Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 20:16:55 +0000
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/Jun/06/t1275855458rxortaiqdinbl2g.htm/, Retrieved Sun, 28 Apr 2024 15:31:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77792, Retrieved Sun, 28 Apr 2024 15:31:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 Oefening 1] [2010-06-06 20:16:55] [5a7cbdb73d36823522b207a888c6ba9b] [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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77792&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77792&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.298636158049011
beta0
gamma0.619823384767296

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.298636158049011 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.619823384767296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77792&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]0.298636158049011[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.619823384767296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77792&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
alpha0.298636158049011
beta0
gamma0.619823384767296







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770240443.7037927351-2741.70379273505
143036431996.9844988044-1632.98449880435
153260933561.8688751679-952.86887516793
163021230629.3187017367-417.31870173672
172996529937.661507874827.3384921251818
182835228050.12836337301.871636629967
192581421460.41407573064353.5859242694
202241420567.60484313081846.39515686924
212050621231.3911255919-725.391125591916
222880627004.35736666911801.64263333094
232222822474.1539274377-246.153927437736
241397113911.154390832559.8456091675198
253684536937.4508844866-92.4508844865995
263533829763.87864866565574.12135133435
273502233776.72645399281245.27354600721
283477731733.43637550323043.56362449683
292688732268.6259188965-5381.62591889647
302397028885.1259418206-4915.12594182057
312278022498.7957062659281.20429373407
321735119299.8958105312-1948.89581053121
332138217712.25964813123669.74035186876
342456125896.3275058556-1335.32750585557
351740919539.0897327482-2130.08973274819
361151410546.5034871906967.49651280944
373151433777.6507673379-2263.65076733789
382707128419.0617150119-1348.06171501192
392946228482.8512417911979.148758208943
402610527141.8424179566-1036.84241795661
412239722795.8623682015-398.862368201477
422384321103.19342234112739.80657765889
432170519261.86039270312443.13960729689
441808915739.11962111252349.8803788875
452076417877.79658726842886.20341273161
462531623652.06032366371663.93967633631
471770417845.0117841157-141.011784115715
481554810793.02412619944754.97587380063
492802933750.5998189922-5721.59981899219
502938327757.3685860671625.63141393296
513643829720.89932163676717.10067836331
523203429217.0552819092816.94471809096
532267926299.2991948781-3620.29919487807
542431925009.0402644495-690.040264449468
551800422014.4633783915-4010.46337839154
561753716523.90159428991013.09840571007
572036618496.51839446491869.48160553511
582278223435.8076544214-653.807654421384
591916916151.94437048193017.05562951808
601380712171.46196092951635.53803907052
612974329643.065818431299.9341815688058
622559128582.3560621918-2991.3560621918
632909631380.4596235772-2284.45962357716
642648226492.9417286765-10.9417286764692
652240519932.26681321612472.73318678387
662704421735.45483847555308.54516152455
671797019088.8124421773-1118.81244217734
681873016645.65355552932084.34644447074
691968419310.4721237642373.527876235796
701978522706.0868862811-2921.08688628111
711847916340.93600901582138.06399098422
721069811497.3792236086-799.379223608617

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 40443.7037927351 & -2741.70379273505 \tabularnewline
14 & 30364 & 31996.9844988044 & -1632.98449880435 \tabularnewline
15 & 32609 & 33561.8688751679 & -952.86887516793 \tabularnewline
16 & 30212 & 30629.3187017367 & -417.31870173672 \tabularnewline
17 & 29965 & 29937.6615078748 & 27.3384921251818 \tabularnewline
18 & 28352 & 28050.12836337 & 301.871636629967 \tabularnewline
19 & 25814 & 21460.4140757306 & 4353.5859242694 \tabularnewline
20 & 22414 & 20567.6048431308 & 1846.39515686924 \tabularnewline
21 & 20506 & 21231.3911255919 & -725.391125591916 \tabularnewline
22 & 28806 & 27004.3573666691 & 1801.64263333094 \tabularnewline
23 & 22228 & 22474.1539274377 & -246.153927437736 \tabularnewline
24 & 13971 & 13911.1543908325 & 59.8456091675198 \tabularnewline
25 & 36845 & 36937.4508844866 & -92.4508844865995 \tabularnewline
26 & 35338 & 29763.8786486656 & 5574.12135133435 \tabularnewline
27 & 35022 & 33776.7264539928 & 1245.27354600721 \tabularnewline
28 & 34777 & 31733.4363755032 & 3043.56362449683 \tabularnewline
29 & 26887 & 32268.6259188965 & -5381.62591889647 \tabularnewline
30 & 23970 & 28885.1259418206 & -4915.12594182057 \tabularnewline
31 & 22780 & 22498.7957062659 & 281.20429373407 \tabularnewline
32 & 17351 & 19299.8958105312 & -1948.89581053121 \tabularnewline
33 & 21382 & 17712.2596481312 & 3669.74035186876 \tabularnewline
34 & 24561 & 25896.3275058556 & -1335.32750585557 \tabularnewline
35 & 17409 & 19539.0897327482 & -2130.08973274819 \tabularnewline
36 & 11514 & 10546.5034871906 & 967.49651280944 \tabularnewline
37 & 31514 & 33777.6507673379 & -2263.65076733789 \tabularnewline
38 & 27071 & 28419.0617150119 & -1348.06171501192 \tabularnewline
39 & 29462 & 28482.8512417911 & 979.148758208943 \tabularnewline
40 & 26105 & 27141.8424179566 & -1036.84241795661 \tabularnewline
41 & 22397 & 22795.8623682015 & -398.862368201477 \tabularnewline
42 & 23843 & 21103.1934223411 & 2739.80657765889 \tabularnewline
43 & 21705 & 19261.8603927031 & 2443.13960729689 \tabularnewline
44 & 18089 & 15739.1196211125 & 2349.8803788875 \tabularnewline
45 & 20764 & 17877.7965872684 & 2886.20341273161 \tabularnewline
46 & 25316 & 23652.0603236637 & 1663.93967633631 \tabularnewline
47 & 17704 & 17845.0117841157 & -141.011784115715 \tabularnewline
48 & 15548 & 10793.0241261994 & 4754.97587380063 \tabularnewline
49 & 28029 & 33750.5998189922 & -5721.59981899219 \tabularnewline
50 & 29383 & 27757.368586067 & 1625.63141393296 \tabularnewline
51 & 36438 & 29720.8993216367 & 6717.10067836331 \tabularnewline
52 & 32034 & 29217.055281909 & 2816.94471809096 \tabularnewline
53 & 22679 & 26299.2991948781 & -3620.29919487807 \tabularnewline
54 & 24319 & 25009.0402644495 & -690.040264449468 \tabularnewline
55 & 18004 & 22014.4633783915 & -4010.46337839154 \tabularnewline
56 & 17537 & 16523.9015942899 & 1013.09840571007 \tabularnewline
57 & 20366 & 18496.5183944649 & 1869.48160553511 \tabularnewline
58 & 22782 & 23435.8076544214 & -653.807654421384 \tabularnewline
59 & 19169 & 16151.9443704819 & 3017.05562951808 \tabularnewline
60 & 13807 & 12171.4619609295 & 1635.53803907052 \tabularnewline
61 & 29743 & 29643.0658184312 & 99.9341815688058 \tabularnewline
62 & 25591 & 28582.3560621918 & -2991.3560621918 \tabularnewline
63 & 29096 & 31380.4596235772 & -2284.45962357716 \tabularnewline
64 & 26482 & 26492.9417286765 & -10.9417286764692 \tabularnewline
65 & 22405 & 19932.2668132161 & 2472.73318678387 \tabularnewline
66 & 27044 & 21735.4548384755 & 5308.54516152455 \tabularnewline
67 & 17970 & 19088.8124421773 & -1118.81244217734 \tabularnewline
68 & 18730 & 16645.6535555293 & 2084.34644447074 \tabularnewline
69 & 19684 & 19310.4721237642 & 373.527876235796 \tabularnewline
70 & 19785 & 22706.0868862811 & -2921.08688628111 \tabularnewline
71 & 18479 & 16340.9360090158 & 2138.06399098422 \tabularnewline
72 & 10698 & 11497.3792236086 & -799.379223608617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77792&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]31996.9844988044[/C][C]-1632.98449880435[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]33561.8688751679[/C][C]-952.86887516793[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30629.3187017367[/C][C]-417.31870173672[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]29937.6615078748[/C][C]27.3384921251818[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28050.12836337[/C][C]301.871636629967[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]21460.4140757306[/C][C]4353.5859242694[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20567.6048431308[/C][C]1846.39515686924[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21231.3911255919[/C][C]-725.391125591916[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]27004.3573666691[/C][C]1801.64263333094[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22474.1539274377[/C][C]-246.153927437736[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13911.1543908325[/C][C]59.8456091675198[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]36937.4508844866[/C][C]-92.4508844865995[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29763.8786486656[/C][C]5574.12135133435[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33776.7264539928[/C][C]1245.27354600721[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31733.4363755032[/C][C]3043.56362449683[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]32268.6259188965[/C][C]-5381.62591889647[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28885.1259418206[/C][C]-4915.12594182057[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22498.7957062659[/C][C]281.20429373407[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]19299.8958105312[/C][C]-1948.89581053121[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]17712.2596481312[/C][C]3669.74035186876[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25896.3275058556[/C][C]-1335.32750585557[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]19539.0897327482[/C][C]-2130.08973274819[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]10546.5034871906[/C][C]967.49651280944[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]33777.6507673379[/C][C]-2263.65076733789[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]28419.0617150119[/C][C]-1348.06171501192[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]28482.8512417911[/C][C]979.148758208943[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27141.8424179566[/C][C]-1036.84241795661[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]22795.8623682015[/C][C]-398.862368201477[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21103.1934223411[/C][C]2739.80657765889[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19261.8603927031[/C][C]2443.13960729689[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]15739.1196211125[/C][C]2349.8803788875[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]17877.7965872684[/C][C]2886.20341273161[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23652.0603236637[/C][C]1663.93967633631[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]17845.0117841157[/C][C]-141.011784115715[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]10793.0241261994[/C][C]4754.97587380063[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33750.5998189922[/C][C]-5721.59981899219[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27757.368586067[/C][C]1625.63141393296[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29720.8993216367[/C][C]6717.10067836331[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]29217.055281909[/C][C]2816.94471809096[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]26299.2991948781[/C][C]-3620.29919487807[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25009.0402644495[/C][C]-690.040264449468[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]22014.4633783915[/C][C]-4010.46337839154[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]16523.9015942899[/C][C]1013.09840571007[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18496.5183944649[/C][C]1869.48160553511[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23435.8076544214[/C][C]-653.807654421384[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]16151.9443704819[/C][C]3017.05562951808[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12171.4619609295[/C][C]1635.53803907052[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29643.0658184312[/C][C]99.9341815688058[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]28582.3560621918[/C][C]-2991.3560621918[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]31380.4596235772[/C][C]-2284.45962357716[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26492.9417286765[/C][C]-10.9417286764692[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]19932.2668132161[/C][C]2472.73318678387[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]21735.4548384755[/C][C]5308.54516152455[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19088.8124421773[/C][C]-1118.81244217734[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16645.6535555293[/C][C]2084.34644447074[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19310.4721237642[/C][C]373.527876235796[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22706.0868862811[/C][C]-2921.08688628111[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]16340.9360090158[/C][C]2138.06399098422[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]11497.3792236086[/C][C]-799.379223608617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77792&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
143036431996.9844988044-1632.98449880435
153260933561.8688751679-952.86887516793
163021230629.3187017367-417.31870173672
172996529937.661507874827.3384921251818
182835228050.12836337301.871636629967
192581421460.41407573064353.5859242694
202241420567.60484313081846.39515686924
212050621231.3911255919-725.391125591916
222880627004.35736666911801.64263333094
232222822474.1539274377-246.153927437736
241397113911.154390832559.8456091675198
253684536937.4508844866-92.4508844865995
263533829763.87864866565574.12135133435
273502233776.72645399281245.27354600721
283477731733.43637550323043.56362449683
292688732268.6259188965-5381.62591889647
302397028885.1259418206-4915.12594182057
312278022498.7957062659281.20429373407
321735119299.8958105312-1948.89581053121
332138217712.25964813123669.74035186876
342456125896.3275058556-1335.32750585557
351740919539.0897327482-2130.08973274819
361151410546.5034871906967.49651280944
373151433777.6507673379-2263.65076733789
382707128419.0617150119-1348.06171501192
392946228482.8512417911979.148758208943
402610527141.8424179566-1036.84241795661
412239722795.8623682015-398.862368201477
422384321103.19342234112739.80657765889
432170519261.86039270312443.13960729689
441808915739.11962111252349.8803788875
452076417877.79658726842886.20341273161
462531623652.06032366371663.93967633631
471770417845.0117841157-141.011784115715
481554810793.02412619944754.97587380063
492802933750.5998189922-5721.59981899219
502938327757.3685860671625.63141393296
513643829720.89932163676717.10067836331
523203429217.0552819092816.94471809096
532267926299.2991948781-3620.29919487807
542431925009.0402644495-690.040264449468
551800422014.4633783915-4010.46337839154
561753716523.90159428991013.09840571007
572036618496.51839446491869.48160553511
582278223435.8076544214-653.807654421384
591916916151.94437048193017.05562951808
601380712171.46196092951635.53803907052
612974329643.065818431299.9341815688058
622559128582.3560621918-2991.3560621918
632909631380.4596235772-2284.45962357716
642648226492.9417286765-10.9417286764692
652240519932.26681321612472.73318678387
662704421735.45483847555308.54516152455
671797019088.8124421773-1118.81244217734
681873016645.65355552932084.34644447074
691968419310.4721237642373.527876235796
701978522706.0868862811-2921.08688628111
711847916340.93600901582138.06399098422
721069811497.3792236086-799.379223608617







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327574.268409076922373.729641692932774.807176461
7425139.863710464719712.375660466330567.351760463
7529138.597582540423493.276546967234783.9186181136
7625921.649520901520066.594213178531776.7048286246
7720443.949608759514386.417461233926501.4817562851
7822741.479127472116488.0225808828994.9356740643
7915715.40130801379271.975057801222158.8275582261
8014998.84298079048370.8896840525521626.7962775282
8116297.4703605169489.9900656089523104.9506554231
8218149.295628243811166.902698355225131.6885581324
8314855.80963892287702.779924936622008.8393529089
848096.77929892456777.08960939678215416.4689884523

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27574.2684090769 & 22373.7296416929 & 32774.807176461 \tabularnewline
74 & 25139.8637104647 & 19712.3756604663 & 30567.351760463 \tabularnewline
75 & 29138.5975825404 & 23493.2765469672 & 34783.9186181136 \tabularnewline
76 & 25921.6495209015 & 20066.5942131785 & 31776.7048286246 \tabularnewline
77 & 20443.9496087595 & 14386.4174612339 & 26501.4817562851 \tabularnewline
78 & 22741.4791274721 & 16488.02258088 & 28994.9356740643 \tabularnewline
79 & 15715.4013080137 & 9271.9750578012 & 22158.8275582261 \tabularnewline
80 & 14998.8429807904 & 8370.88968405255 & 21626.7962775282 \tabularnewline
81 & 16297.470360516 & 9489.99006560895 & 23104.9506554231 \tabularnewline
82 & 18149.2956282438 & 11166.9026983552 & 25131.6885581324 \tabularnewline
83 & 14855.8096389228 & 7702.7799249366 & 22008.8393529089 \tabularnewline
84 & 8096.77929892456 & 777.089609396782 & 15416.4689884523 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77792&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]27574.2684090769[/C][C]22373.7296416929[/C][C]32774.807176461[/C][/ROW]
[ROW][C]74[/C][C]25139.8637104647[/C][C]19712.3756604663[/C][C]30567.351760463[/C][/ROW]
[ROW][C]75[/C][C]29138.5975825404[/C][C]23493.2765469672[/C][C]34783.9186181136[/C][/ROW]
[ROW][C]76[/C][C]25921.6495209015[/C][C]20066.5942131785[/C][C]31776.7048286246[/C][/ROW]
[ROW][C]77[/C][C]20443.9496087595[/C][C]14386.4174612339[/C][C]26501.4817562851[/C][/ROW]
[ROW][C]78[/C][C]22741.4791274721[/C][C]16488.02258088[/C][C]28994.9356740643[/C][/ROW]
[ROW][C]79[/C][C]15715.4013080137[/C][C]9271.9750578012[/C][C]22158.8275582261[/C][/ROW]
[ROW][C]80[/C][C]14998.8429807904[/C][C]8370.88968405255[/C][C]21626.7962775282[/C][/ROW]
[ROW][C]81[/C][C]16297.470360516[/C][C]9489.99006560895[/C][C]23104.9506554231[/C][/ROW]
[ROW][C]82[/C][C]18149.2956282438[/C][C]11166.9026983552[/C][C]25131.6885581324[/C][/ROW]
[ROW][C]83[/C][C]14855.8096389228[/C][C]7702.7799249366[/C][C]22008.8393529089[/C][/ROW]
[ROW][C]84[/C][C]8096.77929892456[/C][C]777.089609396782[/C][C]15416.4689884523[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77792&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77792&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
7327574.268409076922373.729641692932774.807176461
7425139.863710464719712.375660466330567.351760463
7529138.597582540423493.276546967234783.9186181136
7625921.649520901520066.594213178531776.7048286246
7720443.949608759514386.417461233926501.4817562851
7822741.479127472116488.0225808828994.9356740643
7915715.40130801379271.975057801222158.8275582261
8014998.84298079048370.8896840525521626.7962775282
8116297.4703605169489.9900656089523104.9506554231
8218149.295628243811166.902698355225131.6885581324
8314855.80963892287702.779924936622008.8393529089
848096.77929892456777.08960939678215416.4689884523



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')