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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Jan 2010 10:43:41 -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/2010/Jan/25/t1264441506scl60f08hcak6o5.htm/, Retrieved Thu, 31 Oct 2024 23:24:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72476, Retrieved Thu, 31 Oct 2024 23:24:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Autocorrelation F...] [2010-01-25 13:50:04] [830dacb160eeaee72e8ff2204da365bc]
-    D  [(Partial) Autocorrelation Function] [Autocorrelation F...] [2010-01-25 14:02:55] [830dacb160eeaee72e8ff2204da365bc]
- RMPD      [Exponential Smoothing] [Exponential smoot...] [2010-01-25 17:43:41] [3588db8f96a346e7899895ad48978494] [Current]
Feedback Forum

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 time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72476&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]1 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=72476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72476&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.298636157942104
beta0
gamma0.619823384572421

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.298636157942104 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.619823384572421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72476&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]0.298636157942104[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.619823384572421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72476&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
alpha0.298636157942104
beta0
gamma0.619823384572421







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770240443.7037927351-2741.70379273505
143036431996.9844990975-1632.98449909746
153260933561.8688755481-952.868875548083
163021230629.3187021052-417.318702105218
172996529937.661508177927.3384918221163
182835228050.1283635797301.871636420328
192581421460.41407584544353.58592415464
202241420567.60484274581846.39515725418
212050621231.3911251245-725.391125124541
222880627004.35736641881801.64263358119
232222822474.1539270696-246.153927069619
241397113911.154390600659.8456093993864
253684536937.4508845106-92.4508845106393
263533829763.87864848695574.12135151311
273502233776.72645318581245.27354681423
283477731733.43637477143043.56362522861
292688732268.625918055-5381.62591805498
302397028885.125941827-4915.12594182699
312278022498.7957065518281.204293448154
321735119299.8958110955-1948.89581109546
332138217712.25964895233669.74035104774
342456125896.3275057667-1335.32750576675
351740919539.0897330241-2130.08973302409
361151410546.5034875310967.496512468986
373151433777.6507675658-2263.65076756578
382707128419.0617148974-1348.06171489740
392946228482.8512423471979.148757652936
402610527141.8424180499-1036.84241804993
412239722795.8623690159-398.862369015857
422384321103.19342257482739.80657742525
432170519261.86039184262443.13960815737
441808915739.11962067762349.88037932239
452076417877.79658642182886.20341357817
462531623652.0603232371663.93967676299
471770417845.0117837314-141.011783731421
481554810793.02412561804754.97587438204
492802933750.5998184451-5721.59981844506
502938327757.3685858631625.63141413698
513643829720.89932135666717.10067864336
523203429217.05528114562816.94471885435
532267926299.2991943212-3620.29919432120
542431925009.0402640972-690.040264097213
551800422014.4633779833-4010.46337798333
561753716523.90159468371013.09840531626
572036618496.51839448371869.48160551635
582278223435.8076546138-653.80765461384
591916916151.94437088833017.05562911168
601380712171.46196030601635.53803969404
612974329643.065818910899.9341810891783
622559128582.3560614190-2991.35606141904
632909631380.4596230663-2284.45962306634
642648226492.9417291983-10.9417291983009
652240519932.26681422652472.7331857735
662704421735.45483827575308.54516172428
671797019088.8124414929-1118.81244149294
681873016645.65355471782084.34644528216
691968419310.4721229259373.527877074121
701978522706.0868861345-2921.08688613454
711847916340.93600907532138.06399092471
721069811497.3792233808-799.379223380776

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 40443.7037927351 & -2741.70379273505 \tabularnewline
14 & 30364 & 31996.9844990975 & -1632.98449909746 \tabularnewline
15 & 32609 & 33561.8688755481 & -952.868875548083 \tabularnewline
16 & 30212 & 30629.3187021052 & -417.318702105218 \tabularnewline
17 & 29965 & 29937.6615081779 & 27.3384918221163 \tabularnewline
18 & 28352 & 28050.1283635797 & 301.871636420328 \tabularnewline
19 & 25814 & 21460.4140758454 & 4353.58592415464 \tabularnewline
20 & 22414 & 20567.6048427458 & 1846.39515725418 \tabularnewline
21 & 20506 & 21231.3911251245 & -725.391125124541 \tabularnewline
22 & 28806 & 27004.3573664188 & 1801.64263358119 \tabularnewline
23 & 22228 & 22474.1539270696 & -246.153927069619 \tabularnewline
24 & 13971 & 13911.1543906006 & 59.8456093993864 \tabularnewline
25 & 36845 & 36937.4508845106 & -92.4508845106393 \tabularnewline
26 & 35338 & 29763.8786484869 & 5574.12135151311 \tabularnewline
27 & 35022 & 33776.7264531858 & 1245.27354681423 \tabularnewline
28 & 34777 & 31733.4363747714 & 3043.56362522861 \tabularnewline
29 & 26887 & 32268.625918055 & -5381.62591805498 \tabularnewline
30 & 23970 & 28885.125941827 & -4915.12594182699 \tabularnewline
31 & 22780 & 22498.7957065518 & 281.204293448154 \tabularnewline
32 & 17351 & 19299.8958110955 & -1948.89581109546 \tabularnewline
33 & 21382 & 17712.2596489523 & 3669.74035104774 \tabularnewline
34 & 24561 & 25896.3275057667 & -1335.32750576675 \tabularnewline
35 & 17409 & 19539.0897330241 & -2130.08973302409 \tabularnewline
36 & 11514 & 10546.5034875310 & 967.496512468986 \tabularnewline
37 & 31514 & 33777.6507675658 & -2263.65076756578 \tabularnewline
38 & 27071 & 28419.0617148974 & -1348.06171489740 \tabularnewline
39 & 29462 & 28482.8512423471 & 979.148757652936 \tabularnewline
40 & 26105 & 27141.8424180499 & -1036.84241804993 \tabularnewline
41 & 22397 & 22795.8623690159 & -398.862369015857 \tabularnewline
42 & 23843 & 21103.1934225748 & 2739.80657742525 \tabularnewline
43 & 21705 & 19261.8603918426 & 2443.13960815737 \tabularnewline
44 & 18089 & 15739.1196206776 & 2349.88037932239 \tabularnewline
45 & 20764 & 17877.7965864218 & 2886.20341357817 \tabularnewline
46 & 25316 & 23652.060323237 & 1663.93967676299 \tabularnewline
47 & 17704 & 17845.0117837314 & -141.011783731421 \tabularnewline
48 & 15548 & 10793.0241256180 & 4754.97587438204 \tabularnewline
49 & 28029 & 33750.5998184451 & -5721.59981844506 \tabularnewline
50 & 29383 & 27757.368585863 & 1625.63141413698 \tabularnewline
51 & 36438 & 29720.8993213566 & 6717.10067864336 \tabularnewline
52 & 32034 & 29217.0552811456 & 2816.94471885435 \tabularnewline
53 & 22679 & 26299.2991943212 & -3620.29919432120 \tabularnewline
54 & 24319 & 25009.0402640972 & -690.040264097213 \tabularnewline
55 & 18004 & 22014.4633779833 & -4010.46337798333 \tabularnewline
56 & 17537 & 16523.9015946837 & 1013.09840531626 \tabularnewline
57 & 20366 & 18496.5183944837 & 1869.48160551635 \tabularnewline
58 & 22782 & 23435.8076546138 & -653.80765461384 \tabularnewline
59 & 19169 & 16151.9443708883 & 3017.05562911168 \tabularnewline
60 & 13807 & 12171.4619603060 & 1635.53803969404 \tabularnewline
61 & 29743 & 29643.0658189108 & 99.9341810891783 \tabularnewline
62 & 25591 & 28582.3560614190 & -2991.35606141904 \tabularnewline
63 & 29096 & 31380.4596230663 & -2284.45962306634 \tabularnewline
64 & 26482 & 26492.9417291983 & -10.9417291983009 \tabularnewline
65 & 22405 & 19932.2668142265 & 2472.7331857735 \tabularnewline
66 & 27044 & 21735.4548382757 & 5308.54516172428 \tabularnewline
67 & 17970 & 19088.8124414929 & -1118.81244149294 \tabularnewline
68 & 18730 & 16645.6535547178 & 2084.34644528216 \tabularnewline
69 & 19684 & 19310.4721229259 & 373.527877074121 \tabularnewline
70 & 19785 & 22706.0868861345 & -2921.08688613454 \tabularnewline
71 & 18479 & 16340.9360090753 & 2138.06399092471 \tabularnewline
72 & 10698 & 11497.3792233808 & -799.379223380776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72476&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]31996.9844990975[/C][C]-1632.98449909746[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]33561.8688755481[/C][C]-952.868875548083[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30629.3187021052[/C][C]-417.318702105218[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]29937.6615081779[/C][C]27.3384918221163[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28050.1283635797[/C][C]301.871636420328[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]21460.4140758454[/C][C]4353.58592415464[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20567.6048427458[/C][C]1846.39515725418[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21231.3911251245[/C][C]-725.391125124541[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]27004.3573664188[/C][C]1801.64263358119[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22474.1539270696[/C][C]-246.153927069619[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13911.1543906006[/C][C]59.8456093993864[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]36937.4508845106[/C][C]-92.4508845106393[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29763.8786484869[/C][C]5574.12135151311[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33776.7264531858[/C][C]1245.27354681423[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31733.4363747714[/C][C]3043.56362522861[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]32268.625918055[/C][C]-5381.62591805498[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28885.125941827[/C][C]-4915.12594182699[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22498.7957065518[/C][C]281.204293448154[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]19299.8958110955[/C][C]-1948.89581109546[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]17712.2596489523[/C][C]3669.74035104774[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25896.3275057667[/C][C]-1335.32750576675[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]19539.0897330241[/C][C]-2130.08973302409[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]10546.5034875310[/C][C]967.496512468986[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]33777.6507675658[/C][C]-2263.65076756578[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]28419.0617148974[/C][C]-1348.06171489740[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]28482.8512423471[/C][C]979.148757652936[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27141.8424180499[/C][C]-1036.84241804993[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]22795.8623690159[/C][C]-398.862369015857[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21103.1934225748[/C][C]2739.80657742525[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19261.8603918426[/C][C]2443.13960815737[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]15739.1196206776[/C][C]2349.88037932239[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]17877.7965864218[/C][C]2886.20341357817[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23652.060323237[/C][C]1663.93967676299[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]17845.0117837314[/C][C]-141.011783731421[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]10793.0241256180[/C][C]4754.97587438204[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33750.5998184451[/C][C]-5721.59981844506[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27757.368585863[/C][C]1625.63141413698[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29720.8993213566[/C][C]6717.10067864336[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]29217.0552811456[/C][C]2816.94471885435[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]26299.2991943212[/C][C]-3620.29919432120[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25009.0402640972[/C][C]-690.040264097213[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]22014.4633779833[/C][C]-4010.46337798333[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]16523.9015946837[/C][C]1013.09840531626[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18496.5183944837[/C][C]1869.48160551635[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23435.8076546138[/C][C]-653.80765461384[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]16151.9443708883[/C][C]3017.05562911168[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12171.4619603060[/C][C]1635.53803969404[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29643.0658189108[/C][C]99.9341810891783[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]28582.3560614190[/C][C]-2991.35606141904[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]31380.4596230663[/C][C]-2284.45962306634[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26492.9417291983[/C][C]-10.9417291983009[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]19932.2668142265[/C][C]2472.7331857735[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]21735.4548382757[/C][C]5308.54516172428[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19088.8124414929[/C][C]-1118.81244149294[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16645.6535547178[/C][C]2084.34644528216[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19310.4721229259[/C][C]373.527877074121[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22706.0868861345[/C][C]-2921.08688613454[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]16340.9360090753[/C][C]2138.06399092471[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]11497.3792233808[/C][C]-799.379223380776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72476&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72476&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
143036431996.9844990975-1632.98449909746
153260933561.8688755481-952.868875548083
163021230629.3187021052-417.318702105218
172996529937.661508177927.3384918221163
182835228050.1283635797301.871636420328
192581421460.41407584544353.58592415464
202241420567.60484274581846.39515725418
212050621231.3911251245-725.391125124541
222880627004.35736641881801.64263358119
232222822474.1539270696-246.153927069619
241397113911.154390600659.8456093993864
253684536937.4508845106-92.4508845106393
263533829763.87864848695574.12135151311
273502233776.72645318581245.27354681423
283477731733.43637477143043.56362522861
292688732268.625918055-5381.62591805498
302397028885.125941827-4915.12594182699
312278022498.7957065518281.204293448154
321735119299.8958110955-1948.89581109546
332138217712.25964895233669.74035104774
342456125896.3275057667-1335.32750576675
351740919539.0897330241-2130.08973302409
361151410546.5034875310967.496512468986
373151433777.6507675658-2263.65076756578
382707128419.0617148974-1348.06171489740
392946228482.8512423471979.148757652936
402610527141.8424180499-1036.84241804993
412239722795.8623690159-398.862369015857
422384321103.19342257482739.80657742525
432170519261.86039184262443.13960815737
441808915739.11962067762349.88037932239
452076417877.79658642182886.20341357817
462531623652.0603232371663.93967676299
471770417845.0117837314-141.011783731421
481554810793.02412561804754.97587438204
492802933750.5998184451-5721.59981844506
502938327757.3685858631625.63141413698
513643829720.89932135666717.10067864336
523203429217.05528114562816.94471885435
532267926299.2991943212-3620.29919432120
542431925009.0402640972-690.040264097213
551800422014.4633779833-4010.46337798333
561753716523.90159468371013.09840531626
572036618496.51839448371869.48160551635
582278223435.8076546138-653.80765461384
591916916151.94437088833017.05562911168
601380712171.46196030601635.53803969404
612974329643.065818910899.9341810891783
622559128582.3560614190-2991.35606141904
632909631380.4596230663-2284.45962306634
642648226492.9417291983-10.9417291983009
652240519932.26681422652472.7331857735
662704421735.45483827575308.54516172428
671797019088.8124414929-1118.81244149294
681873016645.65355471782084.34644528216
691968419310.4721229259373.527877074121
701978522706.0868861345-2921.08688613454
711847916340.93600907532138.06399092471
721069811497.3792233808-799.379223380776







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327574.268409722922373.729642367332774.8071770786
7425139.863710774419712.375660964730567.351760584
7529138.597582397723493.276547161334783.9186176342
7625921.649520785820066.594213537131776.7048280344
7720443.949608899714386.417461977426501.4817558221
7822741.479127294716488.022581427028994.9356731623
7915715.40130852279271.9750591494522158.8275578959
8014998.84298067808370.8896848883521626.7962764677
8116297.47036048959489.990066634323104.9506543446
8218149.295628629811166.902699892325131.6885573674
8314855.8096387137702.7799259730422008.8393514530
848096.77929900556777.08961081535515416.4689871958

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27574.2684097229 & 22373.7296423673 & 32774.8071770786 \tabularnewline
74 & 25139.8637107744 & 19712.3756609647 & 30567.351760584 \tabularnewline
75 & 29138.5975823977 & 23493.2765471613 & 34783.9186176342 \tabularnewline
76 & 25921.6495207858 & 20066.5942135371 & 31776.7048280344 \tabularnewline
77 & 20443.9496088997 & 14386.4174619774 & 26501.4817558221 \tabularnewline
78 & 22741.4791272947 & 16488.0225814270 & 28994.9356731623 \tabularnewline
79 & 15715.4013085227 & 9271.97505914945 & 22158.8275578959 \tabularnewline
80 & 14998.8429806780 & 8370.88968488835 & 21626.7962764677 \tabularnewline
81 & 16297.4703604895 & 9489.9900666343 & 23104.9506543446 \tabularnewline
82 & 18149.2956286298 & 11166.9026998923 & 25131.6885573674 \tabularnewline
83 & 14855.809638713 & 7702.77992597304 & 22008.8393514530 \tabularnewline
84 & 8096.77929900556 & 777.089610815355 & 15416.4689871958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72476&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]27574.2684097229[/C][C]22373.7296423673[/C][C]32774.8071770786[/C][/ROW]
[ROW][C]74[/C][C]25139.8637107744[/C][C]19712.3756609647[/C][C]30567.351760584[/C][/ROW]
[ROW][C]75[/C][C]29138.5975823977[/C][C]23493.2765471613[/C][C]34783.9186176342[/C][/ROW]
[ROW][C]76[/C][C]25921.6495207858[/C][C]20066.5942135371[/C][C]31776.7048280344[/C][/ROW]
[ROW][C]77[/C][C]20443.9496088997[/C][C]14386.4174619774[/C][C]26501.4817558221[/C][/ROW]
[ROW][C]78[/C][C]22741.4791272947[/C][C]16488.0225814270[/C][C]28994.9356731623[/C][/ROW]
[ROW][C]79[/C][C]15715.4013085227[/C][C]9271.97505914945[/C][C]22158.8275578959[/C][/ROW]
[ROW][C]80[/C][C]14998.8429806780[/C][C]8370.88968488835[/C][C]21626.7962764677[/C][/ROW]
[ROW][C]81[/C][C]16297.4703604895[/C][C]9489.9900666343[/C][C]23104.9506543446[/C][/ROW]
[ROW][C]82[/C][C]18149.2956286298[/C][C]11166.9026998923[/C][C]25131.6885573674[/C][/ROW]
[ROW][C]83[/C][C]14855.809638713[/C][C]7702.77992597304[/C][C]22008.8393514530[/C][/ROW]
[ROW][C]84[/C][C]8096.77929900556[/C][C]777.089610815355[/C][C]15416.4689871958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72476&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72476&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
7327574.268409722922373.729642367332774.8071770786
7425139.863710774419712.375660964730567.351760584
7529138.597582397723493.276547161334783.9186176342
7625921.649520785820066.594213537131776.7048280344
7720443.949608899714386.417461977426501.4817558221
7822741.479127294716488.022581427028994.9356731623
7915715.40130852279271.9750591494522158.8275578959
8014998.84298067808370.8896848883521626.7962764677
8116297.47036048959489.990066634323104.9506543446
8218149.295628629811166.902699892325131.6885573674
8314855.8096387137702.7799259730422008.8393514530
848096.77929900556777.08961081535515416.4689871958



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')