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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 computationSun, 30 Nov 2014 09:44:33 +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/2014/Nov/30/t1417340771hve938ijmkleabe.htm/, Retrieved Tue, 28 May 2024 22:49:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261313, Retrieved Tue, 28 May 2024 22:49:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 09:44:33] [e05db0df8788e4fa845cdc810f8bbe4c] [Current]
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Dataseries X:
564410
658506
574787
611567
565210
638288
524970
505151
605350
517957
510879
622942
459903
486911
545974
481494
492324
609265
573243
524622
540071
564556
465319
458048
492603
606596
776475
749810
832426
895273
643875
348031
301771
411429
350941
425245
447041
449723
514318
445044
532552
469484
442289
532681
524463
590857
487590
612157
598030
577042
755394
697253
476835
510995
527816
482667
531528
628748
472131
445430
551715
561949
769474
583410
480271
576444
550457
534892
541769
741041
482062
586176




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261313&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261313&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.734140568930374
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.734140568930374 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261313&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]0.734140568930374[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261313&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
alpha0.734140568930374
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13459903490872.012673342-30969.0126733425
14486911489964.514298384-3053.51429838355
15545974545410.98680387563.013196129701
16481494479035.48821552458.51178450015
17492324488517.583041253806.41695874964
18609265614295.464355768-5030.46435576805
19573243479738.8618107793504.1381892305
20524622535510.946009414-10888.9460094137
21540071638053.589013703-97982.5890137026
22564556487094.80809815977461.191901841
23465319541803.017289193-76484.0172891926
24458048592986.553325971-134938.553325971
25492603354853.830818905137749.169181095
26606596484951.703703093121644.296296907
27776475644041.785021524132433.214978476
28749810652353.72402909897456.2759709023
29832426737535.65139285694890.3486071441
308952731007460.67039406-112187.670394057
31643875763119.467627178-119244.467627178
32348031628183.353658685-280152.353658685
33301771489537.059027827-187766.059027827
34411429328046.67527953183382.3247204692
35350941356980.985570793-6039.98557079269
36425245415759.1259932659485.87400673464
37447041353552.34862452293488.6513754779
38449723438575.8891081911147.1108918097
39514318495921.17750003618396.8224999637
40445044442231.7026164282812.29738357209
41532552449377.09060232183174.9093976793
42469484596395.924112466-126911.924112466
43442289407469.009451634819.9905484
44532681347191.268218619185489.731781381
45524463584565.554890953-60102.554890953
46590857623723.285108329-32866.2851083291
47487590519269.332487157-31679.3324871567
48612157592644.97791137719512.0220886226
49598030535739.06315883562290.9368411651
50577042575216.1242537441825.87574625621
51755394642911.551242158112482.448757842
52697253626147.97564277371105.0243572269
53476835716377.735573551-239542.735573551
54510995564785.311807226-53790.3118072262
55527816466027.55658528461788.4434147156
56482667442816.0181494239850.9818505801
57531528502403.61043857929124.3895614209
58628748613834.83468596114913.1653140385
59472131539933.655677477-67802.6556774767
60445430600876.17699532-155446.17699532
61551715437440.196540907114274.803459093
62561949501452.67154908660496.328450914
63769474633040.937368488136433.062631512
64583410624594.490797259-41184.4907972589
65480271538278.017928108-58007.0179281078
66576444571272.5568492165171.44315078354
67550457541716.1230201978740.87697980308
68534892470289.54089282164602.4591071791
69541769547068.455113085-5299.45511308452
70741041631345.473247524109695.526752476
71482062589220.193334148-107158.193334148
72586176594880.798951805-8704.79895180475

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 459903 & 490872.012673342 & -30969.0126733425 \tabularnewline
14 & 486911 & 489964.514298384 & -3053.51429838355 \tabularnewline
15 & 545974 & 545410.98680387 & 563.013196129701 \tabularnewline
16 & 481494 & 479035.4882155 & 2458.51178450015 \tabularnewline
17 & 492324 & 488517.58304125 & 3806.41695874964 \tabularnewline
18 & 609265 & 614295.464355768 & -5030.46435576805 \tabularnewline
19 & 573243 & 479738.86181077 & 93504.1381892305 \tabularnewline
20 & 524622 & 535510.946009414 & -10888.9460094137 \tabularnewline
21 & 540071 & 638053.589013703 & -97982.5890137026 \tabularnewline
22 & 564556 & 487094.808098159 & 77461.191901841 \tabularnewline
23 & 465319 & 541803.017289193 & -76484.0172891926 \tabularnewline
24 & 458048 & 592986.553325971 & -134938.553325971 \tabularnewline
25 & 492603 & 354853.830818905 & 137749.169181095 \tabularnewline
26 & 606596 & 484951.703703093 & 121644.296296907 \tabularnewline
27 & 776475 & 644041.785021524 & 132433.214978476 \tabularnewline
28 & 749810 & 652353.724029098 & 97456.2759709023 \tabularnewline
29 & 832426 & 737535.651392856 & 94890.3486071441 \tabularnewline
30 & 895273 & 1007460.67039406 & -112187.670394057 \tabularnewline
31 & 643875 & 763119.467627178 & -119244.467627178 \tabularnewline
32 & 348031 & 628183.353658685 & -280152.353658685 \tabularnewline
33 & 301771 & 489537.059027827 & -187766.059027827 \tabularnewline
34 & 411429 & 328046.675279531 & 83382.3247204692 \tabularnewline
35 & 350941 & 356980.985570793 & -6039.98557079269 \tabularnewline
36 & 425245 & 415759.125993265 & 9485.87400673464 \tabularnewline
37 & 447041 & 353552.348624522 & 93488.6513754779 \tabularnewline
38 & 449723 & 438575.88910819 & 11147.1108918097 \tabularnewline
39 & 514318 & 495921.177500036 & 18396.8224999637 \tabularnewline
40 & 445044 & 442231.702616428 & 2812.29738357209 \tabularnewline
41 & 532552 & 449377.090602321 & 83174.9093976793 \tabularnewline
42 & 469484 & 596395.924112466 & -126911.924112466 \tabularnewline
43 & 442289 & 407469.0094516 & 34819.9905484 \tabularnewline
44 & 532681 & 347191.268218619 & 185489.731781381 \tabularnewline
45 & 524463 & 584565.554890953 & -60102.554890953 \tabularnewline
46 & 590857 & 623723.285108329 & -32866.2851083291 \tabularnewline
47 & 487590 & 519269.332487157 & -31679.3324871567 \tabularnewline
48 & 612157 & 592644.977911377 & 19512.0220886226 \tabularnewline
49 & 598030 & 535739.063158835 & 62290.9368411651 \tabularnewline
50 & 577042 & 575216.124253744 & 1825.87574625621 \tabularnewline
51 & 755394 & 642911.551242158 & 112482.448757842 \tabularnewline
52 & 697253 & 626147.975642773 & 71105.0243572269 \tabularnewline
53 & 476835 & 716377.735573551 & -239542.735573551 \tabularnewline
54 & 510995 & 564785.311807226 & -53790.3118072262 \tabularnewline
55 & 527816 & 466027.556585284 & 61788.4434147156 \tabularnewline
56 & 482667 & 442816.01814942 & 39850.9818505801 \tabularnewline
57 & 531528 & 502403.610438579 & 29124.3895614209 \tabularnewline
58 & 628748 & 613834.834685961 & 14913.1653140385 \tabularnewline
59 & 472131 & 539933.655677477 & -67802.6556774767 \tabularnewline
60 & 445430 & 600876.17699532 & -155446.17699532 \tabularnewline
61 & 551715 & 437440.196540907 & 114274.803459093 \tabularnewline
62 & 561949 & 501452.671549086 & 60496.328450914 \tabularnewline
63 & 769474 & 633040.937368488 & 136433.062631512 \tabularnewline
64 & 583410 & 624594.490797259 & -41184.4907972589 \tabularnewline
65 & 480271 & 538278.017928108 & -58007.0179281078 \tabularnewline
66 & 576444 & 571272.556849216 & 5171.44315078354 \tabularnewline
67 & 550457 & 541716.123020197 & 8740.87697980308 \tabularnewline
68 & 534892 & 470289.540892821 & 64602.4591071791 \tabularnewline
69 & 541769 & 547068.455113085 & -5299.45511308452 \tabularnewline
70 & 741041 & 631345.473247524 & 109695.526752476 \tabularnewline
71 & 482062 & 589220.193334148 & -107158.193334148 \tabularnewline
72 & 586176 & 594880.798951805 & -8704.79895180475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261313&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]459903[/C][C]490872.012673342[/C][C]-30969.0126733425[/C][/ROW]
[ROW][C]14[/C][C]486911[/C][C]489964.514298384[/C][C]-3053.51429838355[/C][/ROW]
[ROW][C]15[/C][C]545974[/C][C]545410.98680387[/C][C]563.013196129701[/C][/ROW]
[ROW][C]16[/C][C]481494[/C][C]479035.4882155[/C][C]2458.51178450015[/C][/ROW]
[ROW][C]17[/C][C]492324[/C][C]488517.58304125[/C][C]3806.41695874964[/C][/ROW]
[ROW][C]18[/C][C]609265[/C][C]614295.464355768[/C][C]-5030.46435576805[/C][/ROW]
[ROW][C]19[/C][C]573243[/C][C]479738.86181077[/C][C]93504.1381892305[/C][/ROW]
[ROW][C]20[/C][C]524622[/C][C]535510.946009414[/C][C]-10888.9460094137[/C][/ROW]
[ROW][C]21[/C][C]540071[/C][C]638053.589013703[/C][C]-97982.5890137026[/C][/ROW]
[ROW][C]22[/C][C]564556[/C][C]487094.808098159[/C][C]77461.191901841[/C][/ROW]
[ROW][C]23[/C][C]465319[/C][C]541803.017289193[/C][C]-76484.0172891926[/C][/ROW]
[ROW][C]24[/C][C]458048[/C][C]592986.553325971[/C][C]-134938.553325971[/C][/ROW]
[ROW][C]25[/C][C]492603[/C][C]354853.830818905[/C][C]137749.169181095[/C][/ROW]
[ROW][C]26[/C][C]606596[/C][C]484951.703703093[/C][C]121644.296296907[/C][/ROW]
[ROW][C]27[/C][C]776475[/C][C]644041.785021524[/C][C]132433.214978476[/C][/ROW]
[ROW][C]28[/C][C]749810[/C][C]652353.724029098[/C][C]97456.2759709023[/C][/ROW]
[ROW][C]29[/C][C]832426[/C][C]737535.651392856[/C][C]94890.3486071441[/C][/ROW]
[ROW][C]30[/C][C]895273[/C][C]1007460.67039406[/C][C]-112187.670394057[/C][/ROW]
[ROW][C]31[/C][C]643875[/C][C]763119.467627178[/C][C]-119244.467627178[/C][/ROW]
[ROW][C]32[/C][C]348031[/C][C]628183.353658685[/C][C]-280152.353658685[/C][/ROW]
[ROW][C]33[/C][C]301771[/C][C]489537.059027827[/C][C]-187766.059027827[/C][/ROW]
[ROW][C]34[/C][C]411429[/C][C]328046.675279531[/C][C]83382.3247204692[/C][/ROW]
[ROW][C]35[/C][C]350941[/C][C]356980.985570793[/C][C]-6039.98557079269[/C][/ROW]
[ROW][C]36[/C][C]425245[/C][C]415759.125993265[/C][C]9485.87400673464[/C][/ROW]
[ROW][C]37[/C][C]447041[/C][C]353552.348624522[/C][C]93488.6513754779[/C][/ROW]
[ROW][C]38[/C][C]449723[/C][C]438575.88910819[/C][C]11147.1108918097[/C][/ROW]
[ROW][C]39[/C][C]514318[/C][C]495921.177500036[/C][C]18396.8224999637[/C][/ROW]
[ROW][C]40[/C][C]445044[/C][C]442231.702616428[/C][C]2812.29738357209[/C][/ROW]
[ROW][C]41[/C][C]532552[/C][C]449377.090602321[/C][C]83174.9093976793[/C][/ROW]
[ROW][C]42[/C][C]469484[/C][C]596395.924112466[/C][C]-126911.924112466[/C][/ROW]
[ROW][C]43[/C][C]442289[/C][C]407469.0094516[/C][C]34819.9905484[/C][/ROW]
[ROW][C]44[/C][C]532681[/C][C]347191.268218619[/C][C]185489.731781381[/C][/ROW]
[ROW][C]45[/C][C]524463[/C][C]584565.554890953[/C][C]-60102.554890953[/C][/ROW]
[ROW][C]46[/C][C]590857[/C][C]623723.285108329[/C][C]-32866.2851083291[/C][/ROW]
[ROW][C]47[/C][C]487590[/C][C]519269.332487157[/C][C]-31679.3324871567[/C][/ROW]
[ROW][C]48[/C][C]612157[/C][C]592644.977911377[/C][C]19512.0220886226[/C][/ROW]
[ROW][C]49[/C][C]598030[/C][C]535739.063158835[/C][C]62290.9368411651[/C][/ROW]
[ROW][C]50[/C][C]577042[/C][C]575216.124253744[/C][C]1825.87574625621[/C][/ROW]
[ROW][C]51[/C][C]755394[/C][C]642911.551242158[/C][C]112482.448757842[/C][/ROW]
[ROW][C]52[/C][C]697253[/C][C]626147.975642773[/C][C]71105.0243572269[/C][/ROW]
[ROW][C]53[/C][C]476835[/C][C]716377.735573551[/C][C]-239542.735573551[/C][/ROW]
[ROW][C]54[/C][C]510995[/C][C]564785.311807226[/C][C]-53790.3118072262[/C][/ROW]
[ROW][C]55[/C][C]527816[/C][C]466027.556585284[/C][C]61788.4434147156[/C][/ROW]
[ROW][C]56[/C][C]482667[/C][C]442816.01814942[/C][C]39850.9818505801[/C][/ROW]
[ROW][C]57[/C][C]531528[/C][C]502403.610438579[/C][C]29124.3895614209[/C][/ROW]
[ROW][C]58[/C][C]628748[/C][C]613834.834685961[/C][C]14913.1653140385[/C][/ROW]
[ROW][C]59[/C][C]472131[/C][C]539933.655677477[/C][C]-67802.6556774767[/C][/ROW]
[ROW][C]60[/C][C]445430[/C][C]600876.17699532[/C][C]-155446.17699532[/C][/ROW]
[ROW][C]61[/C][C]551715[/C][C]437440.196540907[/C][C]114274.803459093[/C][/ROW]
[ROW][C]62[/C][C]561949[/C][C]501452.671549086[/C][C]60496.328450914[/C][/ROW]
[ROW][C]63[/C][C]769474[/C][C]633040.937368488[/C][C]136433.062631512[/C][/ROW]
[ROW][C]64[/C][C]583410[/C][C]624594.490797259[/C][C]-41184.4907972589[/C][/ROW]
[ROW][C]65[/C][C]480271[/C][C]538278.017928108[/C][C]-58007.0179281078[/C][/ROW]
[ROW][C]66[/C][C]576444[/C][C]571272.556849216[/C][C]5171.44315078354[/C][/ROW]
[ROW][C]67[/C][C]550457[/C][C]541716.123020197[/C][C]8740.87697980308[/C][/ROW]
[ROW][C]68[/C][C]534892[/C][C]470289.540892821[/C][C]64602.4591071791[/C][/ROW]
[ROW][C]69[/C][C]541769[/C][C]547068.455113085[/C][C]-5299.45511308452[/C][/ROW]
[ROW][C]70[/C][C]741041[/C][C]631345.473247524[/C][C]109695.526752476[/C][/ROW]
[ROW][C]71[/C][C]482062[/C][C]589220.193334148[/C][C]-107158.193334148[/C][/ROW]
[ROW][C]72[/C][C]586176[/C][C]594880.798951805[/C][C]-8704.79895180475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261313&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
13459903490872.012673342-30969.0126733425
14486911489964.514298384-3053.51429838355
15545974545410.98680387563.013196129701
16481494479035.48821552458.51178450015
17492324488517.583041253806.41695874964
18609265614295.464355768-5030.46435576805
19573243479738.8618107793504.1381892305
20524622535510.946009414-10888.9460094137
21540071638053.589013703-97982.5890137026
22564556487094.80809815977461.191901841
23465319541803.017289193-76484.0172891926
24458048592986.553325971-134938.553325971
25492603354853.830818905137749.169181095
26606596484951.703703093121644.296296907
27776475644041.785021524132433.214978476
28749810652353.72402909897456.2759709023
29832426737535.65139285694890.3486071441
308952731007460.67039406-112187.670394057
31643875763119.467627178-119244.467627178
32348031628183.353658685-280152.353658685
33301771489537.059027827-187766.059027827
34411429328046.67527953183382.3247204692
35350941356980.985570793-6039.98557079269
36425245415759.1259932659485.87400673464
37447041353552.34862452293488.6513754779
38449723438575.8891081911147.1108918097
39514318495921.17750003618396.8224999637
40445044442231.7026164282812.29738357209
41532552449377.09060232183174.9093976793
42469484596395.924112466-126911.924112466
43442289407469.009451634819.9905484
44532681347191.268218619185489.731781381
45524463584565.554890953-60102.554890953
46590857623723.285108329-32866.2851083291
47487590519269.332487157-31679.3324871567
48612157592644.97791137719512.0220886226
49598030535739.06315883562290.9368411651
50577042575216.1242537441825.87574625621
51755394642911.551242158112482.448757842
52697253626147.97564277371105.0243572269
53476835716377.735573551-239542.735573551
54510995564785.311807226-53790.3118072262
55527816466027.55658528461788.4434147156
56482667442816.0181494239850.9818505801
57531528502403.61043857929124.3895614209
58628748613834.83468596114913.1653140385
59472131539933.655677477-67802.6556774767
60445430600876.17699532-155446.17699532
61551715437440.196540907114274.803459093
62561949501452.67154908660496.328450914
63769474633040.937368488136433.062631512
64583410624594.490797259-41184.4907972589
65480271538278.017928108-58007.0179281078
66576444571272.5568492165171.44315078354
67550457541716.1230201978740.87697980308
68534892470289.54089282164602.4591071791
69541769547068.455113085-5299.45511308452
70741041631345.473247524109695.526752476
71482062589220.193334148-107158.193334148
72586176594880.798951805-8704.79895180475







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73612751.107716025427697.847075354797804.368356696
74573706.669414268348733.807926221798679.530902316
75678341.270799532389374.742374531967307.799224534
76540100.858293263261393.23895562818808.477630907
77482603.859003014192353.582307921772854.135698107
78575436.513145687211110.805643767939762.220647606
79543056.275289317169358.867770123916753.682808511
80479319.850022922116133.937567606842505.762478239
81488652.05296062593186.4942667049884117.611654545
82592420.63654726399029.88389349181085811.38920103
83444217.24240941139477.7114863008848956.773332522
84545758.94583602870153.95756870521021363.93410335

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 612751.107716025 & 427697.847075354 & 797804.368356696 \tabularnewline
74 & 573706.669414268 & 348733.807926221 & 798679.530902316 \tabularnewline
75 & 678341.270799532 & 389374.742374531 & 967307.799224534 \tabularnewline
76 & 540100.858293263 & 261393.23895562 & 818808.477630907 \tabularnewline
77 & 482603.859003014 & 192353.582307921 & 772854.135698107 \tabularnewline
78 & 575436.513145687 & 211110.805643767 & 939762.220647606 \tabularnewline
79 & 543056.275289317 & 169358.867770123 & 916753.682808511 \tabularnewline
80 & 479319.850022922 & 116133.937567606 & 842505.762478239 \tabularnewline
81 & 488652.052960625 & 93186.4942667049 & 884117.611654545 \tabularnewline
82 & 592420.636547263 & 99029.8838934918 & 1085811.38920103 \tabularnewline
83 & 444217.242409411 & 39477.7114863008 & 848956.773332522 \tabularnewline
84 & 545758.945836028 & 70153.9575687052 & 1021363.93410335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261313&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]612751.107716025[/C][C]427697.847075354[/C][C]797804.368356696[/C][/ROW]
[ROW][C]74[/C][C]573706.669414268[/C][C]348733.807926221[/C][C]798679.530902316[/C][/ROW]
[ROW][C]75[/C][C]678341.270799532[/C][C]389374.742374531[/C][C]967307.799224534[/C][/ROW]
[ROW][C]76[/C][C]540100.858293263[/C][C]261393.23895562[/C][C]818808.477630907[/C][/ROW]
[ROW][C]77[/C][C]482603.859003014[/C][C]192353.582307921[/C][C]772854.135698107[/C][/ROW]
[ROW][C]78[/C][C]575436.513145687[/C][C]211110.805643767[/C][C]939762.220647606[/C][/ROW]
[ROW][C]79[/C][C]543056.275289317[/C][C]169358.867770123[/C][C]916753.682808511[/C][/ROW]
[ROW][C]80[/C][C]479319.850022922[/C][C]116133.937567606[/C][C]842505.762478239[/C][/ROW]
[ROW][C]81[/C][C]488652.052960625[/C][C]93186.4942667049[/C][C]884117.611654545[/C][/ROW]
[ROW][C]82[/C][C]592420.636547263[/C][C]99029.8838934918[/C][C]1085811.38920103[/C][/ROW]
[ROW][C]83[/C][C]444217.242409411[/C][C]39477.7114863008[/C][C]848956.773332522[/C][/ROW]
[ROW][C]84[/C][C]545758.945836028[/C][C]70153.9575687052[/C][C]1021363.93410335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261313&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261313&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
73612751.107716025427697.847075354797804.368356696
74573706.669414268348733.807926221798679.530902316
75678341.270799532389374.742374531967307.799224534
76540100.858293263261393.23895562818808.477630907
77482603.859003014192353.582307921772854.135698107
78575436.513145687211110.805643767939762.220647606
79543056.275289317169358.867770123916753.682808511
80479319.850022922116133.937567606842505.762478239
81488652.05296062593186.4942667049884117.611654545
82592420.63654726399029.88389349181085811.38920103
83444217.24240941139477.7114863008848956.773332522
84545758.94583602870153.95756870521021363.93410335



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')