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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Nov 2015 15:33:24 +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/2015/Nov/29/t1448811223bjpl2zu8xc8o785.htm/, Retrieved Wed, 15 May 2024 13:17:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284483, Retrieved Wed, 15 May 2024 13:17:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-29 15:33:24] [a9d02bc5e77e4ed95e8bc9cdb21bd9af] [Current]
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Dataseries X:
31025
31068
31619
32020
30467
31960
31389
28863
33143
33350
29079
26505
24975
24644
26626
23977
23898
25583
25974
23529
27491
28053
27913
26706
26788
27600
32770
29623
29300
32152
30700
29463
32709
32823
34073
33551
32168
32833
37341
33747
34482
33309
33057
32809
35316
33989
35799
34508
34646
35203
38084
35005
36734
35716
34543
34340
35094
38730
37805
33815
36486
34960
38054
35283
37361
35536
36103
33886
35416
38053
37181
34787
36074
34966
37482
36109
35520
36123
36256
32456
37748
38461
36344
35865




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=284483&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=284483&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284483&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
alpha0.765367760937519
beta0.0333456453514284
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.765367760937519 \tabularnewline
beta & 0.0333456453514284 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284483&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]0.765367760937519[/C][/ROW]
[ROW][C]beta[/C][C]0.0333456453514284[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284483&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284483&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
alpha0.765367760937519
beta0.0333456453514284
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132497528194.8571047009-3219.85710470087
142464425295.1932051589-651.193205158928
152662626667.7572971601-41.7572971601403
162397723873.1566023787103.843397621302
172389823575.72757685322.272423150043
182558324988.6186864557594.38131354432
192597425856.1927790569117.807220943076
202352923399.3107305705129.689269429466
212749127716.7910405456-225.791040545631
222805327750.8939478339302.106052166073
232791323784.40919221254128.59080778754
242670624479.54442096862226.45557903143
252678824016.1039445172771.89605548304
262760026554.58478444651045.41521555349
273277029661.53055373333108.4694462667
282962329685.4325274384-62.4325274383955
292930029681.0061819135-381.006181913501
303215230970.54160673771181.45839326227
313070032541.6746856743-1841.67468567435
322946328903.8957581757559.104241824261
333270933793.6281841627-1084.62818416272
343282333599.3464194373-776.346419437308
353407329982.82158810044090.17841189961
363355130478.83060255453072.16939744554
373216831088.80981988381079.19018011625
383283332181.6190698745651.380930125495
393734135715.94529713971625.05470286029
403374734067.5369442574-320.536944257445
413448233991.2742145131490.72578548688
423330936537.31387631-3228.31387630997
433305734134.1842697593-1077.18426975933
443280931774.49220264081034.50779735923
453531636784.2140695081-1468.21406950815
463398936500.6946239215-2511.69462392146
473579932785.55858421983013.44141578021
483450832278.85468498062229.14531501938
493464631814.72248387022831.27751612983
503520334231.590480771971.409519229048
513808438330.9246257791-246.924625779109
523500534837.1021558162167.897844183797
533673435381.3227691881352.67723081201
543571637792.7668383134-2076.7668383134
553454336883.409145759-2340.40914575901
563434034127.8074779883212.192522011712
573509437975.4005958432-2881.4005958432
583873036383.83675432872346.16324567132
593780537825.501449129-20.5014491289621
603381534877.6409113709-1062.64091137085
613648632016.29593124244469.70406875763
623496035273.5278470409-313.52784704091
633805438093.5081752899-39.508175289855
643528334851.016197812431.983802188042
653736135877.33695090741483.66304909263
663553637589.7080012677-2053.70800126772
673610336642.0611140511-539.061114051132
683388635915.9705319792-2029.97053197925
693541637316.2986125355-1900.29861253547
703805337721.9039399437331.096060056341
713718137034.2877662726146.712233727441
723478733942.4376775182844.562322481819
733607433860.09609277942213.90390722058
743496634232.1640979534733.835902046609
753748237908.4404298095-426.440429809532
763610934460.93874245761648.06125754242
773552036676.3087181927-1156.30871819268
783612335482.317565457640.682434542985
793625636965.1889867053-709.188986705318
803245635767.664394228-3311.66439422801
813774836193.33133648831554.66866351171
823846139830.8717466596-1369.87174665958
833634437818.7730883187-1474.77308831867
843586533628.89133246622236.10866753381

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 24975 & 28194.8571047009 & -3219.85710470087 \tabularnewline
14 & 24644 & 25295.1932051589 & -651.193205158928 \tabularnewline
15 & 26626 & 26667.7572971601 & -41.7572971601403 \tabularnewline
16 & 23977 & 23873.1566023787 & 103.843397621302 \tabularnewline
17 & 23898 & 23575.72757685 & 322.272423150043 \tabularnewline
18 & 25583 & 24988.6186864557 & 594.38131354432 \tabularnewline
19 & 25974 & 25856.1927790569 & 117.807220943076 \tabularnewline
20 & 23529 & 23399.3107305705 & 129.689269429466 \tabularnewline
21 & 27491 & 27716.7910405456 & -225.791040545631 \tabularnewline
22 & 28053 & 27750.8939478339 & 302.106052166073 \tabularnewline
23 & 27913 & 23784.4091922125 & 4128.59080778754 \tabularnewline
24 & 26706 & 24479.5444209686 & 2226.45557903143 \tabularnewline
25 & 26788 & 24016.103944517 & 2771.89605548304 \tabularnewline
26 & 27600 & 26554.5847844465 & 1045.41521555349 \tabularnewline
27 & 32770 & 29661.5305537333 & 3108.4694462667 \tabularnewline
28 & 29623 & 29685.4325274384 & -62.4325274383955 \tabularnewline
29 & 29300 & 29681.0061819135 & -381.006181913501 \tabularnewline
30 & 32152 & 30970.5416067377 & 1181.45839326227 \tabularnewline
31 & 30700 & 32541.6746856743 & -1841.67468567435 \tabularnewline
32 & 29463 & 28903.8957581757 & 559.104241824261 \tabularnewline
33 & 32709 & 33793.6281841627 & -1084.62818416272 \tabularnewline
34 & 32823 & 33599.3464194373 & -776.346419437308 \tabularnewline
35 & 34073 & 29982.8215881004 & 4090.17841189961 \tabularnewline
36 & 33551 & 30478.8306025545 & 3072.16939744554 \tabularnewline
37 & 32168 & 31088.8098198838 & 1079.19018011625 \tabularnewline
38 & 32833 & 32181.6190698745 & 651.380930125495 \tabularnewline
39 & 37341 & 35715.9452971397 & 1625.05470286029 \tabularnewline
40 & 33747 & 34067.5369442574 & -320.536944257445 \tabularnewline
41 & 34482 & 33991.2742145131 & 490.72578548688 \tabularnewline
42 & 33309 & 36537.31387631 & -3228.31387630997 \tabularnewline
43 & 33057 & 34134.1842697593 & -1077.18426975933 \tabularnewline
44 & 32809 & 31774.4922026408 & 1034.50779735923 \tabularnewline
45 & 35316 & 36784.2140695081 & -1468.21406950815 \tabularnewline
46 & 33989 & 36500.6946239215 & -2511.69462392146 \tabularnewline
47 & 35799 & 32785.5585842198 & 3013.44141578021 \tabularnewline
48 & 34508 & 32278.8546849806 & 2229.14531501938 \tabularnewline
49 & 34646 & 31814.7224838702 & 2831.27751612983 \tabularnewline
50 & 35203 & 34231.590480771 & 971.409519229048 \tabularnewline
51 & 38084 & 38330.9246257791 & -246.924625779109 \tabularnewline
52 & 35005 & 34837.1021558162 & 167.897844183797 \tabularnewline
53 & 36734 & 35381.322769188 & 1352.67723081201 \tabularnewline
54 & 35716 & 37792.7668383134 & -2076.7668383134 \tabularnewline
55 & 34543 & 36883.409145759 & -2340.40914575901 \tabularnewline
56 & 34340 & 34127.8074779883 & 212.192522011712 \tabularnewline
57 & 35094 & 37975.4005958432 & -2881.4005958432 \tabularnewline
58 & 38730 & 36383.8367543287 & 2346.16324567132 \tabularnewline
59 & 37805 & 37825.501449129 & -20.5014491289621 \tabularnewline
60 & 33815 & 34877.6409113709 & -1062.64091137085 \tabularnewline
61 & 36486 & 32016.2959312424 & 4469.70406875763 \tabularnewline
62 & 34960 & 35273.5278470409 & -313.52784704091 \tabularnewline
63 & 38054 & 38093.5081752899 & -39.508175289855 \tabularnewline
64 & 35283 & 34851.016197812 & 431.983802188042 \tabularnewline
65 & 37361 & 35877.3369509074 & 1483.66304909263 \tabularnewline
66 & 35536 & 37589.7080012677 & -2053.70800126772 \tabularnewline
67 & 36103 & 36642.0611140511 & -539.061114051132 \tabularnewline
68 & 33886 & 35915.9705319792 & -2029.97053197925 \tabularnewline
69 & 35416 & 37316.2986125355 & -1900.29861253547 \tabularnewline
70 & 38053 & 37721.9039399437 & 331.096060056341 \tabularnewline
71 & 37181 & 37034.2877662726 & 146.712233727441 \tabularnewline
72 & 34787 & 33942.4376775182 & 844.562322481819 \tabularnewline
73 & 36074 & 33860.0960927794 & 2213.90390722058 \tabularnewline
74 & 34966 & 34232.1640979534 & 733.835902046609 \tabularnewline
75 & 37482 & 37908.4404298095 & -426.440429809532 \tabularnewline
76 & 36109 & 34460.9387424576 & 1648.06125754242 \tabularnewline
77 & 35520 & 36676.3087181927 & -1156.30871819268 \tabularnewline
78 & 36123 & 35482.317565457 & 640.682434542985 \tabularnewline
79 & 36256 & 36965.1889867053 & -709.188986705318 \tabularnewline
80 & 32456 & 35767.664394228 & -3311.66439422801 \tabularnewline
81 & 37748 & 36193.3313364883 & 1554.66866351171 \tabularnewline
82 & 38461 & 39830.8717466596 & -1369.87174665958 \tabularnewline
83 & 36344 & 37818.7730883187 & -1474.77308831867 \tabularnewline
84 & 35865 & 33628.8913324662 & 2236.10866753381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284483&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]24975[/C][C]28194.8571047009[/C][C]-3219.85710470087[/C][/ROW]
[ROW][C]14[/C][C]24644[/C][C]25295.1932051589[/C][C]-651.193205158928[/C][/ROW]
[ROW][C]15[/C][C]26626[/C][C]26667.7572971601[/C][C]-41.7572971601403[/C][/ROW]
[ROW][C]16[/C][C]23977[/C][C]23873.1566023787[/C][C]103.843397621302[/C][/ROW]
[ROW][C]17[/C][C]23898[/C][C]23575.72757685[/C][C]322.272423150043[/C][/ROW]
[ROW][C]18[/C][C]25583[/C][C]24988.6186864557[/C][C]594.38131354432[/C][/ROW]
[ROW][C]19[/C][C]25974[/C][C]25856.1927790569[/C][C]117.807220943076[/C][/ROW]
[ROW][C]20[/C][C]23529[/C][C]23399.3107305705[/C][C]129.689269429466[/C][/ROW]
[ROW][C]21[/C][C]27491[/C][C]27716.7910405456[/C][C]-225.791040545631[/C][/ROW]
[ROW][C]22[/C][C]28053[/C][C]27750.8939478339[/C][C]302.106052166073[/C][/ROW]
[ROW][C]23[/C][C]27913[/C][C]23784.4091922125[/C][C]4128.59080778754[/C][/ROW]
[ROW][C]24[/C][C]26706[/C][C]24479.5444209686[/C][C]2226.45557903143[/C][/ROW]
[ROW][C]25[/C][C]26788[/C][C]24016.103944517[/C][C]2771.89605548304[/C][/ROW]
[ROW][C]26[/C][C]27600[/C][C]26554.5847844465[/C][C]1045.41521555349[/C][/ROW]
[ROW][C]27[/C][C]32770[/C][C]29661.5305537333[/C][C]3108.4694462667[/C][/ROW]
[ROW][C]28[/C][C]29623[/C][C]29685.4325274384[/C][C]-62.4325274383955[/C][/ROW]
[ROW][C]29[/C][C]29300[/C][C]29681.0061819135[/C][C]-381.006181913501[/C][/ROW]
[ROW][C]30[/C][C]32152[/C][C]30970.5416067377[/C][C]1181.45839326227[/C][/ROW]
[ROW][C]31[/C][C]30700[/C][C]32541.6746856743[/C][C]-1841.67468567435[/C][/ROW]
[ROW][C]32[/C][C]29463[/C][C]28903.8957581757[/C][C]559.104241824261[/C][/ROW]
[ROW][C]33[/C][C]32709[/C][C]33793.6281841627[/C][C]-1084.62818416272[/C][/ROW]
[ROW][C]34[/C][C]32823[/C][C]33599.3464194373[/C][C]-776.346419437308[/C][/ROW]
[ROW][C]35[/C][C]34073[/C][C]29982.8215881004[/C][C]4090.17841189961[/C][/ROW]
[ROW][C]36[/C][C]33551[/C][C]30478.8306025545[/C][C]3072.16939744554[/C][/ROW]
[ROW][C]37[/C][C]32168[/C][C]31088.8098198838[/C][C]1079.19018011625[/C][/ROW]
[ROW][C]38[/C][C]32833[/C][C]32181.6190698745[/C][C]651.380930125495[/C][/ROW]
[ROW][C]39[/C][C]37341[/C][C]35715.9452971397[/C][C]1625.05470286029[/C][/ROW]
[ROW][C]40[/C][C]33747[/C][C]34067.5369442574[/C][C]-320.536944257445[/C][/ROW]
[ROW][C]41[/C][C]34482[/C][C]33991.2742145131[/C][C]490.72578548688[/C][/ROW]
[ROW][C]42[/C][C]33309[/C][C]36537.31387631[/C][C]-3228.31387630997[/C][/ROW]
[ROW][C]43[/C][C]33057[/C][C]34134.1842697593[/C][C]-1077.18426975933[/C][/ROW]
[ROW][C]44[/C][C]32809[/C][C]31774.4922026408[/C][C]1034.50779735923[/C][/ROW]
[ROW][C]45[/C][C]35316[/C][C]36784.2140695081[/C][C]-1468.21406950815[/C][/ROW]
[ROW][C]46[/C][C]33989[/C][C]36500.6946239215[/C][C]-2511.69462392146[/C][/ROW]
[ROW][C]47[/C][C]35799[/C][C]32785.5585842198[/C][C]3013.44141578021[/C][/ROW]
[ROW][C]48[/C][C]34508[/C][C]32278.8546849806[/C][C]2229.14531501938[/C][/ROW]
[ROW][C]49[/C][C]34646[/C][C]31814.7224838702[/C][C]2831.27751612983[/C][/ROW]
[ROW][C]50[/C][C]35203[/C][C]34231.590480771[/C][C]971.409519229048[/C][/ROW]
[ROW][C]51[/C][C]38084[/C][C]38330.9246257791[/C][C]-246.924625779109[/C][/ROW]
[ROW][C]52[/C][C]35005[/C][C]34837.1021558162[/C][C]167.897844183797[/C][/ROW]
[ROW][C]53[/C][C]36734[/C][C]35381.322769188[/C][C]1352.67723081201[/C][/ROW]
[ROW][C]54[/C][C]35716[/C][C]37792.7668383134[/C][C]-2076.7668383134[/C][/ROW]
[ROW][C]55[/C][C]34543[/C][C]36883.409145759[/C][C]-2340.40914575901[/C][/ROW]
[ROW][C]56[/C][C]34340[/C][C]34127.8074779883[/C][C]212.192522011712[/C][/ROW]
[ROW][C]57[/C][C]35094[/C][C]37975.4005958432[/C][C]-2881.4005958432[/C][/ROW]
[ROW][C]58[/C][C]38730[/C][C]36383.8367543287[/C][C]2346.16324567132[/C][/ROW]
[ROW][C]59[/C][C]37805[/C][C]37825.501449129[/C][C]-20.5014491289621[/C][/ROW]
[ROW][C]60[/C][C]33815[/C][C]34877.6409113709[/C][C]-1062.64091137085[/C][/ROW]
[ROW][C]61[/C][C]36486[/C][C]32016.2959312424[/C][C]4469.70406875763[/C][/ROW]
[ROW][C]62[/C][C]34960[/C][C]35273.5278470409[/C][C]-313.52784704091[/C][/ROW]
[ROW][C]63[/C][C]38054[/C][C]38093.5081752899[/C][C]-39.508175289855[/C][/ROW]
[ROW][C]64[/C][C]35283[/C][C]34851.016197812[/C][C]431.983802188042[/C][/ROW]
[ROW][C]65[/C][C]37361[/C][C]35877.3369509074[/C][C]1483.66304909263[/C][/ROW]
[ROW][C]66[/C][C]35536[/C][C]37589.7080012677[/C][C]-2053.70800126772[/C][/ROW]
[ROW][C]67[/C][C]36103[/C][C]36642.0611140511[/C][C]-539.061114051132[/C][/ROW]
[ROW][C]68[/C][C]33886[/C][C]35915.9705319792[/C][C]-2029.97053197925[/C][/ROW]
[ROW][C]69[/C][C]35416[/C][C]37316.2986125355[/C][C]-1900.29861253547[/C][/ROW]
[ROW][C]70[/C][C]38053[/C][C]37721.9039399437[/C][C]331.096060056341[/C][/ROW]
[ROW][C]71[/C][C]37181[/C][C]37034.2877662726[/C][C]146.712233727441[/C][/ROW]
[ROW][C]72[/C][C]34787[/C][C]33942.4376775182[/C][C]844.562322481819[/C][/ROW]
[ROW][C]73[/C][C]36074[/C][C]33860.0960927794[/C][C]2213.90390722058[/C][/ROW]
[ROW][C]74[/C][C]34966[/C][C]34232.1640979534[/C][C]733.835902046609[/C][/ROW]
[ROW][C]75[/C][C]37482[/C][C]37908.4404298095[/C][C]-426.440429809532[/C][/ROW]
[ROW][C]76[/C][C]36109[/C][C]34460.9387424576[/C][C]1648.06125754242[/C][/ROW]
[ROW][C]77[/C][C]35520[/C][C]36676.3087181927[/C][C]-1156.30871819268[/C][/ROW]
[ROW][C]78[/C][C]36123[/C][C]35482.317565457[/C][C]640.682434542985[/C][/ROW]
[ROW][C]79[/C][C]36256[/C][C]36965.1889867053[/C][C]-709.188986705318[/C][/ROW]
[ROW][C]80[/C][C]32456[/C][C]35767.664394228[/C][C]-3311.66439422801[/C][/ROW]
[ROW][C]81[/C][C]37748[/C][C]36193.3313364883[/C][C]1554.66866351171[/C][/ROW]
[ROW][C]82[/C][C]38461[/C][C]39830.8717466596[/C][C]-1369.87174665958[/C][/ROW]
[ROW][C]83[/C][C]36344[/C][C]37818.7730883187[/C][C]-1474.77308831867[/C][/ROW]
[ROW][C]84[/C][C]35865[/C][C]33628.8913324662[/C][C]2236.10866753381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284483&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284483&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
132497528194.8571047009-3219.85710470087
142464425295.1932051589-651.193205158928
152662626667.7572971601-41.7572971601403
162397723873.1566023787103.843397621302
172389823575.72757685322.272423150043
182558324988.6186864557594.38131354432
192597425856.1927790569117.807220943076
202352923399.3107305705129.689269429466
212749127716.7910405456-225.791040545631
222805327750.8939478339302.106052166073
232791323784.40919221254128.59080778754
242670624479.54442096862226.45557903143
252678824016.1039445172771.89605548304
262760026554.58478444651045.41521555349
273277029661.53055373333108.4694462667
282962329685.4325274384-62.4325274383955
292930029681.0061819135-381.006181913501
303215230970.54160673771181.45839326227
313070032541.6746856743-1841.67468567435
322946328903.8957581757559.104241824261
333270933793.6281841627-1084.62818416272
343282333599.3464194373-776.346419437308
353407329982.82158810044090.17841189961
363355130478.83060255453072.16939744554
373216831088.80981988381079.19018011625
383283332181.6190698745651.380930125495
393734135715.94529713971625.05470286029
403374734067.5369442574-320.536944257445
413448233991.2742145131490.72578548688
423330936537.31387631-3228.31387630997
433305734134.1842697593-1077.18426975933
443280931774.49220264081034.50779735923
453531636784.2140695081-1468.21406950815
463398936500.6946239215-2511.69462392146
473579932785.55858421983013.44141578021
483450832278.85468498062229.14531501938
493464631814.72248387022831.27751612983
503520334231.590480771971.409519229048
513808438330.9246257791-246.924625779109
523500534837.1021558162167.897844183797
533673435381.3227691881352.67723081201
543571637792.7668383134-2076.7668383134
553454336883.409145759-2340.40914575901
563434034127.8074779883212.192522011712
573509437975.4005958432-2881.4005958432
583873036383.83675432872346.16324567132
593780537825.501449129-20.5014491289621
603381534877.6409113709-1062.64091137085
613648632016.29593124244469.70406875763
623496035273.5278470409-313.52784704091
633805438093.5081752899-39.508175289855
643528334851.016197812431.983802188042
653736135877.33695090741483.66304909263
663553637589.7080012677-2053.70800126772
673610336642.0611140511-539.061114051132
683388635915.9705319792-2029.97053197925
693541637316.2986125355-1900.29861253547
703805337721.9039399437331.096060056341
713718137034.2877662726146.712233727441
723478733942.4376775182844.562322481819
733607433860.09609277942213.90390722058
743496634232.1640979534733.835902046609
753748237908.4404298095-426.440429809532
763610934460.93874245761648.06125754242
773552036676.3087181927-1156.30871819268
783612335482.317565457640.682434542985
793625636965.1889867053-709.188986705318
803245635767.664394228-3311.66439422801
813774836193.33133648831554.66866351171
823846139830.8717466596-1369.87174665958
833634437818.7730883187-1474.77308831867
843586533628.89133246622236.10866753381







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8534947.663537719131460.836670158538434.4904052798
8633236.284042723328790.742356605637681.8257288409
8736018.213919435730739.345473180341297.0823656911
8833334.270561645727294.019449114539374.5216741769
8933538.640277825526783.403531403640293.8770242473
9033589.16184231826150.878411666841027.4452729692
9134186.480180738926088.024617212142284.9357442658
9232860.748990450124118.905467035241602.5925138651
9336987.002609076927614.252972840646359.7522453132
9438732.927414087228738.596845709348727.2579824651
9537764.101755071427155.129617502248373.0738926405
9635630.725525138624412.204544671146849.2465056061

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 34947.6635377191 & 31460.8366701585 & 38434.4904052798 \tabularnewline
86 & 33236.2840427233 & 28790.7423566056 & 37681.8257288409 \tabularnewline
87 & 36018.2139194357 & 30739.3454731803 & 41297.0823656911 \tabularnewline
88 & 33334.2705616457 & 27294.0194491145 & 39374.5216741769 \tabularnewline
89 & 33538.6402778255 & 26783.4035314036 & 40293.8770242473 \tabularnewline
90 & 33589.161842318 & 26150.8784116668 & 41027.4452729692 \tabularnewline
91 & 34186.4801807389 & 26088.0246172121 & 42284.9357442658 \tabularnewline
92 & 32860.7489904501 & 24118.9054670352 & 41602.5925138651 \tabularnewline
93 & 36987.0026090769 & 27614.2529728406 & 46359.7522453132 \tabularnewline
94 & 38732.9274140872 & 28738.5968457093 & 48727.2579824651 \tabularnewline
95 & 37764.1017550714 & 27155.1296175022 & 48373.0738926405 \tabularnewline
96 & 35630.7255251386 & 24412.2045446711 & 46849.2465056061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284483&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]85[/C][C]34947.6635377191[/C][C]31460.8366701585[/C][C]38434.4904052798[/C][/ROW]
[ROW][C]86[/C][C]33236.2840427233[/C][C]28790.7423566056[/C][C]37681.8257288409[/C][/ROW]
[ROW][C]87[/C][C]36018.2139194357[/C][C]30739.3454731803[/C][C]41297.0823656911[/C][/ROW]
[ROW][C]88[/C][C]33334.2705616457[/C][C]27294.0194491145[/C][C]39374.5216741769[/C][/ROW]
[ROW][C]89[/C][C]33538.6402778255[/C][C]26783.4035314036[/C][C]40293.8770242473[/C][/ROW]
[ROW][C]90[/C][C]33589.161842318[/C][C]26150.8784116668[/C][C]41027.4452729692[/C][/ROW]
[ROW][C]91[/C][C]34186.4801807389[/C][C]26088.0246172121[/C][C]42284.9357442658[/C][/ROW]
[ROW][C]92[/C][C]32860.7489904501[/C][C]24118.9054670352[/C][C]41602.5925138651[/C][/ROW]
[ROW][C]93[/C][C]36987.0026090769[/C][C]27614.2529728406[/C][C]46359.7522453132[/C][/ROW]
[ROW][C]94[/C][C]38732.9274140872[/C][C]28738.5968457093[/C][C]48727.2579824651[/C][/ROW]
[ROW][C]95[/C][C]37764.1017550714[/C][C]27155.1296175022[/C][C]48373.0738926405[/C][/ROW]
[ROW][C]96[/C][C]35630.7255251386[/C][C]24412.2045446711[/C][C]46849.2465056061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284483&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284483&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
8534947.663537719131460.836670158538434.4904052798
8633236.284042723328790.742356605637681.8257288409
8736018.213919435730739.345473180341297.0823656911
8833334.270561645727294.019449114539374.5216741769
8933538.640277825526783.403531403640293.8770242473
9033589.16184231826150.878411666841027.4452729692
9134186.480180738926088.024617212142284.9357442658
9232860.748990450124118.905467035241602.5925138651
9336987.002609076927614.252972840646359.7522453132
9438732.927414087228738.596845709348727.2579824651
9537764.101755071427155.129617502248373.0738926405
9635630.725525138624412.204544671146849.2465056061



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')