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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 09:41:52 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243957372qyd3gj2wykn53bt.htm/, Retrieved Fri, 10 May 2024 03:54:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41286, Retrieved Fri, 10 May 2024 03:54:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2009-06-02 15:41:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
4.43
4.44
4.44
4.44
4.45
4.47
4.48
4.48
4.5
4.52
4.52
4.53
4.53
4.63
4.66
4.67
4.68
4.69
4.69
4.7
4.71
4.72
4.72
4.72
4.73
4.74
4.76
4.81
4.82
4.83
4.83
4.84
4.89
4.92
4.95
4.95
5.01
5.05
5.08
5.11
5.14
5.17
5.18
5.2
5.22
5.24
5.28
5.29
5.33
5.4
5.43
5.46
5.46
5.46
5.47
5.49
5.5
5.54
5.55
5.55
5.56
5.6
5.61
5.63
5.64
5.66
5.67
5.69
5.77
5.77
5.78
5.8
5.82
5.85
5.87
5.88
5.9
5.91
5.94
5.97
5.98
6
6.01
6.02




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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41286&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41286&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' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.793999311610606
beta0.0134193323937087
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.793999311610606 \tabularnewline
beta & 0.0134193323937087 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41286&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]0.793999311610606[/C][/ROW]
[ROW][C]beta[/C][C]0.0134193323937087[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41286&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
alpha0.793999311610606
beta0.0134193323937087
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134.534.423015872781060.106984127218944
144.634.608525874091240.0214741259087559
154.664.656760266376290.00323973362370555
164.674.6714010798474-0.00140107984740201
174.684.68275686774525-0.00275686774524875
184.694.69342170442019-0.00342170442019096
194.694.689379288673160.000620711326839718
204.74.696268616705530.00373138329446832
214.714.72139034061084-0.0113903406108378
224.724.73263663761863-0.0126366376186278
234.724.72142954082522-0.00142954082522362
244.724.72999254138796-0.00999254138796157
254.734.74519011869151-0.0151901186915113
264.744.81861215888169-0.0786121588816897
274.764.78245801993673-0.0224580199367317
284.814.773898944474780.0361010555252168
294.824.813296869650320.00670313034968029
304.834.829991584792718.415207288337e-06
314.834.827810291963420.00218970803657914
324.844.835137282833150.00486271716684783
334.894.856957267574390.0330427324256100
344.924.902654450706860.0173455492931449
354.954.916543111151850.0334568888481543
364.954.95061577380595-0.000615773805945352
375.014.972534209285640.0374657907143590
385.055.07832615284318-0.0283261528431797
395.085.09627139944495-0.0162713994449462
405.115.106250709811150.00374929018884895
415.145.114087777200270.0259122227997324
425.175.145345473484520.0246545265154818
435.185.163288002577540.0167119974224645
445.25.183471152354410.0165288476455903
455.225.22249238500372-0.00249238500372240
465.245.237955444507010.00204455549299443
475.285.243199149613940.0368008503860553
485.295.272949657024460.0170503429755353
495.335.318892837351480.0111071626485151
505.45.394062030971450.00593796902855104
515.435.44485234825027-0.0148523482502698
525.465.46218031798748-0.00218031798747997
535.465.47066968608911-0.0106696860891091
545.465.47313146498262-0.0131314649826244
555.475.458818514980910.0111814850190921
565.495.474475818933160.0155241810668363
575.55.50951006943973-0.00951006943972654
585.545.520794556884840.0192054431151565
595.555.546988216319410.00301178368058519
605.555.54498172322430.00501827677569988
615.565.58090218580957-0.0209021858095735
625.65.63143873107618-0.0314387310761832
635.615.6485507245144-0.038550724514403
645.635.64928596073528-0.0192859607352833
655.645.64110475250088-0.00110475250088182
665.665.649471395504980.0105286044950210
675.675.657664575556860.0123354244431413
685.695.674090721267570.0159092787324298
695.775.703592337273280.066407662726724
705.775.78149934471408-0.0114993447140765
715.785.779343511923160.000656488076837825
725.85.774750167901680.0252498320983214
735.825.82174776315338-0.00174776315338043
745.855.8876809894394-0.0376809894394032
755.875.89950454879958-0.0295045487995811
765.885.91244902444505-0.0324490244450510
775.95.897358380931630.00264161906837401
785.915.91096243344079-0.000962433440787613
795.945.909652818558290.0303471814417087
805.975.940837903102440.0291620968975597
815.985.99193331108579-0.0119333110857864
8265.990771808155080.0092281918449233
836.016.006975145950990.00302485404900654
846.026.008355824466290.0116441755337133

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.53 & 4.42301587278106 & 0.106984127218944 \tabularnewline
14 & 4.63 & 4.60852587409124 & 0.0214741259087559 \tabularnewline
15 & 4.66 & 4.65676026637629 & 0.00323973362370555 \tabularnewline
16 & 4.67 & 4.6714010798474 & -0.00140107984740201 \tabularnewline
17 & 4.68 & 4.68275686774525 & -0.00275686774524875 \tabularnewline
18 & 4.69 & 4.69342170442019 & -0.00342170442019096 \tabularnewline
19 & 4.69 & 4.68937928867316 & 0.000620711326839718 \tabularnewline
20 & 4.7 & 4.69626861670553 & 0.00373138329446832 \tabularnewline
21 & 4.71 & 4.72139034061084 & -0.0113903406108378 \tabularnewline
22 & 4.72 & 4.73263663761863 & -0.0126366376186278 \tabularnewline
23 & 4.72 & 4.72142954082522 & -0.00142954082522362 \tabularnewline
24 & 4.72 & 4.72999254138796 & -0.00999254138796157 \tabularnewline
25 & 4.73 & 4.74519011869151 & -0.0151901186915113 \tabularnewline
26 & 4.74 & 4.81861215888169 & -0.0786121588816897 \tabularnewline
27 & 4.76 & 4.78245801993673 & -0.0224580199367317 \tabularnewline
28 & 4.81 & 4.77389894447478 & 0.0361010555252168 \tabularnewline
29 & 4.82 & 4.81329686965032 & 0.00670313034968029 \tabularnewline
30 & 4.83 & 4.82999158479271 & 8.415207288337e-06 \tabularnewline
31 & 4.83 & 4.82781029196342 & 0.00218970803657914 \tabularnewline
32 & 4.84 & 4.83513728283315 & 0.00486271716684783 \tabularnewline
33 & 4.89 & 4.85695726757439 & 0.0330427324256100 \tabularnewline
34 & 4.92 & 4.90265445070686 & 0.0173455492931449 \tabularnewline
35 & 4.95 & 4.91654311115185 & 0.0334568888481543 \tabularnewline
36 & 4.95 & 4.95061577380595 & -0.000615773805945352 \tabularnewline
37 & 5.01 & 4.97253420928564 & 0.0374657907143590 \tabularnewline
38 & 5.05 & 5.07832615284318 & -0.0283261528431797 \tabularnewline
39 & 5.08 & 5.09627139944495 & -0.0162713994449462 \tabularnewline
40 & 5.11 & 5.10625070981115 & 0.00374929018884895 \tabularnewline
41 & 5.14 & 5.11408777720027 & 0.0259122227997324 \tabularnewline
42 & 5.17 & 5.14534547348452 & 0.0246545265154818 \tabularnewline
43 & 5.18 & 5.16328800257754 & 0.0167119974224645 \tabularnewline
44 & 5.2 & 5.18347115235441 & 0.0165288476455903 \tabularnewline
45 & 5.22 & 5.22249238500372 & -0.00249238500372240 \tabularnewline
46 & 5.24 & 5.23795544450701 & 0.00204455549299443 \tabularnewline
47 & 5.28 & 5.24319914961394 & 0.0368008503860553 \tabularnewline
48 & 5.29 & 5.27294965702446 & 0.0170503429755353 \tabularnewline
49 & 5.33 & 5.31889283735148 & 0.0111071626485151 \tabularnewline
50 & 5.4 & 5.39406203097145 & 0.00593796902855104 \tabularnewline
51 & 5.43 & 5.44485234825027 & -0.0148523482502698 \tabularnewline
52 & 5.46 & 5.46218031798748 & -0.00218031798747997 \tabularnewline
53 & 5.46 & 5.47066968608911 & -0.0106696860891091 \tabularnewline
54 & 5.46 & 5.47313146498262 & -0.0131314649826244 \tabularnewline
55 & 5.47 & 5.45881851498091 & 0.0111814850190921 \tabularnewline
56 & 5.49 & 5.47447581893316 & 0.0155241810668363 \tabularnewline
57 & 5.5 & 5.50951006943973 & -0.00951006943972654 \tabularnewline
58 & 5.54 & 5.52079455688484 & 0.0192054431151565 \tabularnewline
59 & 5.55 & 5.54698821631941 & 0.00301178368058519 \tabularnewline
60 & 5.55 & 5.5449817232243 & 0.00501827677569988 \tabularnewline
61 & 5.56 & 5.58090218580957 & -0.0209021858095735 \tabularnewline
62 & 5.6 & 5.63143873107618 & -0.0314387310761832 \tabularnewline
63 & 5.61 & 5.6485507245144 & -0.038550724514403 \tabularnewline
64 & 5.63 & 5.64928596073528 & -0.0192859607352833 \tabularnewline
65 & 5.64 & 5.64110475250088 & -0.00110475250088182 \tabularnewline
66 & 5.66 & 5.64947139550498 & 0.0105286044950210 \tabularnewline
67 & 5.67 & 5.65766457555686 & 0.0123354244431413 \tabularnewline
68 & 5.69 & 5.67409072126757 & 0.0159092787324298 \tabularnewline
69 & 5.77 & 5.70359233727328 & 0.066407662726724 \tabularnewline
70 & 5.77 & 5.78149934471408 & -0.0114993447140765 \tabularnewline
71 & 5.78 & 5.77934351192316 & 0.000656488076837825 \tabularnewline
72 & 5.8 & 5.77475016790168 & 0.0252498320983214 \tabularnewline
73 & 5.82 & 5.82174776315338 & -0.00174776315338043 \tabularnewline
74 & 5.85 & 5.8876809894394 & -0.0376809894394032 \tabularnewline
75 & 5.87 & 5.89950454879958 & -0.0295045487995811 \tabularnewline
76 & 5.88 & 5.91244902444505 & -0.0324490244450510 \tabularnewline
77 & 5.9 & 5.89735838093163 & 0.00264161906837401 \tabularnewline
78 & 5.91 & 5.91096243344079 & -0.000962433440787613 \tabularnewline
79 & 5.94 & 5.90965281855829 & 0.0303471814417087 \tabularnewline
80 & 5.97 & 5.94083790310244 & 0.0291620968975597 \tabularnewline
81 & 5.98 & 5.99193331108579 & -0.0119333110857864 \tabularnewline
82 & 6 & 5.99077180815508 & 0.0092281918449233 \tabularnewline
83 & 6.01 & 6.00697514595099 & 0.00302485404900654 \tabularnewline
84 & 6.02 & 6.00835582446629 & 0.0116441755337133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41286&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]13[/C][C]4.53[/C][C]4.42301587278106[/C][C]0.106984127218944[/C][/ROW]
[ROW][C]14[/C][C]4.63[/C][C]4.60852587409124[/C][C]0.0214741259087559[/C][/ROW]
[ROW][C]15[/C][C]4.66[/C][C]4.65676026637629[/C][C]0.00323973362370555[/C][/ROW]
[ROW][C]16[/C][C]4.67[/C][C]4.6714010798474[/C][C]-0.00140107984740201[/C][/ROW]
[ROW][C]17[/C][C]4.68[/C][C]4.68275686774525[/C][C]-0.00275686774524875[/C][/ROW]
[ROW][C]18[/C][C]4.69[/C][C]4.69342170442019[/C][C]-0.00342170442019096[/C][/ROW]
[ROW][C]19[/C][C]4.69[/C][C]4.68937928867316[/C][C]0.000620711326839718[/C][/ROW]
[ROW][C]20[/C][C]4.7[/C][C]4.69626861670553[/C][C]0.00373138329446832[/C][/ROW]
[ROW][C]21[/C][C]4.71[/C][C]4.72139034061084[/C][C]-0.0113903406108378[/C][/ROW]
[ROW][C]22[/C][C]4.72[/C][C]4.73263663761863[/C][C]-0.0126366376186278[/C][/ROW]
[ROW][C]23[/C][C]4.72[/C][C]4.72142954082522[/C][C]-0.00142954082522362[/C][/ROW]
[ROW][C]24[/C][C]4.72[/C][C]4.72999254138796[/C][C]-0.00999254138796157[/C][/ROW]
[ROW][C]25[/C][C]4.73[/C][C]4.74519011869151[/C][C]-0.0151901186915113[/C][/ROW]
[ROW][C]26[/C][C]4.74[/C][C]4.81861215888169[/C][C]-0.0786121588816897[/C][/ROW]
[ROW][C]27[/C][C]4.76[/C][C]4.78245801993673[/C][C]-0.0224580199367317[/C][/ROW]
[ROW][C]28[/C][C]4.81[/C][C]4.77389894447478[/C][C]0.0361010555252168[/C][/ROW]
[ROW][C]29[/C][C]4.82[/C][C]4.81329686965032[/C][C]0.00670313034968029[/C][/ROW]
[ROW][C]30[/C][C]4.83[/C][C]4.82999158479271[/C][C]8.415207288337e-06[/C][/ROW]
[ROW][C]31[/C][C]4.83[/C][C]4.82781029196342[/C][C]0.00218970803657914[/C][/ROW]
[ROW][C]32[/C][C]4.84[/C][C]4.83513728283315[/C][C]0.00486271716684783[/C][/ROW]
[ROW][C]33[/C][C]4.89[/C][C]4.85695726757439[/C][C]0.0330427324256100[/C][/ROW]
[ROW][C]34[/C][C]4.92[/C][C]4.90265445070686[/C][C]0.0173455492931449[/C][/ROW]
[ROW][C]35[/C][C]4.95[/C][C]4.91654311115185[/C][C]0.0334568888481543[/C][/ROW]
[ROW][C]36[/C][C]4.95[/C][C]4.95061577380595[/C][C]-0.000615773805945352[/C][/ROW]
[ROW][C]37[/C][C]5.01[/C][C]4.97253420928564[/C][C]0.0374657907143590[/C][/ROW]
[ROW][C]38[/C][C]5.05[/C][C]5.07832615284318[/C][C]-0.0283261528431797[/C][/ROW]
[ROW][C]39[/C][C]5.08[/C][C]5.09627139944495[/C][C]-0.0162713994449462[/C][/ROW]
[ROW][C]40[/C][C]5.11[/C][C]5.10625070981115[/C][C]0.00374929018884895[/C][/ROW]
[ROW][C]41[/C][C]5.14[/C][C]5.11408777720027[/C][C]0.0259122227997324[/C][/ROW]
[ROW][C]42[/C][C]5.17[/C][C]5.14534547348452[/C][C]0.0246545265154818[/C][/ROW]
[ROW][C]43[/C][C]5.18[/C][C]5.16328800257754[/C][C]0.0167119974224645[/C][/ROW]
[ROW][C]44[/C][C]5.2[/C][C]5.18347115235441[/C][C]0.0165288476455903[/C][/ROW]
[ROW][C]45[/C][C]5.22[/C][C]5.22249238500372[/C][C]-0.00249238500372240[/C][/ROW]
[ROW][C]46[/C][C]5.24[/C][C]5.23795544450701[/C][C]0.00204455549299443[/C][/ROW]
[ROW][C]47[/C][C]5.28[/C][C]5.24319914961394[/C][C]0.0368008503860553[/C][/ROW]
[ROW][C]48[/C][C]5.29[/C][C]5.27294965702446[/C][C]0.0170503429755353[/C][/ROW]
[ROW][C]49[/C][C]5.33[/C][C]5.31889283735148[/C][C]0.0111071626485151[/C][/ROW]
[ROW][C]50[/C][C]5.4[/C][C]5.39406203097145[/C][C]0.00593796902855104[/C][/ROW]
[ROW][C]51[/C][C]5.43[/C][C]5.44485234825027[/C][C]-0.0148523482502698[/C][/ROW]
[ROW][C]52[/C][C]5.46[/C][C]5.46218031798748[/C][C]-0.00218031798747997[/C][/ROW]
[ROW][C]53[/C][C]5.46[/C][C]5.47066968608911[/C][C]-0.0106696860891091[/C][/ROW]
[ROW][C]54[/C][C]5.46[/C][C]5.47313146498262[/C][C]-0.0131314649826244[/C][/ROW]
[ROW][C]55[/C][C]5.47[/C][C]5.45881851498091[/C][C]0.0111814850190921[/C][/ROW]
[ROW][C]56[/C][C]5.49[/C][C]5.47447581893316[/C][C]0.0155241810668363[/C][/ROW]
[ROW][C]57[/C][C]5.5[/C][C]5.50951006943973[/C][C]-0.00951006943972654[/C][/ROW]
[ROW][C]58[/C][C]5.54[/C][C]5.52079455688484[/C][C]0.0192054431151565[/C][/ROW]
[ROW][C]59[/C][C]5.55[/C][C]5.54698821631941[/C][C]0.00301178368058519[/C][/ROW]
[ROW][C]60[/C][C]5.55[/C][C]5.5449817232243[/C][C]0.00501827677569988[/C][/ROW]
[ROW][C]61[/C][C]5.56[/C][C]5.58090218580957[/C][C]-0.0209021858095735[/C][/ROW]
[ROW][C]62[/C][C]5.6[/C][C]5.63143873107618[/C][C]-0.0314387310761832[/C][/ROW]
[ROW][C]63[/C][C]5.61[/C][C]5.6485507245144[/C][C]-0.038550724514403[/C][/ROW]
[ROW][C]64[/C][C]5.63[/C][C]5.64928596073528[/C][C]-0.0192859607352833[/C][/ROW]
[ROW][C]65[/C][C]5.64[/C][C]5.64110475250088[/C][C]-0.00110475250088182[/C][/ROW]
[ROW][C]66[/C][C]5.66[/C][C]5.64947139550498[/C][C]0.0105286044950210[/C][/ROW]
[ROW][C]67[/C][C]5.67[/C][C]5.65766457555686[/C][C]0.0123354244431413[/C][/ROW]
[ROW][C]68[/C][C]5.69[/C][C]5.67409072126757[/C][C]0.0159092787324298[/C][/ROW]
[ROW][C]69[/C][C]5.77[/C][C]5.70359233727328[/C][C]0.066407662726724[/C][/ROW]
[ROW][C]70[/C][C]5.77[/C][C]5.78149934471408[/C][C]-0.0114993447140765[/C][/ROW]
[ROW][C]71[/C][C]5.78[/C][C]5.77934351192316[/C][C]0.000656488076837825[/C][/ROW]
[ROW][C]72[/C][C]5.8[/C][C]5.77475016790168[/C][C]0.0252498320983214[/C][/ROW]
[ROW][C]73[/C][C]5.82[/C][C]5.82174776315338[/C][C]-0.00174776315338043[/C][/ROW]
[ROW][C]74[/C][C]5.85[/C][C]5.8876809894394[/C][C]-0.0376809894394032[/C][/ROW]
[ROW][C]75[/C][C]5.87[/C][C]5.89950454879958[/C][C]-0.0295045487995811[/C][/ROW]
[ROW][C]76[/C][C]5.88[/C][C]5.91244902444505[/C][C]-0.0324490244450510[/C][/ROW]
[ROW][C]77[/C][C]5.9[/C][C]5.89735838093163[/C][C]0.00264161906837401[/C][/ROW]
[ROW][C]78[/C][C]5.91[/C][C]5.91096243344079[/C][C]-0.000962433440787613[/C][/ROW]
[ROW][C]79[/C][C]5.94[/C][C]5.90965281855829[/C][C]0.0303471814417087[/C][/ROW]
[ROW][C]80[/C][C]5.97[/C][C]5.94083790310244[/C][C]0.0291620968975597[/C][/ROW]
[ROW][C]81[/C][C]5.98[/C][C]5.99193331108579[/C][C]-0.0119333110857864[/C][/ROW]
[ROW][C]82[/C][C]6[/C][C]5.99077180815508[/C][C]0.0092281918449233[/C][/ROW]
[ROW][C]83[/C][C]6.01[/C][C]6.00697514595099[/C][C]0.00302485404900654[/C][/ROW]
[ROW][C]84[/C][C]6.02[/C][C]6.00835582446629[/C][C]0.0116441755337133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41286&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41286&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
134.534.423015872781060.106984127218944
144.634.608525874091240.0214741259087559
154.664.656760266376290.00323973362370555
164.674.6714010798474-0.00140107984740201
174.684.68275686774525-0.00275686774524875
184.694.69342170442019-0.00342170442019096
194.694.689379288673160.000620711326839718
204.74.696268616705530.00373138329446832
214.714.72139034061084-0.0113903406108378
224.724.73263663761863-0.0126366376186278
234.724.72142954082522-0.00142954082522362
244.724.72999254138796-0.00999254138796157
254.734.74519011869151-0.0151901186915113
264.744.81861215888169-0.0786121588816897
274.764.78245801993673-0.0224580199367317
284.814.773898944474780.0361010555252168
294.824.813296869650320.00670313034968029
304.834.829991584792718.415207288337e-06
314.834.827810291963420.00218970803657914
324.844.835137282833150.00486271716684783
334.894.856957267574390.0330427324256100
344.924.902654450706860.0173455492931449
354.954.916543111151850.0334568888481543
364.954.95061577380595-0.000615773805945352
375.014.972534209285640.0374657907143590
385.055.07832615284318-0.0283261528431797
395.085.09627139944495-0.0162713994449462
405.115.106250709811150.00374929018884895
415.145.114087777200270.0259122227997324
425.175.145345473484520.0246545265154818
435.185.163288002577540.0167119974224645
445.25.183471152354410.0165288476455903
455.225.22249238500372-0.00249238500372240
465.245.237955444507010.00204455549299443
475.285.243199149613940.0368008503860553
485.295.272949657024460.0170503429755353
495.335.318892837351480.0111071626485151
505.45.394062030971450.00593796902855104
515.435.44485234825027-0.0148523482502698
525.465.46218031798748-0.00218031798747997
535.465.47066968608911-0.0106696860891091
545.465.47313146498262-0.0131314649826244
555.475.458818514980910.0111814850190921
565.495.474475818933160.0155241810668363
575.55.50951006943973-0.00951006943972654
585.545.520794556884840.0192054431151565
595.555.546988216319410.00301178368058519
605.555.54498172322430.00501827677569988
615.565.58090218580957-0.0209021858095735
625.65.63143873107618-0.0314387310761832
635.615.6485507245144-0.038550724514403
645.635.64928596073528-0.0192859607352833
655.645.64110475250088-0.00110475250088182
665.665.649471395504980.0105286044950210
675.675.657664575556860.0123354244431413
685.695.674090721267570.0159092787324298
695.775.703592337273280.066407662726724
705.775.78149934471408-0.0114993447140765
715.785.779343511923160.000656488076837825
725.85.774750167901680.0252498320983214
735.825.82174776315338-0.00174776315338043
745.855.8876809894394-0.0376809894394032
755.875.89950454879958-0.0295045487995811
765.885.91244902444505-0.0324490244450510
775.95.897358380931630.00264161906837401
785.915.91096243344079-0.000962433440787613
795.945.909652818558290.0303471814417087
805.975.940837903102440.0291620968975597
815.985.99193331108579-0.0119333110857864
8265.990771808155080.0092281918449233
836.016.006975145950990.00302485404900654
846.026.008355824466290.0116441755337133







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
856.038727699073245.989770375946076.08768502220042
866.099804418082096.036799064296146.16280977186804
876.144316868504926.069560616644466.21907312036539
886.181224290413366.096073357511916.26637522331481
896.19981882753796.105340362077236.29429729299858
906.21088394917336.10781303057376.31395486777289
916.216825674277856.105729113125196.32792223543051
926.223476037670316.104737360083836.34221471525679
936.243042851848376.116761666875796.36932403682094
946.25564215826676.122205787030576.38907852950283
956.262862032334766.122597499604736.4031265650648
966.262922093690483.870352031788018.65549215559295

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 6.03872769907324 & 5.98977037594607 & 6.08768502220042 \tabularnewline
86 & 6.09980441808209 & 6.03679906429614 & 6.16280977186804 \tabularnewline
87 & 6.14431686850492 & 6.06956061664446 & 6.21907312036539 \tabularnewline
88 & 6.18122429041336 & 6.09607335751191 & 6.26637522331481 \tabularnewline
89 & 6.1998188275379 & 6.10534036207723 & 6.29429729299858 \tabularnewline
90 & 6.2108839491733 & 6.1078130305737 & 6.31395486777289 \tabularnewline
91 & 6.21682567427785 & 6.10572911312519 & 6.32792223543051 \tabularnewline
92 & 6.22347603767031 & 6.10473736008383 & 6.34221471525679 \tabularnewline
93 & 6.24304285184837 & 6.11676166687579 & 6.36932403682094 \tabularnewline
94 & 6.2556421582667 & 6.12220578703057 & 6.38907852950283 \tabularnewline
95 & 6.26286203233476 & 6.12259749960473 & 6.4031265650648 \tabularnewline
96 & 6.26292209369048 & 3.87035203178801 & 8.65549215559295 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41286&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]85[/C][C]6.03872769907324[/C][C]5.98977037594607[/C][C]6.08768502220042[/C][/ROW]
[ROW][C]86[/C][C]6.09980441808209[/C][C]6.03679906429614[/C][C]6.16280977186804[/C][/ROW]
[ROW][C]87[/C][C]6.14431686850492[/C][C]6.06956061664446[/C][C]6.21907312036539[/C][/ROW]
[ROW][C]88[/C][C]6.18122429041336[/C][C]6.09607335751191[/C][C]6.26637522331481[/C][/ROW]
[ROW][C]89[/C][C]6.1998188275379[/C][C]6.10534036207723[/C][C]6.29429729299858[/C][/ROW]
[ROW][C]90[/C][C]6.2108839491733[/C][C]6.1078130305737[/C][C]6.31395486777289[/C][/ROW]
[ROW][C]91[/C][C]6.21682567427785[/C][C]6.10572911312519[/C][C]6.32792223543051[/C][/ROW]
[ROW][C]92[/C][C]6.22347603767031[/C][C]6.10473736008383[/C][C]6.34221471525679[/C][/ROW]
[ROW][C]93[/C][C]6.24304285184837[/C][C]6.11676166687579[/C][C]6.36932403682094[/C][/ROW]
[ROW][C]94[/C][C]6.2556421582667[/C][C]6.12220578703057[/C][C]6.38907852950283[/C][/ROW]
[ROW][C]95[/C][C]6.26286203233476[/C][C]6.12259749960473[/C][C]6.4031265650648[/C][/ROW]
[ROW][C]96[/C][C]6.26292209369048[/C][C]3.87035203178801[/C][C]8.65549215559295[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41286&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41286&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
856.038727699073245.989770375946076.08768502220042
866.099804418082096.036799064296146.16280977186804
876.144316868504926.069560616644466.21907312036539
886.181224290413366.096073357511916.26637522331481
896.19981882753796.105340362077236.29429729299858
906.21088394917336.10781303057376.31395486777289
916.216825674277856.105729113125196.32792223543051
926.223476037670316.104737360083836.34221471525679
936.243042851848376.116761666875796.36932403682094
946.25564215826676.122205787030576.38907852950283
956.262862032334766.122597499604736.4031265650648
966.262922093690483.870352031788018.65549215559295



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')