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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 04:32:45 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/05/t12441979984u7p0xgp0kch1ub.htm/, Retrieved Fri, 10 May 2024 01:47:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41784, Retrieved Fri, 10 May 2024 01:47:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 - oef 2...] [2009-06-05 10:32:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
266433
267722
266003
262971
265521
264676
270223
269508
268457
265814
266680
263018
269285
269829
270911
266844
271244
269907
271296
270157
271322
267179
264101
265518
269419
268714
272482
268351
268175
270674
272764
272599
270333
270846
270491
269160
274027
273784
276663
274525
271344
271115
270798
273911
273985
271917
273338
270601
273547
275363
281229
277793
279913
282500
280041
282166
290304
283519
287816
285226
287595
289741
289148
288301
290155
289648
288225
289351
294735
305333
309030
310215
321935




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41784&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41784&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.909335006287375
beta0.0820112173986116
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.909335006287375 \tabularnewline
beta & 0.0820112173986116 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41784&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]0.909335006287375[/C][/ROW]
[ROW][C]beta[/C][C]0.0820112173986116[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41784&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
alpha0.909335006287375
beta0.0820112173986116
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13269285267036.9635879382248.03641206183
14269829269956.087441595-127.087441595097
15270911271170.191826702-259.19182670163
16266844267062.253623455-218.253623455414
17271244271674.78701356-430.787013560126
18269907270275.071238274-368.071238273929
19271296272914.495646938-1618.49564693752
20270157270694.894581584-537.894581584318
21271322268996.7168201312325.28317986906
22267179268383.934385677-1204.93438567704
23264101267978.393974333-3877.39397433336
24265518260308.991110185209.00888982008
25269419271628.582124246-2209.58212424570
26268714270038.900248436-1324.90024843649
27272482269817.6277956192664.37220438116
28268351268240.110135488110.889864511730
29268175273069.616157436-4894.61615743616
30270674267210.5801639123463.41983608826
31272764273090.010729606-326.010729606496
32272599272101.221012437497.77898756275
33270333271632.364748922-1299.36474892183
34270846267185.5176994823660.48230051773
35270491271094.687152619-603.687152618659
36269160267511.7079263361648.29207366367
37274027275102.447981403-1075.44798140280
38273784274824.034737523-1040.03473752266
39276663275462.5516643841200.44833561569
40274525272360.7309149482164.2690850519
41271344278947.796646886-7603.79664688563
42271115271430.998603056-315.99860305601
43270798273309.685809758-2511.68580975791
44273911270026.6847240453884.31527595507
45273985272336.4313109921648.56868900813
46271917271064.142755852852.857244147512
47273338271909.1678552471428.83214475308
48270601270373.748501195227.251498804777
49273547276373.387849601-2826.38784960087
50275363274294.3755592871068.62444071274
51281229277007.1457612784221.85423872236
52277793276839.591703434953.408296566282
53279913281538.258895376-1625.25889537612
54282500280645.1351850971854.86481490283
55280041285071.065866953-5030.06586695346
56282166280569.1565703171596.84342968272
57290304280881.2157349229422.78426507779
58283519287335.198788099-3816.19878809917
59287816284532.0505138423283.94948615762
60285226285085.409702811140.590297188726
61287595291692.649041344-4097.64904134435
62289741289440.89696119300.103038810194
63289148292368.828148631-3220.82814863132
64288301284980.2023948833320.79760511749
65290155291869.663409974-1714.66340997408
66289648291381.338234087-1733.33823408716
67288225291839.019646254-3614.01964625437
68289351289230.559528781120.440471219423
69294735288746.4719367575988.5280632429
70305333290445.08946497114887.9105350295
71309030306356.0421431612673.95785683906
72310215306766.5523916783448.44760832243
73321935317666.334086384268.66591362015

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 269285 & 267036.963587938 & 2248.03641206183 \tabularnewline
14 & 269829 & 269956.087441595 & -127.087441595097 \tabularnewline
15 & 270911 & 271170.191826702 & -259.19182670163 \tabularnewline
16 & 266844 & 267062.253623455 & -218.253623455414 \tabularnewline
17 & 271244 & 271674.78701356 & -430.787013560126 \tabularnewline
18 & 269907 & 270275.071238274 & -368.071238273929 \tabularnewline
19 & 271296 & 272914.495646938 & -1618.49564693752 \tabularnewline
20 & 270157 & 270694.894581584 & -537.894581584318 \tabularnewline
21 & 271322 & 268996.716820131 & 2325.28317986906 \tabularnewline
22 & 267179 & 268383.934385677 & -1204.93438567704 \tabularnewline
23 & 264101 & 267978.393974333 & -3877.39397433336 \tabularnewline
24 & 265518 & 260308.99111018 & 5209.00888982008 \tabularnewline
25 & 269419 & 271628.582124246 & -2209.58212424570 \tabularnewline
26 & 268714 & 270038.900248436 & -1324.90024843649 \tabularnewline
27 & 272482 & 269817.627795619 & 2664.37220438116 \tabularnewline
28 & 268351 & 268240.110135488 & 110.889864511730 \tabularnewline
29 & 268175 & 273069.616157436 & -4894.61615743616 \tabularnewline
30 & 270674 & 267210.580163912 & 3463.41983608826 \tabularnewline
31 & 272764 & 273090.010729606 & -326.010729606496 \tabularnewline
32 & 272599 & 272101.221012437 & 497.77898756275 \tabularnewline
33 & 270333 & 271632.364748922 & -1299.36474892183 \tabularnewline
34 & 270846 & 267185.517699482 & 3660.48230051773 \tabularnewline
35 & 270491 & 271094.687152619 & -603.687152618659 \tabularnewline
36 & 269160 & 267511.707926336 & 1648.29207366367 \tabularnewline
37 & 274027 & 275102.447981403 & -1075.44798140280 \tabularnewline
38 & 273784 & 274824.034737523 & -1040.03473752266 \tabularnewline
39 & 276663 & 275462.551664384 & 1200.44833561569 \tabularnewline
40 & 274525 & 272360.730914948 & 2164.2690850519 \tabularnewline
41 & 271344 & 278947.796646886 & -7603.79664688563 \tabularnewline
42 & 271115 & 271430.998603056 & -315.99860305601 \tabularnewline
43 & 270798 & 273309.685809758 & -2511.68580975791 \tabularnewline
44 & 273911 & 270026.684724045 & 3884.31527595507 \tabularnewline
45 & 273985 & 272336.431310992 & 1648.56868900813 \tabularnewline
46 & 271917 & 271064.142755852 & 852.857244147512 \tabularnewline
47 & 273338 & 271909.167855247 & 1428.83214475308 \tabularnewline
48 & 270601 & 270373.748501195 & 227.251498804777 \tabularnewline
49 & 273547 & 276373.387849601 & -2826.38784960087 \tabularnewline
50 & 275363 & 274294.375559287 & 1068.62444071274 \tabularnewline
51 & 281229 & 277007.145761278 & 4221.85423872236 \tabularnewline
52 & 277793 & 276839.591703434 & 953.408296566282 \tabularnewline
53 & 279913 & 281538.258895376 & -1625.25889537612 \tabularnewline
54 & 282500 & 280645.135185097 & 1854.86481490283 \tabularnewline
55 & 280041 & 285071.065866953 & -5030.06586695346 \tabularnewline
56 & 282166 & 280569.156570317 & 1596.84342968272 \tabularnewline
57 & 290304 & 280881.215734922 & 9422.78426507779 \tabularnewline
58 & 283519 & 287335.198788099 & -3816.19878809917 \tabularnewline
59 & 287816 & 284532.050513842 & 3283.94948615762 \tabularnewline
60 & 285226 & 285085.409702811 & 140.590297188726 \tabularnewline
61 & 287595 & 291692.649041344 & -4097.64904134435 \tabularnewline
62 & 289741 & 289440.89696119 & 300.103038810194 \tabularnewline
63 & 289148 & 292368.828148631 & -3220.82814863132 \tabularnewline
64 & 288301 & 284980.202394883 & 3320.79760511749 \tabularnewline
65 & 290155 & 291869.663409974 & -1714.66340997408 \tabularnewline
66 & 289648 & 291381.338234087 & -1733.33823408716 \tabularnewline
67 & 288225 & 291839.019646254 & -3614.01964625437 \tabularnewline
68 & 289351 & 289230.559528781 & 120.440471219423 \tabularnewline
69 & 294735 & 288746.471936757 & 5988.5280632429 \tabularnewline
70 & 305333 & 290445.089464971 & 14887.9105350295 \tabularnewline
71 & 309030 & 306356.042143161 & 2673.95785683906 \tabularnewline
72 & 310215 & 306766.552391678 & 3448.44760832243 \tabularnewline
73 & 321935 & 317666.33408638 & 4268.66591362015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41784&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]269285[/C][C]267036.963587938[/C][C]2248.03641206183[/C][/ROW]
[ROW][C]14[/C][C]269829[/C][C]269956.087441595[/C][C]-127.087441595097[/C][/ROW]
[ROW][C]15[/C][C]270911[/C][C]271170.191826702[/C][C]-259.19182670163[/C][/ROW]
[ROW][C]16[/C][C]266844[/C][C]267062.253623455[/C][C]-218.253623455414[/C][/ROW]
[ROW][C]17[/C][C]271244[/C][C]271674.78701356[/C][C]-430.787013560126[/C][/ROW]
[ROW][C]18[/C][C]269907[/C][C]270275.071238274[/C][C]-368.071238273929[/C][/ROW]
[ROW][C]19[/C][C]271296[/C][C]272914.495646938[/C][C]-1618.49564693752[/C][/ROW]
[ROW][C]20[/C][C]270157[/C][C]270694.894581584[/C][C]-537.894581584318[/C][/ROW]
[ROW][C]21[/C][C]271322[/C][C]268996.716820131[/C][C]2325.28317986906[/C][/ROW]
[ROW][C]22[/C][C]267179[/C][C]268383.934385677[/C][C]-1204.93438567704[/C][/ROW]
[ROW][C]23[/C][C]264101[/C][C]267978.393974333[/C][C]-3877.39397433336[/C][/ROW]
[ROW][C]24[/C][C]265518[/C][C]260308.99111018[/C][C]5209.00888982008[/C][/ROW]
[ROW][C]25[/C][C]269419[/C][C]271628.582124246[/C][C]-2209.58212424570[/C][/ROW]
[ROW][C]26[/C][C]268714[/C][C]270038.900248436[/C][C]-1324.90024843649[/C][/ROW]
[ROW][C]27[/C][C]272482[/C][C]269817.627795619[/C][C]2664.37220438116[/C][/ROW]
[ROW][C]28[/C][C]268351[/C][C]268240.110135488[/C][C]110.889864511730[/C][/ROW]
[ROW][C]29[/C][C]268175[/C][C]273069.616157436[/C][C]-4894.61615743616[/C][/ROW]
[ROW][C]30[/C][C]270674[/C][C]267210.580163912[/C][C]3463.41983608826[/C][/ROW]
[ROW][C]31[/C][C]272764[/C][C]273090.010729606[/C][C]-326.010729606496[/C][/ROW]
[ROW][C]32[/C][C]272599[/C][C]272101.221012437[/C][C]497.77898756275[/C][/ROW]
[ROW][C]33[/C][C]270333[/C][C]271632.364748922[/C][C]-1299.36474892183[/C][/ROW]
[ROW][C]34[/C][C]270846[/C][C]267185.517699482[/C][C]3660.48230051773[/C][/ROW]
[ROW][C]35[/C][C]270491[/C][C]271094.687152619[/C][C]-603.687152618659[/C][/ROW]
[ROW][C]36[/C][C]269160[/C][C]267511.707926336[/C][C]1648.29207366367[/C][/ROW]
[ROW][C]37[/C][C]274027[/C][C]275102.447981403[/C][C]-1075.44798140280[/C][/ROW]
[ROW][C]38[/C][C]273784[/C][C]274824.034737523[/C][C]-1040.03473752266[/C][/ROW]
[ROW][C]39[/C][C]276663[/C][C]275462.551664384[/C][C]1200.44833561569[/C][/ROW]
[ROW][C]40[/C][C]274525[/C][C]272360.730914948[/C][C]2164.2690850519[/C][/ROW]
[ROW][C]41[/C][C]271344[/C][C]278947.796646886[/C][C]-7603.79664688563[/C][/ROW]
[ROW][C]42[/C][C]271115[/C][C]271430.998603056[/C][C]-315.99860305601[/C][/ROW]
[ROW][C]43[/C][C]270798[/C][C]273309.685809758[/C][C]-2511.68580975791[/C][/ROW]
[ROW][C]44[/C][C]273911[/C][C]270026.684724045[/C][C]3884.31527595507[/C][/ROW]
[ROW][C]45[/C][C]273985[/C][C]272336.431310992[/C][C]1648.56868900813[/C][/ROW]
[ROW][C]46[/C][C]271917[/C][C]271064.142755852[/C][C]852.857244147512[/C][/ROW]
[ROW][C]47[/C][C]273338[/C][C]271909.167855247[/C][C]1428.83214475308[/C][/ROW]
[ROW][C]48[/C][C]270601[/C][C]270373.748501195[/C][C]227.251498804777[/C][/ROW]
[ROW][C]49[/C][C]273547[/C][C]276373.387849601[/C][C]-2826.38784960087[/C][/ROW]
[ROW][C]50[/C][C]275363[/C][C]274294.375559287[/C][C]1068.62444071274[/C][/ROW]
[ROW][C]51[/C][C]281229[/C][C]277007.145761278[/C][C]4221.85423872236[/C][/ROW]
[ROW][C]52[/C][C]277793[/C][C]276839.591703434[/C][C]953.408296566282[/C][/ROW]
[ROW][C]53[/C][C]279913[/C][C]281538.258895376[/C][C]-1625.25889537612[/C][/ROW]
[ROW][C]54[/C][C]282500[/C][C]280645.135185097[/C][C]1854.86481490283[/C][/ROW]
[ROW][C]55[/C][C]280041[/C][C]285071.065866953[/C][C]-5030.06586695346[/C][/ROW]
[ROW][C]56[/C][C]282166[/C][C]280569.156570317[/C][C]1596.84342968272[/C][/ROW]
[ROW][C]57[/C][C]290304[/C][C]280881.215734922[/C][C]9422.78426507779[/C][/ROW]
[ROW][C]58[/C][C]283519[/C][C]287335.198788099[/C][C]-3816.19878809917[/C][/ROW]
[ROW][C]59[/C][C]287816[/C][C]284532.050513842[/C][C]3283.94948615762[/C][/ROW]
[ROW][C]60[/C][C]285226[/C][C]285085.409702811[/C][C]140.590297188726[/C][/ROW]
[ROW][C]61[/C][C]287595[/C][C]291692.649041344[/C][C]-4097.64904134435[/C][/ROW]
[ROW][C]62[/C][C]289741[/C][C]289440.89696119[/C][C]300.103038810194[/C][/ROW]
[ROW][C]63[/C][C]289148[/C][C]292368.828148631[/C][C]-3220.82814863132[/C][/ROW]
[ROW][C]64[/C][C]288301[/C][C]284980.202394883[/C][C]3320.79760511749[/C][/ROW]
[ROW][C]65[/C][C]290155[/C][C]291869.663409974[/C][C]-1714.66340997408[/C][/ROW]
[ROW][C]66[/C][C]289648[/C][C]291381.338234087[/C][C]-1733.33823408716[/C][/ROW]
[ROW][C]67[/C][C]288225[/C][C]291839.019646254[/C][C]-3614.01964625437[/C][/ROW]
[ROW][C]68[/C][C]289351[/C][C]289230.559528781[/C][C]120.440471219423[/C][/ROW]
[ROW][C]69[/C][C]294735[/C][C]288746.471936757[/C][C]5988.5280632429[/C][/ROW]
[ROW][C]70[/C][C]305333[/C][C]290445.089464971[/C][C]14887.9105350295[/C][/ROW]
[ROW][C]71[/C][C]309030[/C][C]306356.042143161[/C][C]2673.95785683906[/C][/ROW]
[ROW][C]72[/C][C]310215[/C][C]306766.552391678[/C][C]3448.44760832243[/C][/ROW]
[ROW][C]73[/C][C]321935[/C][C]317666.33408638[/C][C]4268.66591362015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41784&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41784&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
13269285267036.9635879382248.03641206183
14269829269956.087441595-127.087441595097
15270911271170.191826702-259.19182670163
16266844267062.253623455-218.253623455414
17271244271674.78701356-430.787013560126
18269907270275.071238274-368.071238273929
19271296272914.495646938-1618.49564693752
20270157270694.894581584-537.894581584318
21271322268996.7168201312325.28317986906
22267179268383.934385677-1204.93438567704
23264101267978.393974333-3877.39397433336
24265518260308.991110185209.00888982008
25269419271628.582124246-2209.58212424570
26268714270038.900248436-1324.90024843649
27272482269817.6277956192664.37220438116
28268351268240.110135488110.889864511730
29268175273069.616157436-4894.61615743616
30270674267210.5801639123463.41983608826
31272764273090.010729606-326.010729606496
32272599272101.221012437497.77898756275
33270333271632.364748922-1299.36474892183
34270846267185.5176994823660.48230051773
35270491271094.687152619-603.687152618659
36269160267511.7079263361648.29207366367
37274027275102.447981403-1075.44798140280
38273784274824.034737523-1040.03473752266
39276663275462.5516643841200.44833561569
40274525272360.7309149482164.2690850519
41271344278947.796646886-7603.79664688563
42271115271430.998603056-315.99860305601
43270798273309.685809758-2511.68580975791
44273911270026.6847240453884.31527595507
45273985272336.4313109921648.56868900813
46271917271064.142755852852.857244147512
47273338271909.1678552471428.83214475308
48270601270373.748501195227.251498804777
49273547276373.387849601-2826.38784960087
50275363274294.3755592871068.62444071274
51281229277007.1457612784221.85423872236
52277793276839.591703434953.408296566282
53279913281538.258895376-1625.25889537612
54282500280645.1351850971854.86481490283
55280041285071.065866953-5030.06586695346
56282166280569.1565703171596.84342968272
57290304280881.2157349229422.78426507779
58283519287335.198788099-3816.19878809917
59287816284532.0505138423283.94948615762
60285226285085.409702811140.590297188726
61287595291692.649041344-4097.64904134435
62289741289440.89696119300.103038810194
63289148292368.828148631-3220.82814863132
64288301284980.2023948833320.79760511749
65290155291869.663409974-1714.66340997408
66289648291381.338234087-1733.33823408716
67288225291839.019646254-3614.01964625437
68289351289230.559528781120.440471219423
69294735288746.4719367575988.5280632429
70305333290445.08946497114887.9105350295
71309030306356.0421431612673.95785683906
72310215306766.5523916783448.44760832243
73321935317666.334086384268.66591362015







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74325422.61644011318581.935284816332263.297595403
75329803.748539347320181.520720576339425.976358117
76327380.366946838315458.450049121339302.283844554
77332982.676776855318675.494227277347289.859326433
78336076.143786297319534.599115959352617.688456635
79340252.288218566321450.873076376359053.703360755
80343784.157516855322754.771464654364813.543569056
81346015.722146355322825.365145904369206.079146805
82344266.049813088319171.722529072369360.377097103
83346237.360765989318977.958341959373496.763190018
84344379.765529816315241.895051493373517.63600814
85353143.58931973321962.433955165384324.744684294

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 325422.61644011 & 318581.935284816 & 332263.297595403 \tabularnewline
75 & 329803.748539347 & 320181.520720576 & 339425.976358117 \tabularnewline
76 & 327380.366946838 & 315458.450049121 & 339302.283844554 \tabularnewline
77 & 332982.676776855 & 318675.494227277 & 347289.859326433 \tabularnewline
78 & 336076.143786297 & 319534.599115959 & 352617.688456635 \tabularnewline
79 & 340252.288218566 & 321450.873076376 & 359053.703360755 \tabularnewline
80 & 343784.157516855 & 322754.771464654 & 364813.543569056 \tabularnewline
81 & 346015.722146355 & 322825.365145904 & 369206.079146805 \tabularnewline
82 & 344266.049813088 & 319171.722529072 & 369360.377097103 \tabularnewline
83 & 346237.360765989 & 318977.958341959 & 373496.763190018 \tabularnewline
84 & 344379.765529816 & 315241.895051493 & 373517.63600814 \tabularnewline
85 & 353143.58931973 & 321962.433955165 & 384324.744684294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41784&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]74[/C][C]325422.61644011[/C][C]318581.935284816[/C][C]332263.297595403[/C][/ROW]
[ROW][C]75[/C][C]329803.748539347[/C][C]320181.520720576[/C][C]339425.976358117[/C][/ROW]
[ROW][C]76[/C][C]327380.366946838[/C][C]315458.450049121[/C][C]339302.283844554[/C][/ROW]
[ROW][C]77[/C][C]332982.676776855[/C][C]318675.494227277[/C][C]347289.859326433[/C][/ROW]
[ROW][C]78[/C][C]336076.143786297[/C][C]319534.599115959[/C][C]352617.688456635[/C][/ROW]
[ROW][C]79[/C][C]340252.288218566[/C][C]321450.873076376[/C][C]359053.703360755[/C][/ROW]
[ROW][C]80[/C][C]343784.157516855[/C][C]322754.771464654[/C][C]364813.543569056[/C][/ROW]
[ROW][C]81[/C][C]346015.722146355[/C][C]322825.365145904[/C][C]369206.079146805[/C][/ROW]
[ROW][C]82[/C][C]344266.049813088[/C][C]319171.722529072[/C][C]369360.377097103[/C][/ROW]
[ROW][C]83[/C][C]346237.360765989[/C][C]318977.958341959[/C][C]373496.763190018[/C][/ROW]
[ROW][C]84[/C][C]344379.765529816[/C][C]315241.895051493[/C][C]373517.63600814[/C][/ROW]
[ROW][C]85[/C][C]353143.58931973[/C][C]321962.433955165[/C][C]384324.744684294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41784&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41784&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
74325422.61644011318581.935284816332263.297595403
75329803.748539347320181.520720576339425.976358117
76327380.366946838315458.450049121339302.283844554
77332982.676776855318675.494227277347289.859326433
78336076.143786297319534.599115959352617.688456635
79340252.288218566321450.873076376359053.703360755
80343784.157516855322754.771464654364813.543569056
81346015.722146355322825.365145904369206.079146805
82344266.049813088319171.722529072369360.377097103
83346237.360765989318977.958341959373496.763190018
84344379.765529816315241.895051493373517.63600814
85353143.58931973321962.433955165384324.744684294



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')