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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 08:40:07 -0500
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/Jan/15/t1358257241w64srjh9f6css55.htm/, Retrieved Sat, 27 Apr 2024 18:55:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205455, Retrieved Sat, 27 Apr 2024 18:55:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-01-15 13:40:07] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
369,82
373,1
374,55
375,01
374,81
375,31
375,31
375,39
375,59
376,26
377,18
377,26
377,26
381,87
387,09
387,14
388,78
389,16
389,16
389,42
389,49
388,97
388,97
389,09
389,09
391,76
390,96
391,76
392,8
393,06
393,06
393,26
393,87
394,47
394,57
394,57
394,57
399,57
406,13
407,03
409,46
409,9
409,9
410,14
410,54
410,69
410,79
410,97
410,97
413,8
423,31
423,85
426,6
426,26
426,26
426,32
427,14
427,55
428,29
428,8
428,8
434,87
435,66
440,75
440,99
441,04
441,04
441,88
441,92
442,48
442,81
442,81




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205455&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205455&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.819981198634985
beta0
gamma0.36170856285575

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.819981198634985 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.36170856285575 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205455&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]0.819981198634985[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.36170856285575[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205455&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
alpha0.819981198634985
beta0
gamma0.36170856285575







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13377.26371.0094009861736.25059901382747
14381.87380.6534523257781.21654767422211
15387.09386.7846854035840.305314596415542
16387.14387.0567757848510.0832242151486184
17388.78388.825149863074-0.0451498630741298
18389.16389.265075296243-0.105075296243399
19389.16387.8417028858531.31829711414656
20389.42389.3856165633720.0343834366279339
21389.49389.780181762214-0.290181762214388
22388.97390.251480232465-1.28148023246501
23388.97390.108153321152-1.13815332115161
24389.09389.142786199201-0.0527861992012504
25389.09389.411700235456-0.321700235455864
26391.76393.442763553845-1.68276355384546
27390.96397.245105879771-6.28510587977144
28391.76392.08465841396-0.324658413959867
29392.8393.517515622571-0.717515622571284
30393.06393.39566249269-0.335662492690005
31393.06391.8520616521621.20793834783842
32393.26393.2149869192020.0450130807977871
33393.87393.5899158395960.280084160403646
34394.47394.4592924780460.0107075219539183
35394.57395.382508750227-0.812508750226812
36394.57394.739916522341-0.169916522341055
37394.57394.884289398671-0.314289398670951
38399.57398.8766134144120.693386585587859
39406.13404.394697407011.73530259299025
40407.03406.173451415860.856548584140455
41409.46408.5717194908410.888280509158676
42409.9409.7665346507380.133465349261485
43409.9408.611929830671.2880701693299
44410.14409.9314996244890.208500375511392
45410.54410.4247800686920.11521993130782
46410.69411.12222154037-0.432221540369824
47410.79411.61969456224-0.829694562240149
48410.97410.9633245625070.00667543749352717
49410.97411.210047304557-0.240047304556867
50413.8415.463371320798-1.66337132079764
51423.31419.2600274987574.04997250124268
52423.85422.8470908299691.0029091700307
53426.6425.3923754819291.20762451807127
54426.26426.772029721534-0.512029721534475
55426.26425.0718819114551.18811808854525
56426.32426.2039641104760.116035889523857
57427.14426.5853322672710.554667732729229
58427.55427.586994785885-0.036994785884815
59428.29428.372378789186-0.0823787891861798
60428.8428.3411151691620.45888483083786
61428.8428.906076870355-0.106076870355423
62434.87433.3183763748031.55162362519712
63435.66440.342157117929-4.68215711792919
64440.75436.537556922114.21244307789021
65440.99441.752560118548-0.762560118547981
66441.04441.37684357471-0.336843574709519
67441.04439.8528142589921.18718574100774
68441.88440.8801315348570.999868465142526
69441.92441.987223002533-0.0672230025326712
70442.48442.4206876811270.0593123188732534
71442.81443.272939334154-0.462939334153987
72442.81442.930735112249-0.120735112248781

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 377.26 & 371.009400986173 & 6.25059901382747 \tabularnewline
14 & 381.87 & 380.653452325778 & 1.21654767422211 \tabularnewline
15 & 387.09 & 386.784685403584 & 0.305314596415542 \tabularnewline
16 & 387.14 & 387.056775784851 & 0.0832242151486184 \tabularnewline
17 & 388.78 & 388.825149863074 & -0.0451498630741298 \tabularnewline
18 & 389.16 & 389.265075296243 & -0.105075296243399 \tabularnewline
19 & 389.16 & 387.841702885853 & 1.31829711414656 \tabularnewline
20 & 389.42 & 389.385616563372 & 0.0343834366279339 \tabularnewline
21 & 389.49 & 389.780181762214 & -0.290181762214388 \tabularnewline
22 & 388.97 & 390.251480232465 & -1.28148023246501 \tabularnewline
23 & 388.97 & 390.108153321152 & -1.13815332115161 \tabularnewline
24 & 389.09 & 389.142786199201 & -0.0527861992012504 \tabularnewline
25 & 389.09 & 389.411700235456 & -0.321700235455864 \tabularnewline
26 & 391.76 & 393.442763553845 & -1.68276355384546 \tabularnewline
27 & 390.96 & 397.245105879771 & -6.28510587977144 \tabularnewline
28 & 391.76 & 392.08465841396 & -0.324658413959867 \tabularnewline
29 & 392.8 & 393.517515622571 & -0.717515622571284 \tabularnewline
30 & 393.06 & 393.39566249269 & -0.335662492690005 \tabularnewline
31 & 393.06 & 391.852061652162 & 1.20793834783842 \tabularnewline
32 & 393.26 & 393.214986919202 & 0.0450130807977871 \tabularnewline
33 & 393.87 & 393.589915839596 & 0.280084160403646 \tabularnewline
34 & 394.47 & 394.459292478046 & 0.0107075219539183 \tabularnewline
35 & 394.57 & 395.382508750227 & -0.812508750226812 \tabularnewline
36 & 394.57 & 394.739916522341 & -0.169916522341055 \tabularnewline
37 & 394.57 & 394.884289398671 & -0.314289398670951 \tabularnewline
38 & 399.57 & 398.876613414412 & 0.693386585587859 \tabularnewline
39 & 406.13 & 404.39469740701 & 1.73530259299025 \tabularnewline
40 & 407.03 & 406.17345141586 & 0.856548584140455 \tabularnewline
41 & 409.46 & 408.571719490841 & 0.888280509158676 \tabularnewline
42 & 409.9 & 409.766534650738 & 0.133465349261485 \tabularnewline
43 & 409.9 & 408.61192983067 & 1.2880701693299 \tabularnewline
44 & 410.14 & 409.931499624489 & 0.208500375511392 \tabularnewline
45 & 410.54 & 410.424780068692 & 0.11521993130782 \tabularnewline
46 & 410.69 & 411.12222154037 & -0.432221540369824 \tabularnewline
47 & 410.79 & 411.61969456224 & -0.829694562240149 \tabularnewline
48 & 410.97 & 410.963324562507 & 0.00667543749352717 \tabularnewline
49 & 410.97 & 411.210047304557 & -0.240047304556867 \tabularnewline
50 & 413.8 & 415.463371320798 & -1.66337132079764 \tabularnewline
51 & 423.31 & 419.260027498757 & 4.04997250124268 \tabularnewline
52 & 423.85 & 422.847090829969 & 1.0029091700307 \tabularnewline
53 & 426.6 & 425.392375481929 & 1.20762451807127 \tabularnewline
54 & 426.26 & 426.772029721534 & -0.512029721534475 \tabularnewline
55 & 426.26 & 425.071881911455 & 1.18811808854525 \tabularnewline
56 & 426.32 & 426.203964110476 & 0.116035889523857 \tabularnewline
57 & 427.14 & 426.585332267271 & 0.554667732729229 \tabularnewline
58 & 427.55 & 427.586994785885 & -0.036994785884815 \tabularnewline
59 & 428.29 & 428.372378789186 & -0.0823787891861798 \tabularnewline
60 & 428.8 & 428.341115169162 & 0.45888483083786 \tabularnewline
61 & 428.8 & 428.906076870355 & -0.106076870355423 \tabularnewline
62 & 434.87 & 433.318376374803 & 1.55162362519712 \tabularnewline
63 & 435.66 & 440.342157117929 & -4.68215711792919 \tabularnewline
64 & 440.75 & 436.53755692211 & 4.21244307789021 \tabularnewline
65 & 440.99 & 441.752560118548 & -0.762560118547981 \tabularnewline
66 & 441.04 & 441.37684357471 & -0.336843574709519 \tabularnewline
67 & 441.04 & 439.852814258992 & 1.18718574100774 \tabularnewline
68 & 441.88 & 440.880131534857 & 0.999868465142526 \tabularnewline
69 & 441.92 & 441.987223002533 & -0.0672230025326712 \tabularnewline
70 & 442.48 & 442.420687681127 & 0.0593123188732534 \tabularnewline
71 & 442.81 & 443.272939334154 & -0.462939334153987 \tabularnewline
72 & 442.81 & 442.930735112249 & -0.120735112248781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205455&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]377.26[/C][C]371.009400986173[/C][C]6.25059901382747[/C][/ROW]
[ROW][C]14[/C][C]381.87[/C][C]380.653452325778[/C][C]1.21654767422211[/C][/ROW]
[ROW][C]15[/C][C]387.09[/C][C]386.784685403584[/C][C]0.305314596415542[/C][/ROW]
[ROW][C]16[/C][C]387.14[/C][C]387.056775784851[/C][C]0.0832242151486184[/C][/ROW]
[ROW][C]17[/C][C]388.78[/C][C]388.825149863074[/C][C]-0.0451498630741298[/C][/ROW]
[ROW][C]18[/C][C]389.16[/C][C]389.265075296243[/C][C]-0.105075296243399[/C][/ROW]
[ROW][C]19[/C][C]389.16[/C][C]387.841702885853[/C][C]1.31829711414656[/C][/ROW]
[ROW][C]20[/C][C]389.42[/C][C]389.385616563372[/C][C]0.0343834366279339[/C][/ROW]
[ROW][C]21[/C][C]389.49[/C][C]389.780181762214[/C][C]-0.290181762214388[/C][/ROW]
[ROW][C]22[/C][C]388.97[/C][C]390.251480232465[/C][C]-1.28148023246501[/C][/ROW]
[ROW][C]23[/C][C]388.97[/C][C]390.108153321152[/C][C]-1.13815332115161[/C][/ROW]
[ROW][C]24[/C][C]389.09[/C][C]389.142786199201[/C][C]-0.0527861992012504[/C][/ROW]
[ROW][C]25[/C][C]389.09[/C][C]389.411700235456[/C][C]-0.321700235455864[/C][/ROW]
[ROW][C]26[/C][C]391.76[/C][C]393.442763553845[/C][C]-1.68276355384546[/C][/ROW]
[ROW][C]27[/C][C]390.96[/C][C]397.245105879771[/C][C]-6.28510587977144[/C][/ROW]
[ROW][C]28[/C][C]391.76[/C][C]392.08465841396[/C][C]-0.324658413959867[/C][/ROW]
[ROW][C]29[/C][C]392.8[/C][C]393.517515622571[/C][C]-0.717515622571284[/C][/ROW]
[ROW][C]30[/C][C]393.06[/C][C]393.39566249269[/C][C]-0.335662492690005[/C][/ROW]
[ROW][C]31[/C][C]393.06[/C][C]391.852061652162[/C][C]1.20793834783842[/C][/ROW]
[ROW][C]32[/C][C]393.26[/C][C]393.214986919202[/C][C]0.0450130807977871[/C][/ROW]
[ROW][C]33[/C][C]393.87[/C][C]393.589915839596[/C][C]0.280084160403646[/C][/ROW]
[ROW][C]34[/C][C]394.47[/C][C]394.459292478046[/C][C]0.0107075219539183[/C][/ROW]
[ROW][C]35[/C][C]394.57[/C][C]395.382508750227[/C][C]-0.812508750226812[/C][/ROW]
[ROW][C]36[/C][C]394.57[/C][C]394.739916522341[/C][C]-0.169916522341055[/C][/ROW]
[ROW][C]37[/C][C]394.57[/C][C]394.884289398671[/C][C]-0.314289398670951[/C][/ROW]
[ROW][C]38[/C][C]399.57[/C][C]398.876613414412[/C][C]0.693386585587859[/C][/ROW]
[ROW][C]39[/C][C]406.13[/C][C]404.39469740701[/C][C]1.73530259299025[/C][/ROW]
[ROW][C]40[/C][C]407.03[/C][C]406.17345141586[/C][C]0.856548584140455[/C][/ROW]
[ROW][C]41[/C][C]409.46[/C][C]408.571719490841[/C][C]0.888280509158676[/C][/ROW]
[ROW][C]42[/C][C]409.9[/C][C]409.766534650738[/C][C]0.133465349261485[/C][/ROW]
[ROW][C]43[/C][C]409.9[/C][C]408.61192983067[/C][C]1.2880701693299[/C][/ROW]
[ROW][C]44[/C][C]410.14[/C][C]409.931499624489[/C][C]0.208500375511392[/C][/ROW]
[ROW][C]45[/C][C]410.54[/C][C]410.424780068692[/C][C]0.11521993130782[/C][/ROW]
[ROW][C]46[/C][C]410.69[/C][C]411.12222154037[/C][C]-0.432221540369824[/C][/ROW]
[ROW][C]47[/C][C]410.79[/C][C]411.61969456224[/C][C]-0.829694562240149[/C][/ROW]
[ROW][C]48[/C][C]410.97[/C][C]410.963324562507[/C][C]0.00667543749352717[/C][/ROW]
[ROW][C]49[/C][C]410.97[/C][C]411.210047304557[/C][C]-0.240047304556867[/C][/ROW]
[ROW][C]50[/C][C]413.8[/C][C]415.463371320798[/C][C]-1.66337132079764[/C][/ROW]
[ROW][C]51[/C][C]423.31[/C][C]419.260027498757[/C][C]4.04997250124268[/C][/ROW]
[ROW][C]52[/C][C]423.85[/C][C]422.847090829969[/C][C]1.0029091700307[/C][/ROW]
[ROW][C]53[/C][C]426.6[/C][C]425.392375481929[/C][C]1.20762451807127[/C][/ROW]
[ROW][C]54[/C][C]426.26[/C][C]426.772029721534[/C][C]-0.512029721534475[/C][/ROW]
[ROW][C]55[/C][C]426.26[/C][C]425.071881911455[/C][C]1.18811808854525[/C][/ROW]
[ROW][C]56[/C][C]426.32[/C][C]426.203964110476[/C][C]0.116035889523857[/C][/ROW]
[ROW][C]57[/C][C]427.14[/C][C]426.585332267271[/C][C]0.554667732729229[/C][/ROW]
[ROW][C]58[/C][C]427.55[/C][C]427.586994785885[/C][C]-0.036994785884815[/C][/ROW]
[ROW][C]59[/C][C]428.29[/C][C]428.372378789186[/C][C]-0.0823787891861798[/C][/ROW]
[ROW][C]60[/C][C]428.8[/C][C]428.341115169162[/C][C]0.45888483083786[/C][/ROW]
[ROW][C]61[/C][C]428.8[/C][C]428.906076870355[/C][C]-0.106076870355423[/C][/ROW]
[ROW][C]62[/C][C]434.87[/C][C]433.318376374803[/C][C]1.55162362519712[/C][/ROW]
[ROW][C]63[/C][C]435.66[/C][C]440.342157117929[/C][C]-4.68215711792919[/C][/ROW]
[ROW][C]64[/C][C]440.75[/C][C]436.53755692211[/C][C]4.21244307789021[/C][/ROW]
[ROW][C]65[/C][C]440.99[/C][C]441.752560118548[/C][C]-0.762560118547981[/C][/ROW]
[ROW][C]66[/C][C]441.04[/C][C]441.37684357471[/C][C]-0.336843574709519[/C][/ROW]
[ROW][C]67[/C][C]441.04[/C][C]439.852814258992[/C][C]1.18718574100774[/C][/ROW]
[ROW][C]68[/C][C]441.88[/C][C]440.880131534857[/C][C]0.999868465142526[/C][/ROW]
[ROW][C]69[/C][C]441.92[/C][C]441.987223002533[/C][C]-0.0672230025326712[/C][/ROW]
[ROW][C]70[/C][C]442.48[/C][C]442.420687681127[/C][C]0.0593123188732534[/C][/ROW]
[ROW][C]71[/C][C]442.81[/C][C]443.272939334154[/C][C]-0.462939334153987[/C][/ROW]
[ROW][C]72[/C][C]442.81[/C][C]442.930735112249[/C][C]-0.120735112248781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205455&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
13377.26371.0094009861736.25059901382747
14381.87380.6534523257781.21654767422211
15387.09386.7846854035840.305314596415542
16387.14387.0567757848510.0832242151486184
17388.78388.825149863074-0.0451498630741298
18389.16389.265075296243-0.105075296243399
19389.16387.8417028858531.31829711414656
20389.42389.3856165633720.0343834366279339
21389.49389.780181762214-0.290181762214388
22388.97390.251480232465-1.28148023246501
23388.97390.108153321152-1.13815332115161
24389.09389.142786199201-0.0527861992012504
25389.09389.411700235456-0.321700235455864
26391.76393.442763553845-1.68276355384546
27390.96397.245105879771-6.28510587977144
28391.76392.08465841396-0.324658413959867
29392.8393.517515622571-0.717515622571284
30393.06393.39566249269-0.335662492690005
31393.06391.8520616521621.20793834783842
32393.26393.2149869192020.0450130807977871
33393.87393.5899158395960.280084160403646
34394.47394.4592924780460.0107075219539183
35394.57395.382508750227-0.812508750226812
36394.57394.739916522341-0.169916522341055
37394.57394.884289398671-0.314289398670951
38399.57398.8766134144120.693386585587859
39406.13404.394697407011.73530259299025
40407.03406.173451415860.856548584140455
41409.46408.5717194908410.888280509158676
42409.9409.7665346507380.133465349261485
43409.9408.611929830671.2880701693299
44410.14409.9314996244890.208500375511392
45410.54410.4247800686920.11521993130782
46410.69411.12222154037-0.432221540369824
47410.79411.61969456224-0.829694562240149
48410.97410.9633245625070.00667543749352717
49410.97411.210047304557-0.240047304556867
50413.8415.463371320798-1.66337132079764
51423.31419.2600274987574.04997250124268
52423.85422.8470908299691.0029091700307
53426.6425.3923754819291.20762451807127
54426.26426.772029721534-0.512029721534475
55426.26425.0718819114551.18811808854525
56426.32426.2039641104760.116035889523857
57427.14426.5853322672710.554667732729229
58427.55427.586994785885-0.036994785884815
59428.29428.372378789186-0.0823787891861798
60428.8428.3411151691620.45888483083786
61428.8428.906076870355-0.106076870355423
62434.87433.3183763748031.55162362519712
63435.66440.342157117929-4.68215711792919
64440.75436.537556922114.21244307789021
65440.99441.752560118548-0.762560118547981
66441.04441.37684357471-0.336843574709519
67441.04439.8528142589921.18718574100774
68441.88440.8801315348570.999868465142526
69441.92441.987223002533-0.0672230025326712
70442.48442.4206876811270.0593123188732534
71442.81443.272939334154-0.462939334153987
72442.81442.930735112249-0.120735112248781







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73442.953466191857440.039142476251445.867789907462
74447.676735916962443.688840086301451.664631747624
75453.146680611524448.300860102057457.992501120991
76453.739854625222448.19702983131459.282679419134
77455.187359970545449.018151040117461.356568900972
78455.438726850363448.714627965866462.162825734861
79454.217353022748447.002152034425461.432554011071
80454.227550443335446.539271387208461.915829499462
81454.421043813924446.286292900401462.555794727447
82454.901506337178446.340333017753463.462679656603
83455.66251589777446.691237722396464.633794073145
84455.692924282653446.414336077752464.971512487554

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 442.953466191857 & 440.039142476251 & 445.867789907462 \tabularnewline
74 & 447.676735916962 & 443.688840086301 & 451.664631747624 \tabularnewline
75 & 453.146680611524 & 448.300860102057 & 457.992501120991 \tabularnewline
76 & 453.739854625222 & 448.19702983131 & 459.282679419134 \tabularnewline
77 & 455.187359970545 & 449.018151040117 & 461.356568900972 \tabularnewline
78 & 455.438726850363 & 448.714627965866 & 462.162825734861 \tabularnewline
79 & 454.217353022748 & 447.002152034425 & 461.432554011071 \tabularnewline
80 & 454.227550443335 & 446.539271387208 & 461.915829499462 \tabularnewline
81 & 454.421043813924 & 446.286292900401 & 462.555794727447 \tabularnewline
82 & 454.901506337178 & 446.340333017753 & 463.462679656603 \tabularnewline
83 & 455.66251589777 & 446.691237722396 & 464.633794073145 \tabularnewline
84 & 455.692924282653 & 446.414336077752 & 464.971512487554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205455&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]442.953466191857[/C][C]440.039142476251[/C][C]445.867789907462[/C][/ROW]
[ROW][C]74[/C][C]447.676735916962[/C][C]443.688840086301[/C][C]451.664631747624[/C][/ROW]
[ROW][C]75[/C][C]453.146680611524[/C][C]448.300860102057[/C][C]457.992501120991[/C][/ROW]
[ROW][C]76[/C][C]453.739854625222[/C][C]448.19702983131[/C][C]459.282679419134[/C][/ROW]
[ROW][C]77[/C][C]455.187359970545[/C][C]449.018151040117[/C][C]461.356568900972[/C][/ROW]
[ROW][C]78[/C][C]455.438726850363[/C][C]448.714627965866[/C][C]462.162825734861[/C][/ROW]
[ROW][C]79[/C][C]454.217353022748[/C][C]447.002152034425[/C][C]461.432554011071[/C][/ROW]
[ROW][C]80[/C][C]454.227550443335[/C][C]446.539271387208[/C][C]461.915829499462[/C][/ROW]
[ROW][C]81[/C][C]454.421043813924[/C][C]446.286292900401[/C][C]462.555794727447[/C][/ROW]
[ROW][C]82[/C][C]454.901506337178[/C][C]446.340333017753[/C][C]463.462679656603[/C][/ROW]
[ROW][C]83[/C][C]455.66251589777[/C][C]446.691237722396[/C][C]464.633794073145[/C][/ROW]
[ROW][C]84[/C][C]455.692924282653[/C][C]446.414336077752[/C][C]464.971512487554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205455&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205455&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
73442.953466191857440.039142476251445.867789907462
74447.676735916962443.688840086301451.664631747624
75453.146680611524448.300860102057457.992501120991
76453.739854625222448.19702983131459.282679419134
77455.187359970545449.018151040117461.356568900972
78455.438726850363448.714627965866462.162825734861
79454.217353022748447.002152034425461.432554011071
80454.227550443335446.539271387208461.915829499462
81454.421043813924446.286292900401462.555794727447
82454.901506337178446.340333017753463.462679656603
83455.66251589777446.691237722396464.633794073145
84455.692924282653446.414336077752464.971512487554



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')