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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, 26 May 2013 19:58:20 -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/t13696127771oj2kve7tbye7ee.htm/, Retrieved Mon, 29 Apr 2024 09:52:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210693, Retrieved Mon, 29 Apr 2024 09:52:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Inschrijvingen ni...] [2013-05-06 21:00:33] [a12eb5ef392ea8ae41cc1fa625e5276e]
- RMPD  [Exponential Smoothing] [Interesse in de l...] [2013-05-26 18:16:00] [a12eb5ef392ea8ae41cc1fa625e5276e]
- R P       [Exponential Smoothing] [Interesse in de l...] [2013-05-26 23:58:20] [c6583091fa4b3042e72e3a6292788221] [Current]
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Dataseries X:
38
35
33
35
33
32
33
38
45
42
40
44
50
37
37
35
33
40
38
39
52
48
49
50
48
45
42
39
38
44
47
45
51
51
47
49
44
40
40
38
36
45
39
43
50
49
47
49
58
43
39
44
45
57
54
52
61
59
60
58
52
49
60
51
52
56
56
57
58
100
70
70




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210693&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210693&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.576574193139615
beta0.0775949269235273
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.576574193139615 \tabularnewline
beta & 0.0775949269235273 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210693&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]0.576574193139615[/C][/ROW]
[ROW][C]beta[/C][C]0.0775949269235273[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210693&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
alpha0.576574193139615
beta0.0775949269235273
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
333321
43529.62131342552235.37868657447773
53330.00790283830442.99209716169564
63229.15231051628472.84768948371533
73328.34085989541594.65914010458409
83828.78229130652929.21770869347083
94532.264468934924312.7355310650757
104238.3447100426733.65528995732705
114039.35305332703510.646946672964873
124438.65580740707025.34419259292984
135040.90596733770019.09403266229987
143745.7250483213039-8.72504832130386
153739.8797550999001-2.87975509990006
163537.275869068672-2.27586906867203
173334.9183475035118-1.91834750351177
184032.68113825156357.31886174843652
193836.09730572745891.90269427254107
203936.47577589224332.52422410775669
215237.325535969222214.6744640307778
224845.83733508263362.16266491736636
234947.23190968580881.76809031419118
245048.4780857589651.52191424103498
254849.650412336267-1.65041233626705
264548.9198190958463-3.91981909584634
274246.7053747866886-4.70537478668856
283943.827484482888-4.82748448288802
293840.6632109294231-2.66321092942314
304438.62765164112525.37234835887482
314741.46554320757155.53445679242854
324544.64450966184340.355490338156649
335144.85332207629496.14667792370513
345148.67618145221422.32381854778582
354750.3988446260011-3.39884462600112
364948.66990619819680.330093801803152
374449.1057455789781-5.10574557897807
384046.1789931168042-6.17899311680419
394042.3569904125256-2.35699041252556
403840.6332058918541-2.63320589185414
413638.6323550437491-2.63235504374911
424536.51422522868788.48577477131223
433941.1861691904076-2.18616919040757
444339.60713814173013.39286185826987
455041.39662645356418.60337354643585
464946.57526966621582.42473033378417
474748.2999472277038-1.29994722770376
484947.81891318836611.18108681163388
495848.82122026574139.17877973425871
504354.8454422464775-11.8454422464775
513948.2176844089421-9.21768440894208
524442.69263180154821.30736819845176
534543.29454355865471.70545644134526
545744.202283535253812.7977164647462
555452.07809439582371.92190560417629
565253.7691779661642-1.76917796616425
576153.25292634097037.7470736590297
585958.5700979470030.429902052996979
596059.68761072607410.312389273925866
605860.7513447256887-2.75134472568875
615259.9255157154338-7.92551571543377
624955.7618117522549-6.76181175225493
636051.96655119538748.03344880461264
645157.0612663892899-6.06126638928986
655253.7581561372117-1.75815613721171
665652.85744965072863.1425503492714
675654.92295934285381.07704065714616
685755.84573542306551.15426457693446
695856.86467773365881.13532226634119
7010057.923491843508642.0765081564914
717084.4704078504149-14.4704078504149
727077.7664364466141-7.76643644661405

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 33 & 32 & 1 \tabularnewline
4 & 35 & 29.6213134255223 & 5.37868657447773 \tabularnewline
5 & 33 & 30.0079028383044 & 2.99209716169564 \tabularnewline
6 & 32 & 29.1523105162847 & 2.84768948371533 \tabularnewline
7 & 33 & 28.3408598954159 & 4.65914010458409 \tabularnewline
8 & 38 & 28.7822913065292 & 9.21770869347083 \tabularnewline
9 & 45 & 32.2644689349243 & 12.7355310650757 \tabularnewline
10 & 42 & 38.344710042673 & 3.65528995732705 \tabularnewline
11 & 40 & 39.3530533270351 & 0.646946672964873 \tabularnewline
12 & 44 & 38.6558074070702 & 5.34419259292984 \tabularnewline
13 & 50 & 40.9059673377001 & 9.09403266229987 \tabularnewline
14 & 37 & 45.7250483213039 & -8.72504832130386 \tabularnewline
15 & 37 & 39.8797550999001 & -2.87975509990006 \tabularnewline
16 & 35 & 37.275869068672 & -2.27586906867203 \tabularnewline
17 & 33 & 34.9183475035118 & -1.91834750351177 \tabularnewline
18 & 40 & 32.6811382515635 & 7.31886174843652 \tabularnewline
19 & 38 & 36.0973057274589 & 1.90269427254107 \tabularnewline
20 & 39 & 36.4757758922433 & 2.52422410775669 \tabularnewline
21 & 52 & 37.3255359692222 & 14.6744640307778 \tabularnewline
22 & 48 & 45.8373350826336 & 2.16266491736636 \tabularnewline
23 & 49 & 47.2319096858088 & 1.76809031419118 \tabularnewline
24 & 50 & 48.478085758965 & 1.52191424103498 \tabularnewline
25 & 48 & 49.650412336267 & -1.65041233626705 \tabularnewline
26 & 45 & 48.9198190958463 & -3.91981909584634 \tabularnewline
27 & 42 & 46.7053747866886 & -4.70537478668856 \tabularnewline
28 & 39 & 43.827484482888 & -4.82748448288802 \tabularnewline
29 & 38 & 40.6632109294231 & -2.66321092942314 \tabularnewline
30 & 44 & 38.6276516411252 & 5.37234835887482 \tabularnewline
31 & 47 & 41.4655432075715 & 5.53445679242854 \tabularnewline
32 & 45 & 44.6445096618434 & 0.355490338156649 \tabularnewline
33 & 51 & 44.8533220762949 & 6.14667792370513 \tabularnewline
34 & 51 & 48.6761814522142 & 2.32381854778582 \tabularnewline
35 & 47 & 50.3988446260011 & -3.39884462600112 \tabularnewline
36 & 49 & 48.6699061981968 & 0.330093801803152 \tabularnewline
37 & 44 & 49.1057455789781 & -5.10574557897807 \tabularnewline
38 & 40 & 46.1789931168042 & -6.17899311680419 \tabularnewline
39 & 40 & 42.3569904125256 & -2.35699041252556 \tabularnewline
40 & 38 & 40.6332058918541 & -2.63320589185414 \tabularnewline
41 & 36 & 38.6323550437491 & -2.63235504374911 \tabularnewline
42 & 45 & 36.5142252286878 & 8.48577477131223 \tabularnewline
43 & 39 & 41.1861691904076 & -2.18616919040757 \tabularnewline
44 & 43 & 39.6071381417301 & 3.39286185826987 \tabularnewline
45 & 50 & 41.3966264535641 & 8.60337354643585 \tabularnewline
46 & 49 & 46.5752696662158 & 2.42473033378417 \tabularnewline
47 & 47 & 48.2999472277038 & -1.29994722770376 \tabularnewline
48 & 49 & 47.8189131883661 & 1.18108681163388 \tabularnewline
49 & 58 & 48.8212202657413 & 9.17877973425871 \tabularnewline
50 & 43 & 54.8454422464775 & -11.8454422464775 \tabularnewline
51 & 39 & 48.2176844089421 & -9.21768440894208 \tabularnewline
52 & 44 & 42.6926318015482 & 1.30736819845176 \tabularnewline
53 & 45 & 43.2945435586547 & 1.70545644134526 \tabularnewline
54 & 57 & 44.2022835352538 & 12.7977164647462 \tabularnewline
55 & 54 & 52.0780943958237 & 1.92190560417629 \tabularnewline
56 & 52 & 53.7691779661642 & -1.76917796616425 \tabularnewline
57 & 61 & 53.2529263409703 & 7.7470736590297 \tabularnewline
58 & 59 & 58.570097947003 & 0.429902052996979 \tabularnewline
59 & 60 & 59.6876107260741 & 0.312389273925866 \tabularnewline
60 & 58 & 60.7513447256887 & -2.75134472568875 \tabularnewline
61 & 52 & 59.9255157154338 & -7.92551571543377 \tabularnewline
62 & 49 & 55.7618117522549 & -6.76181175225493 \tabularnewline
63 & 60 & 51.9665511953874 & 8.03344880461264 \tabularnewline
64 & 51 & 57.0612663892899 & -6.06126638928986 \tabularnewline
65 & 52 & 53.7581561372117 & -1.75815613721171 \tabularnewline
66 & 56 & 52.8574496507286 & 3.1425503492714 \tabularnewline
67 & 56 & 54.9229593428538 & 1.07704065714616 \tabularnewline
68 & 57 & 55.8457354230655 & 1.15426457693446 \tabularnewline
69 & 58 & 56.8646777336588 & 1.13532226634119 \tabularnewline
70 & 100 & 57.9234918435086 & 42.0765081564914 \tabularnewline
71 & 70 & 84.4704078504149 & -14.4704078504149 \tabularnewline
72 & 70 & 77.7664364466141 & -7.76643644661405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210693&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]3[/C][C]33[/C][C]32[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]35[/C][C]29.6213134255223[/C][C]5.37868657447773[/C][/ROW]
[ROW][C]5[/C][C]33[/C][C]30.0079028383044[/C][C]2.99209716169564[/C][/ROW]
[ROW][C]6[/C][C]32[/C][C]29.1523105162847[/C][C]2.84768948371533[/C][/ROW]
[ROW][C]7[/C][C]33[/C][C]28.3408598954159[/C][C]4.65914010458409[/C][/ROW]
[ROW][C]8[/C][C]38[/C][C]28.7822913065292[/C][C]9.21770869347083[/C][/ROW]
[ROW][C]9[/C][C]45[/C][C]32.2644689349243[/C][C]12.7355310650757[/C][/ROW]
[ROW][C]10[/C][C]42[/C][C]38.344710042673[/C][C]3.65528995732705[/C][/ROW]
[ROW][C]11[/C][C]40[/C][C]39.3530533270351[/C][C]0.646946672964873[/C][/ROW]
[ROW][C]12[/C][C]44[/C][C]38.6558074070702[/C][C]5.34419259292984[/C][/ROW]
[ROW][C]13[/C][C]50[/C][C]40.9059673377001[/C][C]9.09403266229987[/C][/ROW]
[ROW][C]14[/C][C]37[/C][C]45.7250483213039[/C][C]-8.72504832130386[/C][/ROW]
[ROW][C]15[/C][C]37[/C][C]39.8797550999001[/C][C]-2.87975509990006[/C][/ROW]
[ROW][C]16[/C][C]35[/C][C]37.275869068672[/C][C]-2.27586906867203[/C][/ROW]
[ROW][C]17[/C][C]33[/C][C]34.9183475035118[/C][C]-1.91834750351177[/C][/ROW]
[ROW][C]18[/C][C]40[/C][C]32.6811382515635[/C][C]7.31886174843652[/C][/ROW]
[ROW][C]19[/C][C]38[/C][C]36.0973057274589[/C][C]1.90269427254107[/C][/ROW]
[ROW][C]20[/C][C]39[/C][C]36.4757758922433[/C][C]2.52422410775669[/C][/ROW]
[ROW][C]21[/C][C]52[/C][C]37.3255359692222[/C][C]14.6744640307778[/C][/ROW]
[ROW][C]22[/C][C]48[/C][C]45.8373350826336[/C][C]2.16266491736636[/C][/ROW]
[ROW][C]23[/C][C]49[/C][C]47.2319096858088[/C][C]1.76809031419118[/C][/ROW]
[ROW][C]24[/C][C]50[/C][C]48.478085758965[/C][C]1.52191424103498[/C][/ROW]
[ROW][C]25[/C][C]48[/C][C]49.650412336267[/C][C]-1.65041233626705[/C][/ROW]
[ROW][C]26[/C][C]45[/C][C]48.9198190958463[/C][C]-3.91981909584634[/C][/ROW]
[ROW][C]27[/C][C]42[/C][C]46.7053747866886[/C][C]-4.70537478668856[/C][/ROW]
[ROW][C]28[/C][C]39[/C][C]43.827484482888[/C][C]-4.82748448288802[/C][/ROW]
[ROW][C]29[/C][C]38[/C][C]40.6632109294231[/C][C]-2.66321092942314[/C][/ROW]
[ROW][C]30[/C][C]44[/C][C]38.6276516411252[/C][C]5.37234835887482[/C][/ROW]
[ROW][C]31[/C][C]47[/C][C]41.4655432075715[/C][C]5.53445679242854[/C][/ROW]
[ROW][C]32[/C][C]45[/C][C]44.6445096618434[/C][C]0.355490338156649[/C][/ROW]
[ROW][C]33[/C][C]51[/C][C]44.8533220762949[/C][C]6.14667792370513[/C][/ROW]
[ROW][C]34[/C][C]51[/C][C]48.6761814522142[/C][C]2.32381854778582[/C][/ROW]
[ROW][C]35[/C][C]47[/C][C]50.3988446260011[/C][C]-3.39884462600112[/C][/ROW]
[ROW][C]36[/C][C]49[/C][C]48.6699061981968[/C][C]0.330093801803152[/C][/ROW]
[ROW][C]37[/C][C]44[/C][C]49.1057455789781[/C][C]-5.10574557897807[/C][/ROW]
[ROW][C]38[/C][C]40[/C][C]46.1789931168042[/C][C]-6.17899311680419[/C][/ROW]
[ROW][C]39[/C][C]40[/C][C]42.3569904125256[/C][C]-2.35699041252556[/C][/ROW]
[ROW][C]40[/C][C]38[/C][C]40.6332058918541[/C][C]-2.63320589185414[/C][/ROW]
[ROW][C]41[/C][C]36[/C][C]38.6323550437491[/C][C]-2.63235504374911[/C][/ROW]
[ROW][C]42[/C][C]45[/C][C]36.5142252286878[/C][C]8.48577477131223[/C][/ROW]
[ROW][C]43[/C][C]39[/C][C]41.1861691904076[/C][C]-2.18616919040757[/C][/ROW]
[ROW][C]44[/C][C]43[/C][C]39.6071381417301[/C][C]3.39286185826987[/C][/ROW]
[ROW][C]45[/C][C]50[/C][C]41.3966264535641[/C][C]8.60337354643585[/C][/ROW]
[ROW][C]46[/C][C]49[/C][C]46.5752696662158[/C][C]2.42473033378417[/C][/ROW]
[ROW][C]47[/C][C]47[/C][C]48.2999472277038[/C][C]-1.29994722770376[/C][/ROW]
[ROW][C]48[/C][C]49[/C][C]47.8189131883661[/C][C]1.18108681163388[/C][/ROW]
[ROW][C]49[/C][C]58[/C][C]48.8212202657413[/C][C]9.17877973425871[/C][/ROW]
[ROW][C]50[/C][C]43[/C][C]54.8454422464775[/C][C]-11.8454422464775[/C][/ROW]
[ROW][C]51[/C][C]39[/C][C]48.2176844089421[/C][C]-9.21768440894208[/C][/ROW]
[ROW][C]52[/C][C]44[/C][C]42.6926318015482[/C][C]1.30736819845176[/C][/ROW]
[ROW][C]53[/C][C]45[/C][C]43.2945435586547[/C][C]1.70545644134526[/C][/ROW]
[ROW][C]54[/C][C]57[/C][C]44.2022835352538[/C][C]12.7977164647462[/C][/ROW]
[ROW][C]55[/C][C]54[/C][C]52.0780943958237[/C][C]1.92190560417629[/C][/ROW]
[ROW][C]56[/C][C]52[/C][C]53.7691779661642[/C][C]-1.76917796616425[/C][/ROW]
[ROW][C]57[/C][C]61[/C][C]53.2529263409703[/C][C]7.7470736590297[/C][/ROW]
[ROW][C]58[/C][C]59[/C][C]58.570097947003[/C][C]0.429902052996979[/C][/ROW]
[ROW][C]59[/C][C]60[/C][C]59.6876107260741[/C][C]0.312389273925866[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]60.7513447256887[/C][C]-2.75134472568875[/C][/ROW]
[ROW][C]61[/C][C]52[/C][C]59.9255157154338[/C][C]-7.92551571543377[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]55.7618117522549[/C][C]-6.76181175225493[/C][/ROW]
[ROW][C]63[/C][C]60[/C][C]51.9665511953874[/C][C]8.03344880461264[/C][/ROW]
[ROW][C]64[/C][C]51[/C][C]57.0612663892899[/C][C]-6.06126638928986[/C][/ROW]
[ROW][C]65[/C][C]52[/C][C]53.7581561372117[/C][C]-1.75815613721171[/C][/ROW]
[ROW][C]66[/C][C]56[/C][C]52.8574496507286[/C][C]3.1425503492714[/C][/ROW]
[ROW][C]67[/C][C]56[/C][C]54.9229593428538[/C][C]1.07704065714616[/C][/ROW]
[ROW][C]68[/C][C]57[/C][C]55.8457354230655[/C][C]1.15426457693446[/C][/ROW]
[ROW][C]69[/C][C]58[/C][C]56.8646777336588[/C][C]1.13532226634119[/C][/ROW]
[ROW][C]70[/C][C]100[/C][C]57.9234918435086[/C][C]42.0765081564914[/C][/ROW]
[ROW][C]71[/C][C]70[/C][C]84.4704078504149[/C][C]-14.4704078504149[/C][/ROW]
[ROW][C]72[/C][C]70[/C][C]77.7664364466141[/C][C]-7.76643644661405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210693&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
333321
43529.62131342552235.37868657447773
53330.00790283830442.99209716169564
63229.15231051628472.84768948371533
73328.34085989541594.65914010458409
83828.78229130652929.21770869347083
94532.264468934924312.7355310650757
104238.3447100426733.65528995732705
114039.35305332703510.646946672964873
124438.65580740707025.34419259292984
135040.90596733770019.09403266229987
143745.7250483213039-8.72504832130386
153739.8797550999001-2.87975509990006
163537.275869068672-2.27586906867203
173334.9183475035118-1.91834750351177
184032.68113825156357.31886174843652
193836.09730572745891.90269427254107
203936.47577589224332.52422410775669
215237.325535969222214.6744640307778
224845.83733508263362.16266491736636
234947.23190968580881.76809031419118
245048.4780857589651.52191424103498
254849.650412336267-1.65041233626705
264548.9198190958463-3.91981909584634
274246.7053747866886-4.70537478668856
283943.827484482888-4.82748448288802
293840.6632109294231-2.66321092942314
304438.62765164112525.37234835887482
314741.46554320757155.53445679242854
324544.64450966184340.355490338156649
335144.85332207629496.14667792370513
345148.67618145221422.32381854778582
354750.3988446260011-3.39884462600112
364948.66990619819680.330093801803152
374449.1057455789781-5.10574557897807
384046.1789931168042-6.17899311680419
394042.3569904125256-2.35699041252556
403840.6332058918541-2.63320589185414
413638.6323550437491-2.63235504374911
424536.51422522868788.48577477131223
433941.1861691904076-2.18616919040757
444339.60713814173013.39286185826987
455041.39662645356418.60337354643585
464946.57526966621582.42473033378417
474748.2999472277038-1.29994722770376
484947.81891318836611.18108681163388
495848.82122026574139.17877973425871
504354.8454422464775-11.8454422464775
513948.2176844089421-9.21768440894208
524442.69263180154821.30736819845176
534543.29454355865471.70545644134526
545744.202283535253812.7977164647462
555452.07809439582371.92190560417629
565253.7691779661642-1.76917796616425
576153.25292634097037.7470736590297
585958.5700979470030.429902052996979
596059.68761072607410.312389273925866
605860.7513447256887-2.75134472568875
615259.9255157154338-7.92551571543377
624955.7618117522549-6.76181175225493
636051.96655119538748.03344880461264
645157.0612663892899-6.06126638928986
655253.7581561372117-1.75815613721171
665652.85744965072863.1425503492714
675654.92295934285381.07704065714616
685755.84573542306551.15426457693446
695856.86467773365881.13532226634119
7010057.923491843508642.0765081564914
717084.4704078504149-14.4704078504149
727077.7664364466141-7.76643644661405







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7374.580337540820559.748934775116689.4117403065244
7475.872165462803558.4111859601693.3331449654471
7577.163993384786657.102326623239497.2256601463337
7678.455821306769655.7929640809621101.118678532577
7779.747649228752654.4658323674277105.029466090078
7881.039477150735753.1101635675483108.968790733923
7982.331305072718751.7189780890904112.943632056347
8083.623132994701850.2876433831302116.958622606273
8184.914960916684848.8130488404555121.016872992914
8286.206788838667847.2931059936543125.120471683681
8387.498616760650945.7264319469421129.27080157436
8488.790444682633944.1121414956871133.468747869581

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 74.5803375408205 & 59.7489347751166 & 89.4117403065244 \tabularnewline
74 & 75.8721654628035 & 58.41118596016 & 93.3331449654471 \tabularnewline
75 & 77.1639933847866 & 57.1023266232394 & 97.2256601463337 \tabularnewline
76 & 78.4558213067696 & 55.7929640809621 & 101.118678532577 \tabularnewline
77 & 79.7476492287526 & 54.4658323674277 & 105.029466090078 \tabularnewline
78 & 81.0394771507357 & 53.1101635675483 & 108.968790733923 \tabularnewline
79 & 82.3313050727187 & 51.7189780890904 & 112.943632056347 \tabularnewline
80 & 83.6231329947018 & 50.2876433831302 & 116.958622606273 \tabularnewline
81 & 84.9149609166848 & 48.8130488404555 & 121.016872992914 \tabularnewline
82 & 86.2067888386678 & 47.2931059936543 & 125.120471683681 \tabularnewline
83 & 87.4986167606509 & 45.7264319469421 & 129.27080157436 \tabularnewline
84 & 88.7904446826339 & 44.1121414956871 & 133.468747869581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210693&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]74.5803375408205[/C][C]59.7489347751166[/C][C]89.4117403065244[/C][/ROW]
[ROW][C]74[/C][C]75.8721654628035[/C][C]58.41118596016[/C][C]93.3331449654471[/C][/ROW]
[ROW][C]75[/C][C]77.1639933847866[/C][C]57.1023266232394[/C][C]97.2256601463337[/C][/ROW]
[ROW][C]76[/C][C]78.4558213067696[/C][C]55.7929640809621[/C][C]101.118678532577[/C][/ROW]
[ROW][C]77[/C][C]79.7476492287526[/C][C]54.4658323674277[/C][C]105.029466090078[/C][/ROW]
[ROW][C]78[/C][C]81.0394771507357[/C][C]53.1101635675483[/C][C]108.968790733923[/C][/ROW]
[ROW][C]79[/C][C]82.3313050727187[/C][C]51.7189780890904[/C][C]112.943632056347[/C][/ROW]
[ROW][C]80[/C][C]83.6231329947018[/C][C]50.2876433831302[/C][C]116.958622606273[/C][/ROW]
[ROW][C]81[/C][C]84.9149609166848[/C][C]48.8130488404555[/C][C]121.016872992914[/C][/ROW]
[ROW][C]82[/C][C]86.2067888386678[/C][C]47.2931059936543[/C][C]125.120471683681[/C][/ROW]
[ROW][C]83[/C][C]87.4986167606509[/C][C]45.7264319469421[/C][C]129.27080157436[/C][/ROW]
[ROW][C]84[/C][C]88.7904446826339[/C][C]44.1121414956871[/C][C]133.468747869581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210693&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
7374.580337540820559.748934775116689.4117403065244
7475.872165462803558.4111859601693.3331449654471
7577.163993384786657.102326623239497.2256601463337
7678.455821306769655.7929640809621101.118678532577
7779.747649228752654.4658323674277105.029466090078
7881.039477150735753.1101635675483108.968790733923
7982.331305072718751.7189780890904112.943632056347
8083.623132994701850.2876433831302116.958622606273
8184.914960916684848.8130488404555121.016872992914
8286.206788838667847.2931059936543125.120471683681
8387.498616760650945.7264319469421129.27080157436
8488.790444682633944.1121414956871133.468747869581



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