Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 02:53:57 -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/17/t1355730919rymi86v2q16eo0s.htm/, Retrieved Thu, 31 Oct 2024 23:52:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200682, Retrieved Thu, 31 Oct 2024 23:52:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 07:53:57] [946b987ea445738c2c70467dba74cc4f] [Current]
Feedback Forum

Post a new message
Dataseries X:
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,43
3,5
3,52
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,53
3,58
3,58
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,61
3,71
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
4,09
4,09
4,09
4,09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.002012910036564
gamma0.0982581635507916

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.002012910036564 \tabularnewline
gamma & 0.0982581635507916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&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]0.002012910036564[/C][/ROW]
[ROW][C]gamma[/C][C]0.0982581635507916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&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
beta0.002012910036564
gamma0.0982581635507916







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133.533.480325854700850.049674145299146
143.533.529409430145070.000590569854928891
153.533.53024395224239-0.000243952242392709
163.533.53191012785514-0.00191012785514255
173.533.53273961627294-0.00273961627294472
183.533.53273410167185-0.00273410167185206
193.533.519395264837820.0106047351621767
203.533.529416611215670.000583388784333838
213.583.59941778552481-0.019417785524805
223.583.59937869926943-0.0193786992694345
233.593.589339691691180.000660308308821023
243.593.58934102083240.000658979167598606
253.593.589342347298180.000657652701818279
263.593.589343671093910.000656328906094128
273.593.59017832555828-0.000178325558281678
283.593.59184463327164-0.00184463327164286
293.593.59267425352415-0.00267425352414952
303.593.59266887049239-0.00266887049239006
313.593.579330164962860.0106698350371435
323.613.589351642380890.0206483576191085
333.713.679393205667180.0306067943328188
343.833.729454814390680.100545185609319
353.833.83965720280392-0.00965720280392146
363.833.829637763723470.000362236276527206
373.833.829638492872510.000361507127490501
383.833.829639220553830.000360779446165083
393.833.83047328010374-0.000473280103736595
403.833.83213899410013-0.00213899410013241
413.833.83296802183077-0.00296802183077327
423.833.83296204746984-0.00296204746984063
433.833.819622751801430.0103772481985729
443.833.829643640268480.000356359731521927
453.923.899644357588560.0203556424114422
463.923.93968533166547-0.0196853316654688
473.923.92964570686379-0.00964570686378563
483.923.919626290923630.000373709076369799
493.923.919627043166380.000372956833619043
503.923.919627793894930.000372206105065498
513.923.92046187644567-0.000461876445672527
523.923.92212761339661-0.00212761339660616
533.923.92295666403558-0.00295666403557959
543.923.92295071253687-0.00295071253686707
553.923.909611439684650.0103885603153464
563.923.919632350921980.000367649078022225
573.983.9896330909665-0.00963309096649656
583.983.99961370042101-0.0196137004210071
593.983.98957421980657-0.00957421980657491
603.983.979554947763430.000445052236565324
613.983.979555843613550.000444156386451677
623.983.97955673766040.000443262339603567
633.983.98039096324094-0.000390963240942455
643.983.98205684293378-0.0020568429337775
653.983.98288603602733-0.00288603602732573
663.983.98288022669644-0.00288022669643961
673.983.969541095725880.0104589042741181
683.983.979562148559270.000437851440732828
694.094.049563029914830.0404369700851737
704.094.10964442589776-0.0196444258977593
714.094.09960488343571-0.00960488343570631
724.094.089585549669440.000414450330560534

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.53 & 3.48032585470085 & 0.049674145299146 \tabularnewline
14 & 3.53 & 3.52940943014507 & 0.000590569854928891 \tabularnewline
15 & 3.53 & 3.53024395224239 & -0.000243952242392709 \tabularnewline
16 & 3.53 & 3.53191012785514 & -0.00191012785514255 \tabularnewline
17 & 3.53 & 3.53273961627294 & -0.00273961627294472 \tabularnewline
18 & 3.53 & 3.53273410167185 & -0.00273410167185206 \tabularnewline
19 & 3.53 & 3.51939526483782 & 0.0106047351621767 \tabularnewline
20 & 3.53 & 3.52941661121567 & 0.000583388784333838 \tabularnewline
21 & 3.58 & 3.59941778552481 & -0.019417785524805 \tabularnewline
22 & 3.58 & 3.59937869926943 & -0.0193786992694345 \tabularnewline
23 & 3.59 & 3.58933969169118 & 0.000660308308821023 \tabularnewline
24 & 3.59 & 3.5893410208324 & 0.000658979167598606 \tabularnewline
25 & 3.59 & 3.58934234729818 & 0.000657652701818279 \tabularnewline
26 & 3.59 & 3.58934367109391 & 0.000656328906094128 \tabularnewline
27 & 3.59 & 3.59017832555828 & -0.000178325558281678 \tabularnewline
28 & 3.59 & 3.59184463327164 & -0.00184463327164286 \tabularnewline
29 & 3.59 & 3.59267425352415 & -0.00267425352414952 \tabularnewline
30 & 3.59 & 3.59266887049239 & -0.00266887049239006 \tabularnewline
31 & 3.59 & 3.57933016496286 & 0.0106698350371435 \tabularnewline
32 & 3.61 & 3.58935164238089 & 0.0206483576191085 \tabularnewline
33 & 3.71 & 3.67939320566718 & 0.0306067943328188 \tabularnewline
34 & 3.83 & 3.72945481439068 & 0.100545185609319 \tabularnewline
35 & 3.83 & 3.83965720280392 & -0.00965720280392146 \tabularnewline
36 & 3.83 & 3.82963776372347 & 0.000362236276527206 \tabularnewline
37 & 3.83 & 3.82963849287251 & 0.000361507127490501 \tabularnewline
38 & 3.83 & 3.82963922055383 & 0.000360779446165083 \tabularnewline
39 & 3.83 & 3.83047328010374 & -0.000473280103736595 \tabularnewline
40 & 3.83 & 3.83213899410013 & -0.00213899410013241 \tabularnewline
41 & 3.83 & 3.83296802183077 & -0.00296802183077327 \tabularnewline
42 & 3.83 & 3.83296204746984 & -0.00296204746984063 \tabularnewline
43 & 3.83 & 3.81962275180143 & 0.0103772481985729 \tabularnewline
44 & 3.83 & 3.82964364026848 & 0.000356359731521927 \tabularnewline
45 & 3.92 & 3.89964435758856 & 0.0203556424114422 \tabularnewline
46 & 3.92 & 3.93968533166547 & -0.0196853316654688 \tabularnewline
47 & 3.92 & 3.92964570686379 & -0.00964570686378563 \tabularnewline
48 & 3.92 & 3.91962629092363 & 0.000373709076369799 \tabularnewline
49 & 3.92 & 3.91962704316638 & 0.000372956833619043 \tabularnewline
50 & 3.92 & 3.91962779389493 & 0.000372206105065498 \tabularnewline
51 & 3.92 & 3.92046187644567 & -0.000461876445672527 \tabularnewline
52 & 3.92 & 3.92212761339661 & -0.00212761339660616 \tabularnewline
53 & 3.92 & 3.92295666403558 & -0.00295666403557959 \tabularnewline
54 & 3.92 & 3.92295071253687 & -0.00295071253686707 \tabularnewline
55 & 3.92 & 3.90961143968465 & 0.0103885603153464 \tabularnewline
56 & 3.92 & 3.91963235092198 & 0.000367649078022225 \tabularnewline
57 & 3.98 & 3.9896330909665 & -0.00963309096649656 \tabularnewline
58 & 3.98 & 3.99961370042101 & -0.0196137004210071 \tabularnewline
59 & 3.98 & 3.98957421980657 & -0.00957421980657491 \tabularnewline
60 & 3.98 & 3.97955494776343 & 0.000445052236565324 \tabularnewline
61 & 3.98 & 3.97955584361355 & 0.000444156386451677 \tabularnewline
62 & 3.98 & 3.9795567376604 & 0.000443262339603567 \tabularnewline
63 & 3.98 & 3.98039096324094 & -0.000390963240942455 \tabularnewline
64 & 3.98 & 3.98205684293378 & -0.0020568429337775 \tabularnewline
65 & 3.98 & 3.98288603602733 & -0.00288603602732573 \tabularnewline
66 & 3.98 & 3.98288022669644 & -0.00288022669643961 \tabularnewline
67 & 3.98 & 3.96954109572588 & 0.0104589042741181 \tabularnewline
68 & 3.98 & 3.97956214855927 & 0.000437851440732828 \tabularnewline
69 & 4.09 & 4.04956302991483 & 0.0404369700851737 \tabularnewline
70 & 4.09 & 4.10964442589776 & -0.0196444258977593 \tabularnewline
71 & 4.09 & 4.09960488343571 & -0.00960488343570631 \tabularnewline
72 & 4.09 & 4.08958554966944 & 0.000414450330560534 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&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]3.53[/C][C]3.48032585470085[/C][C]0.049674145299146[/C][/ROW]
[ROW][C]14[/C][C]3.53[/C][C]3.52940943014507[/C][C]0.000590569854928891[/C][/ROW]
[ROW][C]15[/C][C]3.53[/C][C]3.53024395224239[/C][C]-0.000243952242392709[/C][/ROW]
[ROW][C]16[/C][C]3.53[/C][C]3.53191012785514[/C][C]-0.00191012785514255[/C][/ROW]
[ROW][C]17[/C][C]3.53[/C][C]3.53273961627294[/C][C]-0.00273961627294472[/C][/ROW]
[ROW][C]18[/C][C]3.53[/C][C]3.53273410167185[/C][C]-0.00273410167185206[/C][/ROW]
[ROW][C]19[/C][C]3.53[/C][C]3.51939526483782[/C][C]0.0106047351621767[/C][/ROW]
[ROW][C]20[/C][C]3.53[/C][C]3.52941661121567[/C][C]0.000583388784333838[/C][/ROW]
[ROW][C]21[/C][C]3.58[/C][C]3.59941778552481[/C][C]-0.019417785524805[/C][/ROW]
[ROW][C]22[/C][C]3.58[/C][C]3.59937869926943[/C][C]-0.0193786992694345[/C][/ROW]
[ROW][C]23[/C][C]3.59[/C][C]3.58933969169118[/C][C]0.000660308308821023[/C][/ROW]
[ROW][C]24[/C][C]3.59[/C][C]3.5893410208324[/C][C]0.000658979167598606[/C][/ROW]
[ROW][C]25[/C][C]3.59[/C][C]3.58934234729818[/C][C]0.000657652701818279[/C][/ROW]
[ROW][C]26[/C][C]3.59[/C][C]3.58934367109391[/C][C]0.000656328906094128[/C][/ROW]
[ROW][C]27[/C][C]3.59[/C][C]3.59017832555828[/C][C]-0.000178325558281678[/C][/ROW]
[ROW][C]28[/C][C]3.59[/C][C]3.59184463327164[/C][C]-0.00184463327164286[/C][/ROW]
[ROW][C]29[/C][C]3.59[/C][C]3.59267425352415[/C][C]-0.00267425352414952[/C][/ROW]
[ROW][C]30[/C][C]3.59[/C][C]3.59266887049239[/C][C]-0.00266887049239006[/C][/ROW]
[ROW][C]31[/C][C]3.59[/C][C]3.57933016496286[/C][C]0.0106698350371435[/C][/ROW]
[ROW][C]32[/C][C]3.61[/C][C]3.58935164238089[/C][C]0.0206483576191085[/C][/ROW]
[ROW][C]33[/C][C]3.71[/C][C]3.67939320566718[/C][C]0.0306067943328188[/C][/ROW]
[ROW][C]34[/C][C]3.83[/C][C]3.72945481439068[/C][C]0.100545185609319[/C][/ROW]
[ROW][C]35[/C][C]3.83[/C][C]3.83965720280392[/C][C]-0.00965720280392146[/C][/ROW]
[ROW][C]36[/C][C]3.83[/C][C]3.82963776372347[/C][C]0.000362236276527206[/C][/ROW]
[ROW][C]37[/C][C]3.83[/C][C]3.82963849287251[/C][C]0.000361507127490501[/C][/ROW]
[ROW][C]38[/C][C]3.83[/C][C]3.82963922055383[/C][C]0.000360779446165083[/C][/ROW]
[ROW][C]39[/C][C]3.83[/C][C]3.83047328010374[/C][C]-0.000473280103736595[/C][/ROW]
[ROW][C]40[/C][C]3.83[/C][C]3.83213899410013[/C][C]-0.00213899410013241[/C][/ROW]
[ROW][C]41[/C][C]3.83[/C][C]3.83296802183077[/C][C]-0.00296802183077327[/C][/ROW]
[ROW][C]42[/C][C]3.83[/C][C]3.83296204746984[/C][C]-0.00296204746984063[/C][/ROW]
[ROW][C]43[/C][C]3.83[/C][C]3.81962275180143[/C][C]0.0103772481985729[/C][/ROW]
[ROW][C]44[/C][C]3.83[/C][C]3.82964364026848[/C][C]0.000356359731521927[/C][/ROW]
[ROW][C]45[/C][C]3.92[/C][C]3.89964435758856[/C][C]0.0203556424114422[/C][/ROW]
[ROW][C]46[/C][C]3.92[/C][C]3.93968533166547[/C][C]-0.0196853316654688[/C][/ROW]
[ROW][C]47[/C][C]3.92[/C][C]3.92964570686379[/C][C]-0.00964570686378563[/C][/ROW]
[ROW][C]48[/C][C]3.92[/C][C]3.91962629092363[/C][C]0.000373709076369799[/C][/ROW]
[ROW][C]49[/C][C]3.92[/C][C]3.91962704316638[/C][C]0.000372956833619043[/C][/ROW]
[ROW][C]50[/C][C]3.92[/C][C]3.91962779389493[/C][C]0.000372206105065498[/C][/ROW]
[ROW][C]51[/C][C]3.92[/C][C]3.92046187644567[/C][C]-0.000461876445672527[/C][/ROW]
[ROW][C]52[/C][C]3.92[/C][C]3.92212761339661[/C][C]-0.00212761339660616[/C][/ROW]
[ROW][C]53[/C][C]3.92[/C][C]3.92295666403558[/C][C]-0.00295666403557959[/C][/ROW]
[ROW][C]54[/C][C]3.92[/C][C]3.92295071253687[/C][C]-0.00295071253686707[/C][/ROW]
[ROW][C]55[/C][C]3.92[/C][C]3.90961143968465[/C][C]0.0103885603153464[/C][/ROW]
[ROW][C]56[/C][C]3.92[/C][C]3.91963235092198[/C][C]0.000367649078022225[/C][/ROW]
[ROW][C]57[/C][C]3.98[/C][C]3.9896330909665[/C][C]-0.00963309096649656[/C][/ROW]
[ROW][C]58[/C][C]3.98[/C][C]3.99961370042101[/C][C]-0.0196137004210071[/C][/ROW]
[ROW][C]59[/C][C]3.98[/C][C]3.98957421980657[/C][C]-0.00957421980657491[/C][/ROW]
[ROW][C]60[/C][C]3.98[/C][C]3.97955494776343[/C][C]0.000445052236565324[/C][/ROW]
[ROW][C]61[/C][C]3.98[/C][C]3.97955584361355[/C][C]0.000444156386451677[/C][/ROW]
[ROW][C]62[/C][C]3.98[/C][C]3.9795567376604[/C][C]0.000443262339603567[/C][/ROW]
[ROW][C]63[/C][C]3.98[/C][C]3.98039096324094[/C][C]-0.000390963240942455[/C][/ROW]
[ROW][C]64[/C][C]3.98[/C][C]3.98205684293378[/C][C]-0.0020568429337775[/C][/ROW]
[ROW][C]65[/C][C]3.98[/C][C]3.98288603602733[/C][C]-0.00288603602732573[/C][/ROW]
[ROW][C]66[/C][C]3.98[/C][C]3.98288022669644[/C][C]-0.00288022669643961[/C][/ROW]
[ROW][C]67[/C][C]3.98[/C][C]3.96954109572588[/C][C]0.0104589042741181[/C][/ROW]
[ROW][C]68[/C][C]3.98[/C][C]3.97956214855927[/C][C]0.000437851440732828[/C][/ROW]
[ROW][C]69[/C][C]4.09[/C][C]4.04956302991483[/C][C]0.0404369700851737[/C][/ROW]
[ROW][C]70[/C][C]4.09[/C][C]4.10964442589776[/C][C]-0.0196444258977593[/C][/ROW]
[ROW][C]71[/C][C]4.09[/C][C]4.09960488343571[/C][C]-0.00960488343570631[/C][/ROW]
[ROW][C]72[/C][C]4.09[/C][C]4.08958554966944[/C][C]0.000414450330560534[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&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
133.533.480325854700850.049674145299146
143.533.529409430145070.000590569854928891
153.533.53024395224239-0.000243952242392709
163.533.53191012785514-0.00191012785514255
173.533.53273961627294-0.00273961627294472
183.533.53273410167185-0.00273410167185206
193.533.519395264837820.0106047351621767
203.533.529416611215670.000583388784333838
213.583.59941778552481-0.019417785524805
223.583.59937869926943-0.0193786992694345
233.593.589339691691180.000660308308821023
243.593.58934102083240.000658979167598606
253.593.589342347298180.000657652701818279
263.593.589343671093910.000656328906094128
273.593.59017832555828-0.000178325558281678
283.593.59184463327164-0.00184463327164286
293.593.59267425352415-0.00267425352414952
303.593.59266887049239-0.00266887049239006
313.593.579330164962860.0106698350371435
323.613.589351642380890.0206483576191085
333.713.679393205667180.0306067943328188
343.833.729454814390680.100545185609319
353.833.83965720280392-0.00965720280392146
363.833.829637763723470.000362236276527206
373.833.829638492872510.000361507127490501
383.833.829639220553830.000360779446165083
393.833.83047328010374-0.000473280103736595
403.833.83213899410013-0.00213899410013241
413.833.83296802183077-0.00296802183077327
423.833.83296204746984-0.00296204746984063
433.833.819622751801430.0103772481985729
443.833.829643640268480.000356359731521927
453.923.899644357588560.0203556424114422
463.923.93968533166547-0.0196853316654688
473.923.92964570686379-0.00964570686378563
483.923.919626290923630.000373709076369799
493.923.919627043166380.000372956833619043
503.923.919627793894930.000372206105065498
513.923.92046187644567-0.000461876445672527
523.923.92212761339661-0.00212761339660616
533.923.92295666403558-0.00295666403557959
543.923.92295071253687-0.00295071253686707
553.923.909611439684650.0103885603153464
563.923.919632350921980.000367649078022225
573.983.9896330909665-0.00963309096649656
583.983.99961370042101-0.0196137004210071
593.983.98957421980657-0.00957421980657491
603.983.979554947763430.000445052236565324
613.983.979555843613550.000444156386451677
623.983.97955673766040.000443262339603567
633.983.98039096324094-0.000390963240942455
643.983.98205684293378-0.0020568429337775
653.983.98288603602733-0.00288603602732573
663.983.98288022669644-0.00288022669643961
673.983.969541095725880.0104589042741181
683.983.979562148559270.000437851440732828
694.094.049563029914830.0404369700851737
704.094.10964442589776-0.0196444258977593
714.094.09960488343571-0.00960488343570631
724.094.089585549669440.000414450330560534







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734.089586383920674.054687937381934.1244848304594
744.089172767841344.039769214032674.13857632165001
754.089592485095344.029024848987164.15016012120352
764.091678869016014.021671057418744.16168668061328
774.094598586270014.016248816512544.17294835602749
784.097518303524024.011604238189124.18343236885891
794.087104687444693.994213761310874.1799956135785
804.086691071365353.987286901949064.18609524078165
814.156277455286024.050737743756154.26181716681589
824.175863839206694.064503794914344.28722388349905
834.185450223127364.068537926803544.30236251945119
844.185036607048034.062803562089014.30726965200705

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.08958638392067 & 4.05468793738193 & 4.1244848304594 \tabularnewline
74 & 4.08917276784134 & 4.03976921403267 & 4.13857632165001 \tabularnewline
75 & 4.08959248509534 & 4.02902484898716 & 4.15016012120352 \tabularnewline
76 & 4.09167886901601 & 4.02167105741874 & 4.16168668061328 \tabularnewline
77 & 4.09459858627001 & 4.01624881651254 & 4.17294835602749 \tabularnewline
78 & 4.09751830352402 & 4.01160423818912 & 4.18343236885891 \tabularnewline
79 & 4.08710468744469 & 3.99421376131087 & 4.1799956135785 \tabularnewline
80 & 4.08669107136535 & 3.98728690194906 & 4.18609524078165 \tabularnewline
81 & 4.15627745528602 & 4.05073774375615 & 4.26181716681589 \tabularnewline
82 & 4.17586383920669 & 4.06450379491434 & 4.28722388349905 \tabularnewline
83 & 4.18545022312736 & 4.06853792680354 & 4.30236251945119 \tabularnewline
84 & 4.18503660704803 & 4.06280356208901 & 4.30726965200705 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200682&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]4.08958638392067[/C][C]4.05468793738193[/C][C]4.1244848304594[/C][/ROW]
[ROW][C]74[/C][C]4.08917276784134[/C][C]4.03976921403267[/C][C]4.13857632165001[/C][/ROW]
[ROW][C]75[/C][C]4.08959248509534[/C][C]4.02902484898716[/C][C]4.15016012120352[/C][/ROW]
[ROW][C]76[/C][C]4.09167886901601[/C][C]4.02167105741874[/C][C]4.16168668061328[/C][/ROW]
[ROW][C]77[/C][C]4.09459858627001[/C][C]4.01624881651254[/C][C]4.17294835602749[/C][/ROW]
[ROW][C]78[/C][C]4.09751830352402[/C][C]4.01160423818912[/C][C]4.18343236885891[/C][/ROW]
[ROW][C]79[/C][C]4.08710468744469[/C][C]3.99421376131087[/C][C]4.1799956135785[/C][/ROW]
[ROW][C]80[/C][C]4.08669107136535[/C][C]3.98728690194906[/C][C]4.18609524078165[/C][/ROW]
[ROW][C]81[/C][C]4.15627745528602[/C][C]4.05073774375615[/C][C]4.26181716681589[/C][/ROW]
[ROW][C]82[/C][C]4.17586383920669[/C][C]4.06450379491434[/C][C]4.28722388349905[/C][/ROW]
[ROW][C]83[/C][C]4.18545022312736[/C][C]4.06853792680354[/C][C]4.30236251945119[/C][/ROW]
[ROW][C]84[/C][C]4.18503660704803[/C][C]4.06280356208901[/C][C]4.30726965200705[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200682&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200682&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
734.089586383920674.054687937381934.1244848304594
744.089172767841344.039769214032674.13857632165001
754.089592485095344.029024848987164.15016012120352
764.091678869016014.021671057418744.16168668061328
774.094598586270014.016248816512544.17294835602749
784.097518303524024.011604238189124.18343236885891
794.087104687444693.994213761310874.1799956135785
804.086691071365353.987286901949064.18609524078165
814.156277455286024.050737743756154.26181716681589
824.175863839206694.064503794914344.28722388349905
834.185450223127364.068537926803544.30236251945119
844.185036607048034.062803562089014.30726965200705



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