Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 15:43:19 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/12/t1386881088zbcfe2n6o4wwzi0.htm/, Retrieved Sun, 05 Dec 2021 16:28:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232272, Retrieved Sun, 05 Dec 2021 16:28:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact37
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 20:43:19] [4fd97498c979c83b38653eaed452295a] [Current]
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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'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232272&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232272&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.594274923316691
beta0.0241142539120853
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.594274923316691 \tabularnewline
beta & 0.0241142539120853 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232272&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]0.594274923316691[/C][/ROW]
[ROW][C]beta[/C][C]0.0241142539120853[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232272&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
alpha0.594274923316691
beta0.0241142539120853
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
343129382944835
43786339840.6072043033-1977.60720430333
53595337310.3126917717-1357.31269177168
62913335129.192688473-5996.19268847296
72469330105.3742131567-5412.37421315672
82220525350.9424083429-3145.94240834287
92172521898.3112741974-173.311274197404
102719220209.7566427556982.24335724496
112179022873.6277044576-1083.6277044576
121325320728.6249365729-7475.62493657291
133770214677.889087532623024.1109124674
143036427082.32835977653281.67164022354
153260927801.35903103114807.64096896886
163021229496.1308896812715.869110318847
172996528769.52410050691195.47589949314
182835228345.06736225866.93263774138904
192581427214.3885164144-1400.38851641443
202241425227.305737017-2813.30573701704
212050622360.2456169724-1854.24561697241
222880620036.5586160958769.44138390503
232222824151.9328411378-1923.93284113783
241397121884.9320059536-7913.93200595359
253684515944.814302354220900.1856976458
263533827427.71422328287910.2857767172
273502231304.40068661233717.59931338768
283477732742.75376701232034.24623298775
292688733209.8840829498-6322.88408294984
302397028619.9713536828-4649.97135368283
312278024957.5923105983-2177.59231059827
321735122733.280154997-5382.28015499698
332138218527.37163005662854.62836994335
342456119257.35952870485303.64047129522
351740921518.7377067368-4109.73770673676
361151418127.0867084793-6613.08670847928
373151413152.989358944318361.0106410557
382707123283.49419349783787.50580650217
392946224807.60739834564654.39260165436
402610526913.5894433031-808.589443303106
412239725761.4707643112-3364.47076431117
422384323042.2413731134800.758626886563
432170522809.7786275816-1104.77862758158
441808921429.0708501344-3340.07085013435
452076418672.12008526412091.87991473585
462531619173.2191222236142.78087777705
471770422169.6961175774-4465.69611757741
481554818797.8256178991-3249.8256178991
492802916101.944851880311927.0551481197
502938322596.22436007036786.7756399297
513643826133.022521542310304.9774784577
523203431908.275253418125.72474658204
532267931636.0550466646-8957.05504666461
542431925837.8075297262-1518.80752972615
551800424438.1587196983-6434.15871969827
561753720025.2352698412-2488.23526984119
572036617921.61752899852444.38247100153
582278218784.36003203293997.63996796707
591916920627.4526801149-1458.4526801149
601380719207.2259372753-5400.22593727535
612974315367.114275981714375.8857240183
622559123485.46343424062105.5365657594
632909624342.02517157024753.97482842984
642648226840.6141734953-358.61417349528
652240526295.7806192313-3890.78061923132
662704423596.11230365033447.88769634968
671797025307.0404807588-7337.04048075883
681873020503.6128602848-1773.61286028477
691968418980.9740096464703.025990353566
701978518940.2142334743844.785766525703
711847918995.8049367975-516.804936797522
721069818234.8303580312-7536.83035803121

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 43129 & 38294 & 4835 \tabularnewline
4 & 37863 & 39840.6072043033 & -1977.60720430333 \tabularnewline
5 & 35953 & 37310.3126917717 & -1357.31269177168 \tabularnewline
6 & 29133 & 35129.192688473 & -5996.19268847296 \tabularnewline
7 & 24693 & 30105.3742131567 & -5412.37421315672 \tabularnewline
8 & 22205 & 25350.9424083429 & -3145.94240834287 \tabularnewline
9 & 21725 & 21898.3112741974 & -173.311274197404 \tabularnewline
10 & 27192 & 20209.756642755 & 6982.24335724496 \tabularnewline
11 & 21790 & 22873.6277044576 & -1083.6277044576 \tabularnewline
12 & 13253 & 20728.6249365729 & -7475.62493657291 \tabularnewline
13 & 37702 & 14677.8890875326 & 23024.1109124674 \tabularnewline
14 & 30364 & 27082.3283597765 & 3281.67164022354 \tabularnewline
15 & 32609 & 27801.3590310311 & 4807.64096896886 \tabularnewline
16 & 30212 & 29496.1308896812 & 715.869110318847 \tabularnewline
17 & 29965 & 28769.5241005069 & 1195.47589949314 \tabularnewline
18 & 28352 & 28345.0673622586 & 6.93263774138904 \tabularnewline
19 & 25814 & 27214.3885164144 & -1400.38851641443 \tabularnewline
20 & 22414 & 25227.305737017 & -2813.30573701704 \tabularnewline
21 & 20506 & 22360.2456169724 & -1854.24561697241 \tabularnewline
22 & 28806 & 20036.558616095 & 8769.44138390503 \tabularnewline
23 & 22228 & 24151.9328411378 & -1923.93284113783 \tabularnewline
24 & 13971 & 21884.9320059536 & -7913.93200595359 \tabularnewline
25 & 36845 & 15944.8143023542 & 20900.1856976458 \tabularnewline
26 & 35338 & 27427.7142232828 & 7910.2857767172 \tabularnewline
27 & 35022 & 31304.4006866123 & 3717.59931338768 \tabularnewline
28 & 34777 & 32742.7537670123 & 2034.24623298775 \tabularnewline
29 & 26887 & 33209.8840829498 & -6322.88408294984 \tabularnewline
30 & 23970 & 28619.9713536828 & -4649.97135368283 \tabularnewline
31 & 22780 & 24957.5923105983 & -2177.59231059827 \tabularnewline
32 & 17351 & 22733.280154997 & -5382.28015499698 \tabularnewline
33 & 21382 & 18527.3716300566 & 2854.62836994335 \tabularnewline
34 & 24561 & 19257.3595287048 & 5303.64047129522 \tabularnewline
35 & 17409 & 21518.7377067368 & -4109.73770673676 \tabularnewline
36 & 11514 & 18127.0867084793 & -6613.08670847928 \tabularnewline
37 & 31514 & 13152.9893589443 & 18361.0106410557 \tabularnewline
38 & 27071 & 23283.4941934978 & 3787.50580650217 \tabularnewline
39 & 29462 & 24807.6073983456 & 4654.39260165436 \tabularnewline
40 & 26105 & 26913.5894433031 & -808.589443303106 \tabularnewline
41 & 22397 & 25761.4707643112 & -3364.47076431117 \tabularnewline
42 & 23843 & 23042.2413731134 & 800.758626886563 \tabularnewline
43 & 21705 & 22809.7786275816 & -1104.77862758158 \tabularnewline
44 & 18089 & 21429.0708501344 & -3340.07085013435 \tabularnewline
45 & 20764 & 18672.1200852641 & 2091.87991473585 \tabularnewline
46 & 25316 & 19173.219122223 & 6142.78087777705 \tabularnewline
47 & 17704 & 22169.6961175774 & -4465.69611757741 \tabularnewline
48 & 15548 & 18797.8256178991 & -3249.8256178991 \tabularnewline
49 & 28029 & 16101.9448518803 & 11927.0551481197 \tabularnewline
50 & 29383 & 22596.2243600703 & 6786.7756399297 \tabularnewline
51 & 36438 & 26133.0225215423 & 10304.9774784577 \tabularnewline
52 & 32034 & 31908.275253418 & 125.72474658204 \tabularnewline
53 & 22679 & 31636.0550466646 & -8957.05504666461 \tabularnewline
54 & 24319 & 25837.8075297262 & -1518.80752972615 \tabularnewline
55 & 18004 & 24438.1587196983 & -6434.15871969827 \tabularnewline
56 & 17537 & 20025.2352698412 & -2488.23526984119 \tabularnewline
57 & 20366 & 17921.6175289985 & 2444.38247100153 \tabularnewline
58 & 22782 & 18784.3600320329 & 3997.63996796707 \tabularnewline
59 & 19169 & 20627.4526801149 & -1458.4526801149 \tabularnewline
60 & 13807 & 19207.2259372753 & -5400.22593727535 \tabularnewline
61 & 29743 & 15367.1142759817 & 14375.8857240183 \tabularnewline
62 & 25591 & 23485.4634342406 & 2105.5365657594 \tabularnewline
63 & 29096 & 24342.0251715702 & 4753.97482842984 \tabularnewline
64 & 26482 & 26840.6141734953 & -358.61417349528 \tabularnewline
65 & 22405 & 26295.7806192313 & -3890.78061923132 \tabularnewline
66 & 27044 & 23596.1123036503 & 3447.88769634968 \tabularnewline
67 & 17970 & 25307.0404807588 & -7337.04048075883 \tabularnewline
68 & 18730 & 20503.6128602848 & -1773.61286028477 \tabularnewline
69 & 19684 & 18980.9740096464 & 703.025990353566 \tabularnewline
70 & 19785 & 18940.2142334743 & 844.785766525703 \tabularnewline
71 & 18479 & 18995.8049367975 & -516.804936797522 \tabularnewline
72 & 10698 & 18234.8303580312 & -7536.83035803121 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232272&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]43129[/C][C]38294[/C][C]4835[/C][/ROW]
[ROW][C]4[/C][C]37863[/C][C]39840.6072043033[/C][C]-1977.60720430333[/C][/ROW]
[ROW][C]5[/C][C]35953[/C][C]37310.3126917717[/C][C]-1357.31269177168[/C][/ROW]
[ROW][C]6[/C][C]29133[/C][C]35129.192688473[/C][C]-5996.19268847296[/C][/ROW]
[ROW][C]7[/C][C]24693[/C][C]30105.3742131567[/C][C]-5412.37421315672[/C][/ROW]
[ROW][C]8[/C][C]22205[/C][C]25350.9424083429[/C][C]-3145.94240834287[/C][/ROW]
[ROW][C]9[/C][C]21725[/C][C]21898.3112741974[/C][C]-173.311274197404[/C][/ROW]
[ROW][C]10[/C][C]27192[/C][C]20209.756642755[/C][C]6982.24335724496[/C][/ROW]
[ROW][C]11[/C][C]21790[/C][C]22873.6277044576[/C][C]-1083.6277044576[/C][/ROW]
[ROW][C]12[/C][C]13253[/C][C]20728.6249365729[/C][C]-7475.62493657291[/C][/ROW]
[ROW][C]13[/C][C]37702[/C][C]14677.8890875326[/C][C]23024.1109124674[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]27082.3283597765[/C][C]3281.67164022354[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]27801.3590310311[/C][C]4807.64096896886[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]29496.1308896812[/C][C]715.869110318847[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]28769.5241005069[/C][C]1195.47589949314[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28345.0673622586[/C][C]6.93263774138904[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]27214.3885164144[/C][C]-1400.38851641443[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]25227.305737017[/C][C]-2813.30573701704[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]22360.2456169724[/C][C]-1854.24561697241[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]20036.558616095[/C][C]8769.44138390503[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]24151.9328411378[/C][C]-1923.93284113783[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]21884.9320059536[/C][C]-7913.93200595359[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]15944.8143023542[/C][C]20900.1856976458[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]27427.7142232828[/C][C]7910.2857767172[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]31304.4006866123[/C][C]3717.59931338768[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]32742.7537670123[/C][C]2034.24623298775[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]33209.8840829498[/C][C]-6322.88408294984[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28619.9713536828[/C][C]-4649.97135368283[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]24957.5923105983[/C][C]-2177.59231059827[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]22733.280154997[/C][C]-5382.28015499698[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18527.3716300566[/C][C]2854.62836994335[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]19257.3595287048[/C][C]5303.64047129522[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]21518.7377067368[/C][C]-4109.73770673676[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]18127.0867084793[/C][C]-6613.08670847928[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]13152.9893589443[/C][C]18361.0106410557[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]23283.4941934978[/C][C]3787.50580650217[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]24807.6073983456[/C][C]4654.39260165436[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]26913.5894433031[/C][C]-808.589443303106[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]25761.4707643112[/C][C]-3364.47076431117[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]23042.2413731134[/C][C]800.758626886563[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]22809.7786275816[/C][C]-1104.77862758158[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]21429.0708501344[/C][C]-3340.07085013435[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18672.1200852641[/C][C]2091.87991473585[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]19173.219122223[/C][C]6142.78087777705[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]22169.6961175774[/C][C]-4465.69611757741[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]18797.8256178991[/C][C]-3249.8256178991[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]16101.9448518803[/C][C]11927.0551481197[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]22596.2243600703[/C][C]6786.7756399297[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]26133.0225215423[/C][C]10304.9774784577[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]31908.275253418[/C][C]125.72474658204[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]31636.0550466646[/C][C]-8957.05504666461[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25837.8075297262[/C][C]-1518.80752972615[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]24438.1587196983[/C][C]-6434.15871969827[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]20025.2352698412[/C][C]-2488.23526984119[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]17921.6175289985[/C][C]2444.38247100153[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]18784.3600320329[/C][C]3997.63996796707[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]20627.4526801149[/C][C]-1458.4526801149[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]19207.2259372753[/C][C]-5400.22593727535[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]15367.1142759817[/C][C]14375.8857240183[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]23485.4634342406[/C][C]2105.5365657594[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]24342.0251715702[/C][C]4753.97482842984[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26840.6141734953[/C][C]-358.61417349528[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]26295.7806192313[/C][C]-3890.78061923132[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]23596.1123036503[/C][C]3447.88769634968[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]25307.0404807588[/C][C]-7337.04048075883[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]20503.6128602848[/C][C]-1773.61286028477[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]18980.9740096464[/C][C]703.025990353566[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]18940.2142334743[/C][C]844.785766525703[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]18995.8049367975[/C][C]-516.804936797522[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]18234.8303580312[/C][C]-7536.83035803121[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232272&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
343129382944835
43786339840.6072043033-1977.60720430333
53595337310.3126917717-1357.31269177168
62913335129.192688473-5996.19268847296
72469330105.3742131567-5412.37421315672
82220525350.9424083429-3145.94240834287
92172521898.3112741974-173.311274197404
102719220209.7566427556982.24335724496
112179022873.6277044576-1083.6277044576
121325320728.6249365729-7475.62493657291
133770214677.889087532623024.1109124674
143036427082.32835977653281.67164022354
153260927801.35903103114807.64096896886
163021229496.1308896812715.869110318847
172996528769.52410050691195.47589949314
182835228345.06736225866.93263774138904
192581427214.3885164144-1400.38851641443
202241425227.305737017-2813.30573701704
212050622360.2456169724-1854.24561697241
222880620036.5586160958769.44138390503
232222824151.9328411378-1923.93284113783
241397121884.9320059536-7913.93200595359
253684515944.814302354220900.1856976458
263533827427.71422328287910.2857767172
273502231304.40068661233717.59931338768
283477732742.75376701232034.24623298775
292688733209.8840829498-6322.88408294984
302397028619.9713536828-4649.97135368283
312278024957.5923105983-2177.59231059827
321735122733.280154997-5382.28015499698
332138218527.37163005662854.62836994335
342456119257.35952870485303.64047129522
351740921518.7377067368-4109.73770673676
361151418127.0867084793-6613.08670847928
373151413152.989358944318361.0106410557
382707123283.49419349783787.50580650217
392946224807.60739834564654.39260165436
402610526913.5894433031-808.589443303106
412239725761.4707643112-3364.47076431117
422384323042.2413731134800.758626886563
432170522809.7786275816-1104.77862758158
441808921429.0708501344-3340.07085013435
452076418672.12008526412091.87991473585
462531619173.2191222236142.78087777705
471770422169.6961175774-4465.69611757741
481554818797.8256178991-3249.8256178991
492802916101.944851880311927.0551481197
502938322596.22436007036786.7756399297
513643826133.022521542310304.9774784577
523203431908.275253418125.72474658204
532267931636.0550466646-8957.05504666461
542431925837.8075297262-1518.80752972615
551800424438.1587196983-6434.15871969827
561753720025.2352698412-2488.23526984119
572036617921.61752899852444.38247100153
582278218784.36003203293997.63996796707
591916920627.4526801149-1458.4526801149
601380719207.2259372753-5400.22593727535
612974315367.114275981714375.8857240183
622559123485.46343424062105.5365657594
632909624342.02517157024753.97482842984
642648226840.6141734953-358.61417349528
652240526295.7806192313-3890.78061923132
662704423596.11230365033447.88769634968
671797025307.0404807588-7337.04048075883
681873020503.6128602848-1773.61286028477
691968418980.9740096464703.025990353566
701978518940.2142334743844.785766525703
711847918995.8049367975-516.804936797522
721069818234.8303580312-7536.83035803121







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7313194.0241901087447.14858639853825940.8997938189
7412632.1673052562-2289.8490200061627554.1836305185
7512070.3104204036-4832.881560973828973.502401781
7611508.453535551-7245.3076196786330262.2146907806
7710946.5966506984-9564.1391260335731457.3324274304
7810384.7397658458-11813.11618992332582.5957216147
799822.88288099327-14008.480366313233654.2461282998
809261.02599614069-16161.881265739434683.9332580208
818699.16911128811-18281.982889016535680.3211115927
828137.31222643554-20375.415791845136650.0402447161
837575.45534158296-22447.373255271337598.2839384372
847013.59845673038-24502.001378362338529.1982918231

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 13194.0241901087 & 447.148586398538 & 25940.8997938189 \tabularnewline
74 & 12632.1673052562 & -2289.84902000616 & 27554.1836305185 \tabularnewline
75 & 12070.3104204036 & -4832.8815609738 & 28973.502401781 \tabularnewline
76 & 11508.453535551 & -7245.30761967863 & 30262.2146907806 \tabularnewline
77 & 10946.5966506984 & -9564.13912603357 & 31457.3324274304 \tabularnewline
78 & 10384.7397658458 & -11813.116189923 & 32582.5957216147 \tabularnewline
79 & 9822.88288099327 & -14008.4803663132 & 33654.2461282998 \tabularnewline
80 & 9261.02599614069 & -16161.8812657394 & 34683.9332580208 \tabularnewline
81 & 8699.16911128811 & -18281.9828890165 & 35680.3211115927 \tabularnewline
82 & 8137.31222643554 & -20375.4157918451 & 36650.0402447161 \tabularnewline
83 & 7575.45534158296 & -22447.3732552713 & 37598.2839384372 \tabularnewline
84 & 7013.59845673038 & -24502.0013783623 & 38529.1982918231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232272&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]13194.0241901087[/C][C]447.148586398538[/C][C]25940.8997938189[/C][/ROW]
[ROW][C]74[/C][C]12632.1673052562[/C][C]-2289.84902000616[/C][C]27554.1836305185[/C][/ROW]
[ROW][C]75[/C][C]12070.3104204036[/C][C]-4832.8815609738[/C][C]28973.502401781[/C][/ROW]
[ROW][C]76[/C][C]11508.453535551[/C][C]-7245.30761967863[/C][C]30262.2146907806[/C][/ROW]
[ROW][C]77[/C][C]10946.5966506984[/C][C]-9564.13912603357[/C][C]31457.3324274304[/C][/ROW]
[ROW][C]78[/C][C]10384.7397658458[/C][C]-11813.116189923[/C][C]32582.5957216147[/C][/ROW]
[ROW][C]79[/C][C]9822.88288099327[/C][C]-14008.4803663132[/C][C]33654.2461282998[/C][/ROW]
[ROW][C]80[/C][C]9261.02599614069[/C][C]-16161.8812657394[/C][C]34683.9332580208[/C][/ROW]
[ROW][C]81[/C][C]8699.16911128811[/C][C]-18281.9828890165[/C][C]35680.3211115927[/C][/ROW]
[ROW][C]82[/C][C]8137.31222643554[/C][C]-20375.4157918451[/C][C]36650.0402447161[/C][/ROW]
[ROW][C]83[/C][C]7575.45534158296[/C][C]-22447.3732552713[/C][C]37598.2839384372[/C][/ROW]
[ROW][C]84[/C][C]7013.59845673038[/C][C]-24502.0013783623[/C][C]38529.1982918231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232272&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232272&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
7313194.0241901087447.14858639853825940.8997938189
7412632.1673052562-2289.8490200061627554.1836305185
7512070.3104204036-4832.881560973828973.502401781
7611508.453535551-7245.3076196786330262.2146907806
7710946.5966506984-9564.1391260335731457.3324274304
7810384.7397658458-11813.11618992332582.5957216147
799822.88288099327-14008.480366313233654.2461282998
809261.02599614069-16161.881265739434683.9332580208
818699.16911128811-18281.982889016535680.3211115927
828137.31222643554-20375.415791845136650.0402447161
837575.45534158296-22447.373255271337598.2839384372
847013.59845673038-24502.001378362338529.1982918231



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