Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 17 Jan 2009 04:04:38 -0700
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/Jan/17/t1232190321t35n77tpd9yzh04.htm/, Retrieved Mon, 29 Apr 2024 15:23:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36924, Retrieved Mon, 29 Apr 2024 15:23:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact224
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [oef1 Inschrijving...] [2008-12-11 08:11:35] [74be16979710d4c4e7c6647856088456]
- RMP   [Standard Deviation Plot] [Standard Deviatio...] [2009-01-06 10:07:20] [74be16979710d4c4e7c6647856088456]
- RMP     [Classical Decomposition] [SDL OPG 9 OEF1 ] [2009-01-15 22:21:28] [74be16979710d4c4e7c6647856088456]
- RMP         [Exponential Smoothing] [SDL OPG 10 OEF1 ] [2009-01-17 11:04:38] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36924&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36924&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.185475284794843
beta0.000362009975189055
gamma0.521962133305563

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.185475284794843 \tabularnewline
beta & 0.000362009975189055 \tabularnewline
gamma & 0.521962133305563 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36924&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]0.185475284794843[/C][/ROW]
[ROW][C]beta[/C][C]0.000362009975189055[/C][/ROW]
[ROW][C]gamma[/C][C]0.521962133305563[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36924&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
alpha0.185475284794843
beta0.000362009975189055
gamma0.521962133305563







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770239722.9017575777-2020.90175757770
143036431535.1647279220-1171.16472792205
153260933590.6706490098-981.670649009757
163021230845.0542818759-633.05428187587
172996530291.5608338424-326.560833842421
182835228469.5184451801-117.518445180067
192581425831.2286456269-17.2286456268739
202241422218.8079229484195.192077051648
212050620072.5399434037433.460056596261
222880627930.4449264666875.555073533356
232222821566.2431248708661.756875129231
241397113746.8693916781224.130608321868
253684537213.4050139222-368.405013922165
263533829947.19894761515390.80105238488
273502233308.61750170571713.38249829426
283477731165.82031567013611.17968432987
292688731520.5411419808-4633.54114198077
302397028958.9890191581-4988.98901915809
312278025492.0388690565-2712.03886905648
321735121581.2380713670-4230.23807136697
332138218854.02966617022527.9703338298
342456126884.760927283-2323.76092728299
351740920297.5845264531-2888.58452645312
361151412446.0767867257-932.07678672567
373151432744.2952985218-1230.29529852177
382707128263.5475890451-1192.54758904512
392946228693.3350317845768.664968215468
402610527404.5074091275-1299.50740912755
412239723992.1600755122-1595.16007551224
422384322093.26021751341749.73978248663
432170521025.8101504192679.189849580791
441808917487.4969484943601.503051505708
452076418432.12201091492331.87798908514
462531623929.2056032311386.794396769
471770418076.7317399466-372.731739946608
481554811701.23901412513846.7609858749
492802933682.2332964645-5653.23329646454
502938328310.7491611431072.25083885702
513643830049.57033363886388.42966636116
523203428761.94411455843272.05588544160
532267925730.3147471643-3051.31474716425
542431924963.3452032993-644.345203299283
551800422866.9428489642-4862.9428489642
561753718177.4902171702-640.490217170161
572036619623.4814012916742.518598708433
582278224395.3863212825-1613.38632128246
591916917424.42240114831744.57759885167
601380713167.5829631344639.417036865627
612974329499.3786647026243.621335297357
622559128109.0855152350-2518.08551523496
632909631165.2654727371-2069.26547273713
642648227303.0021100247-821.002110024696
652240521530.9386521874874.061347812596
662704422431.67960507984612.32039492025
671797019629.5503743844-1659.55037438441
681873017383.67985006391346.32014993611
691968419765.1142051539-81.1142051538809
701978523314.0381640939-3529.03816409394
711847917568.5563000246910.443699975363
721069812888.4569955773-2190.45699557732

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 39722.9017575777 & -2020.90175757770 \tabularnewline
14 & 30364 & 31535.1647279220 & -1171.16472792205 \tabularnewline
15 & 32609 & 33590.6706490098 & -981.670649009757 \tabularnewline
16 & 30212 & 30845.0542818759 & -633.05428187587 \tabularnewline
17 & 29965 & 30291.5608338424 & -326.560833842421 \tabularnewline
18 & 28352 & 28469.5184451801 & -117.518445180067 \tabularnewline
19 & 25814 & 25831.2286456269 & -17.2286456268739 \tabularnewline
20 & 22414 & 22218.8079229484 & 195.192077051648 \tabularnewline
21 & 20506 & 20072.5399434037 & 433.460056596261 \tabularnewline
22 & 28806 & 27930.4449264666 & 875.555073533356 \tabularnewline
23 & 22228 & 21566.2431248708 & 661.756875129231 \tabularnewline
24 & 13971 & 13746.8693916781 & 224.130608321868 \tabularnewline
25 & 36845 & 37213.4050139222 & -368.405013922165 \tabularnewline
26 & 35338 & 29947.1989476151 & 5390.80105238488 \tabularnewline
27 & 35022 & 33308.6175017057 & 1713.38249829426 \tabularnewline
28 & 34777 & 31165.8203156701 & 3611.17968432987 \tabularnewline
29 & 26887 & 31520.5411419808 & -4633.54114198077 \tabularnewline
30 & 23970 & 28958.9890191581 & -4988.98901915809 \tabularnewline
31 & 22780 & 25492.0388690565 & -2712.03886905648 \tabularnewline
32 & 17351 & 21581.2380713670 & -4230.23807136697 \tabularnewline
33 & 21382 & 18854.0296661702 & 2527.9703338298 \tabularnewline
34 & 24561 & 26884.760927283 & -2323.76092728299 \tabularnewline
35 & 17409 & 20297.5845264531 & -2888.58452645312 \tabularnewline
36 & 11514 & 12446.0767867257 & -932.07678672567 \tabularnewline
37 & 31514 & 32744.2952985218 & -1230.29529852177 \tabularnewline
38 & 27071 & 28263.5475890451 & -1192.54758904512 \tabularnewline
39 & 29462 & 28693.3350317845 & 768.664968215468 \tabularnewline
40 & 26105 & 27404.5074091275 & -1299.50740912755 \tabularnewline
41 & 22397 & 23992.1600755122 & -1595.16007551224 \tabularnewline
42 & 23843 & 22093.2602175134 & 1749.73978248663 \tabularnewline
43 & 21705 & 21025.8101504192 & 679.189849580791 \tabularnewline
44 & 18089 & 17487.4969484943 & 601.503051505708 \tabularnewline
45 & 20764 & 18432.1220109149 & 2331.87798908514 \tabularnewline
46 & 25316 & 23929.205603231 & 1386.794396769 \tabularnewline
47 & 17704 & 18076.7317399466 & -372.731739946608 \tabularnewline
48 & 15548 & 11701.2390141251 & 3846.7609858749 \tabularnewline
49 & 28029 & 33682.2332964645 & -5653.23329646454 \tabularnewline
50 & 29383 & 28310.749161143 & 1072.25083885702 \tabularnewline
51 & 36438 & 30049.5703336388 & 6388.42966636116 \tabularnewline
52 & 32034 & 28761.9441145584 & 3272.05588544160 \tabularnewline
53 & 22679 & 25730.3147471643 & -3051.31474716425 \tabularnewline
54 & 24319 & 24963.3452032993 & -644.345203299283 \tabularnewline
55 & 18004 & 22866.9428489642 & -4862.9428489642 \tabularnewline
56 & 17537 & 18177.4902171702 & -640.490217170161 \tabularnewline
57 & 20366 & 19623.4814012916 & 742.518598708433 \tabularnewline
58 & 22782 & 24395.3863212825 & -1613.38632128246 \tabularnewline
59 & 19169 & 17424.4224011483 & 1744.57759885167 \tabularnewline
60 & 13807 & 13167.5829631344 & 639.417036865627 \tabularnewline
61 & 29743 & 29499.3786647026 & 243.621335297357 \tabularnewline
62 & 25591 & 28109.0855152350 & -2518.08551523496 \tabularnewline
63 & 29096 & 31165.2654727371 & -2069.26547273713 \tabularnewline
64 & 26482 & 27303.0021100247 & -821.002110024696 \tabularnewline
65 & 22405 & 21530.9386521874 & 874.061347812596 \tabularnewline
66 & 27044 & 22431.6796050798 & 4612.32039492025 \tabularnewline
67 & 17970 & 19629.5503743844 & -1659.55037438441 \tabularnewline
68 & 18730 & 17383.6798500639 & 1346.32014993611 \tabularnewline
69 & 19684 & 19765.1142051539 & -81.1142051538809 \tabularnewline
70 & 19785 & 23314.0381640939 & -3529.03816409394 \tabularnewline
71 & 18479 & 17568.5563000246 & 910.443699975363 \tabularnewline
72 & 10698 & 12888.4569955773 & -2190.45699557732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36924&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]37702[/C][C]39722.9017575777[/C][C]-2020.90175757770[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]31535.1647279220[/C][C]-1171.16472792205[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]33590.6706490098[/C][C]-981.670649009757[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30845.0542818759[/C][C]-633.05428187587[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30291.5608338424[/C][C]-326.560833842421[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28469.5184451801[/C][C]-117.518445180067[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]25831.2286456269[/C][C]-17.2286456268739[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]22218.8079229484[/C][C]195.192077051648[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]20072.5399434037[/C][C]433.460056596261[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]27930.4449264666[/C][C]875.555073533356[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]21566.2431248708[/C][C]661.756875129231[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13746.8693916781[/C][C]224.130608321868[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]37213.4050139222[/C][C]-368.405013922165[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29947.1989476151[/C][C]5390.80105238488[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33308.6175017057[/C][C]1713.38249829426[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31165.8203156701[/C][C]3611.17968432987[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]31520.5411419808[/C][C]-4633.54114198077[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28958.9890191581[/C][C]-4988.98901915809[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]25492.0388690565[/C][C]-2712.03886905648[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]21581.2380713670[/C][C]-4230.23807136697[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18854.0296661702[/C][C]2527.9703338298[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]26884.760927283[/C][C]-2323.76092728299[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]20297.5845264531[/C][C]-2888.58452645312[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]12446.0767867257[/C][C]-932.07678672567[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]32744.2952985218[/C][C]-1230.29529852177[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]28263.5475890451[/C][C]-1192.54758904512[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]28693.3350317845[/C][C]768.664968215468[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27404.5074091275[/C][C]-1299.50740912755[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]23992.1600755122[/C][C]-1595.16007551224[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]22093.2602175134[/C][C]1749.73978248663[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]21025.8101504192[/C][C]679.189849580791[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]17487.4969484943[/C][C]601.503051505708[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18432.1220109149[/C][C]2331.87798908514[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23929.205603231[/C][C]1386.794396769[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]18076.7317399466[/C][C]-372.731739946608[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]11701.2390141251[/C][C]3846.7609858749[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33682.2332964645[/C][C]-5653.23329646454[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]28310.749161143[/C][C]1072.25083885702[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]30049.5703336388[/C][C]6388.42966636116[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]28761.9441145584[/C][C]3272.05588544160[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]25730.3147471643[/C][C]-3051.31474716425[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]24963.3452032993[/C][C]-644.345203299283[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]22866.9428489642[/C][C]-4862.9428489642[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]18177.4902171702[/C][C]-640.490217170161[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]19623.4814012916[/C][C]742.518598708433[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]24395.3863212825[/C][C]-1613.38632128246[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]17424.4224011483[/C][C]1744.57759885167[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]13167.5829631344[/C][C]639.417036865627[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29499.3786647026[/C][C]243.621335297357[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]28109.0855152350[/C][C]-2518.08551523496[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]31165.2654727371[/C][C]-2069.26547273713[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]27303.0021100247[/C][C]-821.002110024696[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]21530.9386521874[/C][C]874.061347812596[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]22431.6796050798[/C][C]4612.32039492025[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19629.5503743844[/C][C]-1659.55037438441[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]17383.6798500639[/C][C]1346.32014993611[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19765.1142051539[/C][C]-81.1142051538809[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]23314.0381640939[/C][C]-3529.03816409394[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]17568.5563000246[/C][C]910.443699975363[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]12888.4569955773[/C][C]-2190.45699557732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36924&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36924&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
133770239722.9017575777-2020.90175757770
143036431535.1647279220-1171.16472792205
153260933590.6706490098-981.670649009757
163021230845.0542818759-633.05428187587
172996530291.5608338424-326.560833842421
182835228469.5184451801-117.518445180067
192581425831.2286456269-17.2286456268739
202241422218.8079229484195.192077051648
212050620072.5399434037433.460056596261
222880627930.4449264666875.555073533356
232222821566.2431248708661.756875129231
241397113746.8693916781224.130608321868
253684537213.4050139222-368.405013922165
263533829947.19894761515390.80105238488
273502233308.61750170571713.38249829426
283477731165.82031567013611.17968432987
292688731520.5411419808-4633.54114198077
302397028958.9890191581-4988.98901915809
312278025492.0388690565-2712.03886905648
321735121581.2380713670-4230.23807136697
332138218854.02966617022527.9703338298
342456126884.760927283-2323.76092728299
351740920297.5845264531-2888.58452645312
361151412446.0767867257-932.07678672567
373151432744.2952985218-1230.29529852177
382707128263.5475890451-1192.54758904512
392946228693.3350317845768.664968215468
402610527404.5074091275-1299.50740912755
412239723992.1600755122-1595.16007551224
422384322093.26021751341749.73978248663
432170521025.8101504192679.189849580791
441808917487.4969484943601.503051505708
452076418432.12201091492331.87798908514
462531623929.2056032311386.794396769
471770418076.7317399466-372.731739946608
481554811701.23901412513846.7609858749
492802933682.2332964645-5653.23329646454
502938328310.7491611431072.25083885702
513643830049.57033363886388.42966636116
523203428761.94411455843272.05588544160
532267925730.3147471643-3051.31474716425
542431924963.3452032993-644.345203299283
551800422866.9428489642-4862.9428489642
561753718177.4902171702-640.490217170161
572036619623.4814012916742.518598708433
582278224395.3863212825-1613.38632128246
591916917424.42240114831744.57759885167
601380713167.5829631344639.417036865627
612974329499.3786647026243.621335297357
622559128109.0855152350-2518.08551523496
632909631165.2654727371-2069.26547273713
642648227303.0021100247-821.002110024696
652240521530.9386521874874.061347812596
662704422431.67960507984612.32039492025
671797019629.5503743844-1659.55037438441
681873017383.67985006391346.32014993611
691968419765.1142051539-81.1142051538809
701978523314.0381640939-3529.03816409394
711847917568.5563000246910.443699975363
721069812888.4569955773-2190.45699557732







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327245.510322207224298.673526978730192.3471174356
7424823.019525218521764.547317407327881.4917330298
7528275.335183873925018.240534187331532.4298335605
7625480.826151418522176.949704405228784.7025984318
7720816.648159815817541.813627592624091.4826920390
7822940.0238985419452.440250716926427.6075463630
7917177.669132286313845.449555901820509.8887086708
8016556.082254438813135.471623733919976.6928851438
8117936.311376861014302.878373112821569.7443806092
8219798.531623841715897.439720694623699.6235269888
8316793.375588092313050.972784565520535.778391619
8411047.71668241439412.978078371112682.4552864575

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27245.5103222072 & 24298.6735269787 & 30192.3471174356 \tabularnewline
74 & 24823.0195252185 & 21764.5473174073 & 27881.4917330298 \tabularnewline
75 & 28275.3351838739 & 25018.2405341873 & 31532.4298335605 \tabularnewline
76 & 25480.8261514185 & 22176.9497044052 & 28784.7025984318 \tabularnewline
77 & 20816.6481598158 & 17541.8136275926 & 24091.4826920390 \tabularnewline
78 & 22940.02389854 & 19452.4402507169 & 26427.6075463630 \tabularnewline
79 & 17177.6691322863 & 13845.4495559018 & 20509.8887086708 \tabularnewline
80 & 16556.0822544388 & 13135.4716237339 & 19976.6928851438 \tabularnewline
81 & 17936.3113768610 & 14302.8783731128 & 21569.7443806092 \tabularnewline
82 & 19798.5316238417 & 15897.4397206946 & 23699.6235269888 \tabularnewline
83 & 16793.3755880923 & 13050.9727845655 & 20535.778391619 \tabularnewline
84 & 11047.7166824143 & 9412.9780783711 & 12682.4552864575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36924&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]27245.5103222072[/C][C]24298.6735269787[/C][C]30192.3471174356[/C][/ROW]
[ROW][C]74[/C][C]24823.0195252185[/C][C]21764.5473174073[/C][C]27881.4917330298[/C][/ROW]
[ROW][C]75[/C][C]28275.3351838739[/C][C]25018.2405341873[/C][C]31532.4298335605[/C][/ROW]
[ROW][C]76[/C][C]25480.8261514185[/C][C]22176.9497044052[/C][C]28784.7025984318[/C][/ROW]
[ROW][C]77[/C][C]20816.6481598158[/C][C]17541.8136275926[/C][C]24091.4826920390[/C][/ROW]
[ROW][C]78[/C][C]22940.02389854[/C][C]19452.4402507169[/C][C]26427.6075463630[/C][/ROW]
[ROW][C]79[/C][C]17177.6691322863[/C][C]13845.4495559018[/C][C]20509.8887086708[/C][/ROW]
[ROW][C]80[/C][C]16556.0822544388[/C][C]13135.4716237339[/C][C]19976.6928851438[/C][/ROW]
[ROW][C]81[/C][C]17936.3113768610[/C][C]14302.8783731128[/C][C]21569.7443806092[/C][/ROW]
[ROW][C]82[/C][C]19798.5316238417[/C][C]15897.4397206946[/C][C]23699.6235269888[/C][/ROW]
[ROW][C]83[/C][C]16793.3755880923[/C][C]13050.9727845655[/C][C]20535.778391619[/C][/ROW]
[ROW][C]84[/C][C]11047.7166824143[/C][C]9412.9780783711[/C][C]12682.4552864575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36924&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36924&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
7327245.510322207224298.673526978730192.3471174356
7424823.019525218521764.547317407327881.4917330298
7528275.335183873925018.240534187331532.4298335605
7625480.826151418522176.949704405228784.7025984318
7720816.648159815817541.813627592624091.4826920390
7822940.0238985419452.440250716926427.6075463630
7917177.669132286313845.449555901820509.8887086708
8016556.082254438813135.471623733919976.6928851438
8117936.311376861014302.878373112821569.7443806092
8219798.531623841715897.439720694623699.6235269888
8316793.375588092313050.972784565520535.778391619
8411047.71668241439412.978078371112682.4552864575



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')