273942495031
1128.9728.88327394348680.0867260565131822
1229.0829.11274555515-0.0327455551499973
1329.1629.2191693152684-0.0591693152683987
1429.2429.2927072576224-0.0527072576224015
1529.3629.3669509405926-0.00695094059264179
1629.3529.4861918076096-0.13619180760961
1729.4329.461317893526-0.0313178935260332
1829.4929.5378975728345-0.0478975728344935
1929.6129.59266653584590.0173334641541238
2029.6629.7145595752373-0.054559575237338
2129.7529.7586009610684-0.00860096106839237
2229.7429.847661624421-0.107661624420963
2329.9729.82590357685670.144096423143296
2430.0230.071640777612-0.0516407776120396
2530.0930.1160009340496-0.0260009340495522
2630.1630.183161294383-0.0231612943830122
2730.3330.25063178024580.0793682197541727
2830.4130.4292998205803-0.0192998205803399
2930.4430.5071920295305-0.0671920295305029
3030.4530.5298537872979-0.079853787297882
3130.4630.5311327166816-0.0711327166816353
3230.5130.5333641002353-0.023364100235284
3330.5430.5808124370652-0.0408124370652381
3430.8230.60635518891570.213644811084301
3530.8830.9096879768436-0.02968797684359
3630.8930.9664456642211-0.0764456642211364
3731.1330.96809680490540.161903195094588
3831.4131.22577873641040.184221263589599
3931.4731.5258980908348-0.0558980908348268
4031.5631.5797932933796-0.0197932933796316
4131.6231.6676316086915-0.0476316086914892
4231.6531.7224296184413-0.072429618441312
4331.7931.74451936348020.0454806365197733
4431.9831.88948643963510.0905135603649398
4532.1432.08937169590630.0506283040936779
4632.3232.25490096421180.0650990357881582
4732.532.44201062434660.0579893756534418
4832.5532.628343817263-0.0783438172629971
4932.6632.6697876549842-0.00978765498420131
5032.6832.7787187159498-0.0987187159498362
5132.7232.7879373501302-0.0679373501301797
5232.832.8205177092088-0.0205177092087609
5332.9332.89827690890430.0317230910957491
5432.9633.0317414824326-0.0717414824326141
5532.9833.0539063808604-0.0739063808603575
5633.0933.06583484426470.0241651557352824
5733.4633.17847399309850.281526006901494
5833.6533.57922028916760.0707797108324257
5933.8233.77695035279080.043049647209223
6033.8333.9516519333422-0.121651933342186
6133.9233.9483659623547-0.0283659623547052
6233.8734.0352680308832-0.165268030883155
6334.0333.96721861561170.0627813843883231
6434.1134.1340751581147-0.0240751581147123
6534.2934.21144583818990.0785541618101178
6634.4434.40002497282490.0399750271750818
6734.6434.55439076493920.0856092350608151
6834.7734.76374040519590.00625959480414195
6935.0134.89442403424040.115575965759561
7035.1935.14704643066070.0429535693393461
7135.3235.3317375182609-0.0117375182609223
7235.3535.4604556288343-0.110455628834302







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7335.47839243970335.302036818572735.6547480608333
7435.60678487940635.343408906432335.8701608523797
7535.73517731910935.395267457120536.0750871810975
7635.86356975881235.450824487868536.2763150297555
7735.99196219851535.507639313924936.476285083105
7836.12035463821835.564557347830936.676151928605
7936.24874707792135.620952132697336.8765420231446
8036.37713951762435.676455442988137.0778235922598
8136.50553195732735.730840027737137.2802238869168
8236.6339243970335.783961660559337.4838871335007
8336.76231683673335.835727771683137.6889059017828
8436.89070927643635.886079278782437.8953392740896

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 35.478392439703 & 35.3020368185727 & 35.6547480608333 \tabularnewline
74 & 35.606784879406 & 35.3434089064323 & 35.8701608523797 \tabularnewline
75 & 35.735177319109 & 35.3952674571205 & 36.0750871810975 \tabularnewline
76 & 35.863569758812 & 35.4508244878685 & 36.2763150297555 \tabularnewline
77 & 35.991962198515 & 35.5076393139249 & 36.476285083105 \tabularnewline
78 & 36.120354638218 & 35.5645573478309 & 36.676151928605 \tabularnewline
79 & 36.248747077921 & 35.6209521326973 & 36.8765420231446 \tabularnewline
80 & 36.377139517624 & 35.6764554429881 & 37.0778235922598 \tabularnewline
81 & 36.505531957327 & 35.7308400277371 & 37.2802238869168 \tabularnewline
82 & 36.63392439703 & 35.7839616605593 & 37.4838871335007 \tabularnewline
83 & 36.762316836733 & 35.8357277716831 & 37.6889059017828 \tabularnewline
84 & 36.890709276436 & 35.8860792787824 & 37.8953392740896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261673&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]35.478392439703[/C][C]35.3020368185727[/C][C]35.6547480608333[/C][/ROW]
[ROW][C]74[/C][C]35.606784879406[/C][C]35.3434089064323[/C][C]35.8701608523797[/C][/ROW]
[ROW][C]75[/C][C]35.735177319109[/C][C]35.3952674571205[/C][C]36.0750871810975[/C][/ROW]
[ROW][C]76[/C][C]35.863569758812[/C][C]35.4508244878685[/C][C]36.2763150297555[/C][/ROW]
[ROW][C]77[/C][C]35.991962198515[/C][C]35.5076393139249[/C][C]36.476285083105[/C][/ROW]
[ROW][C]78[/C][C]36.120354638218[/C][C]35.5645573478309[/C][C]36.676151928605[/C][/ROW]
[ROW][C]79[/C][C]36.248747077921[/C][C]35.6209521326973[/C][C]36.8765420231446[/C][/ROW]
[ROW][C]80[/C][C]36.377139517624[/C][C]35.6764554429881[/C][C]37.0778235922598[/C][/ROW]
[ROW][C]81[/C][C]36.505531957327[/C][C]35.7308400277371[/C][C]37.2802238869168[/C][/ROW]
[ROW][C]82[/C][C]36.63392439703[/C][C]35.7839616605593[/C][C]37.4838871335007[/C][/ROW]
[ROW][C]83[/C][C]36.762316836733[/C][C]35.8357277716831[/C][C]37.6889059017828[/C][/ROW]
[ROW][C]84[/C][C]36.890709276436[/C][C]35.8860792787824[/C][C]37.8953392740896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261673&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261673&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
7335.47839243970335.302036818572735.6547480608333
7435.60678487940635.343408906432335.8701608523797
7535.73517731910935.395267457120536.0750871810975
7635.86356975881235.450824487868536.2763150297555
7735.99196219851535.507639313924936.476285083105
7836.12035463821835.564557347830936.676151928605
7936.24874707792135.620952132697336.8765420231446
8036.37713951762435.676455442988137.0778235922598
8136.50553195732735.730840027737137.2802238869168
8236.6339243970335.783961660559337.4838871335007
8336.76231683673335.835727771683137.6889059017828
8436.89070927643635.886079278782437.8953392740896



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')