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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 15:35:43 -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/2009/Jun/07/t124441057061focgtvkr2adpw.htm/, Retrieved Sun, 12 May 2024 17:51:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42270, Retrieved Sun, 12 May 2024 17:51:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsFilip Bosschaerts
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2009-06-07 21:35:43] [2fef2e3c8097f11f80164f604c894b1e] [Current]
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Dataseries X:
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141




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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42270&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42270&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42270&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' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.932085622762712
beta0.111072200021140
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.932085622762712 \tabularnewline
beta & 0.111072200021140 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42270&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]0.932085622762712[/C][/ROW]
[ROW][C]beta[/C][C]0.111072200021140[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42270&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42270&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
alpha0.932085622762712
beta0.111072200021140
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13562325543510.78498931618814.2150106835
14560854562257.082625005-1403.08262500470
15555332557528.951675197-2196.95167519711
16543599545005.294025158-1406.29402515769
17536662537360.588402685-698.588402684778
18542722543516.617663201-794.617663201061
19593530608666.040283583-15136.0402835835
20610763604066.9713045426696.02869545808
21612613608304.2417565124308.75824348803
22611324600346.99398279810977.0060172023
23594167594549.310356531-382.310356530594
24595454603634.89945451-8180.89945450972
25590865606458.582762683-15593.5827626829
26589379589295.74140339583.2585966045735
27584428583587.891537619840.10846238141
28573100571951.9531159761148.04688402358
29567456565003.8452849672452.15471503336
30569028572683.977763245-3655.97776324546
31620735632490.008431404-11755.0084314037
32628884631172.725617809-2288.72561780910
33628232624590.7885428083641.21145719173
34612117614112.57236219-1995.57236218941
35595404591757.2110193013646.78898069914
36597141600791.09416101-3650.09416100988
37593408604525.981811363-11117.9818113634
38590072590254.35390812-182.353908119840
39579799581977.72012682-2178.72012681945
40574205564863.7414163479341.25858365325
41572775563804.0624579988970.9375420023
42572942575983.396814138-3041.39681413758
43619567634713.823893817-15146.8238938169
44625809629428.419736452-3619.41973645205
45619916620421.569004207-505.569004206918
46587625603678.747719531-16053.7477195309
47565742565131.102672843610.897327156505
48557274567053.351327952-9779.35132795153
49560576560147.154662156428.845337843522
50548854554155.358965362-5301.35896536184
51531673537216.342017777-5543.34201777703
52525919513644.83434624512274.1656537554
53511038511493.580679156-455.580679156468
54498662509294.721496441-10632.7214964412
55555362554565.269475176796.730524823535
56564591561012.1347444433578.86525555735
57541657555760.042110383-14103.0421103832
58527070520713.4015945896356.59840541077
59509846501932.1380522217913.86194777902
60514258508458.0460258375799.95397416304
61516922516881.60421698940.3957830113941
62507561510213.586354658-2652.58635465812
63492622496076.251735346-3454.25173534575
64490243476227.53461788114015.4653821186
65469357475580.577870247-6223.57787024672
66477580467462.91269343410117.0873065657
67528379535147.121509948-6768.1215099484
68533590536245.502109291-2655.50210929057
69517945524849.811186114-6904.81118611363
70506174499515.4878090456658.51219095493
71501866482766.0969620719099.9030379298
72516141502377.56829974413763.4317002557

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 562325 & 543510.784989316 & 18814.2150106835 \tabularnewline
14 & 560854 & 562257.082625005 & -1403.08262500470 \tabularnewline
15 & 555332 & 557528.951675197 & -2196.95167519711 \tabularnewline
16 & 543599 & 545005.294025158 & -1406.29402515769 \tabularnewline
17 & 536662 & 537360.588402685 & -698.588402684778 \tabularnewline
18 & 542722 & 543516.617663201 & -794.617663201061 \tabularnewline
19 & 593530 & 608666.040283583 & -15136.0402835835 \tabularnewline
20 & 610763 & 604066.971304542 & 6696.02869545808 \tabularnewline
21 & 612613 & 608304.241756512 & 4308.75824348803 \tabularnewline
22 & 611324 & 600346.993982798 & 10977.0060172023 \tabularnewline
23 & 594167 & 594549.310356531 & -382.310356530594 \tabularnewline
24 & 595454 & 603634.89945451 & -8180.89945450972 \tabularnewline
25 & 590865 & 606458.582762683 & -15593.5827626829 \tabularnewline
26 & 589379 & 589295.741403395 & 83.2585966045735 \tabularnewline
27 & 584428 & 583587.891537619 & 840.10846238141 \tabularnewline
28 & 573100 & 571951.953115976 & 1148.04688402358 \tabularnewline
29 & 567456 & 565003.845284967 & 2452.15471503336 \tabularnewline
30 & 569028 & 572683.977763245 & -3655.97776324546 \tabularnewline
31 & 620735 & 632490.008431404 & -11755.0084314037 \tabularnewline
32 & 628884 & 631172.725617809 & -2288.72561780910 \tabularnewline
33 & 628232 & 624590.788542808 & 3641.21145719173 \tabularnewline
34 & 612117 & 614112.57236219 & -1995.57236218941 \tabularnewline
35 & 595404 & 591757.211019301 & 3646.78898069914 \tabularnewline
36 & 597141 & 600791.09416101 & -3650.09416100988 \tabularnewline
37 & 593408 & 604525.981811363 & -11117.9818113634 \tabularnewline
38 & 590072 & 590254.35390812 & -182.353908119840 \tabularnewline
39 & 579799 & 581977.72012682 & -2178.72012681945 \tabularnewline
40 & 574205 & 564863.741416347 & 9341.25858365325 \tabularnewline
41 & 572775 & 563804.062457998 & 8970.9375420023 \tabularnewline
42 & 572942 & 575983.396814138 & -3041.39681413758 \tabularnewline
43 & 619567 & 634713.823893817 & -15146.8238938169 \tabularnewline
44 & 625809 & 629428.419736452 & -3619.41973645205 \tabularnewline
45 & 619916 & 620421.569004207 & -505.569004206918 \tabularnewline
46 & 587625 & 603678.747719531 & -16053.7477195309 \tabularnewline
47 & 565742 & 565131.102672843 & 610.897327156505 \tabularnewline
48 & 557274 & 567053.351327952 & -9779.35132795153 \tabularnewline
49 & 560576 & 560147.154662156 & 428.845337843522 \tabularnewline
50 & 548854 & 554155.358965362 & -5301.35896536184 \tabularnewline
51 & 531673 & 537216.342017777 & -5543.34201777703 \tabularnewline
52 & 525919 & 513644.834346245 & 12274.1656537554 \tabularnewline
53 & 511038 & 511493.580679156 & -455.580679156468 \tabularnewline
54 & 498662 & 509294.721496441 & -10632.7214964412 \tabularnewline
55 & 555362 & 554565.269475176 & 796.730524823535 \tabularnewline
56 & 564591 & 561012.134744443 & 3578.86525555735 \tabularnewline
57 & 541657 & 555760.042110383 & -14103.0421103832 \tabularnewline
58 & 527070 & 520713.401594589 & 6356.59840541077 \tabularnewline
59 & 509846 & 501932.138052221 & 7913.86194777902 \tabularnewline
60 & 514258 & 508458.046025837 & 5799.95397416304 \tabularnewline
61 & 516922 & 516881.604216989 & 40.3957830113941 \tabularnewline
62 & 507561 & 510213.586354658 & -2652.58635465812 \tabularnewline
63 & 492622 & 496076.251735346 & -3454.25173534575 \tabularnewline
64 & 490243 & 476227.534617881 & 14015.4653821186 \tabularnewline
65 & 469357 & 475580.577870247 & -6223.57787024672 \tabularnewline
66 & 477580 & 467462.912693434 & 10117.0873065657 \tabularnewline
67 & 528379 & 535147.121509948 & -6768.1215099484 \tabularnewline
68 & 533590 & 536245.502109291 & -2655.50210929057 \tabularnewline
69 & 517945 & 524849.811186114 & -6904.81118611363 \tabularnewline
70 & 506174 & 499515.487809045 & 6658.51219095493 \tabularnewline
71 & 501866 & 482766.09696207 & 19099.9030379298 \tabularnewline
72 & 516141 & 502377.568299744 & 13763.4317002557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42270&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]562325[/C][C]543510.784989316[/C][C]18814.2150106835[/C][/ROW]
[ROW][C]14[/C][C]560854[/C][C]562257.082625005[/C][C]-1403.08262500470[/C][/ROW]
[ROW][C]15[/C][C]555332[/C][C]557528.951675197[/C][C]-2196.95167519711[/C][/ROW]
[ROW][C]16[/C][C]543599[/C][C]545005.294025158[/C][C]-1406.29402515769[/C][/ROW]
[ROW][C]17[/C][C]536662[/C][C]537360.588402685[/C][C]-698.588402684778[/C][/ROW]
[ROW][C]18[/C][C]542722[/C][C]543516.617663201[/C][C]-794.617663201061[/C][/ROW]
[ROW][C]19[/C][C]593530[/C][C]608666.040283583[/C][C]-15136.0402835835[/C][/ROW]
[ROW][C]20[/C][C]610763[/C][C]604066.971304542[/C][C]6696.02869545808[/C][/ROW]
[ROW][C]21[/C][C]612613[/C][C]608304.241756512[/C][C]4308.75824348803[/C][/ROW]
[ROW][C]22[/C][C]611324[/C][C]600346.993982798[/C][C]10977.0060172023[/C][/ROW]
[ROW][C]23[/C][C]594167[/C][C]594549.310356531[/C][C]-382.310356530594[/C][/ROW]
[ROW][C]24[/C][C]595454[/C][C]603634.89945451[/C][C]-8180.89945450972[/C][/ROW]
[ROW][C]25[/C][C]590865[/C][C]606458.582762683[/C][C]-15593.5827626829[/C][/ROW]
[ROW][C]26[/C][C]589379[/C][C]589295.741403395[/C][C]83.2585966045735[/C][/ROW]
[ROW][C]27[/C][C]584428[/C][C]583587.891537619[/C][C]840.10846238141[/C][/ROW]
[ROW][C]28[/C][C]573100[/C][C]571951.953115976[/C][C]1148.04688402358[/C][/ROW]
[ROW][C]29[/C][C]567456[/C][C]565003.845284967[/C][C]2452.15471503336[/C][/ROW]
[ROW][C]30[/C][C]569028[/C][C]572683.977763245[/C][C]-3655.97776324546[/C][/ROW]
[ROW][C]31[/C][C]620735[/C][C]632490.008431404[/C][C]-11755.0084314037[/C][/ROW]
[ROW][C]32[/C][C]628884[/C][C]631172.725617809[/C][C]-2288.72561780910[/C][/ROW]
[ROW][C]33[/C][C]628232[/C][C]624590.788542808[/C][C]3641.21145719173[/C][/ROW]
[ROW][C]34[/C][C]612117[/C][C]614112.57236219[/C][C]-1995.57236218941[/C][/ROW]
[ROW][C]35[/C][C]595404[/C][C]591757.211019301[/C][C]3646.78898069914[/C][/ROW]
[ROW][C]36[/C][C]597141[/C][C]600791.09416101[/C][C]-3650.09416100988[/C][/ROW]
[ROW][C]37[/C][C]593408[/C][C]604525.981811363[/C][C]-11117.9818113634[/C][/ROW]
[ROW][C]38[/C][C]590072[/C][C]590254.35390812[/C][C]-182.353908119840[/C][/ROW]
[ROW][C]39[/C][C]579799[/C][C]581977.72012682[/C][C]-2178.72012681945[/C][/ROW]
[ROW][C]40[/C][C]574205[/C][C]564863.741416347[/C][C]9341.25858365325[/C][/ROW]
[ROW][C]41[/C][C]572775[/C][C]563804.062457998[/C][C]8970.9375420023[/C][/ROW]
[ROW][C]42[/C][C]572942[/C][C]575983.396814138[/C][C]-3041.39681413758[/C][/ROW]
[ROW][C]43[/C][C]619567[/C][C]634713.823893817[/C][C]-15146.8238938169[/C][/ROW]
[ROW][C]44[/C][C]625809[/C][C]629428.419736452[/C][C]-3619.41973645205[/C][/ROW]
[ROW][C]45[/C][C]619916[/C][C]620421.569004207[/C][C]-505.569004206918[/C][/ROW]
[ROW][C]46[/C][C]587625[/C][C]603678.747719531[/C][C]-16053.7477195309[/C][/ROW]
[ROW][C]47[/C][C]565742[/C][C]565131.102672843[/C][C]610.897327156505[/C][/ROW]
[ROW][C]48[/C][C]557274[/C][C]567053.351327952[/C][C]-9779.35132795153[/C][/ROW]
[ROW][C]49[/C][C]560576[/C][C]560147.154662156[/C][C]428.845337843522[/C][/ROW]
[ROW][C]50[/C][C]548854[/C][C]554155.358965362[/C][C]-5301.35896536184[/C][/ROW]
[ROW][C]51[/C][C]531673[/C][C]537216.342017777[/C][C]-5543.34201777703[/C][/ROW]
[ROW][C]52[/C][C]525919[/C][C]513644.834346245[/C][C]12274.1656537554[/C][/ROW]
[ROW][C]53[/C][C]511038[/C][C]511493.580679156[/C][C]-455.580679156468[/C][/ROW]
[ROW][C]54[/C][C]498662[/C][C]509294.721496441[/C][C]-10632.7214964412[/C][/ROW]
[ROW][C]55[/C][C]555362[/C][C]554565.269475176[/C][C]796.730524823535[/C][/ROW]
[ROW][C]56[/C][C]564591[/C][C]561012.134744443[/C][C]3578.86525555735[/C][/ROW]
[ROW][C]57[/C][C]541657[/C][C]555760.042110383[/C][C]-14103.0421103832[/C][/ROW]
[ROW][C]58[/C][C]527070[/C][C]520713.401594589[/C][C]6356.59840541077[/C][/ROW]
[ROW][C]59[/C][C]509846[/C][C]501932.138052221[/C][C]7913.86194777902[/C][/ROW]
[ROW][C]60[/C][C]514258[/C][C]508458.046025837[/C][C]5799.95397416304[/C][/ROW]
[ROW][C]61[/C][C]516922[/C][C]516881.604216989[/C][C]40.3957830113941[/C][/ROW]
[ROW][C]62[/C][C]507561[/C][C]510213.586354658[/C][C]-2652.58635465812[/C][/ROW]
[ROW][C]63[/C][C]492622[/C][C]496076.251735346[/C][C]-3454.25173534575[/C][/ROW]
[ROW][C]64[/C][C]490243[/C][C]476227.534617881[/C][C]14015.4653821186[/C][/ROW]
[ROW][C]65[/C][C]469357[/C][C]475580.577870247[/C][C]-6223.57787024672[/C][/ROW]
[ROW][C]66[/C][C]477580[/C][C]467462.912693434[/C][C]10117.0873065657[/C][/ROW]
[ROW][C]67[/C][C]528379[/C][C]535147.121509948[/C][C]-6768.1215099484[/C][/ROW]
[ROW][C]68[/C][C]533590[/C][C]536245.502109291[/C][C]-2655.50210929057[/C][/ROW]
[ROW][C]69[/C][C]517945[/C][C]524849.811186114[/C][C]-6904.81118611363[/C][/ROW]
[ROW][C]70[/C][C]506174[/C][C]499515.487809045[/C][C]6658.51219095493[/C][/ROW]
[ROW][C]71[/C][C]501866[/C][C]482766.09696207[/C][C]19099.9030379298[/C][/ROW]
[ROW][C]72[/C][C]516141[/C][C]502377.568299744[/C][C]13763.4317002557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42270&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42270&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
13562325543510.78498931618814.2150106835
14560854562257.082625005-1403.08262500470
15555332557528.951675197-2196.95167519711
16543599545005.294025158-1406.29402515769
17536662537360.588402685-698.588402684778
18542722543516.617663201-794.617663201061
19593530608666.040283583-15136.0402835835
20610763604066.9713045426696.02869545808
21612613608304.2417565124308.75824348803
22611324600346.99398279810977.0060172023
23594167594549.310356531-382.310356530594
24595454603634.89945451-8180.89945450972
25590865606458.582762683-15593.5827626829
26589379589295.74140339583.2585966045735
27584428583587.891537619840.10846238141
28573100571951.9531159761148.04688402358
29567456565003.8452849672452.15471503336
30569028572683.977763245-3655.97776324546
31620735632490.008431404-11755.0084314037
32628884631172.725617809-2288.72561780910
33628232624590.7885428083641.21145719173
34612117614112.57236219-1995.57236218941
35595404591757.2110193013646.78898069914
36597141600791.09416101-3650.09416100988
37593408604525.981811363-11117.9818113634
38590072590254.35390812-182.353908119840
39579799581977.72012682-2178.72012681945
40574205564863.7414163479341.25858365325
41572775563804.0624579988970.9375420023
42572942575983.396814138-3041.39681413758
43619567634713.823893817-15146.8238938169
44625809629428.419736452-3619.41973645205
45619916620421.569004207-505.569004206918
46587625603678.747719531-16053.7477195309
47565742565131.102672843610.897327156505
48557274567053.351327952-9779.35132795153
49560576560147.154662156428.845337843522
50548854554155.358965362-5301.35896536184
51531673537216.342017777-5543.34201777703
52525919513644.83434624512274.1656537554
53511038511493.580679156-455.580679156468
54498662509294.721496441-10632.7214964412
55555362554565.269475176796.730524823535
56564591561012.1347444433578.86525555735
57541657555760.042110383-14103.0421103832
58527070520713.4015945896356.59840541077
59509846501932.1380522217913.86194777902
60514258508458.0460258375799.95397416304
61516922516881.60421698940.3957830113941
62507561510213.586354658-2652.58635465812
63492622496076.251735346-3454.25173534575
64490243476227.53461788114015.4653821186
65469357475580.577870247-6223.57787024672
66477580467462.91269343410117.0873065657
67528379535147.121509948-6768.1215099484
68533590536245.502109291-2655.50210929057
69517945524849.811186114-6904.81118611363
70506174499515.4878090456658.51219095493
71501866482766.0969620719099.9030379298
72516141502377.56829974413763.4317002557







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73521459.842109334505491.395619656537428.288599011
74518194.326917147495205.87918015541182.774654145
75510372.651584692481057.851979475539687.45118991
76499185.318632892463785.832415338534584.804850445
77486904.502592433445489.127710203528319.877474663
78489146.107027434441699.794905610536592.419149259
79548654.761921942495116.481243481602193.042600402
80559442.79890431499724.424258574619161.173550046
81553610.476732566487607.227172478619613.726292654
82539724.822665529467321.455022479612128.190308579
83521016.379281091442091.057282510599941.701279672
84523887.59405124438314.400388579609460.787713901

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 521459.842109334 & 505491.395619656 & 537428.288599011 \tabularnewline
74 & 518194.326917147 & 495205.87918015 & 541182.774654145 \tabularnewline
75 & 510372.651584692 & 481057.851979475 & 539687.45118991 \tabularnewline
76 & 499185.318632892 & 463785.832415338 & 534584.804850445 \tabularnewline
77 & 486904.502592433 & 445489.127710203 & 528319.877474663 \tabularnewline
78 & 489146.107027434 & 441699.794905610 & 536592.419149259 \tabularnewline
79 & 548654.761921942 & 495116.481243481 & 602193.042600402 \tabularnewline
80 & 559442.79890431 & 499724.424258574 & 619161.173550046 \tabularnewline
81 & 553610.476732566 & 487607.227172478 & 619613.726292654 \tabularnewline
82 & 539724.822665529 & 467321.455022479 & 612128.190308579 \tabularnewline
83 & 521016.379281091 & 442091.057282510 & 599941.701279672 \tabularnewline
84 & 523887.59405124 & 438314.400388579 & 609460.787713901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42270&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]521459.842109334[/C][C]505491.395619656[/C][C]537428.288599011[/C][/ROW]
[ROW][C]74[/C][C]518194.326917147[/C][C]495205.87918015[/C][C]541182.774654145[/C][/ROW]
[ROW][C]75[/C][C]510372.651584692[/C][C]481057.851979475[/C][C]539687.45118991[/C][/ROW]
[ROW][C]76[/C][C]499185.318632892[/C][C]463785.832415338[/C][C]534584.804850445[/C][/ROW]
[ROW][C]77[/C][C]486904.502592433[/C][C]445489.127710203[/C][C]528319.877474663[/C][/ROW]
[ROW][C]78[/C][C]489146.107027434[/C][C]441699.794905610[/C][C]536592.419149259[/C][/ROW]
[ROW][C]79[/C][C]548654.761921942[/C][C]495116.481243481[/C][C]602193.042600402[/C][/ROW]
[ROW][C]80[/C][C]559442.79890431[/C][C]499724.424258574[/C][C]619161.173550046[/C][/ROW]
[ROW][C]81[/C][C]553610.476732566[/C][C]487607.227172478[/C][C]619613.726292654[/C][/ROW]
[ROW][C]82[/C][C]539724.822665529[/C][C]467321.455022479[/C][C]612128.190308579[/C][/ROW]
[ROW][C]83[/C][C]521016.379281091[/C][C]442091.057282510[/C][C]599941.701279672[/C][/ROW]
[ROW][C]84[/C][C]523887.59405124[/C][C]438314.400388579[/C][C]609460.787713901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42270&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42270&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
73521459.842109334505491.395619656537428.288599011
74518194.326917147495205.87918015541182.774654145
75510372.651584692481057.851979475539687.45118991
76499185.318632892463785.832415338534584.804850445
77486904.502592433445489.127710203528319.877474663
78489146.107027434441699.794905610536592.419149259
79548654.761921942495116.481243481602193.042600402
80559442.79890431499724.424258574619161.173550046
81553610.476732566487607.227172478619613.726292654
82539724.822665529467321.455022479612128.190308579
83521016.379281091442091.057282510599941.701279672
84523887.59405124438314.400388579609460.787713901



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=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')