Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 20:44:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/28/t1480366011gk1d8mn33qbiqvd.htm/, Retrieved Sat, 04 May 2024 18:55:51 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 18:55:51 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
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
14366
13267
14409
14031
14584
14626
15669
15460
15552
15220
13907
14090
14176
12523
13597
13241
14345
14273
15308
15353
15330
14610
13852
13902




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.536171389087897
beta0
gamma0.570740323553612

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.536171389087897 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.570740323553612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.536171389087897[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.570740323553612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.536171389087897
beta0
gamma0.570740323553612







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131492915039.8680555556-110.86805555556
141390513974.0071095362-69.0071095361945
151499415023.5074717592-29.5074717592324
161475314732.436409637620.5635903623861
171503114965.920351780265.0796482198184
181538615310.439197167675.5608028324477
191616016584.8277377828-424.827737782824
201611615928.2139261594187.786073840598
211621916037.1077795552181.892220444788
221606415335.5915173887728.408482611292
231543615269.1016386671166.898361332858
241540415420.8377648995-16.8377648994756
251511215321.6268811025-209.626881102486
261411914213.8959462853-94.8959462853054
271477515259.9720238698-484.972023869841
281428914737.9489967053-448.948996705334
291512114731.4782670432389.521732956828
301537115252.7283065847118.271693415256
311578216417.5515023172-635.551502317245
321610415810.1282520328293.871747967167
331567415974.3419542718-300.341954271811
341510515158.942420181-53.9424201809652
351422314524.3322160349-301.332216034851
361438514376.37683012258.62316987751547
371455814239.7811389985318.218861001495
381380413445.4382150013358.561784998701
391467214631.382194898440.6178051016486
401424414400.7016171988-156.70161719876
411508914772.8903146472316.109685352754
421458015182.9720603715-602.972060371494
431521815761.5286240322-543.528624032244
441569615449.4876208213246.512379178674
451512915431.0049513072-302.004951307223
461511014679.9420528248430.057947175199
471420414239.3485631942-35.3485631941912
481365514316.0591557591-661.059155759147
491453413902.3568952584631.643104741552
501274613286.7428918521-540.742891852067
511407413906.3374940233167.662505976707
521369913691.53912956017.46087043988882
531418414276.9123550425-92.9123550425411
541411014224.3836345504-114.383634550401
551582015080.6435379639739.356462036099
561536215665.5929642514-303.592964251417
571499315206.9529190121-213.952919012097
581443714696.8968579943-259.896857994287
591369413763.1642817981-69.1642817980519
601368813656.102184272231.8978157278107
611436613956.1551255217409.844874478278
621326712911.2585632853355.741436714748
631440914199.0555219777209.944478022282
641403113964.518052458266.4819475417844
651458414554.965319315429.0346806846155
661462614562.137111049963.8628889501397
671566915739.9746379693-70.9746379693279
681546015614.3522047084-154.352204708412
691555215259.4608077808292.539192219234
701522015008.8087845882211.191215411784
711390714378.1519682114-471.151968211379
721409014082.30930811357.69069188646972
731417614469.4353786123-293.435378612259
741252313033.1374961855-510.137496185542
751359713818.0787439395-221.078743939499
761324113314.4607371908-73.4607371907841
771434513819.9614867699525.038513230053
781427314102.2962639088170.703736091176
791530815301.7238387026.27616129801208
801535315195.4488897847157.551110215316
811533015126.0947605424203.905239457579
821461014806.3848483676-196.384848367641
831385213776.563636613975.4363633861285
841390213900.54795582541.45204417457353

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 14929 & 15039.8680555556 & -110.86805555556 \tabularnewline
14 & 13905 & 13974.0071095362 & -69.0071095361945 \tabularnewline
15 & 14994 & 15023.5074717592 & -29.5074717592324 \tabularnewline
16 & 14753 & 14732.4364096376 & 20.5635903623861 \tabularnewline
17 & 15031 & 14965.9203517802 & 65.0796482198184 \tabularnewline
18 & 15386 & 15310.4391971676 & 75.5608028324477 \tabularnewline
19 & 16160 & 16584.8277377828 & -424.827737782824 \tabularnewline
20 & 16116 & 15928.2139261594 & 187.786073840598 \tabularnewline
21 & 16219 & 16037.1077795552 & 181.892220444788 \tabularnewline
22 & 16064 & 15335.5915173887 & 728.408482611292 \tabularnewline
23 & 15436 & 15269.1016386671 & 166.898361332858 \tabularnewline
24 & 15404 & 15420.8377648995 & -16.8377648994756 \tabularnewline
25 & 15112 & 15321.6268811025 & -209.626881102486 \tabularnewline
26 & 14119 & 14213.8959462853 & -94.8959462853054 \tabularnewline
27 & 14775 & 15259.9720238698 & -484.972023869841 \tabularnewline
28 & 14289 & 14737.9489967053 & -448.948996705334 \tabularnewline
29 & 15121 & 14731.4782670432 & 389.521732956828 \tabularnewline
30 & 15371 & 15252.7283065847 & 118.271693415256 \tabularnewline
31 & 15782 & 16417.5515023172 & -635.551502317245 \tabularnewline
32 & 16104 & 15810.1282520328 & 293.871747967167 \tabularnewline
33 & 15674 & 15974.3419542718 & -300.341954271811 \tabularnewline
34 & 15105 & 15158.942420181 & -53.9424201809652 \tabularnewline
35 & 14223 & 14524.3322160349 & -301.332216034851 \tabularnewline
36 & 14385 & 14376.3768301225 & 8.62316987751547 \tabularnewline
37 & 14558 & 14239.7811389985 & 318.218861001495 \tabularnewline
38 & 13804 & 13445.4382150013 & 358.561784998701 \tabularnewline
39 & 14672 & 14631.3821948984 & 40.6178051016486 \tabularnewline
40 & 14244 & 14400.7016171988 & -156.70161719876 \tabularnewline
41 & 15089 & 14772.8903146472 & 316.109685352754 \tabularnewline
42 & 14580 & 15182.9720603715 & -602.972060371494 \tabularnewline
43 & 15218 & 15761.5286240322 & -543.528624032244 \tabularnewline
44 & 15696 & 15449.4876208213 & 246.512379178674 \tabularnewline
45 & 15129 & 15431.0049513072 & -302.004951307223 \tabularnewline
46 & 15110 & 14679.9420528248 & 430.057947175199 \tabularnewline
47 & 14204 & 14239.3485631942 & -35.3485631941912 \tabularnewline
48 & 13655 & 14316.0591557591 & -661.059155759147 \tabularnewline
49 & 14534 & 13902.3568952584 & 631.643104741552 \tabularnewline
50 & 12746 & 13286.7428918521 & -540.742891852067 \tabularnewline
51 & 14074 & 13906.3374940233 & 167.662505976707 \tabularnewline
52 & 13699 & 13691.5391295601 & 7.46087043988882 \tabularnewline
53 & 14184 & 14276.9123550425 & -92.9123550425411 \tabularnewline
54 & 14110 & 14224.3836345504 & -114.383634550401 \tabularnewline
55 & 15820 & 15080.6435379639 & 739.356462036099 \tabularnewline
56 & 15362 & 15665.5929642514 & -303.592964251417 \tabularnewline
57 & 14993 & 15206.9529190121 & -213.952919012097 \tabularnewline
58 & 14437 & 14696.8968579943 & -259.896857994287 \tabularnewline
59 & 13694 & 13763.1642817981 & -69.1642817980519 \tabularnewline
60 & 13688 & 13656.1021842722 & 31.8978157278107 \tabularnewline
61 & 14366 & 13956.1551255217 & 409.844874478278 \tabularnewline
62 & 13267 & 12911.2585632853 & 355.741436714748 \tabularnewline
63 & 14409 & 14199.0555219777 & 209.944478022282 \tabularnewline
64 & 14031 & 13964.5180524582 & 66.4819475417844 \tabularnewline
65 & 14584 & 14554.9653193154 & 29.0346806846155 \tabularnewline
66 & 14626 & 14562.1371110499 & 63.8628889501397 \tabularnewline
67 & 15669 & 15739.9746379693 & -70.9746379693279 \tabularnewline
68 & 15460 & 15614.3522047084 & -154.352204708412 \tabularnewline
69 & 15552 & 15259.4608077808 & 292.539192219234 \tabularnewline
70 & 15220 & 15008.8087845882 & 211.191215411784 \tabularnewline
71 & 13907 & 14378.1519682114 & -471.151968211379 \tabularnewline
72 & 14090 & 14082.3093081135 & 7.69069188646972 \tabularnewline
73 & 14176 & 14469.4353786123 & -293.435378612259 \tabularnewline
74 & 12523 & 13033.1374961855 & -510.137496185542 \tabularnewline
75 & 13597 & 13818.0787439395 & -221.078743939499 \tabularnewline
76 & 13241 & 13314.4607371908 & -73.4607371907841 \tabularnewline
77 & 14345 & 13819.9614867699 & 525.038513230053 \tabularnewline
78 & 14273 & 14102.2962639088 & 170.703736091176 \tabularnewline
79 & 15308 & 15301.723838702 & 6.27616129801208 \tabularnewline
80 & 15353 & 15195.4488897847 & 157.551110215316 \tabularnewline
81 & 15330 & 15126.0947605424 & 203.905239457579 \tabularnewline
82 & 14610 & 14806.3848483676 & -196.384848367641 \tabularnewline
83 & 13852 & 13776.5636366139 & 75.4363633861285 \tabularnewline
84 & 13902 & 13900.5479558254 & 1.45204417457353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]14929[/C][C]15039.8680555556[/C][C]-110.86805555556[/C][/ROW]
[ROW][C]14[/C][C]13905[/C][C]13974.0071095362[/C][C]-69.0071095361945[/C][/ROW]
[ROW][C]15[/C][C]14994[/C][C]15023.5074717592[/C][C]-29.5074717592324[/C][/ROW]
[ROW][C]16[/C][C]14753[/C][C]14732.4364096376[/C][C]20.5635903623861[/C][/ROW]
[ROW][C]17[/C][C]15031[/C][C]14965.9203517802[/C][C]65.0796482198184[/C][/ROW]
[ROW][C]18[/C][C]15386[/C][C]15310.4391971676[/C][C]75.5608028324477[/C][/ROW]
[ROW][C]19[/C][C]16160[/C][C]16584.8277377828[/C][C]-424.827737782824[/C][/ROW]
[ROW][C]20[/C][C]16116[/C][C]15928.2139261594[/C][C]187.786073840598[/C][/ROW]
[ROW][C]21[/C][C]16219[/C][C]16037.1077795552[/C][C]181.892220444788[/C][/ROW]
[ROW][C]22[/C][C]16064[/C][C]15335.5915173887[/C][C]728.408482611292[/C][/ROW]
[ROW][C]23[/C][C]15436[/C][C]15269.1016386671[/C][C]166.898361332858[/C][/ROW]
[ROW][C]24[/C][C]15404[/C][C]15420.8377648995[/C][C]-16.8377648994756[/C][/ROW]
[ROW][C]25[/C][C]15112[/C][C]15321.6268811025[/C][C]-209.626881102486[/C][/ROW]
[ROW][C]26[/C][C]14119[/C][C]14213.8959462853[/C][C]-94.8959462853054[/C][/ROW]
[ROW][C]27[/C][C]14775[/C][C]15259.9720238698[/C][C]-484.972023869841[/C][/ROW]
[ROW][C]28[/C][C]14289[/C][C]14737.9489967053[/C][C]-448.948996705334[/C][/ROW]
[ROW][C]29[/C][C]15121[/C][C]14731.4782670432[/C][C]389.521732956828[/C][/ROW]
[ROW][C]30[/C][C]15371[/C][C]15252.7283065847[/C][C]118.271693415256[/C][/ROW]
[ROW][C]31[/C][C]15782[/C][C]16417.5515023172[/C][C]-635.551502317245[/C][/ROW]
[ROW][C]32[/C][C]16104[/C][C]15810.1282520328[/C][C]293.871747967167[/C][/ROW]
[ROW][C]33[/C][C]15674[/C][C]15974.3419542718[/C][C]-300.341954271811[/C][/ROW]
[ROW][C]34[/C][C]15105[/C][C]15158.942420181[/C][C]-53.9424201809652[/C][/ROW]
[ROW][C]35[/C][C]14223[/C][C]14524.3322160349[/C][C]-301.332216034851[/C][/ROW]
[ROW][C]36[/C][C]14385[/C][C]14376.3768301225[/C][C]8.62316987751547[/C][/ROW]
[ROW][C]37[/C][C]14558[/C][C]14239.7811389985[/C][C]318.218861001495[/C][/ROW]
[ROW][C]38[/C][C]13804[/C][C]13445.4382150013[/C][C]358.561784998701[/C][/ROW]
[ROW][C]39[/C][C]14672[/C][C]14631.3821948984[/C][C]40.6178051016486[/C][/ROW]
[ROW][C]40[/C][C]14244[/C][C]14400.7016171988[/C][C]-156.70161719876[/C][/ROW]
[ROW][C]41[/C][C]15089[/C][C]14772.8903146472[/C][C]316.109685352754[/C][/ROW]
[ROW][C]42[/C][C]14580[/C][C]15182.9720603715[/C][C]-602.972060371494[/C][/ROW]
[ROW][C]43[/C][C]15218[/C][C]15761.5286240322[/C][C]-543.528624032244[/C][/ROW]
[ROW][C]44[/C][C]15696[/C][C]15449.4876208213[/C][C]246.512379178674[/C][/ROW]
[ROW][C]45[/C][C]15129[/C][C]15431.0049513072[/C][C]-302.004951307223[/C][/ROW]
[ROW][C]46[/C][C]15110[/C][C]14679.9420528248[/C][C]430.057947175199[/C][/ROW]
[ROW][C]47[/C][C]14204[/C][C]14239.3485631942[/C][C]-35.3485631941912[/C][/ROW]
[ROW][C]48[/C][C]13655[/C][C]14316.0591557591[/C][C]-661.059155759147[/C][/ROW]
[ROW][C]49[/C][C]14534[/C][C]13902.3568952584[/C][C]631.643104741552[/C][/ROW]
[ROW][C]50[/C][C]12746[/C][C]13286.7428918521[/C][C]-540.742891852067[/C][/ROW]
[ROW][C]51[/C][C]14074[/C][C]13906.3374940233[/C][C]167.662505976707[/C][/ROW]
[ROW][C]52[/C][C]13699[/C][C]13691.5391295601[/C][C]7.46087043988882[/C][/ROW]
[ROW][C]53[/C][C]14184[/C][C]14276.9123550425[/C][C]-92.9123550425411[/C][/ROW]
[ROW][C]54[/C][C]14110[/C][C]14224.3836345504[/C][C]-114.383634550401[/C][/ROW]
[ROW][C]55[/C][C]15820[/C][C]15080.6435379639[/C][C]739.356462036099[/C][/ROW]
[ROW][C]56[/C][C]15362[/C][C]15665.5929642514[/C][C]-303.592964251417[/C][/ROW]
[ROW][C]57[/C][C]14993[/C][C]15206.9529190121[/C][C]-213.952919012097[/C][/ROW]
[ROW][C]58[/C][C]14437[/C][C]14696.8968579943[/C][C]-259.896857994287[/C][/ROW]
[ROW][C]59[/C][C]13694[/C][C]13763.1642817981[/C][C]-69.1642817980519[/C][/ROW]
[ROW][C]60[/C][C]13688[/C][C]13656.1021842722[/C][C]31.8978157278107[/C][/ROW]
[ROW][C]61[/C][C]14366[/C][C]13956.1551255217[/C][C]409.844874478278[/C][/ROW]
[ROW][C]62[/C][C]13267[/C][C]12911.2585632853[/C][C]355.741436714748[/C][/ROW]
[ROW][C]63[/C][C]14409[/C][C]14199.0555219777[/C][C]209.944478022282[/C][/ROW]
[ROW][C]64[/C][C]14031[/C][C]13964.5180524582[/C][C]66.4819475417844[/C][/ROW]
[ROW][C]65[/C][C]14584[/C][C]14554.9653193154[/C][C]29.0346806846155[/C][/ROW]
[ROW][C]66[/C][C]14626[/C][C]14562.1371110499[/C][C]63.8628889501397[/C][/ROW]
[ROW][C]67[/C][C]15669[/C][C]15739.9746379693[/C][C]-70.9746379693279[/C][/ROW]
[ROW][C]68[/C][C]15460[/C][C]15614.3522047084[/C][C]-154.352204708412[/C][/ROW]
[ROW][C]69[/C][C]15552[/C][C]15259.4608077808[/C][C]292.539192219234[/C][/ROW]
[ROW][C]70[/C][C]15220[/C][C]15008.8087845882[/C][C]211.191215411784[/C][/ROW]
[ROW][C]71[/C][C]13907[/C][C]14378.1519682114[/C][C]-471.151968211379[/C][/ROW]
[ROW][C]72[/C][C]14090[/C][C]14082.3093081135[/C][C]7.69069188646972[/C][/ROW]
[ROW][C]73[/C][C]14176[/C][C]14469.4353786123[/C][C]-293.435378612259[/C][/ROW]
[ROW][C]74[/C][C]12523[/C][C]13033.1374961855[/C][C]-510.137496185542[/C][/ROW]
[ROW][C]75[/C][C]13597[/C][C]13818.0787439395[/C][C]-221.078743939499[/C][/ROW]
[ROW][C]76[/C][C]13241[/C][C]13314.4607371908[/C][C]-73.4607371907841[/C][/ROW]
[ROW][C]77[/C][C]14345[/C][C]13819.9614867699[/C][C]525.038513230053[/C][/ROW]
[ROW][C]78[/C][C]14273[/C][C]14102.2962639088[/C][C]170.703736091176[/C][/ROW]
[ROW][C]79[/C][C]15308[/C][C]15301.723838702[/C][C]6.27616129801208[/C][/ROW]
[ROW][C]80[/C][C]15353[/C][C]15195.4488897847[/C][C]157.551110215316[/C][/ROW]
[ROW][C]81[/C][C]15330[/C][C]15126.0947605424[/C][C]203.905239457579[/C][/ROW]
[ROW][C]82[/C][C]14610[/C][C]14806.3848483676[/C][C]-196.384848367641[/C][/ROW]
[ROW][C]83[/C][C]13852[/C][C]13776.5636366139[/C][C]75.4363633861285[/C][/ROW]
[ROW][C]84[/C][C]13902[/C][C]13900.5479558254[/C][C]1.45204417457353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
131492915039.8680555556-110.86805555556
141390513974.0071095362-69.0071095361945
151499415023.5074717592-29.5074717592324
161475314732.436409637620.5635903623861
171503114965.920351780265.0796482198184
181538615310.439197167675.5608028324477
191616016584.8277377828-424.827737782824
201611615928.2139261594187.786073840598
211621916037.1077795552181.892220444788
221606415335.5915173887728.408482611292
231543615269.1016386671166.898361332858
241540415420.8377648995-16.8377648994756
251511215321.6268811025-209.626881102486
261411914213.8959462853-94.8959462853054
271477515259.9720238698-484.972023869841
281428914737.9489967053-448.948996705334
291512114731.4782670432389.521732956828
301537115252.7283065847118.271693415256
311578216417.5515023172-635.551502317245
321610415810.1282520328293.871747967167
331567415974.3419542718-300.341954271811
341510515158.942420181-53.9424201809652
351422314524.3322160349-301.332216034851
361438514376.37683012258.62316987751547
371455814239.7811389985318.218861001495
381380413445.4382150013358.561784998701
391467214631.382194898440.6178051016486
401424414400.7016171988-156.70161719876
411508914772.8903146472316.109685352754
421458015182.9720603715-602.972060371494
431521815761.5286240322-543.528624032244
441569615449.4876208213246.512379178674
451512915431.0049513072-302.004951307223
461511014679.9420528248430.057947175199
471420414239.3485631942-35.3485631941912
481365514316.0591557591-661.059155759147
491453413902.3568952584631.643104741552
501274613286.7428918521-540.742891852067
511407413906.3374940233167.662505976707
521369913691.53912956017.46087043988882
531418414276.9123550425-92.9123550425411
541411014224.3836345504-114.383634550401
551582015080.6435379639739.356462036099
561536215665.5929642514-303.592964251417
571499315206.9529190121-213.952919012097
581443714696.8968579943-259.896857994287
591369413763.1642817981-69.1642817980519
601368813656.102184272231.8978157278107
611436613956.1551255217409.844874478278
621326712911.2585632853355.741436714748
631440914199.0555219777209.944478022282
641403113964.518052458266.4819475417844
651458414554.965319315429.0346806846155
661462614562.137111049963.8628889501397
671566915739.9746379693-70.9746379693279
681546015614.3522047084-154.352204708412
691555215259.4608077808292.539192219234
701522015008.8087845882211.191215411784
711390714378.1519682114-471.151968211379
721409014082.30930811357.69069188646972
731417614469.4353786123-293.435378612259
741252313033.1374961855-510.137496185542
751359713818.0787439395-221.078743939499
761324113314.4607371908-73.4607371907841
771434513819.9614867699525.038513230053
781427314102.2962639088170.703736091176
791530815301.7238387026.27616129801208
801535315195.4488897847157.551110215316
811533015126.0947605424203.905239457579
821461014806.3848483676-196.384848367641
831385213776.563636613975.4363633861285
841390213900.54795582541.45204417457353







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8514204.613234683413589.547521676714819.6789476901
8612868.280388898212170.382760063113566.1780177332
8714003.264044670213231.372621378914775.1554679615
8813657.260414066612817.872757278814496.6480708544
8914360.58683705813458.740449148815262.4332249672
9014267.609466345313307.35836564215227.8605670486
9115331.982378402914316.680725976816347.2840308289
9215262.388696817814194.871617593316329.9057760424
9315120.83129887514003.536358649616238.1262391004
9414585.826160931713420.878414262215750.7739076012
9513733.258944359512522.532500654114943.9853880648
9613797.210893765712542.374732944515052.0470545869

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 14204.6132346834 & 13589.5475216767 & 14819.6789476901 \tabularnewline
86 & 12868.2803888982 & 12170.3827600631 & 13566.1780177332 \tabularnewline
87 & 14003.2640446702 & 13231.3726213789 & 14775.1554679615 \tabularnewline
88 & 13657.2604140666 & 12817.8727572788 & 14496.6480708544 \tabularnewline
89 & 14360.586837058 & 13458.7404491488 & 15262.4332249672 \tabularnewline
90 & 14267.6094663453 & 13307.358365642 & 15227.8605670486 \tabularnewline
91 & 15331.9823784029 & 14316.6807259768 & 16347.2840308289 \tabularnewline
92 & 15262.3886968178 & 14194.8716175933 & 16329.9057760424 \tabularnewline
93 & 15120.831298875 & 14003.5363586496 & 16238.1262391004 \tabularnewline
94 & 14585.8261609317 & 13420.8784142622 & 15750.7739076012 \tabularnewline
95 & 13733.2589443595 & 12522.5325006541 & 14943.9853880648 \tabularnewline
96 & 13797.2108937657 & 12542.3747329445 & 15052.0470545869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]14204.6132346834[/C][C]13589.5475216767[/C][C]14819.6789476901[/C][/ROW]
[ROW][C]86[/C][C]12868.2803888982[/C][C]12170.3827600631[/C][C]13566.1780177332[/C][/ROW]
[ROW][C]87[/C][C]14003.2640446702[/C][C]13231.3726213789[/C][C]14775.1554679615[/C][/ROW]
[ROW][C]88[/C][C]13657.2604140666[/C][C]12817.8727572788[/C][C]14496.6480708544[/C][/ROW]
[ROW][C]89[/C][C]14360.586837058[/C][C]13458.7404491488[/C][C]15262.4332249672[/C][/ROW]
[ROW][C]90[/C][C]14267.6094663453[/C][C]13307.358365642[/C][C]15227.8605670486[/C][/ROW]
[ROW][C]91[/C][C]15331.9823784029[/C][C]14316.6807259768[/C][C]16347.2840308289[/C][/ROW]
[ROW][C]92[/C][C]15262.3886968178[/C][C]14194.8716175933[/C][C]16329.9057760424[/C][/ROW]
[ROW][C]93[/C][C]15120.831298875[/C][C]14003.5363586496[/C][C]16238.1262391004[/C][/ROW]
[ROW][C]94[/C][C]14585.8261609317[/C][C]13420.8784142622[/C][C]15750.7739076012[/C][/ROW]
[ROW][C]95[/C][C]13733.2589443595[/C][C]12522.5325006541[/C][C]14943.9853880648[/C][/ROW]
[ROW][C]96[/C][C]13797.2108937657[/C][C]12542.3747329445[/C][C]15052.0470545869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
8514204.613234683413589.547521676714819.6789476901
8612868.280388898212170.382760063113566.1780177332
8714003.264044670213231.372621378914775.1554679615
8813657.260414066612817.872757278814496.6480708544
8914360.58683705813458.740449148815262.4332249672
9014267.609466345313307.35836564215227.8605670486
9115331.982378402914316.680725976816347.2840308289
9215262.388696817814194.871617593316329.9057760424
9315120.83129887514003.536358649616238.1262391004
9414585.826160931713420.878414262215750.7739076012
9513733.258944359512522.532500654114943.9853880648
9613797.210893765712542.374732944515052.0470545869



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')