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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 17 Jan 2009 02:21:14 -0700
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/Jan/17/t1232184372a0f81pyzy43kuv5.htm/, Retrieved Mon, 29 Apr 2024 13:28:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36922, Retrieved Mon, 29 Apr 2024 13:28:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact217
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [Opdracht 7_oefeni...] [2008-12-15 09:21:34] [4047c66d272f0b18d63fe49a1610bba9]
- RMPD    [Exponential Smoothing] [Opdracht 10_Opgav...] [2009-01-17 09:21:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMP       [Exponential Smoothing] [] [2013-01-16 07:12:17] [d8b265d30b4f0633bb4f7e2bd1bbc5a6]
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Post a new message
Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36922&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]3 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=36922&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36922&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225645293268359
beta0.000987392360344324
gamma0.443424096464966

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.225645293268359 \tabularnewline
beta & 0.000987392360344324 \tabularnewline
gamma & 0.443424096464966 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36922&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]0.225645293268359[/C][/ROW]
[ROW][C]beta[/C][C]0.000987392360344324[/C][/ROW]
[ROW][C]gamma[/C][C]0.443424096464966[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36922&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36922&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
alpha0.225645293268359
beta0.000987392360344324
gamma0.443424096464966







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.3135659264-2020.31356592642
153260934048.9003449238-1439.90034492376
163021230953.1156725608-741.115672560802
172996530167.1395456753-202.139545675338
182835228194.2073966201157.792603379919
192581422076.43666590623737.56333409381
202241420801.71448943221612.28551056781
212050621128.5686532064-622.568653206425
222880626754.3351088812051.66489111902
232222822075.9028005777152.097199422253
241397113470.7919101911500.208089808935
253684537059.3137240137-214.313724013737
263533829795.39583259325542.60416740679
273502233348.5412928561673.45870714403
283477731163.67558089773613.32441910227
292688731542.0050931574-4655.00509315741
302397028668.5927624313-4698.59276243134
312278022752.574744842227.4252551577847
321735120061.6524014616-2710.65240146157
332138218709.35389209042672.64610790962
342456125499.2125262374-938.212526237432
351740920022.3003500512-2613.30035005118
361151411945.8020671158-431.802067115779
373151431811.4261592252-297.426159225179
382707127135.3806512947-64.3806512946976
392946227863.14396409931598.85603590074
402610526585.9642618326-480.964261832625
412239723768.4658044645-1371.46580446454
422384321869.55173426311973.44826573692
432170519509.00931905342195.99068094658
441808916761.20592048261327.79407951737
452076418040.6501136012723.349886399
462531623196.74519867022119.25480132980
471770418102.2740810676-398.274081067633
481554811461.24841949954086.75158050051
492802933585.732192306-5556.732192306
502938327714.3359364251668.66406357501
513643829460.60678135486977.39321864521
523203428524.46033210133509.53966789867
532267925984.4778564559-3305.47785645586
542431924768.9290462075-449.929046207497
551800421739.1115691862-3735.11156918616
561753717326.7906944695210.209305530538
572036618791.38806959851574.61193040150
582278223365.1325770419-583.132577041892
591916917096.73422453672072.26577546332
601380712536.81758758221270.18241241785
612974329375.9445157682367.055484231823
622559127375.9606757853-1784.96067578530
632909629846.2377203085-750.237720308509
642648226330.5427575017151.457242498342
652240521404.03647799451000.96352200549
662704422063.41261627144980.58738372855
671797019291.7487681347-1321.74876813473
681873016844.38845099601885.61154900405
691968419126.6572632223557.342736777737
701978522649.0312084714-2864.03120847137
711847916986.41544496481492.58455503518
721069812281.3703145697-1583.37031456974

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 41487.9961256583 & -3785.99612565827 \tabularnewline
14 & 30364 & 32384.3135659264 & -2020.31356592642 \tabularnewline
15 & 32609 & 34048.9003449238 & -1439.90034492376 \tabularnewline
16 & 30212 & 30953.1156725608 & -741.115672560802 \tabularnewline
17 & 29965 & 30167.1395456753 & -202.139545675338 \tabularnewline
18 & 28352 & 28194.2073966201 & 157.792603379919 \tabularnewline
19 & 25814 & 22076.4366659062 & 3737.56333409381 \tabularnewline
20 & 22414 & 20801.7144894322 & 1612.28551056781 \tabularnewline
21 & 20506 & 21128.5686532064 & -622.568653206425 \tabularnewline
22 & 28806 & 26754.335108881 & 2051.66489111902 \tabularnewline
23 & 22228 & 22075.9028005777 & 152.097199422253 \tabularnewline
24 & 13971 & 13470.7919101911 & 500.208089808935 \tabularnewline
25 & 36845 & 37059.3137240137 & -214.313724013737 \tabularnewline
26 & 35338 & 29795.3958325932 & 5542.60416740679 \tabularnewline
27 & 35022 & 33348.541292856 & 1673.45870714403 \tabularnewline
28 & 34777 & 31163.6755808977 & 3613.32441910227 \tabularnewline
29 & 26887 & 31542.0050931574 & -4655.00509315741 \tabularnewline
30 & 23970 & 28668.5927624313 & -4698.59276243134 \tabularnewline
31 & 22780 & 22752.5747448422 & 27.4252551577847 \tabularnewline
32 & 17351 & 20061.6524014616 & -2710.65240146157 \tabularnewline
33 & 21382 & 18709.3538920904 & 2672.64610790962 \tabularnewline
34 & 24561 & 25499.2125262374 & -938.212526237432 \tabularnewline
35 & 17409 & 20022.3003500512 & -2613.30035005118 \tabularnewline
36 & 11514 & 11945.8020671158 & -431.802067115779 \tabularnewline
37 & 31514 & 31811.4261592252 & -297.426159225179 \tabularnewline
38 & 27071 & 27135.3806512947 & -64.3806512946976 \tabularnewline
39 & 29462 & 27863.1439640993 & 1598.85603590074 \tabularnewline
40 & 26105 & 26585.9642618326 & -480.964261832625 \tabularnewline
41 & 22397 & 23768.4658044645 & -1371.46580446454 \tabularnewline
42 & 23843 & 21869.5517342631 & 1973.44826573692 \tabularnewline
43 & 21705 & 19509.0093190534 & 2195.99068094658 \tabularnewline
44 & 18089 & 16761.2059204826 & 1327.79407951737 \tabularnewline
45 & 20764 & 18040.650113601 & 2723.349886399 \tabularnewline
46 & 25316 & 23196.7451986702 & 2119.25480132980 \tabularnewline
47 & 17704 & 18102.2740810676 & -398.274081067633 \tabularnewline
48 & 15548 & 11461.2484194995 & 4086.75158050051 \tabularnewline
49 & 28029 & 33585.732192306 & -5556.732192306 \tabularnewline
50 & 29383 & 27714.335936425 & 1668.66406357501 \tabularnewline
51 & 36438 & 29460.6067813548 & 6977.39321864521 \tabularnewline
52 & 32034 & 28524.4603321013 & 3509.53966789867 \tabularnewline
53 & 22679 & 25984.4778564559 & -3305.47785645586 \tabularnewline
54 & 24319 & 24768.9290462075 & -449.929046207497 \tabularnewline
55 & 18004 & 21739.1115691862 & -3735.11156918616 \tabularnewline
56 & 17537 & 17326.7906944695 & 210.209305530538 \tabularnewline
57 & 20366 & 18791.3880695985 & 1574.61193040150 \tabularnewline
58 & 22782 & 23365.1325770419 & -583.132577041892 \tabularnewline
59 & 19169 & 17096.7342245367 & 2072.26577546332 \tabularnewline
60 & 13807 & 12536.8175875822 & 1270.18241241785 \tabularnewline
61 & 29743 & 29375.9445157682 & 367.055484231823 \tabularnewline
62 & 25591 & 27375.9606757853 & -1784.96067578530 \tabularnewline
63 & 29096 & 29846.2377203085 & -750.237720308509 \tabularnewline
64 & 26482 & 26330.5427575017 & 151.457242498342 \tabularnewline
65 & 22405 & 21404.0364779945 & 1000.96352200549 \tabularnewline
66 & 27044 & 22063.4126162714 & 4980.58738372855 \tabularnewline
67 & 17970 & 19291.7487681347 & -1321.74876813473 \tabularnewline
68 & 18730 & 16844.3884509960 & 1885.61154900405 \tabularnewline
69 & 19684 & 19126.6572632223 & 557.342736777737 \tabularnewline
70 & 19785 & 22649.0312084714 & -2864.03120847137 \tabularnewline
71 & 18479 & 16986.4154449648 & 1492.58455503518 \tabularnewline
72 & 10698 & 12281.3703145697 & -1583.37031456974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36922&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]37702[/C][C]41487.9961256583[/C][C]-3785.99612565827[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]32384.3135659264[/C][C]-2020.31356592642[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]34048.9003449238[/C][C]-1439.90034492376[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30953.1156725608[/C][C]-741.115672560802[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30167.1395456753[/C][C]-202.139545675338[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28194.2073966201[/C][C]157.792603379919[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]22076.4366659062[/C][C]3737.56333409381[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20801.7144894322[/C][C]1612.28551056781[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21128.5686532064[/C][C]-622.568653206425[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]26754.335108881[/C][C]2051.66489111902[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22075.9028005777[/C][C]152.097199422253[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13470.7919101911[/C][C]500.208089808935[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]37059.3137240137[/C][C]-214.313724013737[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29795.3958325932[/C][C]5542.60416740679[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33348.541292856[/C][C]1673.45870714403[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31163.6755808977[/C][C]3613.32441910227[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]31542.0050931574[/C][C]-4655.00509315741[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28668.5927624313[/C][C]-4698.59276243134[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22752.5747448422[/C][C]27.4252551577847[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]20061.6524014616[/C][C]-2710.65240146157[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18709.3538920904[/C][C]2672.64610790962[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25499.2125262374[/C][C]-938.212526237432[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]20022.3003500512[/C][C]-2613.30035005118[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]11945.8020671158[/C][C]-431.802067115779[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]31811.4261592252[/C][C]-297.426159225179[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]27135.3806512947[/C][C]-64.3806512946976[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]27863.1439640993[/C][C]1598.85603590074[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]26585.9642618326[/C][C]-480.964261832625[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]23768.4658044645[/C][C]-1371.46580446454[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21869.5517342631[/C][C]1973.44826573692[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19509.0093190534[/C][C]2195.99068094658[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]16761.2059204826[/C][C]1327.79407951737[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18040.650113601[/C][C]2723.349886399[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23196.7451986702[/C][C]2119.25480132980[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]18102.2740810676[/C][C]-398.274081067633[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]11461.2484194995[/C][C]4086.75158050051[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33585.732192306[/C][C]-5556.732192306[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27714.335936425[/C][C]1668.66406357501[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29460.6067813548[/C][C]6977.39321864521[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]28524.4603321013[/C][C]3509.53966789867[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]25984.4778564559[/C][C]-3305.47785645586[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]24768.9290462075[/C][C]-449.929046207497[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]21739.1115691862[/C][C]-3735.11156918616[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]17326.7906944695[/C][C]210.209305530538[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18791.3880695985[/C][C]1574.61193040150[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23365.1325770419[/C][C]-583.132577041892[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]17096.7342245367[/C][C]2072.26577546332[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12536.8175875822[/C][C]1270.18241241785[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29375.9445157682[/C][C]367.055484231823[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]27375.9606757853[/C][C]-1784.96067578530[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]29846.2377203085[/C][C]-750.237720308509[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26330.5427575017[/C][C]151.457242498342[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]21404.0364779945[/C][C]1000.96352200549[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]22063.4126162714[/C][C]4980.58738372855[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19291.7487681347[/C][C]-1321.74876813473[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16844.3884509960[/C][C]1885.61154900405[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19126.6572632223[/C][C]557.342736777737[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22649.0312084714[/C][C]-2864.03120847137[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]16986.4154449648[/C][C]1492.58455503518[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]12281.3703145697[/C][C]-1583.37031456974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36922&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36922&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
133770241487.9961256583-3785.99612565827
143036432384.3135659264-2020.31356592642
153260934048.9003449238-1439.90034492376
163021230953.1156725608-741.115672560802
172996530167.1395456753-202.139545675338
182835228194.2073966201157.792603379919
192581422076.43666590623737.56333409381
202241420801.71448943221612.28551056781
212050621128.5686532064-622.568653206425
222880626754.3351088812051.66489111902
232222822075.9028005777152.097199422253
241397113470.7919101911500.208089808935
253684537059.3137240137-214.313724013737
263533829795.39583259325542.60416740679
273502233348.5412928561673.45870714403
283477731163.67558089773613.32441910227
292688731542.0050931574-4655.00509315741
302397028668.5927624313-4698.59276243134
312278022752.574744842227.4252551577847
321735120061.6524014616-2710.65240146157
332138218709.35389209042672.64610790962
342456125499.2125262374-938.212526237432
351740920022.3003500512-2613.30035005118
361151411945.8020671158-431.802067115779
373151431811.4261592252-297.426159225179
382707127135.3806512947-64.3806512946976
392946227863.14396409931598.85603590074
402610526585.9642618326-480.964261832625
412239723768.4658044645-1371.46580446454
422384321869.55173426311973.44826573692
432170519509.00931905342195.99068094658
441808916761.20592048261327.79407951737
452076418040.6501136012723.349886399
462531623196.74519867022119.25480132980
471770418102.2740810676-398.274081067633
481554811461.24841949954086.75158050051
492802933585.732192306-5556.732192306
502938327714.3359364251668.66406357501
513643829460.60678135486977.39321864521
523203428524.46033210133509.53966789867
532267925984.4778564559-3305.47785645586
542431924768.9290462075-449.929046207497
551800421739.1115691862-3735.11156918616
561753717326.7906944695210.209305530538
572036618791.38806959851574.61193040150
582278223365.1325770419-583.132577041892
591916917096.73422453672072.26577546332
601380712536.81758758221270.18241241785
612974329375.9445157682367.055484231823
622559127375.9606757853-1784.96067578530
632909629846.2377203085-750.237720308509
642648226330.5427575017151.457242498342
652240521404.03647799451000.96352200549
662704422063.41261627144980.58738372855
671797019291.7487681347-1321.74876813473
681873016844.38845099601885.61154900405
691968419126.6572632223557.342736777737
701978522649.0312084714-2864.03120847137
711847916986.41544496481492.58455503518
721069812281.3703145697-1583.37031456974







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326500.469400025523700.500890165229300.4379098858
7423936.429930691720958.012913893226914.8469474903
7526838.754287561423558.733455948830118.7751191740
7624044.394515093420689.163127062427399.6259031244
7719771.041334130316444.482929761323097.5997384992
7821290.888961755817665.054642664924916.7232808467
7916074.261585842412658.628759714219489.8944119707
8015127.007409126511599.807198068518654.2076201845
8116276.306596023712432.098804289420120.5143877580
8218074.023874609113808.728215261622339.3195339565
8315011.181302336411004.409162771419017.9534419013
849844.603480536957800.6299601726111888.5770009013

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 26500.4694000255 & 23700.5008901652 & 29300.4379098858 \tabularnewline
74 & 23936.4299306917 & 20958.0129138932 & 26914.8469474903 \tabularnewline
75 & 26838.7542875614 & 23558.7334559488 & 30118.7751191740 \tabularnewline
76 & 24044.3945150934 & 20689.1631270624 & 27399.6259031244 \tabularnewline
77 & 19771.0413341303 & 16444.4829297613 & 23097.5997384992 \tabularnewline
78 & 21290.8889617558 & 17665.0546426649 & 24916.7232808467 \tabularnewline
79 & 16074.2615858424 & 12658.6287597142 & 19489.8944119707 \tabularnewline
80 & 15127.0074091265 & 11599.8071980685 & 18654.2076201845 \tabularnewline
81 & 16276.3065960237 & 12432.0988042894 & 20120.5143877580 \tabularnewline
82 & 18074.0238746091 & 13808.7282152616 & 22339.3195339565 \tabularnewline
83 & 15011.1813023364 & 11004.4091627714 & 19017.9534419013 \tabularnewline
84 & 9844.60348053695 & 7800.62996017261 & 11888.5770009013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36922&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]26500.4694000255[/C][C]23700.5008901652[/C][C]29300.4379098858[/C][/ROW]
[ROW][C]74[/C][C]23936.4299306917[/C][C]20958.0129138932[/C][C]26914.8469474903[/C][/ROW]
[ROW][C]75[/C][C]26838.7542875614[/C][C]23558.7334559488[/C][C]30118.7751191740[/C][/ROW]
[ROW][C]76[/C][C]24044.3945150934[/C][C]20689.1631270624[/C][C]27399.6259031244[/C][/ROW]
[ROW][C]77[/C][C]19771.0413341303[/C][C]16444.4829297613[/C][C]23097.5997384992[/C][/ROW]
[ROW][C]78[/C][C]21290.8889617558[/C][C]17665.0546426649[/C][C]24916.7232808467[/C][/ROW]
[ROW][C]79[/C][C]16074.2615858424[/C][C]12658.6287597142[/C][C]19489.8944119707[/C][/ROW]
[ROW][C]80[/C][C]15127.0074091265[/C][C]11599.8071980685[/C][C]18654.2076201845[/C][/ROW]
[ROW][C]81[/C][C]16276.3065960237[/C][C]12432.0988042894[/C][C]20120.5143877580[/C][/ROW]
[ROW][C]82[/C][C]18074.0238746091[/C][C]13808.7282152616[/C][C]22339.3195339565[/C][/ROW]
[ROW][C]83[/C][C]15011.1813023364[/C][C]11004.4091627714[/C][C]19017.9534419013[/C][/ROW]
[ROW][C]84[/C][C]9844.60348053695[/C][C]7800.62996017261[/C][C]11888.5770009013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36922&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36922&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
7326500.469400025523700.500890165229300.4379098858
7423936.429930691720958.012913893226914.8469474903
7526838.754287561423558.733455948830118.7751191740
7624044.394515093420689.163127062427399.6259031244
7719771.041334130316444.482929761323097.5997384992
7821290.888961755817665.054642664924916.7232808467
7916074.261585842412658.628759714219489.8944119707
8015127.007409126511599.807198068518654.2076201845
8116276.306596023712432.098804289420120.5143877580
8218074.023874609113808.728215261622339.3195339565
8315011.181302336411004.409162771419017.9534419013
849844.603480536957800.6299601726111888.5770009013



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')