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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Jun 2009 04:54:08 -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/04/t1244112892cibpadqx5u6csad.htm/, Retrieved Tue, 14 May 2024 00:02:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41590, Retrieved Tue, 14 May 2024 00:02:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [TRIMMED MEAN PLOT...] [2009-04-22 16:50:11] [b08470c46dfe3064cb845db99379f9ea]
- RMPD    [Exponential Smoothing] [DOUBLE MULTIPLICA...] [2009-06-04 10:54:08] [23fb7a586ae7811d7719db820c9fb3e7] [Current]
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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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41590&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41590&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41590&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.940153707491614
beta0.00064617126624545
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.940153707491614 \tabularnewline
beta & 0.00064617126624545 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41590&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]0.940153707491614[/C][/ROW]
[ROW][C]beta[/C][C]0.00064617126624545[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41590&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41590&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
alpha0.940153707491614
beta0.00064617126624545
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3982810073-245
4992410018.5135040882-94.5135040882033
51037110105.4500282521265.549971747883
61084610531.0628858462314.937114153763
71041311003.2985728707-590.298572870655
81070910624.114966018484.885033981629
91066210879.7592980704-217.759298070419
101057010850.7391504510-280.739150450972
111029710762.3377119973-465.337711997287
121063510500.1025587032134.89744129684
131087210802.262660382969.7373396170697
141029611043.2046163435-747.204616343482
151038310515.6416365650-132.641636564989
161043110565.7817408768-134.781740876790
171057410613.8279382358-39.8279382358469
181065310751.1211097033-98.1211097033247
191080510833.5501312895-28.5501312894867
201087210981.3692219516-109.369221951580
211062511053.1395030552-428.139503055188
221040710824.9566276596-417.956627659563
231046310606.0933115385-143.093311538509
241055610645.5568318907-89.5568318907499
251064610735.2984662666-89.2984662665986
261070210825.2287551958-123.228755195796
271135310883.1844956848469.815504315238
281134611498.9784085249-152.978408524928
291145111529.1573807744-78.1573807743516
301196411629.6321390286334.367860971364
311257412118.1471613238455.85283867623
321303112721.1536665542309.846333445776
331381213187.0798463185624.920153681498
341454413949.6034854990594.396514500952
351493114683.7913082057247.208691794338
361488615091.7193915560-205.719391556016
371600515073.7004835230931.299516477016
381706416125.2198821118938.78011788824
391516817184.3425050657-2016.34250506574
401605015463.970709257586.029290742999
411583916190.5844185262-351.584418526210
421513716035.4835351872-898.483535187188
431495415365.6675906678-411.667590667834
441564815153.2833730648494.716626935238
451530515793.3401785581-488.340178558137
461557915508.875816881470.1241831186053
471634815749.4963958001598.503604199923
481592816487.2384375367-559.2384375367
491617116136.185268890634.8147311093562
501593716343.6545391543-406.654539154317
511571316135.8277954767-422.827795476715
521559415912.5388368879-318.538836887879
531568315787.1040169241-104.104016924099
541643815863.2076447418574.79235525816
551703216577.9274004043454.072599595715
561769617179.4278794590516.572120541041
571774517840.0013325710-95.0013325710424
581939417925.54402299721468.45597700279
592014819481.8689869877666.131013012273
602010820284.2898362675-176.289836267482
611858420294.5985046982-1710.59850469817
621844118861.3820009425-420.38200094254
631839118640.9119444631-249.911944463052
641917818580.5581220149597.441877985082
651807919317.2100834256-1238.21008342565
661848318327.3148346403155.685165359722
671964418647.9899506419996.010049358109
681919519759.3046982474-564.304698247426
691965019403.3409357577246.659064242271
702083019809.95760667251020.04239332753
712359520944.29315781072650.70684218925
722293723613.3142414538-676.314241453827

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9828 & 10073 & -245 \tabularnewline
4 & 9924 & 10018.5135040882 & -94.5135040882033 \tabularnewline
5 & 10371 & 10105.4500282521 & 265.549971747883 \tabularnewline
6 & 10846 & 10531.0628858462 & 314.937114153763 \tabularnewline
7 & 10413 & 11003.2985728707 & -590.298572870655 \tabularnewline
8 & 10709 & 10624.1149660184 & 84.885033981629 \tabularnewline
9 & 10662 & 10879.7592980704 & -217.759298070419 \tabularnewline
10 & 10570 & 10850.7391504510 & -280.739150450972 \tabularnewline
11 & 10297 & 10762.3377119973 & -465.337711997287 \tabularnewline
12 & 10635 & 10500.1025587032 & 134.89744129684 \tabularnewline
13 & 10872 & 10802.2626603829 & 69.7373396170697 \tabularnewline
14 & 10296 & 11043.2046163435 & -747.204616343482 \tabularnewline
15 & 10383 & 10515.6416365650 & -132.641636564989 \tabularnewline
16 & 10431 & 10565.7817408768 & -134.781740876790 \tabularnewline
17 & 10574 & 10613.8279382358 & -39.8279382358469 \tabularnewline
18 & 10653 & 10751.1211097033 & -98.1211097033247 \tabularnewline
19 & 10805 & 10833.5501312895 & -28.5501312894867 \tabularnewline
20 & 10872 & 10981.3692219516 & -109.369221951580 \tabularnewline
21 & 10625 & 11053.1395030552 & -428.139503055188 \tabularnewline
22 & 10407 & 10824.9566276596 & -417.956627659563 \tabularnewline
23 & 10463 & 10606.0933115385 & -143.093311538509 \tabularnewline
24 & 10556 & 10645.5568318907 & -89.5568318907499 \tabularnewline
25 & 10646 & 10735.2984662666 & -89.2984662665986 \tabularnewline
26 & 10702 & 10825.2287551958 & -123.228755195796 \tabularnewline
27 & 11353 & 10883.1844956848 & 469.815504315238 \tabularnewline
28 & 11346 & 11498.9784085249 & -152.978408524928 \tabularnewline
29 & 11451 & 11529.1573807744 & -78.1573807743516 \tabularnewline
30 & 11964 & 11629.6321390286 & 334.367860971364 \tabularnewline
31 & 12574 & 12118.1471613238 & 455.85283867623 \tabularnewline
32 & 13031 & 12721.1536665542 & 309.846333445776 \tabularnewline
33 & 13812 & 13187.0798463185 & 624.920153681498 \tabularnewline
34 & 14544 & 13949.6034854990 & 594.396514500952 \tabularnewline
35 & 14931 & 14683.7913082057 & 247.208691794338 \tabularnewline
36 & 14886 & 15091.7193915560 & -205.719391556016 \tabularnewline
37 & 16005 & 15073.7004835230 & 931.299516477016 \tabularnewline
38 & 17064 & 16125.2198821118 & 938.78011788824 \tabularnewline
39 & 15168 & 17184.3425050657 & -2016.34250506574 \tabularnewline
40 & 16050 & 15463.970709257 & 586.029290742999 \tabularnewline
41 & 15839 & 16190.5844185262 & -351.584418526210 \tabularnewline
42 & 15137 & 16035.4835351872 & -898.483535187188 \tabularnewline
43 & 14954 & 15365.6675906678 & -411.667590667834 \tabularnewline
44 & 15648 & 15153.2833730648 & 494.716626935238 \tabularnewline
45 & 15305 & 15793.3401785581 & -488.340178558137 \tabularnewline
46 & 15579 & 15508.8758168814 & 70.1241831186053 \tabularnewline
47 & 16348 & 15749.4963958001 & 598.503604199923 \tabularnewline
48 & 15928 & 16487.2384375367 & -559.2384375367 \tabularnewline
49 & 16171 & 16136.1852688906 & 34.8147311093562 \tabularnewline
50 & 15937 & 16343.6545391543 & -406.654539154317 \tabularnewline
51 & 15713 & 16135.8277954767 & -422.827795476715 \tabularnewline
52 & 15594 & 15912.5388368879 & -318.538836887879 \tabularnewline
53 & 15683 & 15787.1040169241 & -104.104016924099 \tabularnewline
54 & 16438 & 15863.2076447418 & 574.79235525816 \tabularnewline
55 & 17032 & 16577.9274004043 & 454.072599595715 \tabularnewline
56 & 17696 & 17179.4278794590 & 516.572120541041 \tabularnewline
57 & 17745 & 17840.0013325710 & -95.0013325710424 \tabularnewline
58 & 19394 & 17925.5440229972 & 1468.45597700279 \tabularnewline
59 & 20148 & 19481.8689869877 & 666.131013012273 \tabularnewline
60 & 20108 & 20284.2898362675 & -176.289836267482 \tabularnewline
61 & 18584 & 20294.5985046982 & -1710.59850469817 \tabularnewline
62 & 18441 & 18861.3820009425 & -420.38200094254 \tabularnewline
63 & 18391 & 18640.9119444631 & -249.911944463052 \tabularnewline
64 & 19178 & 18580.5581220149 & 597.441877985082 \tabularnewline
65 & 18079 & 19317.2100834256 & -1238.21008342565 \tabularnewline
66 & 18483 & 18327.3148346403 & 155.685165359722 \tabularnewline
67 & 19644 & 18647.9899506419 & 996.010049358109 \tabularnewline
68 & 19195 & 19759.3046982474 & -564.304698247426 \tabularnewline
69 & 19650 & 19403.3409357577 & 246.659064242271 \tabularnewline
70 & 20830 & 19809.9576066725 & 1020.04239332753 \tabularnewline
71 & 23595 & 20944.2931578107 & 2650.70684218925 \tabularnewline
72 & 22937 & 23613.3142414538 & -676.314241453827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41590&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]3[/C][C]9828[/C][C]10073[/C][C]-245[/C][/ROW]
[ROW][C]4[/C][C]9924[/C][C]10018.5135040882[/C][C]-94.5135040882033[/C][/ROW]
[ROW][C]5[/C][C]10371[/C][C]10105.4500282521[/C][C]265.549971747883[/C][/ROW]
[ROW][C]6[/C][C]10846[/C][C]10531.0628858462[/C][C]314.937114153763[/C][/ROW]
[ROW][C]7[/C][C]10413[/C][C]11003.2985728707[/C][C]-590.298572870655[/C][/ROW]
[ROW][C]8[/C][C]10709[/C][C]10624.1149660184[/C][C]84.885033981629[/C][/ROW]
[ROW][C]9[/C][C]10662[/C][C]10879.7592980704[/C][C]-217.759298070419[/C][/ROW]
[ROW][C]10[/C][C]10570[/C][C]10850.7391504510[/C][C]-280.739150450972[/C][/ROW]
[ROW][C]11[/C][C]10297[/C][C]10762.3377119973[/C][C]-465.337711997287[/C][/ROW]
[ROW][C]12[/C][C]10635[/C][C]10500.1025587032[/C][C]134.89744129684[/C][/ROW]
[ROW][C]13[/C][C]10872[/C][C]10802.2626603829[/C][C]69.7373396170697[/C][/ROW]
[ROW][C]14[/C][C]10296[/C][C]11043.2046163435[/C][C]-747.204616343482[/C][/ROW]
[ROW][C]15[/C][C]10383[/C][C]10515.6416365650[/C][C]-132.641636564989[/C][/ROW]
[ROW][C]16[/C][C]10431[/C][C]10565.7817408768[/C][C]-134.781740876790[/C][/ROW]
[ROW][C]17[/C][C]10574[/C][C]10613.8279382358[/C][C]-39.8279382358469[/C][/ROW]
[ROW][C]18[/C][C]10653[/C][C]10751.1211097033[/C][C]-98.1211097033247[/C][/ROW]
[ROW][C]19[/C][C]10805[/C][C]10833.5501312895[/C][C]-28.5501312894867[/C][/ROW]
[ROW][C]20[/C][C]10872[/C][C]10981.3692219516[/C][C]-109.369221951580[/C][/ROW]
[ROW][C]21[/C][C]10625[/C][C]11053.1395030552[/C][C]-428.139503055188[/C][/ROW]
[ROW][C]22[/C][C]10407[/C][C]10824.9566276596[/C][C]-417.956627659563[/C][/ROW]
[ROW][C]23[/C][C]10463[/C][C]10606.0933115385[/C][C]-143.093311538509[/C][/ROW]
[ROW][C]24[/C][C]10556[/C][C]10645.5568318907[/C][C]-89.5568318907499[/C][/ROW]
[ROW][C]25[/C][C]10646[/C][C]10735.2984662666[/C][C]-89.2984662665986[/C][/ROW]
[ROW][C]26[/C][C]10702[/C][C]10825.2287551958[/C][C]-123.228755195796[/C][/ROW]
[ROW][C]27[/C][C]11353[/C][C]10883.1844956848[/C][C]469.815504315238[/C][/ROW]
[ROW][C]28[/C][C]11346[/C][C]11498.9784085249[/C][C]-152.978408524928[/C][/ROW]
[ROW][C]29[/C][C]11451[/C][C]11529.1573807744[/C][C]-78.1573807743516[/C][/ROW]
[ROW][C]30[/C][C]11964[/C][C]11629.6321390286[/C][C]334.367860971364[/C][/ROW]
[ROW][C]31[/C][C]12574[/C][C]12118.1471613238[/C][C]455.85283867623[/C][/ROW]
[ROW][C]32[/C][C]13031[/C][C]12721.1536665542[/C][C]309.846333445776[/C][/ROW]
[ROW][C]33[/C][C]13812[/C][C]13187.0798463185[/C][C]624.920153681498[/C][/ROW]
[ROW][C]34[/C][C]14544[/C][C]13949.6034854990[/C][C]594.396514500952[/C][/ROW]
[ROW][C]35[/C][C]14931[/C][C]14683.7913082057[/C][C]247.208691794338[/C][/ROW]
[ROW][C]36[/C][C]14886[/C][C]15091.7193915560[/C][C]-205.719391556016[/C][/ROW]
[ROW][C]37[/C][C]16005[/C][C]15073.7004835230[/C][C]931.299516477016[/C][/ROW]
[ROW][C]38[/C][C]17064[/C][C]16125.2198821118[/C][C]938.78011788824[/C][/ROW]
[ROW][C]39[/C][C]15168[/C][C]17184.3425050657[/C][C]-2016.34250506574[/C][/ROW]
[ROW][C]40[/C][C]16050[/C][C]15463.970709257[/C][C]586.029290742999[/C][/ROW]
[ROW][C]41[/C][C]15839[/C][C]16190.5844185262[/C][C]-351.584418526210[/C][/ROW]
[ROW][C]42[/C][C]15137[/C][C]16035.4835351872[/C][C]-898.483535187188[/C][/ROW]
[ROW][C]43[/C][C]14954[/C][C]15365.6675906678[/C][C]-411.667590667834[/C][/ROW]
[ROW][C]44[/C][C]15648[/C][C]15153.2833730648[/C][C]494.716626935238[/C][/ROW]
[ROW][C]45[/C][C]15305[/C][C]15793.3401785581[/C][C]-488.340178558137[/C][/ROW]
[ROW][C]46[/C][C]15579[/C][C]15508.8758168814[/C][C]70.1241831186053[/C][/ROW]
[ROW][C]47[/C][C]16348[/C][C]15749.4963958001[/C][C]598.503604199923[/C][/ROW]
[ROW][C]48[/C][C]15928[/C][C]16487.2384375367[/C][C]-559.2384375367[/C][/ROW]
[ROW][C]49[/C][C]16171[/C][C]16136.1852688906[/C][C]34.8147311093562[/C][/ROW]
[ROW][C]50[/C][C]15937[/C][C]16343.6545391543[/C][C]-406.654539154317[/C][/ROW]
[ROW][C]51[/C][C]15713[/C][C]16135.8277954767[/C][C]-422.827795476715[/C][/ROW]
[ROW][C]52[/C][C]15594[/C][C]15912.5388368879[/C][C]-318.538836887879[/C][/ROW]
[ROW][C]53[/C][C]15683[/C][C]15787.1040169241[/C][C]-104.104016924099[/C][/ROW]
[ROW][C]54[/C][C]16438[/C][C]15863.2076447418[/C][C]574.79235525816[/C][/ROW]
[ROW][C]55[/C][C]17032[/C][C]16577.9274004043[/C][C]454.072599595715[/C][/ROW]
[ROW][C]56[/C][C]17696[/C][C]17179.4278794590[/C][C]516.572120541041[/C][/ROW]
[ROW][C]57[/C][C]17745[/C][C]17840.0013325710[/C][C]-95.0013325710424[/C][/ROW]
[ROW][C]58[/C][C]19394[/C][C]17925.5440229972[/C][C]1468.45597700279[/C][/ROW]
[ROW][C]59[/C][C]20148[/C][C]19481.8689869877[/C][C]666.131013012273[/C][/ROW]
[ROW][C]60[/C][C]20108[/C][C]20284.2898362675[/C][C]-176.289836267482[/C][/ROW]
[ROW][C]61[/C][C]18584[/C][C]20294.5985046982[/C][C]-1710.59850469817[/C][/ROW]
[ROW][C]62[/C][C]18441[/C][C]18861.3820009425[/C][C]-420.38200094254[/C][/ROW]
[ROW][C]63[/C][C]18391[/C][C]18640.9119444631[/C][C]-249.911944463052[/C][/ROW]
[ROW][C]64[/C][C]19178[/C][C]18580.5581220149[/C][C]597.441877985082[/C][/ROW]
[ROW][C]65[/C][C]18079[/C][C]19317.2100834256[/C][C]-1238.21008342565[/C][/ROW]
[ROW][C]66[/C][C]18483[/C][C]18327.3148346403[/C][C]155.685165359722[/C][/ROW]
[ROW][C]67[/C][C]19644[/C][C]18647.9899506419[/C][C]996.010049358109[/C][/ROW]
[ROW][C]68[/C][C]19195[/C][C]19759.3046982474[/C][C]-564.304698247426[/C][/ROW]
[ROW][C]69[/C][C]19650[/C][C]19403.3409357577[/C][C]246.659064242271[/C][/ROW]
[ROW][C]70[/C][C]20830[/C][C]19809.9576066725[/C][C]1020.04239332753[/C][/ROW]
[ROW][C]71[/C][C]23595[/C][C]20944.2931578107[/C][C]2650.70684218925[/C][/ROW]
[ROW][C]72[/C][C]22937[/C][C]23613.3142414538[/C][C]-676.314241453827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41590&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41590&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
3982810073-245
4992410018.5135040882-94.5135040882033
51037110105.4500282521265.549971747883
61084610531.0628858462314.937114153763
71041311003.2985728707-590.298572870655
81070910624.114966018484.885033981629
91066210879.7592980704-217.759298070419
101057010850.7391504510-280.739150450972
111029710762.3377119973-465.337711997287
121063510500.1025587032134.89744129684
131087210802.262660382969.7373396170697
141029611043.2046163435-747.204616343482
151038310515.6416365650-132.641636564989
161043110565.7817408768-134.781740876790
171057410613.8279382358-39.8279382358469
181065310751.1211097033-98.1211097033247
191080510833.5501312895-28.5501312894867
201087210981.3692219516-109.369221951580
211062511053.1395030552-428.139503055188
221040710824.9566276596-417.956627659563
231046310606.0933115385-143.093311538509
241055610645.5568318907-89.5568318907499
251064610735.2984662666-89.2984662665986
261070210825.2287551958-123.228755195796
271135310883.1844956848469.815504315238
281134611498.9784085249-152.978408524928
291145111529.1573807744-78.1573807743516
301196411629.6321390286334.367860971364
311257412118.1471613238455.85283867623
321303112721.1536665542309.846333445776
331381213187.0798463185624.920153681498
341454413949.6034854990594.396514500952
351493114683.7913082057247.208691794338
361488615091.7193915560-205.719391556016
371600515073.7004835230931.299516477016
381706416125.2198821118938.78011788824
391516817184.3425050657-2016.34250506574
401605015463.970709257586.029290742999
411583916190.5844185262-351.584418526210
421513716035.4835351872-898.483535187188
431495415365.6675906678-411.667590667834
441564815153.2833730648494.716626935238
451530515793.3401785581-488.340178558137
461557915508.875816881470.1241831186053
471634815749.4963958001598.503604199923
481592816487.2384375367-559.2384375367
491617116136.185268890634.8147311093562
501593716343.6545391543-406.654539154317
511571316135.8277954767-422.827795476715
521559415912.5388368879-318.538836887879
531568315787.1040169241-104.104016924099
541643815863.2076447418574.79235525816
551703216577.9274004043454.072599595715
561769617179.4278794590516.572120541041
571774517840.0013325710-95.0013325710424
581939417925.54402299721468.45597700279
592014819481.8689869877666.131013012273
602010820284.2898362675-176.289836267482
611858420294.5985046982-1710.59850469817
621844118861.3820009425-420.38200094254
631839118640.9119444631-249.911944463052
641917818580.5581220149597.441877985082
651807919317.2100834256-1238.21008342565
661848318327.3148346403155.685165359722
671964418647.9899506419996.010049358109
681919519759.3046982474-564.304698247426
691965019403.3409357577246.659064242271
702083019809.95760667251020.04239332753
712359520944.29315781072650.70684218925
722293723613.3142414538-676.314241453827







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7323154.013257294621844.888414844624463.1380997447
7423330.551614667721533.169617057425127.9336122780
7523507.089972040721327.797473077225686.3824710042
7623683.628329413721179.629453571526187.6272052559
7723860.166686786721068.631798439626651.7015751339
7824036.705044159720984.281900337127089.1281879823
7924213.243401532820920.239957341327506.2468457242
8024389.781758905820872.33635046227907.2271673496
8124566.320116278820837.655493695428294.9847388622
8224742.858473651820814.064008754428671.6529385493
8324919.396831024820799.945204232929038.8484578167
8425095.935188397920794.039279975929397.8310968198

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 23154.0132572946 & 21844.8884148446 & 24463.1380997447 \tabularnewline
74 & 23330.5516146677 & 21533.1696170574 & 25127.9336122780 \tabularnewline
75 & 23507.0899720407 & 21327.7974730772 & 25686.3824710042 \tabularnewline
76 & 23683.6283294137 & 21179.6294535715 & 26187.6272052559 \tabularnewline
77 & 23860.1666867867 & 21068.6317984396 & 26651.7015751339 \tabularnewline
78 & 24036.7050441597 & 20984.2819003371 & 27089.1281879823 \tabularnewline
79 & 24213.2434015328 & 20920.2399573413 & 27506.2468457242 \tabularnewline
80 & 24389.7817589058 & 20872.336350462 & 27907.2271673496 \tabularnewline
81 & 24566.3201162788 & 20837.6554936954 & 28294.9847388622 \tabularnewline
82 & 24742.8584736518 & 20814.0640087544 & 28671.6529385493 \tabularnewline
83 & 24919.3968310248 & 20799.9452042329 & 29038.8484578167 \tabularnewline
84 & 25095.9351883979 & 20794.0392799759 & 29397.8310968198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41590&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]23154.0132572946[/C][C]21844.8884148446[/C][C]24463.1380997447[/C][/ROW]
[ROW][C]74[/C][C]23330.5516146677[/C][C]21533.1696170574[/C][C]25127.9336122780[/C][/ROW]
[ROW][C]75[/C][C]23507.0899720407[/C][C]21327.7974730772[/C][C]25686.3824710042[/C][/ROW]
[ROW][C]76[/C][C]23683.6283294137[/C][C]21179.6294535715[/C][C]26187.6272052559[/C][/ROW]
[ROW][C]77[/C][C]23860.1666867867[/C][C]21068.6317984396[/C][C]26651.7015751339[/C][/ROW]
[ROW][C]78[/C][C]24036.7050441597[/C][C]20984.2819003371[/C][C]27089.1281879823[/C][/ROW]
[ROW][C]79[/C][C]24213.2434015328[/C][C]20920.2399573413[/C][C]27506.2468457242[/C][/ROW]
[ROW][C]80[/C][C]24389.7817589058[/C][C]20872.336350462[/C][C]27907.2271673496[/C][/ROW]
[ROW][C]81[/C][C]24566.3201162788[/C][C]20837.6554936954[/C][C]28294.9847388622[/C][/ROW]
[ROW][C]82[/C][C]24742.8584736518[/C][C]20814.0640087544[/C][C]28671.6529385493[/C][/ROW]
[ROW][C]83[/C][C]24919.3968310248[/C][C]20799.9452042329[/C][C]29038.8484578167[/C][/ROW]
[ROW][C]84[/C][C]25095.9351883979[/C][C]20794.0392799759[/C][C]29397.8310968198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41590&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41590&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
7323154.013257294621844.888414844624463.1380997447
7423330.551614667721533.169617057425127.9336122780
7523507.089972040721327.797473077225686.3824710042
7623683.628329413721179.629453571526187.6272052559
7723860.166686786721068.631798439626651.7015751339
7824036.705044159720984.281900337127089.1281879823
7924213.243401532820920.239957341327506.2468457242
8024389.781758905820872.33635046227907.2271673496
8124566.320116278820837.655493695428294.9847388622
8224742.858473651820814.064008754428671.6529385493
8324919.396831024820799.945204232929038.8484578167
8425095.935188397920794.039279975929397.8310968198



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')