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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 Apr 2008 08:39:21 -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/2008/Apr/29/t1209480004ic7gpgfjtnb5qtn.htm/, Retrieved Sun, 12 May 2024 15:07:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11059, Retrieved Sun, 12 May 2024 15:07:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact230
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [test 3 (es)] [2008-04-29 14:39:21] [5c345a6bce6e2ca5a97592a5f60e5400] [Current]
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Dataseries X:
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387
50556
43901
48572
43899
37532
40357
35489
29027
34485
42598
30306
26451
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577




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=11059&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=11059&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11059&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
alpha0.0512572023235812
beta0.000425534174427011
gamma0.368605978860725

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0512572023235812 \tabularnewline
beta & 0.000425534174427011 \tabularnewline
gamma & 0.368605978860725 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11059&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]0.0512572023235812[/C][/ROW]
[ROW][C]beta[/C][C]0.000425534174427011[/C][/ROW]
[ROW][C]gamma[/C][C]0.368605978860725[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11059&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11059&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
alpha0.0512572023235812
beta0.000425534174427011
gamma0.368605978860725







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135055650513.913472222342.0865277777484
144390143931.2207583048-30.2207583047712
154857248571.44611602930.553883970744209
164389943787.7905745671111.209425432899
173753237307.3093522476224.690647752446
184035739878.9830941167478.016905883254
193548935015.15205761473.847942389999
202902728634.6593337897392.340666210319
213448533503.7889993035981.211000696465
224259840907.12391256591690.87608743407
233030628398.03782029511907.96217970492
242645124599.16223632611851.83776367391
254746053185.4184385885-5725.41843858849
265010446281.86421886053822.13578113946
276146551130.448299631410334.5517003686
285372646915.54301190186810.45698809817
293947740818.6392113434-1341.63921134340
304389543399.0913610316495.908638968445
313148138535.1926514119-7054.1926514119
322989631740.6385184782-1844.63851847820
333384236701.3022621234-2859.30226212342
343912044156.1382214790-5036.13822147904
353370231378.19156247612323.80843752393
362509427581.0424649262-2487.04246492615
375144253294.9844857177-1852.98448571766
384559449928.8458265101-4334.84582651011
395251856636.6482653951-4118.64826539515
404856450448.0286568089-1884.02865680889
414174541053.9275843764691.072415623552
424958544380.57399340015204.42600659989
433274737117.1504914156-4370.15049141558
443337932281.56920649461097.43079350543
453564537037.8103717865-1392.81037178655
463703443806.1958880855-6772.19588808546
473568133512.73706438932168.26293561075
482097228024.8078272207-7052.80782722075
495855253725.96602166814826.03397833186
505495549833.89016534435121.10983465568
516554057101.84398602198438.15601397814
525157052338.4574206093-768.457420609338
535114543902.23867172667242.7613282734
544664149143.3811748015-2502.3811748015
553570438136.7130716886-2432.71307168862
563325335312.6935494417-2059.69354944170
573519339036.3464977491-3843.34649774914
584166843797.9388594381-2129.93885943813
593486536869.170106545-2004.17010654498
602121027942.7138847439-6732.71388474385
615612657814.5247119143-1688.52471191430
624923153691.6491642265-4460.6491642265
635972361628.1982867343-1905.19828673426
644810353114.4667700878-5011.46677008781
654747247261.784274631210.215725368987
665049748733.70845710411763.29154289586
674005937969.38981067672089.61018932334
683414935507.0592861316-1358.05928613158
693686038642.3638867991-1782.36388679905
704635644108.29423541462247.7057645854
713657737447.4877720121-870.487772012071

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 50556 & 50513.9134722223 & 42.0865277777484 \tabularnewline
14 & 43901 & 43931.2207583048 & -30.2207583047712 \tabularnewline
15 & 48572 & 48571.4461160293 & 0.553883970744209 \tabularnewline
16 & 43899 & 43787.7905745671 & 111.209425432899 \tabularnewline
17 & 37532 & 37307.3093522476 & 224.690647752446 \tabularnewline
18 & 40357 & 39878.9830941167 & 478.016905883254 \tabularnewline
19 & 35489 & 35015.15205761 & 473.847942389999 \tabularnewline
20 & 29027 & 28634.6593337897 & 392.340666210319 \tabularnewline
21 & 34485 & 33503.7889993035 & 981.211000696465 \tabularnewline
22 & 42598 & 40907.1239125659 & 1690.87608743407 \tabularnewline
23 & 30306 & 28398.0378202951 & 1907.96217970492 \tabularnewline
24 & 26451 & 24599.1622363261 & 1851.83776367391 \tabularnewline
25 & 47460 & 53185.4184385885 & -5725.41843858849 \tabularnewline
26 & 50104 & 46281.8642188605 & 3822.13578113946 \tabularnewline
27 & 61465 & 51130.4482996314 & 10334.5517003686 \tabularnewline
28 & 53726 & 46915.5430119018 & 6810.45698809817 \tabularnewline
29 & 39477 & 40818.6392113434 & -1341.63921134340 \tabularnewline
30 & 43895 & 43399.0913610316 & 495.908638968445 \tabularnewline
31 & 31481 & 38535.1926514119 & -7054.1926514119 \tabularnewline
32 & 29896 & 31740.6385184782 & -1844.63851847820 \tabularnewline
33 & 33842 & 36701.3022621234 & -2859.30226212342 \tabularnewline
34 & 39120 & 44156.1382214790 & -5036.13822147904 \tabularnewline
35 & 33702 & 31378.1915624761 & 2323.80843752393 \tabularnewline
36 & 25094 & 27581.0424649262 & -2487.04246492615 \tabularnewline
37 & 51442 & 53294.9844857177 & -1852.98448571766 \tabularnewline
38 & 45594 & 49928.8458265101 & -4334.84582651011 \tabularnewline
39 & 52518 & 56636.6482653951 & -4118.64826539515 \tabularnewline
40 & 48564 & 50448.0286568089 & -1884.02865680889 \tabularnewline
41 & 41745 & 41053.9275843764 & 691.072415623552 \tabularnewline
42 & 49585 & 44380.5739934001 & 5204.42600659989 \tabularnewline
43 & 32747 & 37117.1504914156 & -4370.15049141558 \tabularnewline
44 & 33379 & 32281.5692064946 & 1097.43079350543 \tabularnewline
45 & 35645 & 37037.8103717865 & -1392.81037178655 \tabularnewline
46 & 37034 & 43806.1958880855 & -6772.19588808546 \tabularnewline
47 & 35681 & 33512.7370643893 & 2168.26293561075 \tabularnewline
48 & 20972 & 28024.8078272207 & -7052.80782722075 \tabularnewline
49 & 58552 & 53725.9660216681 & 4826.03397833186 \tabularnewline
50 & 54955 & 49833.8901653443 & 5121.10983465568 \tabularnewline
51 & 65540 & 57101.8439860219 & 8438.15601397814 \tabularnewline
52 & 51570 & 52338.4574206093 & -768.457420609338 \tabularnewline
53 & 51145 & 43902.2386717266 & 7242.7613282734 \tabularnewline
54 & 46641 & 49143.3811748015 & -2502.3811748015 \tabularnewline
55 & 35704 & 38136.7130716886 & -2432.71307168862 \tabularnewline
56 & 33253 & 35312.6935494417 & -2059.69354944170 \tabularnewline
57 & 35193 & 39036.3464977491 & -3843.34649774914 \tabularnewline
58 & 41668 & 43797.9388594381 & -2129.93885943813 \tabularnewline
59 & 34865 & 36869.170106545 & -2004.17010654498 \tabularnewline
60 & 21210 & 27942.7138847439 & -6732.71388474385 \tabularnewline
61 & 56126 & 57814.5247119143 & -1688.52471191430 \tabularnewline
62 & 49231 & 53691.6491642265 & -4460.6491642265 \tabularnewline
63 & 59723 & 61628.1982867343 & -1905.19828673426 \tabularnewline
64 & 48103 & 53114.4667700878 & -5011.46677008781 \tabularnewline
65 & 47472 & 47261.784274631 & 210.215725368987 \tabularnewline
66 & 50497 & 48733.7084571041 & 1763.29154289586 \tabularnewline
67 & 40059 & 37969.3898106767 & 2089.61018932334 \tabularnewline
68 & 34149 & 35507.0592861316 & -1358.05928613158 \tabularnewline
69 & 36860 & 38642.3638867991 & -1782.36388679905 \tabularnewline
70 & 46356 & 44108.2942354146 & 2247.7057645854 \tabularnewline
71 & 36577 & 37447.4877720121 & -870.487772012071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11059&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]50556[/C][C]50513.9134722223[/C][C]42.0865277777484[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]43931.2207583048[/C][C]-30.2207583047712[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]48571.4461160293[/C][C]0.553883970744209[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]43787.7905745671[/C][C]111.209425432899[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]37307.3093522476[/C][C]224.690647752446[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]39878.9830941167[/C][C]478.016905883254[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]35015.15205761[/C][C]473.847942389999[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]28634.6593337897[/C][C]392.340666210319[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]33503.7889993035[/C][C]981.211000696465[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]40907.1239125659[/C][C]1690.87608743407[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]28398.0378202951[/C][C]1907.96217970492[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]24599.1622363261[/C][C]1851.83776367391[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]53185.4184385885[/C][C]-5725.41843858849[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]46281.8642188605[/C][C]3822.13578113946[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]51130.4482996314[/C][C]10334.5517003686[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]46915.5430119018[/C][C]6810.45698809817[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]40818.6392113434[/C][C]-1341.63921134340[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]43399.0913610316[/C][C]495.908638968445[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]38535.1926514119[/C][C]-7054.1926514119[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]31740.6385184782[/C][C]-1844.63851847820[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]36701.3022621234[/C][C]-2859.30226212342[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]44156.1382214790[/C][C]-5036.13822147904[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]31378.1915624761[/C][C]2323.80843752393[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]27581.0424649262[/C][C]-2487.04246492615[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]53294.9844857177[/C][C]-1852.98448571766[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]49928.8458265101[/C][C]-4334.84582651011[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]56636.6482653951[/C][C]-4118.64826539515[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]50448.0286568089[/C][C]-1884.02865680889[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]41053.9275843764[/C][C]691.072415623552[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44380.5739934001[/C][C]5204.42600659989[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]37117.1504914156[/C][C]-4370.15049141558[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]32281.5692064946[/C][C]1097.43079350543[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]37037.8103717865[/C][C]-1392.81037178655[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]43806.1958880855[/C][C]-6772.19588808546[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]33512.7370643893[/C][C]2168.26293561075[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]28024.8078272207[/C][C]-7052.80782722075[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]53725.9660216681[/C][C]4826.03397833186[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]49833.8901653443[/C][C]5121.10983465568[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]57101.8439860219[/C][C]8438.15601397814[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]52338.4574206093[/C][C]-768.457420609338[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]43902.2386717266[/C][C]7242.7613282734[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]49143.3811748015[/C][C]-2502.3811748015[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]38136.7130716886[/C][C]-2432.71307168862[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]35312.6935494417[/C][C]-2059.69354944170[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]39036.3464977491[/C][C]-3843.34649774914[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]43797.9388594381[/C][C]-2129.93885943813[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]36869.170106545[/C][C]-2004.17010654498[/C][/ROW]
[ROW][C]60[/C][C]21210[/C][C]27942.7138847439[/C][C]-6732.71388474385[/C][/ROW]
[ROW][C]61[/C][C]56126[/C][C]57814.5247119143[/C][C]-1688.52471191430[/C][/ROW]
[ROW][C]62[/C][C]49231[/C][C]53691.6491642265[/C][C]-4460.6491642265[/C][/ROW]
[ROW][C]63[/C][C]59723[/C][C]61628.1982867343[/C][C]-1905.19828673426[/C][/ROW]
[ROW][C]64[/C][C]48103[/C][C]53114.4667700878[/C][C]-5011.46677008781[/C][/ROW]
[ROW][C]65[/C][C]47472[/C][C]47261.784274631[/C][C]210.215725368987[/C][/ROW]
[ROW][C]66[/C][C]50497[/C][C]48733.7084571041[/C][C]1763.29154289586[/C][/ROW]
[ROW][C]67[/C][C]40059[/C][C]37969.3898106767[/C][C]2089.61018932334[/C][/ROW]
[ROW][C]68[/C][C]34149[/C][C]35507.0592861316[/C][C]-1358.05928613158[/C][/ROW]
[ROW][C]69[/C][C]36860[/C][C]38642.3638867991[/C][C]-1782.36388679905[/C][/ROW]
[ROW][C]70[/C][C]46356[/C][C]44108.2942354146[/C][C]2247.7057645854[/C][/ROW]
[ROW][C]71[/C][C]36577[/C][C]37447.4877720121[/C][C]-870.487772012071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11059&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11059&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
135055650513.913472222342.0865277777484
144390143931.2207583048-30.2207583047712
154857248571.44611602930.553883970744209
164389943787.7905745671111.209425432899
173753237307.3093522476224.690647752446
184035739878.9830941167478.016905883254
193548935015.15205761473.847942389999
202902728634.6593337897392.340666210319
213448533503.7889993035981.211000696465
224259840907.12391256591690.87608743407
233030628398.03782029511907.96217970492
242645124599.16223632611851.83776367391
254746053185.4184385885-5725.41843858849
265010446281.86421886053822.13578113946
276146551130.448299631410334.5517003686
285372646915.54301190186810.45698809817
293947740818.6392113434-1341.63921134340
304389543399.0913610316495.908638968445
313148138535.1926514119-7054.1926514119
322989631740.6385184782-1844.63851847820
333384236701.3022621234-2859.30226212342
343912044156.1382214790-5036.13822147904
353370231378.19156247612323.80843752393
362509427581.0424649262-2487.04246492615
375144253294.9844857177-1852.98448571766
384559449928.8458265101-4334.84582651011
395251856636.6482653951-4118.64826539515
404856450448.0286568089-1884.02865680889
414174541053.9275843764691.072415623552
424958544380.57399340015204.42600659989
433274737117.1504914156-4370.15049141558
443337932281.56920649461097.43079350543
453564537037.8103717865-1392.81037178655
463703443806.1958880855-6772.19588808546
473568133512.73706438932168.26293561075
482097228024.8078272207-7052.80782722075
495855253725.96602166814826.03397833186
505495549833.89016534435121.10983465568
516554057101.84398602198438.15601397814
525157052338.4574206093-768.457420609338
535114543902.23867172667242.7613282734
544664149143.3811748015-2502.3811748015
553570438136.7130716886-2432.71307168862
563325335312.6935494417-2059.69354944170
573519339036.3464977491-3843.34649774914
584166843797.9388594381-2129.93885943813
593486536869.170106545-2004.17010654498
602121027942.7138847439-6732.71388474385
615612657814.5247119143-1688.52471191430
624923153691.6491642265-4460.6491642265
635972361628.1982867343-1905.19828673426
644810353114.4667700878-5011.46677008781
654747247261.784274631210.215725368987
665049748733.70845710411763.29154289586
674005937969.38981067672089.61018932334
683414935507.0592861316-1358.05928613158
693686038642.3638867991-1782.36388679905
704635644108.29423541462247.7057645854
713657737447.4877720121-870.487772012071







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7226925.129492821619538.982034010334311.2769516328
7358905.820408658251509.968250332766301.6725669837
7453899.84999191346494.297610339461305.4023734865
7562958.611333110755543.363183488270373.8594827331
7653456.175611760146031.236128339160881.1150951812
7749686.503473753942251.877069952957121.129877555
7851690.827832016544246.518900538659135.1367634944
7940950.25254747533496.265460423348404.2396345266
8037175.083681909929711.422790902344638.7445729175
8140231.605241193932758.274877476447704.9356049115
8247198.289412093739715.293886653354681.2849375341
8339331.782320165631839.125923842646824.4387164886

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 26925.1294928216 & 19538.9820340103 & 34311.2769516328 \tabularnewline
73 & 58905.8204086582 & 51509.9682503327 & 66301.6725669837 \tabularnewline
74 & 53899.849991913 & 46494.2976103394 & 61305.4023734865 \tabularnewline
75 & 62958.6113331107 & 55543.3631834882 & 70373.8594827331 \tabularnewline
76 & 53456.1756117601 & 46031.2361283391 & 60881.1150951812 \tabularnewline
77 & 49686.5034737539 & 42251.8770699529 & 57121.129877555 \tabularnewline
78 & 51690.8278320165 & 44246.5189005386 & 59135.1367634944 \tabularnewline
79 & 40950.252547475 & 33496.2654604233 & 48404.2396345266 \tabularnewline
80 & 37175.0836819099 & 29711.4227909023 & 44638.7445729175 \tabularnewline
81 & 40231.6052411939 & 32758.2748774764 & 47704.9356049115 \tabularnewline
82 & 47198.2894120937 & 39715.2938866533 & 54681.2849375341 \tabularnewline
83 & 39331.7823201656 & 31839.1259238426 & 46824.4387164886 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11059&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]72[/C][C]26925.1294928216[/C][C]19538.9820340103[/C][C]34311.2769516328[/C][/ROW]
[ROW][C]73[/C][C]58905.8204086582[/C][C]51509.9682503327[/C][C]66301.6725669837[/C][/ROW]
[ROW][C]74[/C][C]53899.849991913[/C][C]46494.2976103394[/C][C]61305.4023734865[/C][/ROW]
[ROW][C]75[/C][C]62958.6113331107[/C][C]55543.3631834882[/C][C]70373.8594827331[/C][/ROW]
[ROW][C]76[/C][C]53456.1756117601[/C][C]46031.2361283391[/C][C]60881.1150951812[/C][/ROW]
[ROW][C]77[/C][C]49686.5034737539[/C][C]42251.8770699529[/C][C]57121.129877555[/C][/ROW]
[ROW][C]78[/C][C]51690.8278320165[/C][C]44246.5189005386[/C][C]59135.1367634944[/C][/ROW]
[ROW][C]79[/C][C]40950.252547475[/C][C]33496.2654604233[/C][C]48404.2396345266[/C][/ROW]
[ROW][C]80[/C][C]37175.0836819099[/C][C]29711.4227909023[/C][C]44638.7445729175[/C][/ROW]
[ROW][C]81[/C][C]40231.6052411939[/C][C]32758.2748774764[/C][C]47704.9356049115[/C][/ROW]
[ROW][C]82[/C][C]47198.2894120937[/C][C]39715.2938866533[/C][C]54681.2849375341[/C][/ROW]
[ROW][C]83[/C][C]39331.7823201656[/C][C]31839.1259238426[/C][C]46824.4387164886[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11059&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11059&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
7226925.129492821619538.982034010334311.2769516328
7358905.820408658251509.968250332766301.6725669837
7453899.84999191346494.297610339461305.4023734865
7562958.611333110755543.363183488270373.8594827331
7653456.175611760146031.236128339160881.1150951812
7749686.503473753942251.877069952957121.129877555
7851690.827832016544246.518900538659135.1367634944
7940950.25254747533496.265460423348404.2396345266
8037175.083681909929711.422790902344638.7445729175
8140231.605241193932758.274877476447704.9356049115
8247198.289412093739715.293886653354681.2849375341
8339331.782320165631839.125923842646824.4387164886



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