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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 30 Mar 2015 13:46:31 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/30/t14277196141c3kx69ic70gcfq.htm/, Retrieved Sun, 19 May 2024 14:07:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278455, Retrieved Sun, 19 May 2024 14:07:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-03-30 12:46:31] [76397d743865651feb25fadce13a6a2d] [Current]
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Dataseries X:
15071
14236
14771
14804
15597
15418
16903
16350
16393
15685
14556
14850
15391
13704
15409
15098
15254
15522
16669
16238
16246
15424
14952
15008
14929
13905
14994
14753
15031
15386
16160
16116
16219
16064
15436
15404
15112
14119
14775
14289
15121
15371
15782
16104
15674
15105
14223
14385
14558
13804
14672
14244
15089
14580
15218
15696
15129
15110
14204
13655
14534
12746
14074
13699
14184
14110
15820
15362
14993
14437
13694
13688




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=278455&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=278455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278455&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
alpha0.377667552873066
beta0
gamma0.591196775356442

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.377667552873066 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.591196775356442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278455&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]0.377667552873066[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.591196775356442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278455&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
alpha0.377667552873066
beta0
gamma0.591196775356442







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131539115364.60308713726.3969128629924
141370413700.59696282293.40303717714596
151540915415.6325397335-6.63253973348947
161509815116.9889000232-18.9889000232033
171525415258.584317437-4.58431743704023
181552215499.836764786422.1632352135621
191666916889.8573118688-220.857311868796
201623816264.0379862461-26.0379862460977
211624616290.3746331177-44.3746331176808
221542415529.7786341687-105.778634168704
231495214375.0944873499576.905512650052
241500814895.6128895815112.387110418545
251492915495.704426151-566.704426150978
261390513610.4535566033294.546443396704
271499415434.0704346967-440.070434696663
281475314969.9522385599-216.952238559932
291503115039.8663241057-8.86632410565653
301538615285.6887513943100.311248605693
311616016599.332546588-439.332546588044
321611615970.8536252308145.146374769247
331621916054.6558222764164.344177723589
341606415356.8059744913707.194025508679
351543614747.475718338688.524281662016
361540415140.9471844808263.052815519181
371511215550.5085689774-438.508568977397
381411914001.6729657218117.327034278163
391477515508.8309707124-733.83097071237
401428915013.6340236765-724.634023676514
411512114967.3110085059153.688991494068
421537115314.449799654556.5502003454694
431578216409.6574548677-627.657454867745
441610415926.4115569048177.588443095177
451567416029.0956760443-355.095676044293
461510515340.1658810124-235.165881012426
471422314398.9691076692-175.969107669167
481438514310.116775027574.8832249725383
491455814385.3642182767172.635781723269
501380413331.4819942977472.518005702263
511467214607.578773760664.4212262393812
521424414417.0926341872-173.09263418716
531508914897.3643773156191.635622684389
541458015221.1686251464-641.168625146407
551521815777.573384484-559.573384484023
561569615614.815783139181.1842168609455
571512915488.1107420006-359.110742000599
581511014854.5930580573255.40694194266
591420414131.838000076372.16199992369
601365514228.3909629239-573.390962923901
611453414092.4046556804441.595344319627
621274613265.8638181051-519.863818105141
631407413974.374516787799.6254832123323
641369913722.7167515361-23.716751536067
651418414365.8706148958-181.870614895846
661411014241.2106353251-131.210635325067
671582014986.4770702275833.522929772545
681536215584.4354337519-222.435433751887
691499315183.4579191271-190.457919127084
701443714841.0572700995-404.057270099513
711369413822.7463572319-128.746357231868
721368813607.57455383480.4254461660294

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15391 & 15364.603087137 & 26.3969128629924 \tabularnewline
14 & 13704 & 13700.5969628229 & 3.40303717714596 \tabularnewline
15 & 15409 & 15415.6325397335 & -6.63253973348947 \tabularnewline
16 & 15098 & 15116.9889000232 & -18.9889000232033 \tabularnewline
17 & 15254 & 15258.584317437 & -4.58431743704023 \tabularnewline
18 & 15522 & 15499.8367647864 & 22.1632352135621 \tabularnewline
19 & 16669 & 16889.8573118688 & -220.857311868796 \tabularnewline
20 & 16238 & 16264.0379862461 & -26.0379862460977 \tabularnewline
21 & 16246 & 16290.3746331177 & -44.3746331176808 \tabularnewline
22 & 15424 & 15529.7786341687 & -105.778634168704 \tabularnewline
23 & 14952 & 14375.0944873499 & 576.905512650052 \tabularnewline
24 & 15008 & 14895.6128895815 & 112.387110418545 \tabularnewline
25 & 14929 & 15495.704426151 & -566.704426150978 \tabularnewline
26 & 13905 & 13610.4535566033 & 294.546443396704 \tabularnewline
27 & 14994 & 15434.0704346967 & -440.070434696663 \tabularnewline
28 & 14753 & 14969.9522385599 & -216.952238559932 \tabularnewline
29 & 15031 & 15039.8663241057 & -8.86632410565653 \tabularnewline
30 & 15386 & 15285.6887513943 & 100.311248605693 \tabularnewline
31 & 16160 & 16599.332546588 & -439.332546588044 \tabularnewline
32 & 16116 & 15970.8536252308 & 145.146374769247 \tabularnewline
33 & 16219 & 16054.6558222764 & 164.344177723589 \tabularnewline
34 & 16064 & 15356.8059744913 & 707.194025508679 \tabularnewline
35 & 15436 & 14747.475718338 & 688.524281662016 \tabularnewline
36 & 15404 & 15140.9471844808 & 263.052815519181 \tabularnewline
37 & 15112 & 15550.5085689774 & -438.508568977397 \tabularnewline
38 & 14119 & 14001.6729657218 & 117.327034278163 \tabularnewline
39 & 14775 & 15508.8309707124 & -733.83097071237 \tabularnewline
40 & 14289 & 15013.6340236765 & -724.634023676514 \tabularnewline
41 & 15121 & 14967.3110085059 & 153.688991494068 \tabularnewline
42 & 15371 & 15314.4497996545 & 56.5502003454694 \tabularnewline
43 & 15782 & 16409.6574548677 & -627.657454867745 \tabularnewline
44 & 16104 & 15926.4115569048 & 177.588443095177 \tabularnewline
45 & 15674 & 16029.0956760443 & -355.095676044293 \tabularnewline
46 & 15105 & 15340.1658810124 & -235.165881012426 \tabularnewline
47 & 14223 & 14398.9691076692 & -175.969107669167 \tabularnewline
48 & 14385 & 14310.1167750275 & 74.8832249725383 \tabularnewline
49 & 14558 & 14385.3642182767 & 172.635781723269 \tabularnewline
50 & 13804 & 13331.4819942977 & 472.518005702263 \tabularnewline
51 & 14672 & 14607.5787737606 & 64.4212262393812 \tabularnewline
52 & 14244 & 14417.0926341872 & -173.09263418716 \tabularnewline
53 & 15089 & 14897.3643773156 & 191.635622684389 \tabularnewline
54 & 14580 & 15221.1686251464 & -641.168625146407 \tabularnewline
55 & 15218 & 15777.573384484 & -559.573384484023 \tabularnewline
56 & 15696 & 15614.8157831391 & 81.1842168609455 \tabularnewline
57 & 15129 & 15488.1107420006 & -359.110742000599 \tabularnewline
58 & 15110 & 14854.5930580573 & 255.40694194266 \tabularnewline
59 & 14204 & 14131.8380000763 & 72.16199992369 \tabularnewline
60 & 13655 & 14228.3909629239 & -573.390962923901 \tabularnewline
61 & 14534 & 14092.4046556804 & 441.595344319627 \tabularnewline
62 & 12746 & 13265.8638181051 & -519.863818105141 \tabularnewline
63 & 14074 & 13974.3745167877 & 99.6254832123323 \tabularnewline
64 & 13699 & 13722.7167515361 & -23.716751536067 \tabularnewline
65 & 14184 & 14365.8706148958 & -181.870614895846 \tabularnewline
66 & 14110 & 14241.2106353251 & -131.210635325067 \tabularnewline
67 & 15820 & 14986.4770702275 & 833.522929772545 \tabularnewline
68 & 15362 & 15584.4354337519 & -222.435433751887 \tabularnewline
69 & 14993 & 15183.4579191271 & -190.457919127084 \tabularnewline
70 & 14437 & 14841.0572700995 & -404.057270099513 \tabularnewline
71 & 13694 & 13822.7463572319 & -128.746357231868 \tabularnewline
72 & 13688 & 13607.574553834 & 80.4254461660294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278455&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]15391[/C][C]15364.603087137[/C][C]26.3969128629924[/C][/ROW]
[ROW][C]14[/C][C]13704[/C][C]13700.5969628229[/C][C]3.40303717714596[/C][/ROW]
[ROW][C]15[/C][C]15409[/C][C]15415.6325397335[/C][C]-6.63253973348947[/C][/ROW]
[ROW][C]16[/C][C]15098[/C][C]15116.9889000232[/C][C]-18.9889000232033[/C][/ROW]
[ROW][C]17[/C][C]15254[/C][C]15258.584317437[/C][C]-4.58431743704023[/C][/ROW]
[ROW][C]18[/C][C]15522[/C][C]15499.8367647864[/C][C]22.1632352135621[/C][/ROW]
[ROW][C]19[/C][C]16669[/C][C]16889.8573118688[/C][C]-220.857311868796[/C][/ROW]
[ROW][C]20[/C][C]16238[/C][C]16264.0379862461[/C][C]-26.0379862460977[/C][/ROW]
[ROW][C]21[/C][C]16246[/C][C]16290.3746331177[/C][C]-44.3746331176808[/C][/ROW]
[ROW][C]22[/C][C]15424[/C][C]15529.7786341687[/C][C]-105.778634168704[/C][/ROW]
[ROW][C]23[/C][C]14952[/C][C]14375.0944873499[/C][C]576.905512650052[/C][/ROW]
[ROW][C]24[/C][C]15008[/C][C]14895.6128895815[/C][C]112.387110418545[/C][/ROW]
[ROW][C]25[/C][C]14929[/C][C]15495.704426151[/C][C]-566.704426150978[/C][/ROW]
[ROW][C]26[/C][C]13905[/C][C]13610.4535566033[/C][C]294.546443396704[/C][/ROW]
[ROW][C]27[/C][C]14994[/C][C]15434.0704346967[/C][C]-440.070434696663[/C][/ROW]
[ROW][C]28[/C][C]14753[/C][C]14969.9522385599[/C][C]-216.952238559932[/C][/ROW]
[ROW][C]29[/C][C]15031[/C][C]15039.8663241057[/C][C]-8.86632410565653[/C][/ROW]
[ROW][C]30[/C][C]15386[/C][C]15285.6887513943[/C][C]100.311248605693[/C][/ROW]
[ROW][C]31[/C][C]16160[/C][C]16599.332546588[/C][C]-439.332546588044[/C][/ROW]
[ROW][C]32[/C][C]16116[/C][C]15970.8536252308[/C][C]145.146374769247[/C][/ROW]
[ROW][C]33[/C][C]16219[/C][C]16054.6558222764[/C][C]164.344177723589[/C][/ROW]
[ROW][C]34[/C][C]16064[/C][C]15356.8059744913[/C][C]707.194025508679[/C][/ROW]
[ROW][C]35[/C][C]15436[/C][C]14747.475718338[/C][C]688.524281662016[/C][/ROW]
[ROW][C]36[/C][C]15404[/C][C]15140.9471844808[/C][C]263.052815519181[/C][/ROW]
[ROW][C]37[/C][C]15112[/C][C]15550.5085689774[/C][C]-438.508568977397[/C][/ROW]
[ROW][C]38[/C][C]14119[/C][C]14001.6729657218[/C][C]117.327034278163[/C][/ROW]
[ROW][C]39[/C][C]14775[/C][C]15508.8309707124[/C][C]-733.83097071237[/C][/ROW]
[ROW][C]40[/C][C]14289[/C][C]15013.6340236765[/C][C]-724.634023676514[/C][/ROW]
[ROW][C]41[/C][C]15121[/C][C]14967.3110085059[/C][C]153.688991494068[/C][/ROW]
[ROW][C]42[/C][C]15371[/C][C]15314.4497996545[/C][C]56.5502003454694[/C][/ROW]
[ROW][C]43[/C][C]15782[/C][C]16409.6574548677[/C][C]-627.657454867745[/C][/ROW]
[ROW][C]44[/C][C]16104[/C][C]15926.4115569048[/C][C]177.588443095177[/C][/ROW]
[ROW][C]45[/C][C]15674[/C][C]16029.0956760443[/C][C]-355.095676044293[/C][/ROW]
[ROW][C]46[/C][C]15105[/C][C]15340.1658810124[/C][C]-235.165881012426[/C][/ROW]
[ROW][C]47[/C][C]14223[/C][C]14398.9691076692[/C][C]-175.969107669167[/C][/ROW]
[ROW][C]48[/C][C]14385[/C][C]14310.1167750275[/C][C]74.8832249725383[/C][/ROW]
[ROW][C]49[/C][C]14558[/C][C]14385.3642182767[/C][C]172.635781723269[/C][/ROW]
[ROW][C]50[/C][C]13804[/C][C]13331.4819942977[/C][C]472.518005702263[/C][/ROW]
[ROW][C]51[/C][C]14672[/C][C]14607.5787737606[/C][C]64.4212262393812[/C][/ROW]
[ROW][C]52[/C][C]14244[/C][C]14417.0926341872[/C][C]-173.09263418716[/C][/ROW]
[ROW][C]53[/C][C]15089[/C][C]14897.3643773156[/C][C]191.635622684389[/C][/ROW]
[ROW][C]54[/C][C]14580[/C][C]15221.1686251464[/C][C]-641.168625146407[/C][/ROW]
[ROW][C]55[/C][C]15218[/C][C]15777.573384484[/C][C]-559.573384484023[/C][/ROW]
[ROW][C]56[/C][C]15696[/C][C]15614.8157831391[/C][C]81.1842168609455[/C][/ROW]
[ROW][C]57[/C][C]15129[/C][C]15488.1107420006[/C][C]-359.110742000599[/C][/ROW]
[ROW][C]58[/C][C]15110[/C][C]14854.5930580573[/C][C]255.40694194266[/C][/ROW]
[ROW][C]59[/C][C]14204[/C][C]14131.8380000763[/C][C]72.16199992369[/C][/ROW]
[ROW][C]60[/C][C]13655[/C][C]14228.3909629239[/C][C]-573.390962923901[/C][/ROW]
[ROW][C]61[/C][C]14534[/C][C]14092.4046556804[/C][C]441.595344319627[/C][/ROW]
[ROW][C]62[/C][C]12746[/C][C]13265.8638181051[/C][C]-519.863818105141[/C][/ROW]
[ROW][C]63[/C][C]14074[/C][C]13974.3745167877[/C][C]99.6254832123323[/C][/ROW]
[ROW][C]64[/C][C]13699[/C][C]13722.7167515361[/C][C]-23.716751536067[/C][/ROW]
[ROW][C]65[/C][C]14184[/C][C]14365.8706148958[/C][C]-181.870614895846[/C][/ROW]
[ROW][C]66[/C][C]14110[/C][C]14241.2106353251[/C][C]-131.210635325067[/C][/ROW]
[ROW][C]67[/C][C]15820[/C][C]14986.4770702275[/C][C]833.522929772545[/C][/ROW]
[ROW][C]68[/C][C]15362[/C][C]15584.4354337519[/C][C]-222.435433751887[/C][/ROW]
[ROW][C]69[/C][C]14993[/C][C]15183.4579191271[/C][C]-190.457919127084[/C][/ROW]
[ROW][C]70[/C][C]14437[/C][C]14841.0572700995[/C][C]-404.057270099513[/C][/ROW]
[ROW][C]71[/C][C]13694[/C][C]13822.7463572319[/C][C]-128.746357231868[/C][/ROW]
[ROW][C]72[/C][C]13688[/C][C]13607.574553834[/C][C]80.4254461660294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278455&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
131539115364.60308713726.3969128629924
141370413700.59696282293.40303717714596
151540915415.6325397335-6.63253973348947
161509815116.9889000232-18.9889000232033
171525415258.584317437-4.58431743704023
181552215499.836764786422.1632352135621
191666916889.8573118688-220.857311868796
201623816264.0379862461-26.0379862460977
211624616290.3746331177-44.3746331176808
221542415529.7786341687-105.778634168704
231495214375.0944873499576.905512650052
241500814895.6128895815112.387110418545
251492915495.704426151-566.704426150978
261390513610.4535566033294.546443396704
271499415434.0704346967-440.070434696663
281475314969.9522385599-216.952238559932
291503115039.8663241057-8.86632410565653
301538615285.6887513943100.311248605693
311616016599.332546588-439.332546588044
321611615970.8536252308145.146374769247
331621916054.6558222764164.344177723589
341606415356.8059744913707.194025508679
351543614747.475718338688.524281662016
361540415140.9471844808263.052815519181
371511215550.5085689774-438.508568977397
381411914001.6729657218117.327034278163
391477515508.8309707124-733.83097071237
401428915013.6340236765-724.634023676514
411512114967.3110085059153.688991494068
421537115314.449799654556.5502003454694
431578216409.6574548677-627.657454867745
441610415926.4115569048177.588443095177
451567416029.0956760443-355.095676044293
461510515340.1658810124-235.165881012426
471422314398.9691076692-175.969107669167
481438514310.116775027574.8832249725383
491455814385.3642182767172.635781723269
501380413331.4819942977472.518005702263
511467214607.578773760664.4212262393812
521424414417.0926341872-173.09263418716
531508914897.3643773156191.635622684389
541458015221.1686251464-641.168625146407
551521815777.573384484-559.573384484023
561569615614.815783139181.1842168609455
571512915488.1107420006-359.110742000599
581511014854.5930580573255.40694194266
591420414131.838000076372.16199992369
601365514228.3909629239-573.390962923901
611453414092.4046556804441.595344319627
621274613265.8638181051-519.863818105141
631407413974.374516787799.6254832123323
641369913722.7167515361-23.716751536067
651418414365.8706148958-181.870614895846
661411014241.2106353251-131.210635325067
671582014986.4770702275833.522929772545
681536215584.4354337519-222.435433751887
691499315183.4579191271-190.457919127084
701443714841.0572700995-404.057270099513
711369413822.7463572319-128.746357231868
721368813607.57455383480.4254461660294







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7314084.689692364313573.714297644914595.6650870836
7412766.26215325512203.993022617713328.5312838922
7513889.067630931313252.211195013314525.9240668493
7613558.180998840712877.981026222214238.3809714592
7714145.40268753913401.423522499314889.3818525787
7814108.112725265613321.541572649514894.6838778816
7915248.713500423314378.518337817216118.9086630295
8015145.315555785614241.56783786816049.0632737033
8114845.158539390213918.084385630815772.2326931497
8214499.107234656913552.555996253415445.6584730604
8313736.655934874112792.603685857414680.7081838908
8413646.93680426212773.251766184114520.6218423398

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 14084.6896923643 & 13573.7142976449 & 14595.6650870836 \tabularnewline
74 & 12766.262153255 & 12203.9930226177 & 13328.5312838922 \tabularnewline
75 & 13889.0676309313 & 13252.2111950133 & 14525.9240668493 \tabularnewline
76 & 13558.1809988407 & 12877.9810262222 & 14238.3809714592 \tabularnewline
77 & 14145.402687539 & 13401.4235224993 & 14889.3818525787 \tabularnewline
78 & 14108.1127252656 & 13321.5415726495 & 14894.6838778816 \tabularnewline
79 & 15248.7135004233 & 14378.5183378172 & 16118.9086630295 \tabularnewline
80 & 15145.3155557856 & 14241.567837868 & 16049.0632737033 \tabularnewline
81 & 14845.1585393902 & 13918.0843856308 & 15772.2326931497 \tabularnewline
82 & 14499.1072346569 & 13552.5559962534 & 15445.6584730604 \tabularnewline
83 & 13736.6559348741 & 12792.6036858574 & 14680.7081838908 \tabularnewline
84 & 13646.936804262 & 12773.2517661841 & 14520.6218423398 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278455&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]14084.6896923643[/C][C]13573.7142976449[/C][C]14595.6650870836[/C][/ROW]
[ROW][C]74[/C][C]12766.262153255[/C][C]12203.9930226177[/C][C]13328.5312838922[/C][/ROW]
[ROW][C]75[/C][C]13889.0676309313[/C][C]13252.2111950133[/C][C]14525.9240668493[/C][/ROW]
[ROW][C]76[/C][C]13558.1809988407[/C][C]12877.9810262222[/C][C]14238.3809714592[/C][/ROW]
[ROW][C]77[/C][C]14145.402687539[/C][C]13401.4235224993[/C][C]14889.3818525787[/C][/ROW]
[ROW][C]78[/C][C]14108.1127252656[/C][C]13321.5415726495[/C][C]14894.6838778816[/C][/ROW]
[ROW][C]79[/C][C]15248.7135004233[/C][C]14378.5183378172[/C][C]16118.9086630295[/C][/ROW]
[ROW][C]80[/C][C]15145.3155557856[/C][C]14241.567837868[/C][C]16049.0632737033[/C][/ROW]
[ROW][C]81[/C][C]14845.1585393902[/C][C]13918.0843856308[/C][C]15772.2326931497[/C][/ROW]
[ROW][C]82[/C][C]14499.1072346569[/C][C]13552.5559962534[/C][C]15445.6584730604[/C][/ROW]
[ROW][C]83[/C][C]13736.6559348741[/C][C]12792.6036858574[/C][C]14680.7081838908[/C][/ROW]
[ROW][C]84[/C][C]13646.936804262[/C][C]12773.2517661841[/C][C]14520.6218423398[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278455&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278455&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
7314084.689692364313573.714297644914595.6650870836
7412766.26215325512203.993022617713328.5312838922
7513889.067630931313252.211195013314525.9240668493
7613558.180998840712877.981026222214238.3809714592
7714145.40268753913401.423522499314889.3818525787
7814108.112725265613321.541572649514894.6838778816
7915248.713500423314378.518337817216118.9086630295
8015145.315555785614241.56783786816049.0632737033
8114845.158539390213918.084385630815772.2326931497
8214499.107234656913552.555996253415445.6584730604
8313736.655934874112792.603685857414680.7081838908
8413646.93680426212773.251766184114520.6218423398



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=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')