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Author's title

module Exponential Smoothing -Time Series Analysis (new) - goudkoers te bru...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 29 May 2008 12:59:02 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/29/t1212087600w6kp7yi0pfypf7t.htm/, Retrieved Wed, 15 May 2024 06:08:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13519, Retrieved Wed, 15 May 2024 06:08:18 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact236
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [module Exponentia...] [2008-05-29 18:59:02] [b82ef19bb71ab1d2d730136b4505428a] [Current]
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Dataseries X:
10236
10893
10756
10940
10997
10827
10166
10186
10457
10368
10244
10511
10812
10738
10171
9721
9897
9828
9924
10371
10846
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13519&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13519&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.7740580389191
beta0.0233317689039484
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.7740580389191 \tabularnewline
beta & 0.0233317689039484 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13519&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]0.7740580389191[/C][/ROW]
[ROW][C]beta[/C][C]0.0233317689039484[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13519&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
alpha0.7740580389191
beta0.0233317689039484
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131081210920.0551455554-108.055145555360
141073810768.0070828160-30.007082816026
151017110156.293648508014.7063514919719
1697219703.4515027169217.54849728308
1798979875.6450406951621.3549593048374
1898289802.2394481574925.7605518425116
1999249925.69474894115-1.69474894114501
201037110404.1371366797-33.137136679743
211084610856.4696915348-10.4696915348159
221041310350.990744823062.0092551770394
231070910632.920996277276.0790037228471
241066210610.335240159351.6647598406635
251057011021.3949629194-451.394962919412
261029710617.5002892705-320.500289270507
27106359801.84290402755833.15709597245
28108729975.9195173201896.080482679901
291029610865.8636989703-569.863698970299
301038310341.702600136741.2973998633333
311043110487.3761114264-56.3761114263925
321057410951.6135144414-377.613514441362
331065311160.4413436224-507.441343622368
341080510285.9948531293519.005146870748
351087210935.1365574079-63.1365574079264
361062510799.4126465267-174.412646526654
371040710916.1111901584-509.111190158443
381046310491.9685123756-28.9685123755607
391055610147.4295947097408.570405290346
40106469995.5940031531650.405996846908
411070210353.7617773491348.238222650894
421135310685.5011588257667.498841174334
431134611317.119959690928.8800403091282
441145111828.4726973284-377.472697328396
451196412066.1079164284-102.107916428353
461257411728.1716539189845.82834608114
471303112547.4314616023483.56853839774
481381212829.1155601624982.884439837619
491454413872.7694725202671.23052747978
501493114588.8458552917342.154144708347
511488614625.9389543208260.061045679249
521600514320.41672967401684.58327032598
531706415402.56655288911661.43344711093
541516817001.7396022744-1833.73960227444
551605015610.0889008407439.911099159297
561583916582.5158785322-743.515878532206
571513716910.8253601221-1773.82536012207
581495415515.8897181854-561.889718185401
591564815199.6018931586448.398106841354
601530515576.9985206996-271.998520699552
611557915596.8681645326-17.8681645326051
621634815701.9913755013646.008624498674
631592815927.40805282170.591947178261762
641617115685.9521902165485.047809783482
651593715778.5474661450158.452533854954
661571315380.3011200495332.698879950489
671559416176.9310734336-582.93107343364
681568316046.9900869157-363.990086915701
691643816371.85428606866.14571393199
701703216691.2449586921340.755041307923
711769617358.3267908446337.673209155368
721774517479.5206287904265.479371209582

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 10812 & 10920.0551455554 & -108.055145555360 \tabularnewline
14 & 10738 & 10768.0070828160 & -30.007082816026 \tabularnewline
15 & 10171 & 10156.2936485080 & 14.7063514919719 \tabularnewline
16 & 9721 & 9703.45150271692 & 17.54849728308 \tabularnewline
17 & 9897 & 9875.64504069516 & 21.3549593048374 \tabularnewline
18 & 9828 & 9802.23944815749 & 25.7605518425116 \tabularnewline
19 & 9924 & 9925.69474894115 & -1.69474894114501 \tabularnewline
20 & 10371 & 10404.1371366797 & -33.137136679743 \tabularnewline
21 & 10846 & 10856.4696915348 & -10.4696915348159 \tabularnewline
22 & 10413 & 10350.9907448230 & 62.0092551770394 \tabularnewline
23 & 10709 & 10632.9209962772 & 76.0790037228471 \tabularnewline
24 & 10662 & 10610.3352401593 & 51.6647598406635 \tabularnewline
25 & 10570 & 11021.3949629194 & -451.394962919412 \tabularnewline
26 & 10297 & 10617.5002892705 & -320.500289270507 \tabularnewline
27 & 10635 & 9801.84290402755 & 833.15709597245 \tabularnewline
28 & 10872 & 9975.9195173201 & 896.080482679901 \tabularnewline
29 & 10296 & 10865.8636989703 & -569.863698970299 \tabularnewline
30 & 10383 & 10341.7026001367 & 41.2973998633333 \tabularnewline
31 & 10431 & 10487.3761114264 & -56.3761114263925 \tabularnewline
32 & 10574 & 10951.6135144414 & -377.613514441362 \tabularnewline
33 & 10653 & 11160.4413436224 & -507.441343622368 \tabularnewline
34 & 10805 & 10285.9948531293 & 519.005146870748 \tabularnewline
35 & 10872 & 10935.1365574079 & -63.1365574079264 \tabularnewline
36 & 10625 & 10799.4126465267 & -174.412646526654 \tabularnewline
37 & 10407 & 10916.1111901584 & -509.111190158443 \tabularnewline
38 & 10463 & 10491.9685123756 & -28.9685123755607 \tabularnewline
39 & 10556 & 10147.4295947097 & 408.570405290346 \tabularnewline
40 & 10646 & 9995.5940031531 & 650.405996846908 \tabularnewline
41 & 10702 & 10353.7617773491 & 348.238222650894 \tabularnewline
42 & 11353 & 10685.5011588257 & 667.498841174334 \tabularnewline
43 & 11346 & 11317.1199596909 & 28.8800403091282 \tabularnewline
44 & 11451 & 11828.4726973284 & -377.472697328396 \tabularnewline
45 & 11964 & 12066.1079164284 & -102.107916428353 \tabularnewline
46 & 12574 & 11728.1716539189 & 845.82834608114 \tabularnewline
47 & 13031 & 12547.4314616023 & 483.56853839774 \tabularnewline
48 & 13812 & 12829.1155601624 & 982.884439837619 \tabularnewline
49 & 14544 & 13872.7694725202 & 671.23052747978 \tabularnewline
50 & 14931 & 14588.8458552917 & 342.154144708347 \tabularnewline
51 & 14886 & 14625.9389543208 & 260.061045679249 \tabularnewline
52 & 16005 & 14320.4167296740 & 1684.58327032598 \tabularnewline
53 & 17064 & 15402.5665528891 & 1661.43344711093 \tabularnewline
54 & 15168 & 17001.7396022744 & -1833.73960227444 \tabularnewline
55 & 16050 & 15610.0889008407 & 439.911099159297 \tabularnewline
56 & 15839 & 16582.5158785322 & -743.515878532206 \tabularnewline
57 & 15137 & 16910.8253601221 & -1773.82536012207 \tabularnewline
58 & 14954 & 15515.8897181854 & -561.889718185401 \tabularnewline
59 & 15648 & 15199.6018931586 & 448.398106841354 \tabularnewline
60 & 15305 & 15576.9985206996 & -271.998520699552 \tabularnewline
61 & 15579 & 15596.8681645326 & -17.8681645326051 \tabularnewline
62 & 16348 & 15701.9913755013 & 646.008624498674 \tabularnewline
63 & 15928 & 15927.4080528217 & 0.591947178261762 \tabularnewline
64 & 16171 & 15685.9521902165 & 485.047809783482 \tabularnewline
65 & 15937 & 15778.5474661450 & 158.452533854954 \tabularnewline
66 & 15713 & 15380.3011200495 & 332.698879950489 \tabularnewline
67 & 15594 & 16176.9310734336 & -582.93107343364 \tabularnewline
68 & 15683 & 16046.9900869157 & -363.990086915701 \tabularnewline
69 & 16438 & 16371.854286068 & 66.14571393199 \tabularnewline
70 & 17032 & 16691.2449586921 & 340.755041307923 \tabularnewline
71 & 17696 & 17358.3267908446 & 337.673209155368 \tabularnewline
72 & 17745 & 17479.5206287904 & 265.479371209582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13519&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]10812[/C][C]10920.0551455554[/C][C]-108.055145555360[/C][/ROW]
[ROW][C]14[/C][C]10738[/C][C]10768.0070828160[/C][C]-30.007082816026[/C][/ROW]
[ROW][C]15[/C][C]10171[/C][C]10156.2936485080[/C][C]14.7063514919719[/C][/ROW]
[ROW][C]16[/C][C]9721[/C][C]9703.45150271692[/C][C]17.54849728308[/C][/ROW]
[ROW][C]17[/C][C]9897[/C][C]9875.64504069516[/C][C]21.3549593048374[/C][/ROW]
[ROW][C]18[/C][C]9828[/C][C]9802.23944815749[/C][C]25.7605518425116[/C][/ROW]
[ROW][C]19[/C][C]9924[/C][C]9925.69474894115[/C][C]-1.69474894114501[/C][/ROW]
[ROW][C]20[/C][C]10371[/C][C]10404.1371366797[/C][C]-33.137136679743[/C][/ROW]
[ROW][C]21[/C][C]10846[/C][C]10856.4696915348[/C][C]-10.4696915348159[/C][/ROW]
[ROW][C]22[/C][C]10413[/C][C]10350.9907448230[/C][C]62.0092551770394[/C][/ROW]
[ROW][C]23[/C][C]10709[/C][C]10632.9209962772[/C][C]76.0790037228471[/C][/ROW]
[ROW][C]24[/C][C]10662[/C][C]10610.3352401593[/C][C]51.6647598406635[/C][/ROW]
[ROW][C]25[/C][C]10570[/C][C]11021.3949629194[/C][C]-451.394962919412[/C][/ROW]
[ROW][C]26[/C][C]10297[/C][C]10617.5002892705[/C][C]-320.500289270507[/C][/ROW]
[ROW][C]27[/C][C]10635[/C][C]9801.84290402755[/C][C]833.15709597245[/C][/ROW]
[ROW][C]28[/C][C]10872[/C][C]9975.9195173201[/C][C]896.080482679901[/C][/ROW]
[ROW][C]29[/C][C]10296[/C][C]10865.8636989703[/C][C]-569.863698970299[/C][/ROW]
[ROW][C]30[/C][C]10383[/C][C]10341.7026001367[/C][C]41.2973998633333[/C][/ROW]
[ROW][C]31[/C][C]10431[/C][C]10487.3761114264[/C][C]-56.3761114263925[/C][/ROW]
[ROW][C]32[/C][C]10574[/C][C]10951.6135144414[/C][C]-377.613514441362[/C][/ROW]
[ROW][C]33[/C][C]10653[/C][C]11160.4413436224[/C][C]-507.441343622368[/C][/ROW]
[ROW][C]34[/C][C]10805[/C][C]10285.9948531293[/C][C]519.005146870748[/C][/ROW]
[ROW][C]35[/C][C]10872[/C][C]10935.1365574079[/C][C]-63.1365574079264[/C][/ROW]
[ROW][C]36[/C][C]10625[/C][C]10799.4126465267[/C][C]-174.412646526654[/C][/ROW]
[ROW][C]37[/C][C]10407[/C][C]10916.1111901584[/C][C]-509.111190158443[/C][/ROW]
[ROW][C]38[/C][C]10463[/C][C]10491.9685123756[/C][C]-28.9685123755607[/C][/ROW]
[ROW][C]39[/C][C]10556[/C][C]10147.4295947097[/C][C]408.570405290346[/C][/ROW]
[ROW][C]40[/C][C]10646[/C][C]9995.5940031531[/C][C]650.405996846908[/C][/ROW]
[ROW][C]41[/C][C]10702[/C][C]10353.7617773491[/C][C]348.238222650894[/C][/ROW]
[ROW][C]42[/C][C]11353[/C][C]10685.5011588257[/C][C]667.498841174334[/C][/ROW]
[ROW][C]43[/C][C]11346[/C][C]11317.1199596909[/C][C]28.8800403091282[/C][/ROW]
[ROW][C]44[/C][C]11451[/C][C]11828.4726973284[/C][C]-377.472697328396[/C][/ROW]
[ROW][C]45[/C][C]11964[/C][C]12066.1079164284[/C][C]-102.107916428353[/C][/ROW]
[ROW][C]46[/C][C]12574[/C][C]11728.1716539189[/C][C]845.82834608114[/C][/ROW]
[ROW][C]47[/C][C]13031[/C][C]12547.4314616023[/C][C]483.56853839774[/C][/ROW]
[ROW][C]48[/C][C]13812[/C][C]12829.1155601624[/C][C]982.884439837619[/C][/ROW]
[ROW][C]49[/C][C]14544[/C][C]13872.7694725202[/C][C]671.23052747978[/C][/ROW]
[ROW][C]50[/C][C]14931[/C][C]14588.8458552917[/C][C]342.154144708347[/C][/ROW]
[ROW][C]51[/C][C]14886[/C][C]14625.9389543208[/C][C]260.061045679249[/C][/ROW]
[ROW][C]52[/C][C]16005[/C][C]14320.4167296740[/C][C]1684.58327032598[/C][/ROW]
[ROW][C]53[/C][C]17064[/C][C]15402.5665528891[/C][C]1661.43344711093[/C][/ROW]
[ROW][C]54[/C][C]15168[/C][C]17001.7396022744[/C][C]-1833.73960227444[/C][/ROW]
[ROW][C]55[/C][C]16050[/C][C]15610.0889008407[/C][C]439.911099159297[/C][/ROW]
[ROW][C]56[/C][C]15839[/C][C]16582.5158785322[/C][C]-743.515878532206[/C][/ROW]
[ROW][C]57[/C][C]15137[/C][C]16910.8253601221[/C][C]-1773.82536012207[/C][/ROW]
[ROW][C]58[/C][C]14954[/C][C]15515.8897181854[/C][C]-561.889718185401[/C][/ROW]
[ROW][C]59[/C][C]15648[/C][C]15199.6018931586[/C][C]448.398106841354[/C][/ROW]
[ROW][C]60[/C][C]15305[/C][C]15576.9985206996[/C][C]-271.998520699552[/C][/ROW]
[ROW][C]61[/C][C]15579[/C][C]15596.8681645326[/C][C]-17.8681645326051[/C][/ROW]
[ROW][C]62[/C][C]16348[/C][C]15701.9913755013[/C][C]646.008624498674[/C][/ROW]
[ROW][C]63[/C][C]15928[/C][C]15927.4080528217[/C][C]0.591947178261762[/C][/ROW]
[ROW][C]64[/C][C]16171[/C][C]15685.9521902165[/C][C]485.047809783482[/C][/ROW]
[ROW][C]65[/C][C]15937[/C][C]15778.5474661450[/C][C]158.452533854954[/C][/ROW]
[ROW][C]66[/C][C]15713[/C][C]15380.3011200495[/C][C]332.698879950489[/C][/ROW]
[ROW][C]67[/C][C]15594[/C][C]16176.9310734336[/C][C]-582.93107343364[/C][/ROW]
[ROW][C]68[/C][C]15683[/C][C]16046.9900869157[/C][C]-363.990086915701[/C][/ROW]
[ROW][C]69[/C][C]16438[/C][C]16371.854286068[/C][C]66.14571393199[/C][/ROW]
[ROW][C]70[/C][C]17032[/C][C]16691.2449586921[/C][C]340.755041307923[/C][/ROW]
[ROW][C]71[/C][C]17696[/C][C]17358.3267908446[/C][C]337.673209155368[/C][/ROW]
[ROW][C]72[/C][C]17745[/C][C]17479.5206287904[/C][C]265.479371209582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13519&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13519&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
131081210920.0551455554-108.055145555360
141073810768.0070828160-30.007082816026
151017110156.293648508014.7063514919719
1697219703.4515027169217.54849728308
1798979875.6450406951621.3549593048374
1898289802.2394481574925.7605518425116
1999249925.69474894115-1.69474894114501
201037110404.1371366797-33.137136679743
211084610856.4696915348-10.4696915348159
221041310350.990744823062.0092551770394
231070910632.920996277276.0790037228471
241066210610.335240159351.6647598406635
251057011021.3949629194-451.394962919412
261029710617.5002892705-320.500289270507
27106359801.84290402755833.15709597245
28108729975.9195173201896.080482679901
291029610865.8636989703-569.863698970299
301038310341.702600136741.2973998633333
311043110487.3761114264-56.3761114263925
321057410951.6135144414-377.613514441362
331065311160.4413436224-507.441343622368
341080510285.9948531293519.005146870748
351087210935.1365574079-63.1365574079264
361062510799.4126465267-174.412646526654
371040710916.1111901584-509.111190158443
381046310491.9685123756-28.9685123755607
391055610147.4295947097408.570405290346
40106469995.5940031531650.405996846908
411070210353.7617773491348.238222650894
421135310685.5011588257667.498841174334
431134611317.119959690928.8800403091282
441145111828.4726973284-377.472697328396
451196412066.1079164284-102.107916428353
461257411728.1716539189845.82834608114
471303112547.4314616023483.56853839774
481381212829.1155601624982.884439837619
491454413872.7694725202671.23052747978
501493114588.8458552917342.154144708347
511488614625.9389543208260.061045679249
521600514320.41672967401684.58327032598
531706415402.56655288911661.43344711093
541516817001.7396022744-1833.73960227444
551605015610.0889008407439.911099159297
561583916582.5158785322-743.515878532206
571513716910.8253601221-1773.82536012207
581495415515.8897181854-561.889718185401
591564815199.6018931586448.398106841354
601530515576.9985206996-271.998520699552
611557915596.8681645326-17.8681645326051
621634815701.9913755013646.008624498674
631592815927.40805282170.591947178261762
641617115685.9521902165485.047809783482
651593715778.5474661450158.452533854954
661571315380.3011200495332.698879950489
671559416176.9310734336-582.93107343364
681568316046.9900869157-363.990086915701
691643816371.85428606866.14571393199
701703216691.2449586921340.755041307923
711769617358.3267908446337.673209155368
721774517479.5206287904265.479371209582







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7318035.807316473716851.607228851519220.0074040958
7418360.585007204916842.892180529619878.2778338802
7517896.222643947416131.733659289719660.7116286052
7617752.219106261415752.776178523519751.6620339993
7717360.616021834615170.200717072519551.0313265967
7816832.681687572714484.091780865919181.2715942795
7917177.572544050814583.459400938019771.6856871637
8017585.923118363014744.360346884120427.4858898418
8118382.465816061915240.585058605021524.3465735188
8218756.844900252515380.71919185522132.9706086501
8319200.146441623315579.758747463222820.5341357834
8419025.739641694015462.998426066422588.4808573215

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 18035.8073164737 & 16851.6072288515 & 19220.0074040958 \tabularnewline
74 & 18360.5850072049 & 16842.8921805296 & 19878.2778338802 \tabularnewline
75 & 17896.2226439474 & 16131.7336592897 & 19660.7116286052 \tabularnewline
76 & 17752.2191062614 & 15752.7761785235 & 19751.6620339993 \tabularnewline
77 & 17360.6160218346 & 15170.2007170725 & 19551.0313265967 \tabularnewline
78 & 16832.6816875727 & 14484.0917808659 & 19181.2715942795 \tabularnewline
79 & 17177.5725440508 & 14583.4594009380 & 19771.6856871637 \tabularnewline
80 & 17585.9231183630 & 14744.3603468841 & 20427.4858898418 \tabularnewline
81 & 18382.4658160619 & 15240.5850586050 & 21524.3465735188 \tabularnewline
82 & 18756.8449002525 & 15380.719191855 & 22132.9706086501 \tabularnewline
83 & 19200.1464416233 & 15579.7587474632 & 22820.5341357834 \tabularnewline
84 & 19025.7396416940 & 15462.9984260664 & 22588.4808573215 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13519&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]18035.8073164737[/C][C]16851.6072288515[/C][C]19220.0074040958[/C][/ROW]
[ROW][C]74[/C][C]18360.5850072049[/C][C]16842.8921805296[/C][C]19878.2778338802[/C][/ROW]
[ROW][C]75[/C][C]17896.2226439474[/C][C]16131.7336592897[/C][C]19660.7116286052[/C][/ROW]
[ROW][C]76[/C][C]17752.2191062614[/C][C]15752.7761785235[/C][C]19751.6620339993[/C][/ROW]
[ROW][C]77[/C][C]17360.6160218346[/C][C]15170.2007170725[/C][C]19551.0313265967[/C][/ROW]
[ROW][C]78[/C][C]16832.6816875727[/C][C]14484.0917808659[/C][C]19181.2715942795[/C][/ROW]
[ROW][C]79[/C][C]17177.5725440508[/C][C]14583.4594009380[/C][C]19771.6856871637[/C][/ROW]
[ROW][C]80[/C][C]17585.9231183630[/C][C]14744.3603468841[/C][C]20427.4858898418[/C][/ROW]
[ROW][C]81[/C][C]18382.4658160619[/C][C]15240.5850586050[/C][C]21524.3465735188[/C][/ROW]
[ROW][C]82[/C][C]18756.8449002525[/C][C]15380.719191855[/C][C]22132.9706086501[/C][/ROW]
[ROW][C]83[/C][C]19200.1464416233[/C][C]15579.7587474632[/C][C]22820.5341357834[/C][/ROW]
[ROW][C]84[/C][C]19025.7396416940[/C][C]15462.9984260664[/C][C]22588.4808573215[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13519&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13519&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
7318035.807316473716851.607228851519220.0074040958
7418360.585007204916842.892180529619878.2778338802
7517896.222643947416131.733659289719660.7116286052
7617752.219106261415752.776178523519751.6620339993
7717360.616021834615170.200717072519551.0313265967
7816832.681687572714484.091780865919181.2715942795
7917177.572544050814583.459400938019771.6856871637
8017585.923118363014744.360346884120427.4858898418
8118382.465816061915240.585058605021524.3465735188
8218756.844900252515380.71919185522132.9706086501
8319200.146441623315579.758747463222820.5341357834
8419025.739641694015462.998426066422588.4808573215



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')