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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 computationThu, 30 Dec 2010 10:47:18 +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/30/t1293705932d9582nd1fku2rhf.htm/, Retrieved Fri, 03 May 2024 12:58:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117213, Retrieved Fri, 03 May 2024 12:58:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact210
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 2 nieuw] [2010-12-30 10:47:18] [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=117213&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=117213&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117213&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
alpha0.277819840158911
beta0.00090316977252793
gamma0.294847015488245

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.277819840158911 \tabularnewline
beta & 0.00090316977252793 \tabularnewline
gamma & 0.294847015488245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117213&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]0.277819840158911[/C][/ROW]
[ROW][C]beta[/C][C]0.00090316977252793[/C][/ROW]
[ROW][C]gamma[/C][C]0.294847015488245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117213&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117213&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
alpha0.277819840158911
beta0.00090316977252793
gamma0.294847015488245







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137024971014.3015814803-765.301581480278
143925339710.8527884234-457.852788423377
154706047635.4527672573-575.452767257251
164169741988.7273060676-291.727306067616
173870838660.95900439947.040995600968
184926748949.3990594912317.600940508848
193901839929.8661094887-911.866109488743
203222835309.4845196682-3081.48451966818
214087040094.9834112898775.016588710161
223938335911.82691986943471.17308013055
233457130958.29521593913612.70478406090
241206611475.7971259764590.202874023604
257093871750.0461991928-812.046199192831
263407740112.0952689126-6035.09526891258
274540946245.4962690537-836.496269053707
284080940737.497619828371.5023801717034
293701337663.1892276532-650.189227653245
304495347491.0277001042-2538.0277001042
313784837852.9863447481-4.98634474810387
323274533202.8648412825-457.864841282499
334341239397.86755429024014.1324457098
343493136666.7510991591-1735.75109915911
353300830494.57525016492513.42474983514
36862011053.1716924139-2433.17169241385
376890663108.16690708725797.83309291278
383955635157.34860501444398.65139498561
395066945108.63906317705560.36093682295
403643241483.5710994757-5051.57109947571
414089136885.73214922524005.26785077483
424842847768.6412092459659.358790754122
433622239253.8308082136-3031.83080821356
443342533597.9757201134-172.975720113449
453940140929.7030661447-1528.70306614474
463796735533.80313151082433.19686848923
473480131361.56075910853439.43924089148
481265710697.12409712171959.87590287834
496911673361.285399745-4245.28539974494
504151939479.78070197932039.21929802069
515132149649.13077428591671.86922571412
523852942297.7842967754-3768.78429677542
534154739893.07788633871653.92211366131
545207349766.34582290272306.65417709729
553840140458.2728678946-2057.27286789462
564089835452.26699055265445.73300944739
574043944796.7423514500-4357.74235144995
584188839108.37272514342779.62727485658
593789834834.47376562543063.52623437461
60877111982.0036238100-3211.00362381003
616818468898.50359516-714.503595159971
625053038461.203550519912068.7964494801
634722151654.8489989598-4433.84899895985
644175641437.4011455228318.598854477248
654563341317.35354507194315.64645492812
664813852495.176788684-4357.17678868401
673948640319.3352204068-833.335220406778
683934137159.28000716522181.71999283475
694111743429.5369687552-2312.53696875516
704162939809.87752936881819.12247063118
712972235333.79127047-5611.79127047003
72705410448.2665921740-3394.26659217402
735667662778.1260751-6102.12607509996
743487036366.7567259867-1496.75672598666
753511741031.6350956609-5914.63509566088
763016933017.9210381851-2848.92103818506
773093632678.4925929045-1742.49259290455
783569938170.4897376950-2471.48973769496
793322829851.66445881013376.33554118988
802773328996.6041595666-1263.60415956665
813366632138.20919937091527.79080062906
823542930918.99466427904510.00533572104
832743826921.1605618068516.83943819315
8481708015.10017403475154.899825965254

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 70249 & 71014.3015814803 & -765.301581480278 \tabularnewline
14 & 39253 & 39710.8527884234 & -457.852788423377 \tabularnewline
15 & 47060 & 47635.4527672573 & -575.452767257251 \tabularnewline
16 & 41697 & 41988.7273060676 & -291.727306067616 \tabularnewline
17 & 38708 & 38660.959004399 & 47.040995600968 \tabularnewline
18 & 49267 & 48949.3990594912 & 317.600940508848 \tabularnewline
19 & 39018 & 39929.8661094887 & -911.866109488743 \tabularnewline
20 & 32228 & 35309.4845196682 & -3081.48451966818 \tabularnewline
21 & 40870 & 40094.9834112898 & 775.016588710161 \tabularnewline
22 & 39383 & 35911.8269198694 & 3471.17308013055 \tabularnewline
23 & 34571 & 30958.2952159391 & 3612.70478406090 \tabularnewline
24 & 12066 & 11475.7971259764 & 590.202874023604 \tabularnewline
25 & 70938 & 71750.0461991928 & -812.046199192831 \tabularnewline
26 & 34077 & 40112.0952689126 & -6035.09526891258 \tabularnewline
27 & 45409 & 46245.4962690537 & -836.496269053707 \tabularnewline
28 & 40809 & 40737.4976198283 & 71.5023801717034 \tabularnewline
29 & 37013 & 37663.1892276532 & -650.189227653245 \tabularnewline
30 & 44953 & 47491.0277001042 & -2538.0277001042 \tabularnewline
31 & 37848 & 37852.9863447481 & -4.98634474810387 \tabularnewline
32 & 32745 & 33202.8648412825 & -457.864841282499 \tabularnewline
33 & 43412 & 39397.8675542902 & 4014.1324457098 \tabularnewline
34 & 34931 & 36666.7510991591 & -1735.75109915911 \tabularnewline
35 & 33008 & 30494.5752501649 & 2513.42474983514 \tabularnewline
36 & 8620 & 11053.1716924139 & -2433.17169241385 \tabularnewline
37 & 68906 & 63108.1669070872 & 5797.83309291278 \tabularnewline
38 & 39556 & 35157.3486050144 & 4398.65139498561 \tabularnewline
39 & 50669 & 45108.6390631770 & 5560.36093682295 \tabularnewline
40 & 36432 & 41483.5710994757 & -5051.57109947571 \tabularnewline
41 & 40891 & 36885.7321492252 & 4005.26785077483 \tabularnewline
42 & 48428 & 47768.6412092459 & 659.358790754122 \tabularnewline
43 & 36222 & 39253.8308082136 & -3031.83080821356 \tabularnewline
44 & 33425 & 33597.9757201134 & -172.975720113449 \tabularnewline
45 & 39401 & 40929.7030661447 & -1528.70306614474 \tabularnewline
46 & 37967 & 35533.8031315108 & 2433.19686848923 \tabularnewline
47 & 34801 & 31361.5607591085 & 3439.43924089148 \tabularnewline
48 & 12657 & 10697.1240971217 & 1959.87590287834 \tabularnewline
49 & 69116 & 73361.285399745 & -4245.28539974494 \tabularnewline
50 & 41519 & 39479.7807019793 & 2039.21929802069 \tabularnewline
51 & 51321 & 49649.1307742859 & 1671.86922571412 \tabularnewline
52 & 38529 & 42297.7842967754 & -3768.78429677542 \tabularnewline
53 & 41547 & 39893.0778863387 & 1653.92211366131 \tabularnewline
54 & 52073 & 49766.3458229027 & 2306.65417709729 \tabularnewline
55 & 38401 & 40458.2728678946 & -2057.27286789462 \tabularnewline
56 & 40898 & 35452.2669905526 & 5445.73300944739 \tabularnewline
57 & 40439 & 44796.7423514500 & -4357.74235144995 \tabularnewline
58 & 41888 & 39108.3727251434 & 2779.62727485658 \tabularnewline
59 & 37898 & 34834.4737656254 & 3063.52623437461 \tabularnewline
60 & 8771 & 11982.0036238100 & -3211.00362381003 \tabularnewline
61 & 68184 & 68898.50359516 & -714.503595159971 \tabularnewline
62 & 50530 & 38461.2035505199 & 12068.7964494801 \tabularnewline
63 & 47221 & 51654.8489989598 & -4433.84899895985 \tabularnewline
64 & 41756 & 41437.4011455228 & 318.598854477248 \tabularnewline
65 & 45633 & 41317.3535450719 & 4315.64645492812 \tabularnewline
66 & 48138 & 52495.176788684 & -4357.17678868401 \tabularnewline
67 & 39486 & 40319.3352204068 & -833.335220406778 \tabularnewline
68 & 39341 & 37159.2800071652 & 2181.71999283475 \tabularnewline
69 & 41117 & 43429.5369687552 & -2312.53696875516 \tabularnewline
70 & 41629 & 39809.8775293688 & 1819.12247063118 \tabularnewline
71 & 29722 & 35333.79127047 & -5611.79127047003 \tabularnewline
72 & 7054 & 10448.2665921740 & -3394.26659217402 \tabularnewline
73 & 56676 & 62778.1260751 & -6102.12607509996 \tabularnewline
74 & 34870 & 36366.7567259867 & -1496.75672598666 \tabularnewline
75 & 35117 & 41031.6350956609 & -5914.63509566088 \tabularnewline
76 & 30169 & 33017.9210381851 & -2848.92103818506 \tabularnewline
77 & 30936 & 32678.4925929045 & -1742.49259290455 \tabularnewline
78 & 35699 & 38170.4897376950 & -2471.48973769496 \tabularnewline
79 & 33228 & 29851.6644588101 & 3376.33554118988 \tabularnewline
80 & 27733 & 28996.6041595666 & -1263.60415956665 \tabularnewline
81 & 33666 & 32138.2091993709 & 1527.79080062906 \tabularnewline
82 & 35429 & 30918.9946642790 & 4510.00533572104 \tabularnewline
83 & 27438 & 26921.1605618068 & 516.83943819315 \tabularnewline
84 & 8170 & 8015.10017403475 & 154.899825965254 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117213&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]70249[/C][C]71014.3015814803[/C][C]-765.301581480278[/C][/ROW]
[ROW][C]14[/C][C]39253[/C][C]39710.8527884234[/C][C]-457.852788423377[/C][/ROW]
[ROW][C]15[/C][C]47060[/C][C]47635.4527672573[/C][C]-575.452767257251[/C][/ROW]
[ROW][C]16[/C][C]41697[/C][C]41988.7273060676[/C][C]-291.727306067616[/C][/ROW]
[ROW][C]17[/C][C]38708[/C][C]38660.959004399[/C][C]47.040995600968[/C][/ROW]
[ROW][C]18[/C][C]49267[/C][C]48949.3990594912[/C][C]317.600940508848[/C][/ROW]
[ROW][C]19[/C][C]39018[/C][C]39929.8661094887[/C][C]-911.866109488743[/C][/ROW]
[ROW][C]20[/C][C]32228[/C][C]35309.4845196682[/C][C]-3081.48451966818[/C][/ROW]
[ROW][C]21[/C][C]40870[/C][C]40094.9834112898[/C][C]775.016588710161[/C][/ROW]
[ROW][C]22[/C][C]39383[/C][C]35911.8269198694[/C][C]3471.17308013055[/C][/ROW]
[ROW][C]23[/C][C]34571[/C][C]30958.2952159391[/C][C]3612.70478406090[/C][/ROW]
[ROW][C]24[/C][C]12066[/C][C]11475.7971259764[/C][C]590.202874023604[/C][/ROW]
[ROW][C]25[/C][C]70938[/C][C]71750.0461991928[/C][C]-812.046199192831[/C][/ROW]
[ROW][C]26[/C][C]34077[/C][C]40112.0952689126[/C][C]-6035.09526891258[/C][/ROW]
[ROW][C]27[/C][C]45409[/C][C]46245.4962690537[/C][C]-836.496269053707[/C][/ROW]
[ROW][C]28[/C][C]40809[/C][C]40737.4976198283[/C][C]71.5023801717034[/C][/ROW]
[ROW][C]29[/C][C]37013[/C][C]37663.1892276532[/C][C]-650.189227653245[/C][/ROW]
[ROW][C]30[/C][C]44953[/C][C]47491.0277001042[/C][C]-2538.0277001042[/C][/ROW]
[ROW][C]31[/C][C]37848[/C][C]37852.9863447481[/C][C]-4.98634474810387[/C][/ROW]
[ROW][C]32[/C][C]32745[/C][C]33202.8648412825[/C][C]-457.864841282499[/C][/ROW]
[ROW][C]33[/C][C]43412[/C][C]39397.8675542902[/C][C]4014.1324457098[/C][/ROW]
[ROW][C]34[/C][C]34931[/C][C]36666.7510991591[/C][C]-1735.75109915911[/C][/ROW]
[ROW][C]35[/C][C]33008[/C][C]30494.5752501649[/C][C]2513.42474983514[/C][/ROW]
[ROW][C]36[/C][C]8620[/C][C]11053.1716924139[/C][C]-2433.17169241385[/C][/ROW]
[ROW][C]37[/C][C]68906[/C][C]63108.1669070872[/C][C]5797.83309291278[/C][/ROW]
[ROW][C]38[/C][C]39556[/C][C]35157.3486050144[/C][C]4398.65139498561[/C][/ROW]
[ROW][C]39[/C][C]50669[/C][C]45108.6390631770[/C][C]5560.36093682295[/C][/ROW]
[ROW][C]40[/C][C]36432[/C][C]41483.5710994757[/C][C]-5051.57109947571[/C][/ROW]
[ROW][C]41[/C][C]40891[/C][C]36885.7321492252[/C][C]4005.26785077483[/C][/ROW]
[ROW][C]42[/C][C]48428[/C][C]47768.6412092459[/C][C]659.358790754122[/C][/ROW]
[ROW][C]43[/C][C]36222[/C][C]39253.8308082136[/C][C]-3031.83080821356[/C][/ROW]
[ROW][C]44[/C][C]33425[/C][C]33597.9757201134[/C][C]-172.975720113449[/C][/ROW]
[ROW][C]45[/C][C]39401[/C][C]40929.7030661447[/C][C]-1528.70306614474[/C][/ROW]
[ROW][C]46[/C][C]37967[/C][C]35533.8031315108[/C][C]2433.19686848923[/C][/ROW]
[ROW][C]47[/C][C]34801[/C][C]31361.5607591085[/C][C]3439.43924089148[/C][/ROW]
[ROW][C]48[/C][C]12657[/C][C]10697.1240971217[/C][C]1959.87590287834[/C][/ROW]
[ROW][C]49[/C][C]69116[/C][C]73361.285399745[/C][C]-4245.28539974494[/C][/ROW]
[ROW][C]50[/C][C]41519[/C][C]39479.7807019793[/C][C]2039.21929802069[/C][/ROW]
[ROW][C]51[/C][C]51321[/C][C]49649.1307742859[/C][C]1671.86922571412[/C][/ROW]
[ROW][C]52[/C][C]38529[/C][C]42297.7842967754[/C][C]-3768.78429677542[/C][/ROW]
[ROW][C]53[/C][C]41547[/C][C]39893.0778863387[/C][C]1653.92211366131[/C][/ROW]
[ROW][C]54[/C][C]52073[/C][C]49766.3458229027[/C][C]2306.65417709729[/C][/ROW]
[ROW][C]55[/C][C]38401[/C][C]40458.2728678946[/C][C]-2057.27286789462[/C][/ROW]
[ROW][C]56[/C][C]40898[/C][C]35452.2669905526[/C][C]5445.73300944739[/C][/ROW]
[ROW][C]57[/C][C]40439[/C][C]44796.7423514500[/C][C]-4357.74235144995[/C][/ROW]
[ROW][C]58[/C][C]41888[/C][C]39108.3727251434[/C][C]2779.62727485658[/C][/ROW]
[ROW][C]59[/C][C]37898[/C][C]34834.4737656254[/C][C]3063.52623437461[/C][/ROW]
[ROW][C]60[/C][C]8771[/C][C]11982.0036238100[/C][C]-3211.00362381003[/C][/ROW]
[ROW][C]61[/C][C]68184[/C][C]68898.50359516[/C][C]-714.503595159971[/C][/ROW]
[ROW][C]62[/C][C]50530[/C][C]38461.2035505199[/C][C]12068.7964494801[/C][/ROW]
[ROW][C]63[/C][C]47221[/C][C]51654.8489989598[/C][C]-4433.84899895985[/C][/ROW]
[ROW][C]64[/C][C]41756[/C][C]41437.4011455228[/C][C]318.598854477248[/C][/ROW]
[ROW][C]65[/C][C]45633[/C][C]41317.3535450719[/C][C]4315.64645492812[/C][/ROW]
[ROW][C]66[/C][C]48138[/C][C]52495.176788684[/C][C]-4357.17678868401[/C][/ROW]
[ROW][C]67[/C][C]39486[/C][C]40319.3352204068[/C][C]-833.335220406778[/C][/ROW]
[ROW][C]68[/C][C]39341[/C][C]37159.2800071652[/C][C]2181.71999283475[/C][/ROW]
[ROW][C]69[/C][C]41117[/C][C]43429.5369687552[/C][C]-2312.53696875516[/C][/ROW]
[ROW][C]70[/C][C]41629[/C][C]39809.8775293688[/C][C]1819.12247063118[/C][/ROW]
[ROW][C]71[/C][C]29722[/C][C]35333.79127047[/C][C]-5611.79127047003[/C][/ROW]
[ROW][C]72[/C][C]7054[/C][C]10448.2665921740[/C][C]-3394.26659217402[/C][/ROW]
[ROW][C]73[/C][C]56676[/C][C]62778.1260751[/C][C]-6102.12607509996[/C][/ROW]
[ROW][C]74[/C][C]34870[/C][C]36366.7567259867[/C][C]-1496.75672598666[/C][/ROW]
[ROW][C]75[/C][C]35117[/C][C]41031.6350956609[/C][C]-5914.63509566088[/C][/ROW]
[ROW][C]76[/C][C]30169[/C][C]33017.9210381851[/C][C]-2848.92103818506[/C][/ROW]
[ROW][C]77[/C][C]30936[/C][C]32678.4925929045[/C][C]-1742.49259290455[/C][/ROW]
[ROW][C]78[/C][C]35699[/C][C]38170.4897376950[/C][C]-2471.48973769496[/C][/ROW]
[ROW][C]79[/C][C]33228[/C][C]29851.6644588101[/C][C]3376.33554118988[/C][/ROW]
[ROW][C]80[/C][C]27733[/C][C]28996.6041595666[/C][C]-1263.60415956665[/C][/ROW]
[ROW][C]81[/C][C]33666[/C][C]32138.2091993709[/C][C]1527.79080062906[/C][/ROW]
[ROW][C]82[/C][C]35429[/C][C]30918.9946642790[/C][C]4510.00533572104[/C][/ROW]
[ROW][C]83[/C][C]27438[/C][C]26921.1605618068[/C][C]516.83943819315[/C][/ROW]
[ROW][C]84[/C][C]8170[/C][C]8015.10017403475[/C][C]154.899825965254[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117213&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117213&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
137024971014.3015814803-765.301581480278
143925339710.8527884234-457.852788423377
154706047635.4527672573-575.452767257251
164169741988.7273060676-291.727306067616
173870838660.95900439947.040995600968
184926748949.3990594912317.600940508848
193901839929.8661094887-911.866109488743
203222835309.4845196682-3081.48451966818
214087040094.9834112898775.016588710161
223938335911.82691986943471.17308013055
233457130958.29521593913612.70478406090
241206611475.7971259764590.202874023604
257093871750.0461991928-812.046199192831
263407740112.0952689126-6035.09526891258
274540946245.4962690537-836.496269053707
284080940737.497619828371.5023801717034
293701337663.1892276532-650.189227653245
304495347491.0277001042-2538.0277001042
313784837852.9863447481-4.98634474810387
323274533202.8648412825-457.864841282499
334341239397.86755429024014.1324457098
343493136666.7510991591-1735.75109915911
353300830494.57525016492513.42474983514
36862011053.1716924139-2433.17169241385
376890663108.16690708725797.83309291278
383955635157.34860501444398.65139498561
395066945108.63906317705560.36093682295
403643241483.5710994757-5051.57109947571
414089136885.73214922524005.26785077483
424842847768.6412092459659.358790754122
433622239253.8308082136-3031.83080821356
443342533597.9757201134-172.975720113449
453940140929.7030661447-1528.70306614474
463796735533.80313151082433.19686848923
473480131361.56075910853439.43924089148
481265710697.12409712171959.87590287834
496911673361.285399745-4245.28539974494
504151939479.78070197932039.21929802069
515132149649.13077428591671.86922571412
523852942297.7842967754-3768.78429677542
534154739893.07788633871653.92211366131
545207349766.34582290272306.65417709729
553840140458.2728678946-2057.27286789462
564089835452.26699055265445.73300944739
574043944796.7423514500-4357.74235144995
584188839108.37272514342779.62727485658
593789834834.47376562543063.52623437461
60877111982.0036238100-3211.00362381003
616818468898.50359516-714.503595159971
625053038461.203550519912068.7964494801
634722151654.8489989598-4433.84899895985
644175641437.4011455228318.598854477248
654563341317.35354507194315.64645492812
664813852495.176788684-4357.17678868401
673948640319.3352204068-833.335220406778
683934137159.28000716522181.71999283475
694111743429.5369687552-2312.53696875516
704162939809.87752936881819.12247063118
712972235333.79127047-5611.79127047003
72705410448.2665921740-3394.26659217402
735667662778.1260751-6102.12607509996
743487036366.7567259867-1496.75672598666
753511741031.6350956609-5914.63509566088
763016933017.9210381851-2848.92103818506
773093632678.4925929045-1742.49259290455
783569938170.4897376950-2471.48973769496
793322829851.66445881013376.33554118988
802773328996.6041595666-1263.60415956665
813366632138.20919937091527.79080062906
823542930918.99466427904510.00533572104
832743826921.1605618068516.83943819315
8481708015.10017403475154.899825965254







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8556360.218750908653154.188989139259566.248512678
8633974.560400165530585.759337986537363.3614623445
8737866.749012910433878.386693890541855.1113319303
8832173.693286875228079.195050532936268.1915232175
8932870.676028858528336.494078958237404.8579787587
9038878.774389914733456.434536758744301.1142430707
9132143.535820000827073.103461564337213.9681784373
9229305.988525659124211.590005776734400.3870455416
9333527.375875992627587.660360142039467.0913918432
9432464.153310638426381.757398531438546.5492227455
9526484.38738174220971.367479901931997.4072835820
967842.951655195856405.071612593449280.83169779825

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 56360.2187509086 & 53154.1889891392 & 59566.248512678 \tabularnewline
86 & 33974.5604001655 & 30585.7593379865 & 37363.3614623445 \tabularnewline
87 & 37866.7490129104 & 33878.3866938905 & 41855.1113319303 \tabularnewline
88 & 32173.6932868752 & 28079.1950505329 & 36268.1915232175 \tabularnewline
89 & 32870.6760288585 & 28336.4940789582 & 37404.8579787587 \tabularnewline
90 & 38878.7743899147 & 33456.4345367587 & 44301.1142430707 \tabularnewline
91 & 32143.5358200008 & 27073.1034615643 & 37213.9681784373 \tabularnewline
92 & 29305.9885256591 & 24211.5900057767 & 34400.3870455416 \tabularnewline
93 & 33527.3758759926 & 27587.6603601420 & 39467.0913918432 \tabularnewline
94 & 32464.1533106384 & 26381.7573985314 & 38546.5492227455 \tabularnewline
95 & 26484.387381742 & 20971.3674799019 & 31997.4072835820 \tabularnewline
96 & 7842.95165519585 & 6405.07161259344 & 9280.83169779825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117213&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]56360.2187509086[/C][C]53154.1889891392[/C][C]59566.248512678[/C][/ROW]
[ROW][C]86[/C][C]33974.5604001655[/C][C]30585.7593379865[/C][C]37363.3614623445[/C][/ROW]
[ROW][C]87[/C][C]37866.7490129104[/C][C]33878.3866938905[/C][C]41855.1113319303[/C][/ROW]
[ROW][C]88[/C][C]32173.6932868752[/C][C]28079.1950505329[/C][C]36268.1915232175[/C][/ROW]
[ROW][C]89[/C][C]32870.6760288585[/C][C]28336.4940789582[/C][C]37404.8579787587[/C][/ROW]
[ROW][C]90[/C][C]38878.7743899147[/C][C]33456.4345367587[/C][C]44301.1142430707[/C][/ROW]
[ROW][C]91[/C][C]32143.5358200008[/C][C]27073.1034615643[/C][C]37213.9681784373[/C][/ROW]
[ROW][C]92[/C][C]29305.9885256591[/C][C]24211.5900057767[/C][C]34400.3870455416[/C][/ROW]
[ROW][C]93[/C][C]33527.3758759926[/C][C]27587.6603601420[/C][C]39467.0913918432[/C][/ROW]
[ROW][C]94[/C][C]32464.1533106384[/C][C]26381.7573985314[/C][C]38546.5492227455[/C][/ROW]
[ROW][C]95[/C][C]26484.387381742[/C][C]20971.3674799019[/C][C]31997.4072835820[/C][/ROW]
[ROW][C]96[/C][C]7842.95165519585[/C][C]6405.07161259344[/C][C]9280.83169779825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117213&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117213&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
8556360.218750908653154.188989139259566.248512678
8633974.560400165530585.759337986537363.3614623445
8737866.749012910433878.386693890541855.1113319303
8832173.693286875228079.195050532936268.1915232175
8932870.676028858528336.494078958237404.8579787587
9038878.774389914733456.434536758744301.1142430707
9132143.535820000827073.103461564337213.9681784373
9229305.988525659124211.590005776734400.3870455416
9333527.375875992627587.660360142039467.0913918432
9432464.153310638426381.757398531438546.5492227455
9526484.38738174220971.367479901931997.4072835820
967842.951655195856405.071612593449280.83169779825



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')