Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 31 May 2010 13:20:15 +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/May/31/t1275312074xjfbfqpnbgfq97v.htm/, Retrieved Mon, 29 Apr 2024 10:52:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76734, Retrieved Mon, 29 Apr 2024 10:52:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact169
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Inschrijving nieu...] [2010-05-31 13:20:15] [181f2439255053cc457d7672472fa443] [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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76734&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76734&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.594274923316697
beta0.0241142539120687
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.594274923316697 \tabularnewline
beta & 0.0241142539120687 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76734&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]0.594274923316697[/C][/ROW]
[ROW][C]beta[/C][C]0.0241142539120687[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76734&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
alpha0.594274923316697
beta0.0241142539120687
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
343129382944835
43786339840.6072043033-1977.60720430332
53595337310.3126917716-1357.31269177163
62913335129.1926884729-5996.19268847293
72469330105.3742131567-5412.3742131567
82220525350.9424083429-3145.94240834294
92172521898.3112741975-173.311274197535
102719220209.75664275526982.24335724478
112179022873.6277044578-1083.62770445777
121325320728.624936573-7475.62493657304
133770214677.889087532823024.1109124672
143036427082.32835977663281.67164022343
153260927801.35903103114807.64096896892
163021229496.130889681715.86911031901
172996528769.52410050661195.47589949338
182835228345.06736225836.93263774165825
192581427214.3885164141-1400.38851641414
202241425227.3057370168-2813.30573701676
212050622360.2456169722-1854.24561697216
222880620036.55861609478769.44138390525
232222824151.9328411376-1923.9328411376
241397121884.9320059533-7913.93200595332
253684515944.81430235420900.185697646
263533827427.71422328257910.28577671746
273502231304.40068661193717.5993133881
283477732742.75376701172034.24623298828
292688733209.8840829492-6322.88408294923
302397028619.9713536822-4649.97135368221
312278024957.5923105977-2177.59231059771
321735122733.2801549965-5382.28015499649
332138218527.37163005622854.62836994377
342456119257.35952870445303.64047129559
351740921518.7377067364-4109.73770673639
361151418127.0867084789-6613.08670847889
373151413152.98935894418361.010641056
382707123283.49419349753787.50580650251
392946224807.60739834524654.39260165482
402610526913.5894433026-808.58944330256
412239725761.4707643106-3364.47076431058
422384323042.2413731128800.758626887156
432170522809.778627581-1104.77862758102
441808921429.0708501338-3340.0708501338
452076418672.12008526362091.87991473636
462531619173.21912222256142.78087777753
471770422169.6961175769-4465.69611757692
481554818797.8256178986-3249.82561789859
492802916101.944851879811927.0551481202
502938322596.22436006986786.77563993018
513643826133.022521541710304.9774784583
523203431908.2752534173125.724746582709
532267931636.0550466638-8957.05504666383
542431925837.8075297254-1518.80752972539
551800424438.1587196976-6434.15871969757
561753720025.2352698406-2488.23526984057
572036617921.61752899792444.38247100207
582278218784.36003203243997.63996796756
591916920627.4526801144-1458.45268011441
601380719207.2259372748-5400.22593727484
612974315367.114275981214375.8857240188
622559123485.46343424012105.53656575987
632909624342.02517156964753.9748284304
642648226840.6141734947-358.614173494661
652240526295.7806192307-3890.78061923066
662704423596.11230364973447.88769635033
671797025307.0404807582-7337.0404807582
681873020503.6128602842-1773.61286028416
691968418980.9740096459703.025990354101
701978518940.2142334738844.78576652619
711847918995.804936797-516.804936797049
721069818234.8303580307-7536.83035803075

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 43129 & 38294 & 4835 \tabularnewline
4 & 37863 & 39840.6072043033 & -1977.60720430332 \tabularnewline
5 & 35953 & 37310.3126917716 & -1357.31269177163 \tabularnewline
6 & 29133 & 35129.1926884729 & -5996.19268847293 \tabularnewline
7 & 24693 & 30105.3742131567 & -5412.3742131567 \tabularnewline
8 & 22205 & 25350.9424083429 & -3145.94240834294 \tabularnewline
9 & 21725 & 21898.3112741975 & -173.311274197535 \tabularnewline
10 & 27192 & 20209.7566427552 & 6982.24335724478 \tabularnewline
11 & 21790 & 22873.6277044578 & -1083.62770445777 \tabularnewline
12 & 13253 & 20728.624936573 & -7475.62493657304 \tabularnewline
13 & 37702 & 14677.8890875328 & 23024.1109124672 \tabularnewline
14 & 30364 & 27082.3283597766 & 3281.67164022343 \tabularnewline
15 & 32609 & 27801.3590310311 & 4807.64096896892 \tabularnewline
16 & 30212 & 29496.130889681 & 715.86911031901 \tabularnewline
17 & 29965 & 28769.5241005066 & 1195.47589949338 \tabularnewline
18 & 28352 & 28345.0673622583 & 6.93263774165825 \tabularnewline
19 & 25814 & 27214.3885164141 & -1400.38851641414 \tabularnewline
20 & 22414 & 25227.3057370168 & -2813.30573701676 \tabularnewline
21 & 20506 & 22360.2456169722 & -1854.24561697216 \tabularnewline
22 & 28806 & 20036.5586160947 & 8769.44138390525 \tabularnewline
23 & 22228 & 24151.9328411376 & -1923.9328411376 \tabularnewline
24 & 13971 & 21884.9320059533 & -7913.93200595332 \tabularnewline
25 & 36845 & 15944.814302354 & 20900.185697646 \tabularnewline
26 & 35338 & 27427.7142232825 & 7910.28577671746 \tabularnewline
27 & 35022 & 31304.4006866119 & 3717.5993133881 \tabularnewline
28 & 34777 & 32742.7537670117 & 2034.24623298828 \tabularnewline
29 & 26887 & 33209.8840829492 & -6322.88408294923 \tabularnewline
30 & 23970 & 28619.9713536822 & -4649.97135368221 \tabularnewline
31 & 22780 & 24957.5923105977 & -2177.59231059771 \tabularnewline
32 & 17351 & 22733.2801549965 & -5382.28015499649 \tabularnewline
33 & 21382 & 18527.3716300562 & 2854.62836994377 \tabularnewline
34 & 24561 & 19257.3595287044 & 5303.64047129559 \tabularnewline
35 & 17409 & 21518.7377067364 & -4109.73770673639 \tabularnewline
36 & 11514 & 18127.0867084789 & -6613.08670847889 \tabularnewline
37 & 31514 & 13152.989358944 & 18361.010641056 \tabularnewline
38 & 27071 & 23283.4941934975 & 3787.50580650251 \tabularnewline
39 & 29462 & 24807.6073983452 & 4654.39260165482 \tabularnewline
40 & 26105 & 26913.5894433026 & -808.58944330256 \tabularnewline
41 & 22397 & 25761.4707643106 & -3364.47076431058 \tabularnewline
42 & 23843 & 23042.2413731128 & 800.758626887156 \tabularnewline
43 & 21705 & 22809.778627581 & -1104.77862758102 \tabularnewline
44 & 18089 & 21429.0708501338 & -3340.0708501338 \tabularnewline
45 & 20764 & 18672.1200852636 & 2091.87991473636 \tabularnewline
46 & 25316 & 19173.2191222225 & 6142.78087777753 \tabularnewline
47 & 17704 & 22169.6961175769 & -4465.69611757692 \tabularnewline
48 & 15548 & 18797.8256178986 & -3249.82561789859 \tabularnewline
49 & 28029 & 16101.9448518798 & 11927.0551481202 \tabularnewline
50 & 29383 & 22596.2243600698 & 6786.77563993018 \tabularnewline
51 & 36438 & 26133.0225215417 & 10304.9774784583 \tabularnewline
52 & 32034 & 31908.2752534173 & 125.724746582709 \tabularnewline
53 & 22679 & 31636.0550466638 & -8957.05504666383 \tabularnewline
54 & 24319 & 25837.8075297254 & -1518.80752972539 \tabularnewline
55 & 18004 & 24438.1587196976 & -6434.15871969757 \tabularnewline
56 & 17537 & 20025.2352698406 & -2488.23526984057 \tabularnewline
57 & 20366 & 17921.6175289979 & 2444.38247100207 \tabularnewline
58 & 22782 & 18784.3600320324 & 3997.63996796756 \tabularnewline
59 & 19169 & 20627.4526801144 & -1458.45268011441 \tabularnewline
60 & 13807 & 19207.2259372748 & -5400.22593727484 \tabularnewline
61 & 29743 & 15367.1142759812 & 14375.8857240188 \tabularnewline
62 & 25591 & 23485.4634342401 & 2105.53656575987 \tabularnewline
63 & 29096 & 24342.0251715696 & 4753.9748284304 \tabularnewline
64 & 26482 & 26840.6141734947 & -358.614173494661 \tabularnewline
65 & 22405 & 26295.7806192307 & -3890.78061923066 \tabularnewline
66 & 27044 & 23596.1123036497 & 3447.88769635033 \tabularnewline
67 & 17970 & 25307.0404807582 & -7337.0404807582 \tabularnewline
68 & 18730 & 20503.6128602842 & -1773.61286028416 \tabularnewline
69 & 19684 & 18980.9740096459 & 703.025990354101 \tabularnewline
70 & 19785 & 18940.2142334738 & 844.78576652619 \tabularnewline
71 & 18479 & 18995.804936797 & -516.804936797049 \tabularnewline
72 & 10698 & 18234.8303580307 & -7536.83035803075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76734&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]-1977.60720430332[/C][/ROW]
[ROW][C]5[/C][C]35953[/C][C]37310.3126917716[/C][C]-1357.31269177163[/C][/ROW]
[ROW][C]6[/C][C]29133[/C][C]35129.1926884729[/C][C]-5996.19268847293[/C][/ROW]
[ROW][C]7[/C][C]24693[/C][C]30105.3742131567[/C][C]-5412.3742131567[/C][/ROW]
[ROW][C]8[/C][C]22205[/C][C]25350.9424083429[/C][C]-3145.94240834294[/C][/ROW]
[ROW][C]9[/C][C]21725[/C][C]21898.3112741975[/C][C]-173.311274197535[/C][/ROW]
[ROW][C]10[/C][C]27192[/C][C]20209.7566427552[/C][C]6982.24335724478[/C][/ROW]
[ROW][C]11[/C][C]21790[/C][C]22873.6277044578[/C][C]-1083.62770445777[/C][/ROW]
[ROW][C]12[/C][C]13253[/C][C]20728.624936573[/C][C]-7475.62493657304[/C][/ROW]
[ROW][C]13[/C][C]37702[/C][C]14677.8890875328[/C][C]23024.1109124672[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]27082.3283597766[/C][C]3281.67164022343[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]27801.3590310311[/C][C]4807.64096896892[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]29496.130889681[/C][C]715.86911031901[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]28769.5241005066[/C][C]1195.47589949338[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28345.0673622583[/C][C]6.93263774165825[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]27214.3885164141[/C][C]-1400.38851641414[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]25227.3057370168[/C][C]-2813.30573701676[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]22360.2456169722[/C][C]-1854.24561697216[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]20036.5586160947[/C][C]8769.44138390525[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]24151.9328411376[/C][C]-1923.9328411376[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]21884.9320059533[/C][C]-7913.93200595332[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]15944.814302354[/C][C]20900.185697646[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]27427.7142232825[/C][C]7910.28577671746[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]31304.4006866119[/C][C]3717.5993133881[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]32742.7537670117[/C][C]2034.24623298828[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]33209.8840829492[/C][C]-6322.88408294923[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28619.9713536822[/C][C]-4649.97135368221[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]24957.5923105977[/C][C]-2177.59231059771[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]22733.2801549965[/C][C]-5382.28015499649[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18527.3716300562[/C][C]2854.62836994377[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]19257.3595287044[/C][C]5303.64047129559[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]21518.7377067364[/C][C]-4109.73770673639[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]18127.0867084789[/C][C]-6613.08670847889[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]13152.989358944[/C][C]18361.010641056[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]23283.4941934975[/C][C]3787.50580650251[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]24807.6073983452[/C][C]4654.39260165482[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]26913.5894433026[/C][C]-808.58944330256[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]25761.4707643106[/C][C]-3364.47076431058[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]23042.2413731128[/C][C]800.758626887156[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]22809.778627581[/C][C]-1104.77862758102[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]21429.0708501338[/C][C]-3340.0708501338[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18672.1200852636[/C][C]2091.87991473636[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]19173.2191222225[/C][C]6142.78087777753[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]22169.6961175769[/C][C]-4465.69611757692[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]18797.8256178986[/C][C]-3249.82561789859[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]16101.9448518798[/C][C]11927.0551481202[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]22596.2243600698[/C][C]6786.77563993018[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]26133.0225215417[/C][C]10304.9774784583[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]31908.2752534173[/C][C]125.724746582709[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]31636.0550466638[/C][C]-8957.05504666383[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25837.8075297254[/C][C]-1518.80752972539[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]24438.1587196976[/C][C]-6434.15871969757[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]20025.2352698406[/C][C]-2488.23526984057[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]17921.6175289979[/C][C]2444.38247100207[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]18784.3600320324[/C][C]3997.63996796756[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]20627.4526801144[/C][C]-1458.45268011441[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]19207.2259372748[/C][C]-5400.22593727484[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]15367.1142759812[/C][C]14375.8857240188[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]23485.4634342401[/C][C]2105.53656575987[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]24342.0251715696[/C][C]4753.9748284304[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26840.6141734947[/C][C]-358.614173494661[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]26295.7806192307[/C][C]-3890.78061923066[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]23596.1123036497[/C][C]3447.88769635033[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]25307.0404807582[/C][C]-7337.0404807582[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]20503.6128602842[/C][C]-1773.61286028416[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]18980.9740096459[/C][C]703.025990354101[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]18940.2142334738[/C][C]844.78576652619[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]18995.804936797[/C][C]-516.804936797049[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]18234.8303580307[/C][C]-7536.83035803075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76734&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
43786339840.6072043033-1977.60720430332
53595337310.3126917716-1357.31269177163
62913335129.1926884729-5996.19268847293
72469330105.3742131567-5412.3742131567
82220525350.9424083429-3145.94240834294
92172521898.3112741975-173.311274197535
102719220209.75664275526982.24335724478
112179022873.6277044578-1083.62770445777
121325320728.624936573-7475.62493657304
133770214677.889087532823024.1109124672
143036427082.32835977663281.67164022343
153260927801.35903103114807.64096896892
163021229496.130889681715.86911031901
172996528769.52410050661195.47589949338
182835228345.06736225836.93263774165825
192581427214.3885164141-1400.38851641414
202241425227.3057370168-2813.30573701676
212050622360.2456169722-1854.24561697216
222880620036.55861609478769.44138390525
232222824151.9328411376-1923.9328411376
241397121884.9320059533-7913.93200595332
253684515944.81430235420900.185697646
263533827427.71422328257910.28577671746
273502231304.40068661193717.5993133881
283477732742.75376701172034.24623298828
292688733209.8840829492-6322.88408294923
302397028619.9713536822-4649.97135368221
312278024957.5923105977-2177.59231059771
321735122733.2801549965-5382.28015499649
332138218527.37163005622854.62836994377
342456119257.35952870445303.64047129559
351740921518.7377067364-4109.73770673639
361151418127.0867084789-6613.08670847889
373151413152.98935894418361.010641056
382707123283.49419349753787.50580650251
392946224807.60739834524654.39260165482
402610526913.5894433026-808.58944330256
412239725761.4707643106-3364.47076431058
422384323042.2413731128800.758626887156
432170522809.778627581-1104.77862758102
441808921429.0708501338-3340.0708501338
452076418672.12008526362091.87991473636
462531619173.21912222256142.78087777753
471770422169.6961175769-4465.69611757692
481554818797.8256178986-3249.82561789859
492802916101.944851879811927.0551481202
502938322596.22436006986786.77563993018
513643826133.022521541710304.9774784583
523203431908.2752534173125.724746582709
532267931636.0550466638-8957.05504666383
542431925837.8075297254-1518.80752972539
551800424438.1587196976-6434.15871969757
561753720025.2352698406-2488.23526984057
572036617921.61752899792444.38247100207
582278218784.36003203243997.63996796756
591916920627.4526801144-1458.45268011441
601380719207.2259372748-5400.22593727484
612974315367.114275981214375.8857240188
622559123485.46343424012105.53656575987
632909624342.02517156964753.9748284304
642648226840.6141734947-358.614173494661
652240526295.7806192307-3890.78061923066
662704423596.11230364973447.88769635033
671797025307.0404807582-7337.0404807582
681873020503.6128602842-1773.61286028416
691968418980.9740096459703.025990354101
701978518940.2142334738844.78576652619
711847918995.804936797-516.804936797049
721069818234.8303580307-7536.83035803075







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7313194.0241901083447.14858639821125940.8997938184
7412632.1673052555-2289.8490200066327554.1836305177
7512070.3104204028-4832.8815609743728973.5024017799
7611508.45353555-7245.3076196792630262.2146907793
7710946.5966506972-9564.1391260342231457.3324274287
7810384.7397658445-11813.116189923732582.5957216126
799822.88288099172-14008.480366313833654.2461282973
809261.02599613895-16161.8812657434683.9332580179
818699.16911128618-18281.98288901735680.3211115893
828137.31222643342-20375.415791845536650.0402447123
837575.45534158065-22447.373255271637598.2839384329
847013.59845672789-24502.001378362538529.1982918183

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 13194.0241901083 & 447.148586398211 & 25940.8997938184 \tabularnewline
74 & 12632.1673052555 & -2289.84902000663 & 27554.1836305177 \tabularnewline
75 & 12070.3104204028 & -4832.88156097437 & 28973.5024017799 \tabularnewline
76 & 11508.45353555 & -7245.30761967926 & 30262.2146907793 \tabularnewline
77 & 10946.5966506972 & -9564.13912603422 & 31457.3324274287 \tabularnewline
78 & 10384.7397658445 & -11813.1161899237 & 32582.5957216126 \tabularnewline
79 & 9822.88288099172 & -14008.4803663138 & 33654.2461282973 \tabularnewline
80 & 9261.02599613895 & -16161.88126574 & 34683.9332580179 \tabularnewline
81 & 8699.16911128618 & -18281.982889017 & 35680.3211115893 \tabularnewline
82 & 8137.31222643342 & -20375.4157918455 & 36650.0402447123 \tabularnewline
83 & 7575.45534158065 & -22447.3732552716 & 37598.2839384329 \tabularnewline
84 & 7013.59845672789 & -24502.0013783625 & 38529.1982918183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76734&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]13194.0241901083[/C][C]447.148586398211[/C][C]25940.8997938184[/C][/ROW]
[ROW][C]74[/C][C]12632.1673052555[/C][C]-2289.84902000663[/C][C]27554.1836305177[/C][/ROW]
[ROW][C]75[/C][C]12070.3104204028[/C][C]-4832.88156097437[/C][C]28973.5024017799[/C][/ROW]
[ROW][C]76[/C][C]11508.45353555[/C][C]-7245.30761967926[/C][C]30262.2146907793[/C][/ROW]
[ROW][C]77[/C][C]10946.5966506972[/C][C]-9564.13912603422[/C][C]31457.3324274287[/C][/ROW]
[ROW][C]78[/C][C]10384.7397658445[/C][C]-11813.1161899237[/C][C]32582.5957216126[/C][/ROW]
[ROW][C]79[/C][C]9822.88288099172[/C][C]-14008.4803663138[/C][C]33654.2461282973[/C][/ROW]
[ROW][C]80[/C][C]9261.02599613895[/C][C]-16161.88126574[/C][C]34683.9332580179[/C][/ROW]
[ROW][C]81[/C][C]8699.16911128618[/C][C]-18281.982889017[/C][C]35680.3211115893[/C][/ROW]
[ROW][C]82[/C][C]8137.31222643342[/C][C]-20375.4157918455[/C][C]36650.0402447123[/C][/ROW]
[ROW][C]83[/C][C]7575.45534158065[/C][C]-22447.3732552716[/C][C]37598.2839384329[/C][/ROW]
[ROW][C]84[/C][C]7013.59845672789[/C][C]-24502.0013783625[/C][C]38529.1982918183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76734&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76734&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
7313194.0241901083447.14858639821125940.8997938184
7412632.1673052555-2289.8490200066327554.1836305177
7512070.3104204028-4832.8815609743728973.5024017799
7611508.45353555-7245.3076196792630262.2146907793
7710946.5966506972-9564.1391260342231457.3324274287
7810384.7397658445-11813.116189923732582.5957216126
799822.88288099172-14008.480366313833654.2461282973
809261.02599613895-16161.8812657434683.9332580179
818699.16911128618-18281.98288901735680.3211115893
828137.31222643342-20375.415791845536650.0402447123
837575.45534158065-22447.373255271637598.2839384329
847013.59845672789-24502.001378362538529.1982918183



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')