Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 09:45:02 -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/t1244216793lobv0kl0pkwae4t.htm/, Retrieved Fri, 10 May 2024 08:05:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41881, Retrieved Fri, 10 May 2024 08:05:27 +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] [Goudprijs-Exponen...] [2009-06-05 15:45:02] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
9721
9897
9828
9924
10371
10846
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41881&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41881&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.784666830625502
beta0.0378641310094148
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.784666830625502 \tabularnewline
beta & 0.0378641310094148 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41881&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]0.784666830625502[/C][/ROW]
[ROW][C]beta[/C][C]0.0378641310094148[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41881&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
alpha0.784666830625502
beta0.0378641310094148
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131087210741.6474358974130.352564102563
141029610265.303347394030.6966526059896
151038310392.5495905495-9.54959054953906
161043110462.5155496928-31.5155496927582
171057410600.8508660457-26.8508660456828
181065310674.5486461629-21.5486461629444
191080510647.0583430597157.941656940338
201087211025.8506887781-153.850688778106
211062510837.2522401850-212.252240185027
221040710547.0218628396-140.021862839627
231046310142.9747819922320.025218007779
241055610749.5862347794-193.58623477943
251064610866.6264595966-220.626459596553
261070210078.5323568813623.467643118718
271135310664.9624480266688.037551973386
281134611301.020186069344.9798139306604
291145111526.1043572766-75.1043572765575
301196411587.3683400464376.631659953608
311257411947.0847311115626.915268888459
321303112676.7770273560354.222972644035
331381212939.4177222090872.582277791016
341454413613.3522118249930.647788175129
351493114277.6754710051653.324528994903
361488615174.3088032397-288.308803239657
371600515347.4769841290657.523015871013
381706415592.56583641971471.43416358034
391516817045.8316060251-1877.83160602512
401605015641.3918566917408.608143308275
411583916248.0752671819-409.075267181917
421513716256.7648398332-1119.76483983325
431495415563.9516028764-609.951602876434
441564815295.3962878081352.603712191883
451530515699.3387386149-394.338738614941
461557915384.9769985834194.023001416555
471634815383.0039047665964.996095233517
481592816302.1162564163-374.116256416339
491617116589.7593055656-418.759305565622
501593716111.7462231936-174.746223193579
511571315449.3506519834263.649348016603
521559416178.4810701130-584.481070112979
531568315761.2153280806-78.2153280806397
541643815817.6841453827620.315854617282
551703216592.9327386944439.067261305561
561769617378.8434581587317.156541841337
571774517617.1426840708127.857315929232
581939417877.75196930351516.24803069650
592014819157.1126501077990.887349892266
602010819886.7665234069221.233476593101
611858420728.2167249392-2144.21672493916
621844118993.8430463573-552.843046357306
631839118162.9395133201228.060486679875
641917818714.2275167589463.772483241082
651807919292.3653460815-1213.36534608155
661848318638.6683680733-155.668368073348
671964418773.0758289109870.924171089078
681919519891.5064846986-696.506484698646
691965019283.4464530862366.55354691379
702083020027.2020641329802.797935867071
712359520609.30015610352985.69984389645
722293722773.4381660234163.561833976615

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 10872 & 10741.6474358974 & 130.352564102563 \tabularnewline
14 & 10296 & 10265.3033473940 & 30.6966526059896 \tabularnewline
15 & 10383 & 10392.5495905495 & -9.54959054953906 \tabularnewline
16 & 10431 & 10462.5155496928 & -31.5155496927582 \tabularnewline
17 & 10574 & 10600.8508660457 & -26.8508660456828 \tabularnewline
18 & 10653 & 10674.5486461629 & -21.5486461629444 \tabularnewline
19 & 10805 & 10647.0583430597 & 157.941656940338 \tabularnewline
20 & 10872 & 11025.8506887781 & -153.850688778106 \tabularnewline
21 & 10625 & 10837.2522401850 & -212.252240185027 \tabularnewline
22 & 10407 & 10547.0218628396 & -140.021862839627 \tabularnewline
23 & 10463 & 10142.9747819922 & 320.025218007779 \tabularnewline
24 & 10556 & 10749.5862347794 & -193.58623477943 \tabularnewline
25 & 10646 & 10866.6264595966 & -220.626459596553 \tabularnewline
26 & 10702 & 10078.5323568813 & 623.467643118718 \tabularnewline
27 & 11353 & 10664.9624480266 & 688.037551973386 \tabularnewline
28 & 11346 & 11301.0201860693 & 44.9798139306604 \tabularnewline
29 & 11451 & 11526.1043572766 & -75.1043572765575 \tabularnewline
30 & 11964 & 11587.3683400464 & 376.631659953608 \tabularnewline
31 & 12574 & 11947.0847311115 & 626.915268888459 \tabularnewline
32 & 13031 & 12676.7770273560 & 354.222972644035 \tabularnewline
33 & 13812 & 12939.4177222090 & 872.582277791016 \tabularnewline
34 & 14544 & 13613.3522118249 & 930.647788175129 \tabularnewline
35 & 14931 & 14277.6754710051 & 653.324528994903 \tabularnewline
36 & 14886 & 15174.3088032397 & -288.308803239657 \tabularnewline
37 & 16005 & 15347.4769841290 & 657.523015871013 \tabularnewline
38 & 17064 & 15592.5658364197 & 1471.43416358034 \tabularnewline
39 & 15168 & 17045.8316060251 & -1877.83160602512 \tabularnewline
40 & 16050 & 15641.3918566917 & 408.608143308275 \tabularnewline
41 & 15839 & 16248.0752671819 & -409.075267181917 \tabularnewline
42 & 15137 & 16256.7648398332 & -1119.76483983325 \tabularnewline
43 & 14954 & 15563.9516028764 & -609.951602876434 \tabularnewline
44 & 15648 & 15295.3962878081 & 352.603712191883 \tabularnewline
45 & 15305 & 15699.3387386149 & -394.338738614941 \tabularnewline
46 & 15579 & 15384.9769985834 & 194.023001416555 \tabularnewline
47 & 16348 & 15383.0039047665 & 964.996095233517 \tabularnewline
48 & 15928 & 16302.1162564163 & -374.116256416339 \tabularnewline
49 & 16171 & 16589.7593055656 & -418.759305565622 \tabularnewline
50 & 15937 & 16111.7462231936 & -174.746223193579 \tabularnewline
51 & 15713 & 15449.3506519834 & 263.649348016603 \tabularnewline
52 & 15594 & 16178.4810701130 & -584.481070112979 \tabularnewline
53 & 15683 & 15761.2153280806 & -78.2153280806397 \tabularnewline
54 & 16438 & 15817.6841453827 & 620.315854617282 \tabularnewline
55 & 17032 & 16592.9327386944 & 439.067261305561 \tabularnewline
56 & 17696 & 17378.8434581587 & 317.156541841337 \tabularnewline
57 & 17745 & 17617.1426840708 & 127.857315929232 \tabularnewline
58 & 19394 & 17877.7519693035 & 1516.24803069650 \tabularnewline
59 & 20148 & 19157.1126501077 & 990.887349892266 \tabularnewline
60 & 20108 & 19886.7665234069 & 221.233476593101 \tabularnewline
61 & 18584 & 20728.2167249392 & -2144.21672493916 \tabularnewline
62 & 18441 & 18993.8430463573 & -552.843046357306 \tabularnewline
63 & 18391 & 18162.9395133201 & 228.060486679875 \tabularnewline
64 & 19178 & 18714.2275167589 & 463.772483241082 \tabularnewline
65 & 18079 & 19292.3653460815 & -1213.36534608155 \tabularnewline
66 & 18483 & 18638.6683680733 & -155.668368073348 \tabularnewline
67 & 19644 & 18773.0758289109 & 870.924171089078 \tabularnewline
68 & 19195 & 19891.5064846986 & -696.506484698646 \tabularnewline
69 & 19650 & 19283.4464530862 & 366.55354691379 \tabularnewline
70 & 20830 & 20027.2020641329 & 802.797935867071 \tabularnewline
71 & 23595 & 20609.3001561035 & 2985.69984389645 \tabularnewline
72 & 22937 & 22773.4381660234 & 163.561833976615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41881&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]10872[/C][C]10741.6474358974[/C][C]130.352564102563[/C][/ROW]
[ROW][C]14[/C][C]10296[/C][C]10265.3033473940[/C][C]30.6966526059896[/C][/ROW]
[ROW][C]15[/C][C]10383[/C][C]10392.5495905495[/C][C]-9.54959054953906[/C][/ROW]
[ROW][C]16[/C][C]10431[/C][C]10462.5155496928[/C][C]-31.5155496927582[/C][/ROW]
[ROW][C]17[/C][C]10574[/C][C]10600.8508660457[/C][C]-26.8508660456828[/C][/ROW]
[ROW][C]18[/C][C]10653[/C][C]10674.5486461629[/C][C]-21.5486461629444[/C][/ROW]
[ROW][C]19[/C][C]10805[/C][C]10647.0583430597[/C][C]157.941656940338[/C][/ROW]
[ROW][C]20[/C][C]10872[/C][C]11025.8506887781[/C][C]-153.850688778106[/C][/ROW]
[ROW][C]21[/C][C]10625[/C][C]10837.2522401850[/C][C]-212.252240185027[/C][/ROW]
[ROW][C]22[/C][C]10407[/C][C]10547.0218628396[/C][C]-140.021862839627[/C][/ROW]
[ROW][C]23[/C][C]10463[/C][C]10142.9747819922[/C][C]320.025218007779[/C][/ROW]
[ROW][C]24[/C][C]10556[/C][C]10749.5862347794[/C][C]-193.58623477943[/C][/ROW]
[ROW][C]25[/C][C]10646[/C][C]10866.6264595966[/C][C]-220.626459596553[/C][/ROW]
[ROW][C]26[/C][C]10702[/C][C]10078.5323568813[/C][C]623.467643118718[/C][/ROW]
[ROW][C]27[/C][C]11353[/C][C]10664.9624480266[/C][C]688.037551973386[/C][/ROW]
[ROW][C]28[/C][C]11346[/C][C]11301.0201860693[/C][C]44.9798139306604[/C][/ROW]
[ROW][C]29[/C][C]11451[/C][C]11526.1043572766[/C][C]-75.1043572765575[/C][/ROW]
[ROW][C]30[/C][C]11964[/C][C]11587.3683400464[/C][C]376.631659953608[/C][/ROW]
[ROW][C]31[/C][C]12574[/C][C]11947.0847311115[/C][C]626.915268888459[/C][/ROW]
[ROW][C]32[/C][C]13031[/C][C]12676.7770273560[/C][C]354.222972644035[/C][/ROW]
[ROW][C]33[/C][C]13812[/C][C]12939.4177222090[/C][C]872.582277791016[/C][/ROW]
[ROW][C]34[/C][C]14544[/C][C]13613.3522118249[/C][C]930.647788175129[/C][/ROW]
[ROW][C]35[/C][C]14931[/C][C]14277.6754710051[/C][C]653.324528994903[/C][/ROW]
[ROW][C]36[/C][C]14886[/C][C]15174.3088032397[/C][C]-288.308803239657[/C][/ROW]
[ROW][C]37[/C][C]16005[/C][C]15347.4769841290[/C][C]657.523015871013[/C][/ROW]
[ROW][C]38[/C][C]17064[/C][C]15592.5658364197[/C][C]1471.43416358034[/C][/ROW]
[ROW][C]39[/C][C]15168[/C][C]17045.8316060251[/C][C]-1877.83160602512[/C][/ROW]
[ROW][C]40[/C][C]16050[/C][C]15641.3918566917[/C][C]408.608143308275[/C][/ROW]
[ROW][C]41[/C][C]15839[/C][C]16248.0752671819[/C][C]-409.075267181917[/C][/ROW]
[ROW][C]42[/C][C]15137[/C][C]16256.7648398332[/C][C]-1119.76483983325[/C][/ROW]
[ROW][C]43[/C][C]14954[/C][C]15563.9516028764[/C][C]-609.951602876434[/C][/ROW]
[ROW][C]44[/C][C]15648[/C][C]15295.3962878081[/C][C]352.603712191883[/C][/ROW]
[ROW][C]45[/C][C]15305[/C][C]15699.3387386149[/C][C]-394.338738614941[/C][/ROW]
[ROW][C]46[/C][C]15579[/C][C]15384.9769985834[/C][C]194.023001416555[/C][/ROW]
[ROW][C]47[/C][C]16348[/C][C]15383.0039047665[/C][C]964.996095233517[/C][/ROW]
[ROW][C]48[/C][C]15928[/C][C]16302.1162564163[/C][C]-374.116256416339[/C][/ROW]
[ROW][C]49[/C][C]16171[/C][C]16589.7593055656[/C][C]-418.759305565622[/C][/ROW]
[ROW][C]50[/C][C]15937[/C][C]16111.7462231936[/C][C]-174.746223193579[/C][/ROW]
[ROW][C]51[/C][C]15713[/C][C]15449.3506519834[/C][C]263.649348016603[/C][/ROW]
[ROW][C]52[/C][C]15594[/C][C]16178.4810701130[/C][C]-584.481070112979[/C][/ROW]
[ROW][C]53[/C][C]15683[/C][C]15761.2153280806[/C][C]-78.2153280806397[/C][/ROW]
[ROW][C]54[/C][C]16438[/C][C]15817.6841453827[/C][C]620.315854617282[/C][/ROW]
[ROW][C]55[/C][C]17032[/C][C]16592.9327386944[/C][C]439.067261305561[/C][/ROW]
[ROW][C]56[/C][C]17696[/C][C]17378.8434581587[/C][C]317.156541841337[/C][/ROW]
[ROW][C]57[/C][C]17745[/C][C]17617.1426840708[/C][C]127.857315929232[/C][/ROW]
[ROW][C]58[/C][C]19394[/C][C]17877.7519693035[/C][C]1516.24803069650[/C][/ROW]
[ROW][C]59[/C][C]20148[/C][C]19157.1126501077[/C][C]990.887349892266[/C][/ROW]
[ROW][C]60[/C][C]20108[/C][C]19886.7665234069[/C][C]221.233476593101[/C][/ROW]
[ROW][C]61[/C][C]18584[/C][C]20728.2167249392[/C][C]-2144.21672493916[/C][/ROW]
[ROW][C]62[/C][C]18441[/C][C]18993.8430463573[/C][C]-552.843046357306[/C][/ROW]
[ROW][C]63[/C][C]18391[/C][C]18162.9395133201[/C][C]228.060486679875[/C][/ROW]
[ROW][C]64[/C][C]19178[/C][C]18714.2275167589[/C][C]463.772483241082[/C][/ROW]
[ROW][C]65[/C][C]18079[/C][C]19292.3653460815[/C][C]-1213.36534608155[/C][/ROW]
[ROW][C]66[/C][C]18483[/C][C]18638.6683680733[/C][C]-155.668368073348[/C][/ROW]
[ROW][C]67[/C][C]19644[/C][C]18773.0758289109[/C][C]870.924171089078[/C][/ROW]
[ROW][C]68[/C][C]19195[/C][C]19891.5064846986[/C][C]-696.506484698646[/C][/ROW]
[ROW][C]69[/C][C]19650[/C][C]19283.4464530862[/C][C]366.55354691379[/C][/ROW]
[ROW][C]70[/C][C]20830[/C][C]20027.2020641329[/C][C]802.797935867071[/C][/ROW]
[ROW][C]71[/C][C]23595[/C][C]20609.3001561035[/C][C]2985.69984389645[/C][/ROW]
[ROW][C]72[/C][C]22937[/C][C]22773.4381660234[/C][C]163.561833976615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41881&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
131087210741.6474358974130.352564102563
141029610265.303347394030.6966526059896
151038310392.5495905495-9.54959054953906
161043110462.5155496928-31.5155496927582
171057410600.8508660457-26.8508660456828
181065310674.5486461629-21.5486461629444
191080510647.0583430597157.941656940338
201087211025.8506887781-153.850688778106
211062510837.2522401850-212.252240185027
221040710547.0218628396-140.021862839627
231046310142.9747819922320.025218007779
241055610749.5862347794-193.58623477943
251064610866.6264595966-220.626459596553
261070210078.5323568813623.467643118718
271135310664.9624480266688.037551973386
281134611301.020186069344.9798139306604
291145111526.1043572766-75.1043572765575
301196411587.3683400464376.631659953608
311257411947.0847311115626.915268888459
321303112676.7770273560354.222972644035
331381212939.4177222090872.582277791016
341454413613.3522118249930.647788175129
351493114277.6754710051653.324528994903
361488615174.3088032397-288.308803239657
371600515347.4769841290657.523015871013
381706415592.56583641971471.43416358034
391516817045.8316060251-1877.83160602512
401605015641.3918566917408.608143308275
411583916248.0752671819-409.075267181917
421513716256.7648398332-1119.76483983325
431495415563.9516028764-609.951602876434
441564815295.3962878081352.603712191883
451530515699.3387386149-394.338738614941
461557915384.9769985834194.023001416555
471634815383.0039047665964.996095233517
481592816302.1162564163-374.116256416339
491617116589.7593055656-418.759305565622
501593716111.7462231936-174.746223193579
511571315449.3506519834263.649348016603
521559416178.4810701130-584.481070112979
531568315761.2153280806-78.2153280806397
541643815817.6841453827620.315854617282
551703216592.9327386944439.067261305561
561769617378.8434581587317.156541841337
571774517617.1426840708127.857315929232
581939417877.75196930351516.24803069650
592014819157.1126501077990.887349892266
602010819886.7665234069221.233476593101
611858420728.2167249392-2144.21672493916
621844118993.8430463573-552.843046357306
631839118162.9395133201228.060486679875
641917818714.2275167589463.772483241082
651807919292.3653460815-1213.36534608155
661848318638.6683680733-155.668368073348
671964418773.0758289109870.924171089078
681919519891.5064846986-696.506484698646
691965019283.4464530862366.55354691379
702083020027.2020641329802.797935867071
712359520609.30015610352985.69984389645
722293722773.4381660234163.561833976615







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7323093.514934282221591.338555947324595.6913126171
7423481.258255137321543.968518754825418.5479915197
7523365.677844896421050.329461584325681.0262282085
7623895.366206360621233.833279615826556.8991331053
7723841.269974929420853.656632628726828.8833172302
7824496.283975368321196.124913561527796.4430371752
7925107.389882250121504.142683011228710.6370814891
8025312.530843162621412.936129841029212.1255564841
8125608.217572794821417.110405287629799.3247403019
8226275.707227758721796.533724622530754.8807308949
8326791.494450133422026.657550359531556.3313499074
8426010.012445362820961.112631684831058.9122590408

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 23093.5149342822 & 21591.3385559473 & 24595.6913126171 \tabularnewline
74 & 23481.2582551373 & 21543.9685187548 & 25418.5479915197 \tabularnewline
75 & 23365.6778448964 & 21050.3294615843 & 25681.0262282085 \tabularnewline
76 & 23895.3662063606 & 21233.8332796158 & 26556.8991331053 \tabularnewline
77 & 23841.2699749294 & 20853.6566326287 & 26828.8833172302 \tabularnewline
78 & 24496.2839753683 & 21196.1249135615 & 27796.4430371752 \tabularnewline
79 & 25107.3898822501 & 21504.1426830112 & 28710.6370814891 \tabularnewline
80 & 25312.5308431626 & 21412.9361298410 & 29212.1255564841 \tabularnewline
81 & 25608.2175727948 & 21417.1104052876 & 29799.3247403019 \tabularnewline
82 & 26275.7072277587 & 21796.5337246225 & 30754.8807308949 \tabularnewline
83 & 26791.4944501334 & 22026.6575503595 & 31556.3313499074 \tabularnewline
84 & 26010.0124453628 & 20961.1126316848 & 31058.9122590408 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41881&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]23093.5149342822[/C][C]21591.3385559473[/C][C]24595.6913126171[/C][/ROW]
[ROW][C]74[/C][C]23481.2582551373[/C][C]21543.9685187548[/C][C]25418.5479915197[/C][/ROW]
[ROW][C]75[/C][C]23365.6778448964[/C][C]21050.3294615843[/C][C]25681.0262282085[/C][/ROW]
[ROW][C]76[/C][C]23895.3662063606[/C][C]21233.8332796158[/C][C]26556.8991331053[/C][/ROW]
[ROW][C]77[/C][C]23841.2699749294[/C][C]20853.6566326287[/C][C]26828.8833172302[/C][/ROW]
[ROW][C]78[/C][C]24496.2839753683[/C][C]21196.1249135615[/C][C]27796.4430371752[/C][/ROW]
[ROW][C]79[/C][C]25107.3898822501[/C][C]21504.1426830112[/C][C]28710.6370814891[/C][/ROW]
[ROW][C]80[/C][C]25312.5308431626[/C][C]21412.9361298410[/C][C]29212.1255564841[/C][/ROW]
[ROW][C]81[/C][C]25608.2175727948[/C][C]21417.1104052876[/C][C]29799.3247403019[/C][/ROW]
[ROW][C]82[/C][C]26275.7072277587[/C][C]21796.5337246225[/C][C]30754.8807308949[/C][/ROW]
[ROW][C]83[/C][C]26791.4944501334[/C][C]22026.6575503595[/C][C]31556.3313499074[/C][/ROW]
[ROW][C]84[/C][C]26010.0124453628[/C][C]20961.1126316848[/C][C]31058.9122590408[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41881&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41881&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
7323093.514934282221591.338555947324595.6913126171
7423481.258255137321543.968518754825418.5479915197
7523365.677844896421050.329461584325681.0262282085
7623895.366206360621233.833279615826556.8991331053
7723841.269974929420853.656632628726828.8833172302
7824496.283975368321196.124913561527796.4430371752
7925107.389882250121504.142683011228710.6370814891
8025312.530843162621412.936129841029212.1255564841
8125608.217572794821417.110405287629799.3247403019
8226275.707227758721796.533724622530754.8807308949
8326791.494450133422026.657550359531556.3313499074
8426010.012445362820961.112631684831058.9122590408



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')