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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 19:53:04 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/26/t1369612445qkmlmep8j7tgu4e.htm/, Retrieved Thu, 31 Oct 2024 23:26:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210690, Retrieved Thu, 31 Oct 2024 23:26:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2013-04-29 18:07:56] [2350abd9e4ab4c416741d11e9cf0d058]
- RMPD    [Exponential Smoothing] [] [2013-05-26 23:53:04] [fd383db316336f22794dc1afa7a19318] [Current]
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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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210690&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210690&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210690&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' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.29863615794017
beta0
gamma0.619823384568793

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.29863615794017 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.619823384568793 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210690&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]0.29863615794017[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.619823384568793[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210690&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210690&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
alpha0.29863615794017
beta0
gamma0.619823384568793







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770240443.7037927351-2741.70379273505
143036431996.9844991028-1632.98449910276
153260933561.868875555-952.868875554952
163021230629.3187021119-417.318702111876
172996529937.661508183427.3384918166375
182835228050.1283635835301.871636416538
192581421460.41407584744353.58592415257
202241420567.60484273891846.39515726114
212050621231.3911251161-725.391125116083
222880627004.35736641431801.64263358572
232222822474.1539270629-246.153927062947
241397113911.154390596459.8456094035901
253684536937.4508845113-92.450884511265
263533829763.87864848375574.12135151628
273502233776.72645317121245.27354682884
283477731733.43637475813043.56362524189
292688732268.6259180397-5381.62591803969
302397028885.125941827-4915.12594182705
312278022498.7957065567281.204293443327
321735119299.8958111056-1948.8958111056
332138217712.25964896733669.74035103275
342456125896.3275057651-1335.32750576507
351740919539.0897330292-2130.08973302917
361151410546.5034875372967.496512462789
373151433777.65076757-2263.65076757005
382707128419.061714895-1348.06171489501
392946228482.8512423572979.148757642815
402610527141.8424180515-1036.8424180515
412239722795.8623690311-398.862369031092
422384321103.19342257932739.80657742071
432170519261.86039182672443.13960817328
441808915739.11962066972349.88037933027
452076417877.79658640622886.20341359381
462531623652.06032322931663.93967677065
471770417845.0117837246-141.011783724636
481554810793.02412560734754.97587439267
492802933750.5998184354-5721.5998184354
502938327757.36858585921625.6314141408
513643829720.89932135146717.10067864856
523203429217.05528113182816.94471886819
532267926299.2991943114-3620.29919431138
542431925009.0402640908-690.040264090829
551800422014.4633779757-4010.46337797569
561753716523.90159469081013.09840530923
572036618496.51839448371869.48160551629
582278223435.8076546173-653.807654617329
591916916151.94437089593017.05562910411
601380712171.46196029441635.53803970563
612974329643.065818920299.9341810798032
622559128582.3560614049-2991.35606140488
632909631380.4596230566-2284.45962305657
642648226492.9417292077-10.9417292076687
652240519932.26681424532472.73318575467
662704421735.45483827225308.54516172778
671797019088.8124414807-1118.81244148074
681873016645.65355470292084.34644529707
691968419310.4721229104373.52787708964
701978522706.0868861319-2921.0868861319
711847916340.93600907622138.06399092377
721069811497.3792233764-799.379223376427

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 40443.7037927351 & -2741.70379273505 \tabularnewline
14 & 30364 & 31996.9844991028 & -1632.98449910276 \tabularnewline
15 & 32609 & 33561.868875555 & -952.868875554952 \tabularnewline
16 & 30212 & 30629.3187021119 & -417.318702111876 \tabularnewline
17 & 29965 & 29937.6615081834 & 27.3384918166375 \tabularnewline
18 & 28352 & 28050.1283635835 & 301.871636416538 \tabularnewline
19 & 25814 & 21460.4140758474 & 4353.58592415257 \tabularnewline
20 & 22414 & 20567.6048427389 & 1846.39515726114 \tabularnewline
21 & 20506 & 21231.3911251161 & -725.391125116083 \tabularnewline
22 & 28806 & 27004.3573664143 & 1801.64263358572 \tabularnewline
23 & 22228 & 22474.1539270629 & -246.153927062947 \tabularnewline
24 & 13971 & 13911.1543905964 & 59.8456094035901 \tabularnewline
25 & 36845 & 36937.4508845113 & -92.450884511265 \tabularnewline
26 & 35338 & 29763.8786484837 & 5574.12135151628 \tabularnewline
27 & 35022 & 33776.7264531712 & 1245.27354682884 \tabularnewline
28 & 34777 & 31733.4363747581 & 3043.56362524189 \tabularnewline
29 & 26887 & 32268.6259180397 & -5381.62591803969 \tabularnewline
30 & 23970 & 28885.125941827 & -4915.12594182705 \tabularnewline
31 & 22780 & 22498.7957065567 & 281.204293443327 \tabularnewline
32 & 17351 & 19299.8958111056 & -1948.8958111056 \tabularnewline
33 & 21382 & 17712.2596489673 & 3669.74035103275 \tabularnewline
34 & 24561 & 25896.3275057651 & -1335.32750576507 \tabularnewline
35 & 17409 & 19539.0897330292 & -2130.08973302917 \tabularnewline
36 & 11514 & 10546.5034875372 & 967.496512462789 \tabularnewline
37 & 31514 & 33777.65076757 & -2263.65076757005 \tabularnewline
38 & 27071 & 28419.061714895 & -1348.06171489501 \tabularnewline
39 & 29462 & 28482.8512423572 & 979.148757642815 \tabularnewline
40 & 26105 & 27141.8424180515 & -1036.8424180515 \tabularnewline
41 & 22397 & 22795.8623690311 & -398.862369031092 \tabularnewline
42 & 23843 & 21103.1934225793 & 2739.80657742071 \tabularnewline
43 & 21705 & 19261.8603918267 & 2443.13960817328 \tabularnewline
44 & 18089 & 15739.1196206697 & 2349.88037933027 \tabularnewline
45 & 20764 & 17877.7965864062 & 2886.20341359381 \tabularnewline
46 & 25316 & 23652.0603232293 & 1663.93967677065 \tabularnewline
47 & 17704 & 17845.0117837246 & -141.011783724636 \tabularnewline
48 & 15548 & 10793.0241256073 & 4754.97587439267 \tabularnewline
49 & 28029 & 33750.5998184354 & -5721.5998184354 \tabularnewline
50 & 29383 & 27757.3685858592 & 1625.6314141408 \tabularnewline
51 & 36438 & 29720.8993213514 & 6717.10067864856 \tabularnewline
52 & 32034 & 29217.0552811318 & 2816.94471886819 \tabularnewline
53 & 22679 & 26299.2991943114 & -3620.29919431138 \tabularnewline
54 & 24319 & 25009.0402640908 & -690.040264090829 \tabularnewline
55 & 18004 & 22014.4633779757 & -4010.46337797569 \tabularnewline
56 & 17537 & 16523.9015946908 & 1013.09840530923 \tabularnewline
57 & 20366 & 18496.5183944837 & 1869.48160551629 \tabularnewline
58 & 22782 & 23435.8076546173 & -653.807654617329 \tabularnewline
59 & 19169 & 16151.9443708959 & 3017.05562910411 \tabularnewline
60 & 13807 & 12171.4619602944 & 1635.53803970563 \tabularnewline
61 & 29743 & 29643.0658189202 & 99.9341810798032 \tabularnewline
62 & 25591 & 28582.3560614049 & -2991.35606140488 \tabularnewline
63 & 29096 & 31380.4596230566 & -2284.45962305657 \tabularnewline
64 & 26482 & 26492.9417292077 & -10.9417292076687 \tabularnewline
65 & 22405 & 19932.2668142453 & 2472.73318575467 \tabularnewline
66 & 27044 & 21735.4548382722 & 5308.54516172778 \tabularnewline
67 & 17970 & 19088.8124414807 & -1118.81244148074 \tabularnewline
68 & 18730 & 16645.6535547029 & 2084.34644529707 \tabularnewline
69 & 19684 & 19310.4721229104 & 373.52787708964 \tabularnewline
70 & 19785 & 22706.0868861319 & -2921.0868861319 \tabularnewline
71 & 18479 & 16340.9360090762 & 2138.06399092377 \tabularnewline
72 & 10698 & 11497.3792233764 & -799.379223376427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210690&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]40443.7037927351[/C][C]-2741.70379273505[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]31996.9844991028[/C][C]-1632.98449910276[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]33561.868875555[/C][C]-952.868875554952[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30629.3187021119[/C][C]-417.318702111876[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]29937.6615081834[/C][C]27.3384918166375[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28050.1283635835[/C][C]301.871636416538[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]21460.4140758474[/C][C]4353.58592415257[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20567.6048427389[/C][C]1846.39515726114[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21231.3911251161[/C][C]-725.391125116083[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]27004.3573664143[/C][C]1801.64263358572[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22474.1539270629[/C][C]-246.153927062947[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13911.1543905964[/C][C]59.8456094035901[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]36937.4508845113[/C][C]-92.450884511265[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29763.8786484837[/C][C]5574.12135151628[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33776.7264531712[/C][C]1245.27354682884[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31733.4363747581[/C][C]3043.56362524189[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]32268.6259180397[/C][C]-5381.62591803969[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28885.125941827[/C][C]-4915.12594182705[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22498.7957065567[/C][C]281.204293443327[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]19299.8958111056[/C][C]-1948.8958111056[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]17712.2596489673[/C][C]3669.74035103275[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25896.3275057651[/C][C]-1335.32750576507[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]19539.0897330292[/C][C]-2130.08973302917[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]10546.5034875372[/C][C]967.496512462789[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]33777.65076757[/C][C]-2263.65076757005[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]28419.061714895[/C][C]-1348.06171489501[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]28482.8512423572[/C][C]979.148757642815[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27141.8424180515[/C][C]-1036.8424180515[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]22795.8623690311[/C][C]-398.862369031092[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21103.1934225793[/C][C]2739.80657742071[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19261.8603918267[/C][C]2443.13960817328[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]15739.1196206697[/C][C]2349.88037933027[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]17877.7965864062[/C][C]2886.20341359381[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23652.0603232293[/C][C]1663.93967677065[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]17845.0117837246[/C][C]-141.011783724636[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]10793.0241256073[/C][C]4754.97587439267[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33750.5998184354[/C][C]-5721.5998184354[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27757.3685858592[/C][C]1625.6314141408[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29720.8993213514[/C][C]6717.10067864856[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]29217.0552811318[/C][C]2816.94471886819[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]26299.2991943114[/C][C]-3620.29919431138[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25009.0402640908[/C][C]-690.040264090829[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]22014.4633779757[/C][C]-4010.46337797569[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]16523.9015946908[/C][C]1013.09840530923[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18496.5183944837[/C][C]1869.48160551629[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23435.8076546173[/C][C]-653.807654617329[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]16151.9443708959[/C][C]3017.05562910411[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12171.4619602944[/C][C]1635.53803970563[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29643.0658189202[/C][C]99.9341810798032[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]28582.3560614049[/C][C]-2991.35606140488[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]31380.4596230566[/C][C]-2284.45962305657[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26492.9417292077[/C][C]-10.9417292076687[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]19932.2668142453[/C][C]2472.73318575467[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]21735.4548382722[/C][C]5308.54516172778[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19088.8124414807[/C][C]-1118.81244148074[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16645.6535547029[/C][C]2084.34644529707[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19310.4721229104[/C][C]373.52787708964[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22706.0868861319[/C][C]-2921.0868861319[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]16340.9360090762[/C][C]2138.06399092377[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]11497.3792233764[/C][C]-799.379223376427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210690&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210690&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
133770240443.7037927351-2741.70379273505
143036431996.9844991028-1632.98449910276
153260933561.868875555-952.868875554952
163021230629.3187021119-417.318702111876
172996529937.661508183427.3384918166375
182835228050.1283635835301.871636416538
192581421460.41407584744353.58592415257
202241420567.60484273891846.39515726114
212050621231.3911251161-725.391125116083
222880627004.35736641431801.64263358572
232222822474.1539270629-246.153927062947
241397113911.154390596459.8456094035901
253684536937.4508845113-92.450884511265
263533829763.87864848375574.12135151628
273502233776.72645317121245.27354682884
283477731733.43637475813043.56362524189
292688732268.6259180397-5381.62591803969
302397028885.125941827-4915.12594182705
312278022498.7957065567281.204293443327
321735119299.8958111056-1948.8958111056
332138217712.25964896733669.74035103275
342456125896.3275057651-1335.32750576507
351740919539.0897330292-2130.08973302917
361151410546.5034875372967.496512462789
373151433777.65076757-2263.65076757005
382707128419.061714895-1348.06171489501
392946228482.8512423572979.148757642815
402610527141.8424180515-1036.8424180515
412239722795.8623690311-398.862369031092
422384321103.19342257932739.80657742071
432170519261.86039182672443.13960817328
441808915739.11962066972349.88037933027
452076417877.79658640622886.20341359381
462531623652.06032322931663.93967677065
471770417845.0117837246-141.011783724636
481554810793.02412560734754.97587439267
492802933750.5998184354-5721.5998184354
502938327757.36858585921625.6314141408
513643829720.89932135146717.10067864856
523203429217.05528113182816.94471886819
532267926299.2991943114-3620.29919431138
542431925009.0402640908-690.040264090829
551800422014.4633779757-4010.46337797569
561753716523.90159469081013.09840530923
572036618496.51839448371869.48160551629
582278223435.8076546173-653.807654617329
591916916151.94437089593017.05562910411
601380712171.46196029441635.53803970563
612974329643.065818920299.9341810798032
622559128582.3560614049-2991.35606140488
632909631380.4596230566-2284.45962305657
642648226492.9417292077-10.9417292076687
652240519932.26681424532472.73318575467
662704421735.45483827225308.54516172778
671797019088.8124414807-1118.81244148074
681873016645.65355470292084.34644529707
691968419310.4721229104373.52787708964
701978522706.0868861319-2921.0868861319
711847916340.93600907622138.06399092377
721069811497.3792233764-799.379223376427







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327574.26840973522373.729642379932774.8071770902
7425139.863710780319712.375660974130567.3517605865
7529138.597582395223493.276547164934783.9186176256
7625921.649520783720066.594213543631776.7048280238
7720443.949608902414386.41746199126501.4817558139
7822741.479127291316488.022581436828994.9356731459
7915715.40130853239271.9750591742422158.8275578904
8014998.8429806768370.8896849034721626.7962764485
8116297.4703604899489.9900666528323104.9506543251
8218149.295628637211166.902699920525131.6885573538
8314855.80963870917702.7799259916722008.8393514265
848096.77929900702777.08961084101715416.468987173

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27574.268409735 & 22373.7296423799 & 32774.8071770902 \tabularnewline
74 & 25139.8637107803 & 19712.3756609741 & 30567.3517605865 \tabularnewline
75 & 29138.5975823952 & 23493.2765471649 & 34783.9186176256 \tabularnewline
76 & 25921.6495207837 & 20066.5942135436 & 31776.7048280238 \tabularnewline
77 & 20443.9496089024 & 14386.417461991 & 26501.4817558139 \tabularnewline
78 & 22741.4791272913 & 16488.0225814368 & 28994.9356731459 \tabularnewline
79 & 15715.4013085323 & 9271.97505917424 & 22158.8275578904 \tabularnewline
80 & 14998.842980676 & 8370.88968490347 & 21626.7962764485 \tabularnewline
81 & 16297.470360489 & 9489.99006665283 & 23104.9506543251 \tabularnewline
82 & 18149.2956286372 & 11166.9026999205 & 25131.6885573538 \tabularnewline
83 & 14855.8096387091 & 7702.77992599167 & 22008.8393514265 \tabularnewline
84 & 8096.77929900702 & 777.089610841017 & 15416.468987173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210690&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]27574.268409735[/C][C]22373.7296423799[/C][C]32774.8071770902[/C][/ROW]
[ROW][C]74[/C][C]25139.8637107803[/C][C]19712.3756609741[/C][C]30567.3517605865[/C][/ROW]
[ROW][C]75[/C][C]29138.5975823952[/C][C]23493.2765471649[/C][C]34783.9186176256[/C][/ROW]
[ROW][C]76[/C][C]25921.6495207837[/C][C]20066.5942135436[/C][C]31776.7048280238[/C][/ROW]
[ROW][C]77[/C][C]20443.9496089024[/C][C]14386.417461991[/C][C]26501.4817558139[/C][/ROW]
[ROW][C]78[/C][C]22741.4791272913[/C][C]16488.0225814368[/C][C]28994.9356731459[/C][/ROW]
[ROW][C]79[/C][C]15715.4013085323[/C][C]9271.97505917424[/C][C]22158.8275578904[/C][/ROW]
[ROW][C]80[/C][C]14998.842980676[/C][C]8370.88968490347[/C][C]21626.7962764485[/C][/ROW]
[ROW][C]81[/C][C]16297.470360489[/C][C]9489.99006665283[/C][C]23104.9506543251[/C][/ROW]
[ROW][C]82[/C][C]18149.2956286372[/C][C]11166.9026999205[/C][C]25131.6885573538[/C][/ROW]
[ROW][C]83[/C][C]14855.8096387091[/C][C]7702.77992599167[/C][C]22008.8393514265[/C][/ROW]
[ROW][C]84[/C][C]8096.77929900702[/C][C]777.089610841017[/C][C]15416.468987173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210690&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210690&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
7327574.26840973522373.729642379932774.8071770902
7425139.863710780319712.375660974130567.3517605865
7529138.597582395223493.276547164934783.9186176256
7625921.649520783720066.594213543631776.7048280238
7720443.949608902414386.41746199126501.4817558139
7822741.479127291316488.022581436828994.9356731459
7915715.40130853239271.9750591742422158.8275578904
8014998.8429806768370.8896849034721626.7962764485
8116297.4703604899489.9900666528323104.9506543251
8218149.295628637211166.902699920525131.6885573538
8314855.80963870917702.7799259916722008.8393514265
848096.77929900702777.08961084101715416.468987173



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