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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 computationSat, 18 Dec 2010 11:21:12 +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/2010/Dec/18/t1292671163puau5zq94y9pjvb.htm/, Retrieved Tue, 30 Apr 2024 06:36:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111849, Retrieved Tue, 30 Apr 2024 06:36:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 deel 2] [2010-12-18 11:21:12] [6724f75f9c1330f68e70e1e39953a3c7] [Current]
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Dataseries X:
68897
38683
44720
39525
45315
50380
40600
36279
42438
38064
31879
11379
70249
39253
47060
41697
38708
49267
39018
32228
40870
39383
34571
12066
70938
34077
45409
40809
37013
44953
37848
32745
43412
34931
33008
8620
68906
39556
50669
36432
40891
48428
36222
33425
39401
37967
34801
12657
69116
41519
51321
38529
41547
52073
38401
40898
40439
41888
37898
8771
68184
50530
47221
41756
45633
48138
39486
39341
41117
41629
29722
7054
56676
34870
35117
30169
30936
35699
33228
27733
33666
35429
27438
8170




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111849&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111849&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.422758923913050
beta0.477844184477007
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.422758923913050 \tabularnewline
beta & 0.477844184477007 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111849&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]0.422758923913050[/C][/ROW]
[ROW][C]beta[/C][C]0.477844184477007[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111849&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
alpha0.422758923913050
beta0.477844184477007
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
344720846936251
439525903.60314316598738621.396856834
5453152142.3328303147043172.6671696853
65038014026.588060662536353.4119393375
74060030371.800212500710228.1997874993
83627937738.5740196104-1459.57401961042
94243839869.38437850592568.61562149406
103806444222.0413286801-6158.04132868013
113187943641.4224318185-11762.4224318185
121137938315.3404237785-26936.3404237785
137024921132.861111941349116.1388880587
143925346024.3394358417-6771.33943584168
154706045920.98969285551139.01030714453
164169749391.9056625523-7694.9056625523
173870847573.7346669561-8865.7346669561
184926743469.59255071195797.40744928814
193901846735.5756687651-7717.57566876514
203222842728.9292775769-10500.9292775769
214087035424.27220491615445.72779508385
223938335961.31394391873421.68605608126
233457136333.8986752910-1762.89867529104
241206634158.5256828297-22092.5256828297
257093818925.646421214052012.353578786
263407745528.4322029733-11451.4322029733
274540942987.99924926532421.00075073470
284080946801.334489285-5992.33448928497
293701345847.3283493461-8834.32834934613
304495341907.19571378633045.80428621374
313784843604.7869032431-5756.78690324306
323274540418.0589357797-7673.05893577969
334341234871.15303039368540.84696960635
343493137904.1817449405-2973.18174494048
353300835468.9310238346-2460.93102383461
36862032753.0990701987-24133.0990701987
376890615999.967508699852906.0324913002
383955642503.5169980974-2947.51699809745
395066944799.04357200995869.95642799015
403643252008.0426043053-15576.0426043053
414089147003.9927319350-6112.99273193495
424842844765.62829248593662.37170751409
433622247399.7327090261-11177.7327090261
443342541502.0044273972-8077.00442739722
453940135283.47766446584117.52233553418
463796735052.08851339072914.91148660926
473480134901.1345968503-100.134596850323
481265733455.3145628964-20798.3145628964
496911619057.626540429550058.3734595705
504151944727.6725512194-3208.67255121942
515132147230.4062849694090.59371503098
523852953645.3226421855-15116.3226421855
534154748886.6516366273-7339.65163662735
545207345932.93343460696140.0665653931
553840149918.2590058089-11517.2590058089
564089844112.157805532-3214.15780553204
574043941166.9654162397-727.96541623972
584188839125.77464618122762.22535381879
593789839118.0983057955-1220.09830579548
60877137180.3835116219-28409.3835116219
616818418009.094003872750174.9059961273
625053042195.9920925928334.00790740797
634722150377.8541793261-3156.85417932607
644175653064.1265291758-11308.1265291758
654563350019.9883947382-4386.98839473825
664813849015.594952092-877.594952092048
673948649317.5434094924-9831.5434094924
683934143848.0317232249-4507.03172322489
694111739719.0263495291397.97365047099
704162938368.82339510523260.17660489482
712972238464.481066189-8742.48106618904
72705431719.8142019803-24665.8142019803
735667613260.603665418843415.3963345812
743487032353.80225816392516.19774183613
753511734664.804050695452.195949305002
763016936194.580078486-6025.58007848597
773093633768.5736183887-2832.5736183887
783569932120.22274147873578.77725852134
793322833905.2868103312-677.286810331163
802773333754.2411452307-6021.24114523068
813366630127.62275149843538.37724850156
823542931257.21616822044171.78383177962
832743833497.3419922664-6059.34199226636
84817030188.1028656064-22018.1028656064

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 44720 & 8469 & 36251 \tabularnewline
4 & 39525 & 903.603143165987 & 38621.396856834 \tabularnewline
5 & 45315 & 2142.33283031470 & 43172.6671696853 \tabularnewline
6 & 50380 & 14026.5880606625 & 36353.4119393375 \tabularnewline
7 & 40600 & 30371.8002125007 & 10228.1997874993 \tabularnewline
8 & 36279 & 37738.5740196104 & -1459.57401961042 \tabularnewline
9 & 42438 & 39869.3843785059 & 2568.61562149406 \tabularnewline
10 & 38064 & 44222.0413286801 & -6158.04132868013 \tabularnewline
11 & 31879 & 43641.4224318185 & -11762.4224318185 \tabularnewline
12 & 11379 & 38315.3404237785 & -26936.3404237785 \tabularnewline
13 & 70249 & 21132.8611119413 & 49116.1388880587 \tabularnewline
14 & 39253 & 46024.3394358417 & -6771.33943584168 \tabularnewline
15 & 47060 & 45920.9896928555 & 1139.01030714453 \tabularnewline
16 & 41697 & 49391.9056625523 & -7694.9056625523 \tabularnewline
17 & 38708 & 47573.7346669561 & -8865.7346669561 \tabularnewline
18 & 49267 & 43469.5925507119 & 5797.40744928814 \tabularnewline
19 & 39018 & 46735.5756687651 & -7717.57566876514 \tabularnewline
20 & 32228 & 42728.9292775769 & -10500.9292775769 \tabularnewline
21 & 40870 & 35424.2722049161 & 5445.72779508385 \tabularnewline
22 & 39383 & 35961.3139439187 & 3421.68605608126 \tabularnewline
23 & 34571 & 36333.8986752910 & -1762.89867529104 \tabularnewline
24 & 12066 & 34158.5256828297 & -22092.5256828297 \tabularnewline
25 & 70938 & 18925.6464212140 & 52012.353578786 \tabularnewline
26 & 34077 & 45528.4322029733 & -11451.4322029733 \tabularnewline
27 & 45409 & 42987.9992492653 & 2421.00075073470 \tabularnewline
28 & 40809 & 46801.334489285 & -5992.33448928497 \tabularnewline
29 & 37013 & 45847.3283493461 & -8834.32834934613 \tabularnewline
30 & 44953 & 41907.1957137863 & 3045.80428621374 \tabularnewline
31 & 37848 & 43604.7869032431 & -5756.78690324306 \tabularnewline
32 & 32745 & 40418.0589357797 & -7673.05893577969 \tabularnewline
33 & 43412 & 34871.1530303936 & 8540.84696960635 \tabularnewline
34 & 34931 & 37904.1817449405 & -2973.18174494048 \tabularnewline
35 & 33008 & 35468.9310238346 & -2460.93102383461 \tabularnewline
36 & 8620 & 32753.0990701987 & -24133.0990701987 \tabularnewline
37 & 68906 & 15999.9675086998 & 52906.0324913002 \tabularnewline
38 & 39556 & 42503.5169980974 & -2947.51699809745 \tabularnewline
39 & 50669 & 44799.0435720099 & 5869.95642799015 \tabularnewline
40 & 36432 & 52008.0426043053 & -15576.0426043053 \tabularnewline
41 & 40891 & 47003.9927319350 & -6112.99273193495 \tabularnewline
42 & 48428 & 44765.6282924859 & 3662.37170751409 \tabularnewline
43 & 36222 & 47399.7327090261 & -11177.7327090261 \tabularnewline
44 & 33425 & 41502.0044273972 & -8077.00442739722 \tabularnewline
45 & 39401 & 35283.4776644658 & 4117.52233553418 \tabularnewline
46 & 37967 & 35052.0885133907 & 2914.91148660926 \tabularnewline
47 & 34801 & 34901.1345968503 & -100.134596850323 \tabularnewline
48 & 12657 & 33455.3145628964 & -20798.3145628964 \tabularnewline
49 & 69116 & 19057.6265404295 & 50058.3734595705 \tabularnewline
50 & 41519 & 44727.6725512194 & -3208.67255121942 \tabularnewline
51 & 51321 & 47230.406284969 & 4090.59371503098 \tabularnewline
52 & 38529 & 53645.3226421855 & -15116.3226421855 \tabularnewline
53 & 41547 & 48886.6516366273 & -7339.65163662735 \tabularnewline
54 & 52073 & 45932.9334346069 & 6140.0665653931 \tabularnewline
55 & 38401 & 49918.2590058089 & -11517.2590058089 \tabularnewline
56 & 40898 & 44112.157805532 & -3214.15780553204 \tabularnewline
57 & 40439 & 41166.9654162397 & -727.96541623972 \tabularnewline
58 & 41888 & 39125.7746461812 & 2762.22535381879 \tabularnewline
59 & 37898 & 39118.0983057955 & -1220.09830579548 \tabularnewline
60 & 8771 & 37180.3835116219 & -28409.3835116219 \tabularnewline
61 & 68184 & 18009.0940038727 & 50174.9059961273 \tabularnewline
62 & 50530 & 42195.992092592 & 8334.00790740797 \tabularnewline
63 & 47221 & 50377.8541793261 & -3156.85417932607 \tabularnewline
64 & 41756 & 53064.1265291758 & -11308.1265291758 \tabularnewline
65 & 45633 & 50019.9883947382 & -4386.98839473825 \tabularnewline
66 & 48138 & 49015.594952092 & -877.594952092048 \tabularnewline
67 & 39486 & 49317.5434094924 & -9831.5434094924 \tabularnewline
68 & 39341 & 43848.0317232249 & -4507.03172322489 \tabularnewline
69 & 41117 & 39719.026349529 & 1397.97365047099 \tabularnewline
70 & 41629 & 38368.8233951052 & 3260.17660489482 \tabularnewline
71 & 29722 & 38464.481066189 & -8742.48106618904 \tabularnewline
72 & 7054 & 31719.8142019803 & -24665.8142019803 \tabularnewline
73 & 56676 & 13260.6036654188 & 43415.3963345812 \tabularnewline
74 & 34870 & 32353.8022581639 & 2516.19774183613 \tabularnewline
75 & 35117 & 34664.804050695 & 452.195949305002 \tabularnewline
76 & 30169 & 36194.580078486 & -6025.58007848597 \tabularnewline
77 & 30936 & 33768.5736183887 & -2832.5736183887 \tabularnewline
78 & 35699 & 32120.2227414787 & 3578.77725852134 \tabularnewline
79 & 33228 & 33905.2868103312 & -677.286810331163 \tabularnewline
80 & 27733 & 33754.2411452307 & -6021.24114523068 \tabularnewline
81 & 33666 & 30127.6227514984 & 3538.37724850156 \tabularnewline
82 & 35429 & 31257.2161682204 & 4171.78383177962 \tabularnewline
83 & 27438 & 33497.3419922664 & -6059.34199226636 \tabularnewline
84 & 8170 & 30188.1028656064 & -22018.1028656064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111849&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]3[/C][C]44720[/C][C]8469[/C][C]36251[/C][/ROW]
[ROW][C]4[/C][C]39525[/C][C]903.603143165987[/C][C]38621.396856834[/C][/ROW]
[ROW][C]5[/C][C]45315[/C][C]2142.33283031470[/C][C]43172.6671696853[/C][/ROW]
[ROW][C]6[/C][C]50380[/C][C]14026.5880606625[/C][C]36353.4119393375[/C][/ROW]
[ROW][C]7[/C][C]40600[/C][C]30371.8002125007[/C][C]10228.1997874993[/C][/ROW]
[ROW][C]8[/C][C]36279[/C][C]37738.5740196104[/C][C]-1459.57401961042[/C][/ROW]
[ROW][C]9[/C][C]42438[/C][C]39869.3843785059[/C][C]2568.61562149406[/C][/ROW]
[ROW][C]10[/C][C]38064[/C][C]44222.0413286801[/C][C]-6158.04132868013[/C][/ROW]
[ROW][C]11[/C][C]31879[/C][C]43641.4224318185[/C][C]-11762.4224318185[/C][/ROW]
[ROW][C]12[/C][C]11379[/C][C]38315.3404237785[/C][C]-26936.3404237785[/C][/ROW]
[ROW][C]13[/C][C]70249[/C][C]21132.8611119413[/C][C]49116.1388880587[/C][/ROW]
[ROW][C]14[/C][C]39253[/C][C]46024.3394358417[/C][C]-6771.33943584168[/C][/ROW]
[ROW][C]15[/C][C]47060[/C][C]45920.9896928555[/C][C]1139.01030714453[/C][/ROW]
[ROW][C]16[/C][C]41697[/C][C]49391.9056625523[/C][C]-7694.9056625523[/C][/ROW]
[ROW][C]17[/C][C]38708[/C][C]47573.7346669561[/C][C]-8865.7346669561[/C][/ROW]
[ROW][C]18[/C][C]49267[/C][C]43469.5925507119[/C][C]5797.40744928814[/C][/ROW]
[ROW][C]19[/C][C]39018[/C][C]46735.5756687651[/C][C]-7717.57566876514[/C][/ROW]
[ROW][C]20[/C][C]32228[/C][C]42728.9292775769[/C][C]-10500.9292775769[/C][/ROW]
[ROW][C]21[/C][C]40870[/C][C]35424.2722049161[/C][C]5445.72779508385[/C][/ROW]
[ROW][C]22[/C][C]39383[/C][C]35961.3139439187[/C][C]3421.68605608126[/C][/ROW]
[ROW][C]23[/C][C]34571[/C][C]36333.8986752910[/C][C]-1762.89867529104[/C][/ROW]
[ROW][C]24[/C][C]12066[/C][C]34158.5256828297[/C][C]-22092.5256828297[/C][/ROW]
[ROW][C]25[/C][C]70938[/C][C]18925.6464212140[/C][C]52012.353578786[/C][/ROW]
[ROW][C]26[/C][C]34077[/C][C]45528.4322029733[/C][C]-11451.4322029733[/C][/ROW]
[ROW][C]27[/C][C]45409[/C][C]42987.9992492653[/C][C]2421.00075073470[/C][/ROW]
[ROW][C]28[/C][C]40809[/C][C]46801.334489285[/C][C]-5992.33448928497[/C][/ROW]
[ROW][C]29[/C][C]37013[/C][C]45847.3283493461[/C][C]-8834.32834934613[/C][/ROW]
[ROW][C]30[/C][C]44953[/C][C]41907.1957137863[/C][C]3045.80428621374[/C][/ROW]
[ROW][C]31[/C][C]37848[/C][C]43604.7869032431[/C][C]-5756.78690324306[/C][/ROW]
[ROW][C]32[/C][C]32745[/C][C]40418.0589357797[/C][C]-7673.05893577969[/C][/ROW]
[ROW][C]33[/C][C]43412[/C][C]34871.1530303936[/C][C]8540.84696960635[/C][/ROW]
[ROW][C]34[/C][C]34931[/C][C]37904.1817449405[/C][C]-2973.18174494048[/C][/ROW]
[ROW][C]35[/C][C]33008[/C][C]35468.9310238346[/C][C]-2460.93102383461[/C][/ROW]
[ROW][C]36[/C][C]8620[/C][C]32753.0990701987[/C][C]-24133.0990701987[/C][/ROW]
[ROW][C]37[/C][C]68906[/C][C]15999.9675086998[/C][C]52906.0324913002[/C][/ROW]
[ROW][C]38[/C][C]39556[/C][C]42503.5169980974[/C][C]-2947.51699809745[/C][/ROW]
[ROW][C]39[/C][C]50669[/C][C]44799.0435720099[/C][C]5869.95642799015[/C][/ROW]
[ROW][C]40[/C][C]36432[/C][C]52008.0426043053[/C][C]-15576.0426043053[/C][/ROW]
[ROW][C]41[/C][C]40891[/C][C]47003.9927319350[/C][C]-6112.99273193495[/C][/ROW]
[ROW][C]42[/C][C]48428[/C][C]44765.6282924859[/C][C]3662.37170751409[/C][/ROW]
[ROW][C]43[/C][C]36222[/C][C]47399.7327090261[/C][C]-11177.7327090261[/C][/ROW]
[ROW][C]44[/C][C]33425[/C][C]41502.0044273972[/C][C]-8077.00442739722[/C][/ROW]
[ROW][C]45[/C][C]39401[/C][C]35283.4776644658[/C][C]4117.52233553418[/C][/ROW]
[ROW][C]46[/C][C]37967[/C][C]35052.0885133907[/C][C]2914.91148660926[/C][/ROW]
[ROW][C]47[/C][C]34801[/C][C]34901.1345968503[/C][C]-100.134596850323[/C][/ROW]
[ROW][C]48[/C][C]12657[/C][C]33455.3145628964[/C][C]-20798.3145628964[/C][/ROW]
[ROW][C]49[/C][C]69116[/C][C]19057.6265404295[/C][C]50058.3734595705[/C][/ROW]
[ROW][C]50[/C][C]41519[/C][C]44727.6725512194[/C][C]-3208.67255121942[/C][/ROW]
[ROW][C]51[/C][C]51321[/C][C]47230.406284969[/C][C]4090.59371503098[/C][/ROW]
[ROW][C]52[/C][C]38529[/C][C]53645.3226421855[/C][C]-15116.3226421855[/C][/ROW]
[ROW][C]53[/C][C]41547[/C][C]48886.6516366273[/C][C]-7339.65163662735[/C][/ROW]
[ROW][C]54[/C][C]52073[/C][C]45932.9334346069[/C][C]6140.0665653931[/C][/ROW]
[ROW][C]55[/C][C]38401[/C][C]49918.2590058089[/C][C]-11517.2590058089[/C][/ROW]
[ROW][C]56[/C][C]40898[/C][C]44112.157805532[/C][C]-3214.15780553204[/C][/ROW]
[ROW][C]57[/C][C]40439[/C][C]41166.9654162397[/C][C]-727.96541623972[/C][/ROW]
[ROW][C]58[/C][C]41888[/C][C]39125.7746461812[/C][C]2762.22535381879[/C][/ROW]
[ROW][C]59[/C][C]37898[/C][C]39118.0983057955[/C][C]-1220.09830579548[/C][/ROW]
[ROW][C]60[/C][C]8771[/C][C]37180.3835116219[/C][C]-28409.3835116219[/C][/ROW]
[ROW][C]61[/C][C]68184[/C][C]18009.0940038727[/C][C]50174.9059961273[/C][/ROW]
[ROW][C]62[/C][C]50530[/C][C]42195.992092592[/C][C]8334.00790740797[/C][/ROW]
[ROW][C]63[/C][C]47221[/C][C]50377.8541793261[/C][C]-3156.85417932607[/C][/ROW]
[ROW][C]64[/C][C]41756[/C][C]53064.1265291758[/C][C]-11308.1265291758[/C][/ROW]
[ROW][C]65[/C][C]45633[/C][C]50019.9883947382[/C][C]-4386.98839473825[/C][/ROW]
[ROW][C]66[/C][C]48138[/C][C]49015.594952092[/C][C]-877.594952092048[/C][/ROW]
[ROW][C]67[/C][C]39486[/C][C]49317.5434094924[/C][C]-9831.5434094924[/C][/ROW]
[ROW][C]68[/C][C]39341[/C][C]43848.0317232249[/C][C]-4507.03172322489[/C][/ROW]
[ROW][C]69[/C][C]41117[/C][C]39719.026349529[/C][C]1397.97365047099[/C][/ROW]
[ROW][C]70[/C][C]41629[/C][C]38368.8233951052[/C][C]3260.17660489482[/C][/ROW]
[ROW][C]71[/C][C]29722[/C][C]38464.481066189[/C][C]-8742.48106618904[/C][/ROW]
[ROW][C]72[/C][C]7054[/C][C]31719.8142019803[/C][C]-24665.8142019803[/C][/ROW]
[ROW][C]73[/C][C]56676[/C][C]13260.6036654188[/C][C]43415.3963345812[/C][/ROW]
[ROW][C]74[/C][C]34870[/C][C]32353.8022581639[/C][C]2516.19774183613[/C][/ROW]
[ROW][C]75[/C][C]35117[/C][C]34664.804050695[/C][C]452.195949305002[/C][/ROW]
[ROW][C]76[/C][C]30169[/C][C]36194.580078486[/C][C]-6025.58007848597[/C][/ROW]
[ROW][C]77[/C][C]30936[/C][C]33768.5736183887[/C][C]-2832.5736183887[/C][/ROW]
[ROW][C]78[/C][C]35699[/C][C]32120.2227414787[/C][C]3578.77725852134[/C][/ROW]
[ROW][C]79[/C][C]33228[/C][C]33905.2868103312[/C][C]-677.286810331163[/C][/ROW]
[ROW][C]80[/C][C]27733[/C][C]33754.2411452307[/C][C]-6021.24114523068[/C][/ROW]
[ROW][C]81[/C][C]33666[/C][C]30127.6227514984[/C][C]3538.37724850156[/C][/ROW]
[ROW][C]82[/C][C]35429[/C][C]31257.2161682204[/C][C]4171.78383177962[/C][/ROW]
[ROW][C]83[/C][C]27438[/C][C]33497.3419922664[/C][C]-6059.34199226636[/C][/ROW]
[ROW][C]84[/C][C]8170[/C][C]30188.1028656064[/C][C]-22018.1028656064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111849&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111849&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
344720846936251
439525903.60314316598738621.396856834
5453152142.3328303147043172.6671696853
65038014026.588060662536353.4119393375
74060030371.800212500710228.1997874993
83627937738.5740196104-1459.57401961042
94243839869.38437850592568.61562149406
103806444222.0413286801-6158.04132868013
113187943641.4224318185-11762.4224318185
121137938315.3404237785-26936.3404237785
137024921132.861111941349116.1388880587
143925346024.3394358417-6771.33943584168
154706045920.98969285551139.01030714453
164169749391.9056625523-7694.9056625523
173870847573.7346669561-8865.7346669561
184926743469.59255071195797.40744928814
193901846735.5756687651-7717.57566876514
203222842728.9292775769-10500.9292775769
214087035424.27220491615445.72779508385
223938335961.31394391873421.68605608126
233457136333.8986752910-1762.89867529104
241206634158.5256828297-22092.5256828297
257093818925.646421214052012.353578786
263407745528.4322029733-11451.4322029733
274540942987.99924926532421.00075073470
284080946801.334489285-5992.33448928497
293701345847.3283493461-8834.32834934613
304495341907.19571378633045.80428621374
313784843604.7869032431-5756.78690324306
323274540418.0589357797-7673.05893577969
334341234871.15303039368540.84696960635
343493137904.1817449405-2973.18174494048
353300835468.9310238346-2460.93102383461
36862032753.0990701987-24133.0990701987
376890615999.967508699852906.0324913002
383955642503.5169980974-2947.51699809745
395066944799.04357200995869.95642799015
403643252008.0426043053-15576.0426043053
414089147003.9927319350-6112.99273193495
424842844765.62829248593662.37170751409
433622247399.7327090261-11177.7327090261
443342541502.0044273972-8077.00442739722
453940135283.47766446584117.52233553418
463796735052.08851339072914.91148660926
473480134901.1345968503-100.134596850323
481265733455.3145628964-20798.3145628964
496911619057.626540429550058.3734595705
504151944727.6725512194-3208.67255121942
515132147230.4062849694090.59371503098
523852953645.3226421855-15116.3226421855
534154748886.6516366273-7339.65163662735
545207345932.93343460696140.0665653931
553840149918.2590058089-11517.2590058089
564089844112.157805532-3214.15780553204
574043941166.9654162397-727.96541623972
584188839125.77464618122762.22535381879
593789839118.0983057955-1220.09830579548
60877137180.3835116219-28409.3835116219
616818418009.094003872750174.9059961273
625053042195.9920925928334.00790740797
634722150377.8541793261-3156.85417932607
644175653064.1265291758-11308.1265291758
654563350019.9883947382-4386.98839473825
664813849015.594952092-877.594952092048
673948649317.5434094924-9831.5434094924
683934143848.0317232249-4507.03172322489
694111739719.0263495291397.97365047099
704162938368.82339510523260.17660489482
712972238464.481066189-8742.48106618904
72705431719.8142019803-24665.8142019803
735667613260.603665418843415.3963345812
743487032353.80225816392516.19774183613
753511734664.804050695452.195949305002
763016936194.580078486-6025.58007848597
773093633768.5736183887-2832.5736183887
783569932120.22274147873578.77725852134
793322833905.2868103312-677.286810331163
802773333754.2411452307-6021.24114523068
813366630127.62275149843538.37724850156
823542931257.21616822044171.78383177962
832743833497.3419922664-6059.34199226636
84817030188.1028656064-22018.1028656064







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8515684.2145018833-20477.293587426751845.7225911932
8610488.6756122307-32150.324837059653127.676061521
875293.13672257817-46783.362078336957369.6355234932
8897.597832925625-63902.523079056764097.718744908
89-5097.94105672692-83052.891590918672857.0094774648
90-10293.4799463795-103896.72209533183309.7622025718
91-15489.018836032-126198.19671249895220.1590404335
92-20684.5577256845-149791.367747329108422.252295960
93-25880.0966153371-174555.698614305122795.505383631
94-31075.6355049896-200400.322065361138249.051055381
95-36271.1743946422-227254.266961278154711.918171993
96-41466.7132842947-255060.345768303172126.919199714

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 15684.2145018833 & -20477.2935874267 & 51845.7225911932 \tabularnewline
86 & 10488.6756122307 & -32150.3248370596 & 53127.676061521 \tabularnewline
87 & 5293.13672257817 & -46783.3620783369 & 57369.6355234932 \tabularnewline
88 & 97.597832925625 & -63902.5230790567 & 64097.718744908 \tabularnewline
89 & -5097.94105672692 & -83052.8915909186 & 72857.0094774648 \tabularnewline
90 & -10293.4799463795 & -103896.722095331 & 83309.7622025718 \tabularnewline
91 & -15489.018836032 & -126198.196712498 & 95220.1590404335 \tabularnewline
92 & -20684.5577256845 & -149791.367747329 & 108422.252295960 \tabularnewline
93 & -25880.0966153371 & -174555.698614305 & 122795.505383631 \tabularnewline
94 & -31075.6355049896 & -200400.322065361 & 138249.051055381 \tabularnewline
95 & -36271.1743946422 & -227254.266961278 & 154711.918171993 \tabularnewline
96 & -41466.7132842947 & -255060.345768303 & 172126.919199714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111849&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]15684.2145018833[/C][C]-20477.2935874267[/C][C]51845.7225911932[/C][/ROW]
[ROW][C]86[/C][C]10488.6756122307[/C][C]-32150.3248370596[/C][C]53127.676061521[/C][/ROW]
[ROW][C]87[/C][C]5293.13672257817[/C][C]-46783.3620783369[/C][C]57369.6355234932[/C][/ROW]
[ROW][C]88[/C][C]97.597832925625[/C][C]-63902.5230790567[/C][C]64097.718744908[/C][/ROW]
[ROW][C]89[/C][C]-5097.94105672692[/C][C]-83052.8915909186[/C][C]72857.0094774648[/C][/ROW]
[ROW][C]90[/C][C]-10293.4799463795[/C][C]-103896.722095331[/C][C]83309.7622025718[/C][/ROW]
[ROW][C]91[/C][C]-15489.018836032[/C][C]-126198.196712498[/C][C]95220.1590404335[/C][/ROW]
[ROW][C]92[/C][C]-20684.5577256845[/C][C]-149791.367747329[/C][C]108422.252295960[/C][/ROW]
[ROW][C]93[/C][C]-25880.0966153371[/C][C]-174555.698614305[/C][C]122795.505383631[/C][/ROW]
[ROW][C]94[/C][C]-31075.6355049896[/C][C]-200400.322065361[/C][C]138249.051055381[/C][/ROW]
[ROW][C]95[/C][C]-36271.1743946422[/C][C]-227254.266961278[/C][C]154711.918171993[/C][/ROW]
[ROW][C]96[/C][C]-41466.7132842947[/C][C]-255060.345768303[/C][C]172126.919199714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111849&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111849&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
8515684.2145018833-20477.293587426751845.7225911932
8610488.6756122307-32150.324837059653127.676061521
875293.13672257817-46783.362078336957369.6355234932
8897.597832925625-63902.523079056764097.718744908
89-5097.94105672692-83052.891590918672857.0094774648
90-10293.4799463795-103896.72209533183309.7622025718
91-15489.018836032-126198.19671249895220.1590404335
92-20684.5577256845-149791.367747329108422.252295960
93-25880.0966153371-174555.698614305122795.505383631
94-31075.6355049896-200400.322065361138249.051055381
95-36271.1743946422-227254.266961278154711.918171993
96-41466.7132842947-255060.345768303172126.919199714



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')