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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Dec 2012 14:25:21 -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/2012/Dec/29/t1356809228fznjwlyxhleio80.htm/, Retrieved Thu, 02 May 2024 04:13:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204904, Retrieved Thu, 02 May 2024 04:13:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-29 19:25:21] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
31,5
31,29
31,3
31,06
31,09
31,11
31,13
31,1
31,03
30,74
30,83
30,82
30,8
30,74
30,71
30,58
30,71
30,7
30,7
30,72
30,68
30,78
30,84
30,8
30,8
30,88
30,87
30,92
30,82
30,75
30,75
30,75
30,63
30,52
30,58
30,6
30,6
30,63
30,56
30,61
30,53
30,6
30,6
30,63
30,66
30,34
30,32
30,3
30,3
30,08
29,96
29,91
29,83
29,89
29,85
30,06
29,83
29,95
30,02
30,03
30,03
29,96
29,85
30,12
29,91
29,9
29,92
29,89
29,96
29,72
29,6
29,54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204904&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204904&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.699900770302555
beta0.342238653113147
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.699900770302555 \tabularnewline
beta & 0.342238653113147 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204904&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]0.699900770302555[/C][/ROW]
[ROW][C]beta[/C][C]0.342238653113147[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204904&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
alpha0.699900770302555
beta0.342238653113147
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
331.331.080.220000000000002
431.0631.0766754507936-0.016675450793624
531.0930.90370724889360.1862927511064
631.1130.91741992746050.192580072539457
731.1330.98166240832620.148337591673844
831.131.05047130548030.0495286945197364
931.0331.0619875409892-0.0319875409892383
1030.7431.0087884257166-0.268788425716629
1130.8330.72546846478110.104531535218861
1230.8230.72847419443270.0915258055672936
1330.830.74430066354040.0556993364596323
1430.7430.7483939938821-0.00839399388210538
1530.7130.70561771359610.00438228640388871
1630.5830.6728332643579-0.0928332643579033
1730.7130.54977093694530.16022906305469
1830.730.64220729111680.0577927088831665
1930.730.67679162863610.0232083713638715
2030.7230.6927295347530.0272704652469891
2130.6830.7180426825034-0.0380426825033666
2230.7830.68853062627640.0914693737236156
2330.8430.77157410032940.0684258996705722
2430.830.8548796968014-0.0548796968013754
2530.830.838738107586-0.0387381075859636
2630.8830.82461497021660.0553850297833804
2730.8730.8896352369036-0.0196352369035644
2830.9230.89744547204330.0225545279566717
2930.8230.9401869120392-0.120186912039166
3030.7530.8542347649753-0.104234764975278
3130.7530.7544798618659-0.00447986186592075
3230.7530.72347041709760.0265295829023557
3330.6330.7205192197625-0.090519219762502
3430.5230.6139631262368-0.0939631262368152
3530.5830.48248936129110.0975106387088722
3630.630.50838525719830.091614742801692
3730.630.55209937408720.0479006259128099
3830.6330.57669173216280.053308267837231
3930.5630.6178379974744-0.0578379974743903
4030.6130.56733879142220.0426612085777656
4130.5330.5973978285107-0.0673978285106678
4230.630.53428245017190.0657175498281255
4330.630.58007615590520.0199238440947624
4430.6330.59859123179980.0314087682001905
4530.6630.63266805444070.0273319455592684
4630.3430.6704384113401-0.330438411340126
4730.3230.3786540838376-0.0586540838375811
4830.330.26304222216040.0369577778396319
4930.330.22320178710310.0767982128969109
5030.0830.2296414170063-0.149641417006336
5129.9630.0417517034671-0.0817517034670736
5229.9129.88179581401790.0282041859821227
5329.8329.80555397230850.0244460276915213
5429.8929.73253742543740.157462574562572
5529.8529.79033676032170.0596632396782795
5630.0629.79397758595910.266022414040894
5729.8330.0057705293829-0.175770529382874
5829.9529.8662493921360.0837506078639656
5930.0229.92842834123040.0915716587695812
6030.0330.01801569289530.0119843071046617
6130.0330.0547704340191-0.0247704340191177
6229.9630.0598671647449-0.0998671647449143
6329.8529.9884821445344-0.138482144534436
6430.1229.85689941327270.263100586727337
6529.9130.0694060433071-0.159406043307055
6629.929.948016934298-0.0480169342979586
6729.9229.89308750350960.0269124964903753
6829.8929.8970476726791-0.00704767267914264
6929.9629.87555094242420.0844490575757568
7029.7229.9383211884498-0.218321188449806
7129.629.7368871556601-0.136887155660112
7229.5429.559659860822-0.0196598608220349

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 31.3 & 31.08 & 0.220000000000002 \tabularnewline
4 & 31.06 & 31.0766754507936 & -0.016675450793624 \tabularnewline
5 & 31.09 & 30.9037072488936 & 0.1862927511064 \tabularnewline
6 & 31.11 & 30.9174199274605 & 0.192580072539457 \tabularnewline
7 & 31.13 & 30.9816624083262 & 0.148337591673844 \tabularnewline
8 & 31.1 & 31.0504713054803 & 0.0495286945197364 \tabularnewline
9 & 31.03 & 31.0619875409892 & -0.0319875409892383 \tabularnewline
10 & 30.74 & 31.0087884257166 & -0.268788425716629 \tabularnewline
11 & 30.83 & 30.7254684647811 & 0.104531535218861 \tabularnewline
12 & 30.82 & 30.7284741944327 & 0.0915258055672936 \tabularnewline
13 & 30.8 & 30.7443006635404 & 0.0556993364596323 \tabularnewline
14 & 30.74 & 30.7483939938821 & -0.00839399388210538 \tabularnewline
15 & 30.71 & 30.7056177135961 & 0.00438228640388871 \tabularnewline
16 & 30.58 & 30.6728332643579 & -0.0928332643579033 \tabularnewline
17 & 30.71 & 30.5497709369453 & 0.16022906305469 \tabularnewline
18 & 30.7 & 30.6422072911168 & 0.0577927088831665 \tabularnewline
19 & 30.7 & 30.6767916286361 & 0.0232083713638715 \tabularnewline
20 & 30.72 & 30.692729534753 & 0.0272704652469891 \tabularnewline
21 & 30.68 & 30.7180426825034 & -0.0380426825033666 \tabularnewline
22 & 30.78 & 30.6885306262764 & 0.0914693737236156 \tabularnewline
23 & 30.84 & 30.7715741003294 & 0.0684258996705722 \tabularnewline
24 & 30.8 & 30.8548796968014 & -0.0548796968013754 \tabularnewline
25 & 30.8 & 30.838738107586 & -0.0387381075859636 \tabularnewline
26 & 30.88 & 30.8246149702166 & 0.0553850297833804 \tabularnewline
27 & 30.87 & 30.8896352369036 & -0.0196352369035644 \tabularnewline
28 & 30.92 & 30.8974454720433 & 0.0225545279566717 \tabularnewline
29 & 30.82 & 30.9401869120392 & -0.120186912039166 \tabularnewline
30 & 30.75 & 30.8542347649753 & -0.104234764975278 \tabularnewline
31 & 30.75 & 30.7544798618659 & -0.00447986186592075 \tabularnewline
32 & 30.75 & 30.7234704170976 & 0.0265295829023557 \tabularnewline
33 & 30.63 & 30.7205192197625 & -0.090519219762502 \tabularnewline
34 & 30.52 & 30.6139631262368 & -0.0939631262368152 \tabularnewline
35 & 30.58 & 30.4824893612911 & 0.0975106387088722 \tabularnewline
36 & 30.6 & 30.5083852571983 & 0.091614742801692 \tabularnewline
37 & 30.6 & 30.5520993740872 & 0.0479006259128099 \tabularnewline
38 & 30.63 & 30.5766917321628 & 0.053308267837231 \tabularnewline
39 & 30.56 & 30.6178379974744 & -0.0578379974743903 \tabularnewline
40 & 30.61 & 30.5673387914222 & 0.0426612085777656 \tabularnewline
41 & 30.53 & 30.5973978285107 & -0.0673978285106678 \tabularnewline
42 & 30.6 & 30.5342824501719 & 0.0657175498281255 \tabularnewline
43 & 30.6 & 30.5800761559052 & 0.0199238440947624 \tabularnewline
44 & 30.63 & 30.5985912317998 & 0.0314087682001905 \tabularnewline
45 & 30.66 & 30.6326680544407 & 0.0273319455592684 \tabularnewline
46 & 30.34 & 30.6704384113401 & -0.330438411340126 \tabularnewline
47 & 30.32 & 30.3786540838376 & -0.0586540838375811 \tabularnewline
48 & 30.3 & 30.2630422221604 & 0.0369577778396319 \tabularnewline
49 & 30.3 & 30.2232017871031 & 0.0767982128969109 \tabularnewline
50 & 30.08 & 30.2296414170063 & -0.149641417006336 \tabularnewline
51 & 29.96 & 30.0417517034671 & -0.0817517034670736 \tabularnewline
52 & 29.91 & 29.8817958140179 & 0.0282041859821227 \tabularnewline
53 & 29.83 & 29.8055539723085 & 0.0244460276915213 \tabularnewline
54 & 29.89 & 29.7325374254374 & 0.157462574562572 \tabularnewline
55 & 29.85 & 29.7903367603217 & 0.0596632396782795 \tabularnewline
56 & 30.06 & 29.7939775859591 & 0.266022414040894 \tabularnewline
57 & 29.83 & 30.0057705293829 & -0.175770529382874 \tabularnewline
58 & 29.95 & 29.866249392136 & 0.0837506078639656 \tabularnewline
59 & 30.02 & 29.9284283412304 & 0.0915716587695812 \tabularnewline
60 & 30.03 & 30.0180156928953 & 0.0119843071046617 \tabularnewline
61 & 30.03 & 30.0547704340191 & -0.0247704340191177 \tabularnewline
62 & 29.96 & 30.0598671647449 & -0.0998671647449143 \tabularnewline
63 & 29.85 & 29.9884821445344 & -0.138482144534436 \tabularnewline
64 & 30.12 & 29.8568994132727 & 0.263100586727337 \tabularnewline
65 & 29.91 & 30.0694060433071 & -0.159406043307055 \tabularnewline
66 & 29.9 & 29.948016934298 & -0.0480169342979586 \tabularnewline
67 & 29.92 & 29.8930875035096 & 0.0269124964903753 \tabularnewline
68 & 29.89 & 29.8970476726791 & -0.00704767267914264 \tabularnewline
69 & 29.96 & 29.8755509424242 & 0.0844490575757568 \tabularnewline
70 & 29.72 & 29.9383211884498 & -0.218321188449806 \tabularnewline
71 & 29.6 & 29.7368871556601 & -0.136887155660112 \tabularnewline
72 & 29.54 & 29.559659860822 & -0.0196598608220349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204904&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]31.3[/C][C]31.08[/C][C]0.220000000000002[/C][/ROW]
[ROW][C]4[/C][C]31.06[/C][C]31.0766754507936[/C][C]-0.016675450793624[/C][/ROW]
[ROW][C]5[/C][C]31.09[/C][C]30.9037072488936[/C][C]0.1862927511064[/C][/ROW]
[ROW][C]6[/C][C]31.11[/C][C]30.9174199274605[/C][C]0.192580072539457[/C][/ROW]
[ROW][C]7[/C][C]31.13[/C][C]30.9816624083262[/C][C]0.148337591673844[/C][/ROW]
[ROW][C]8[/C][C]31.1[/C][C]31.0504713054803[/C][C]0.0495286945197364[/C][/ROW]
[ROW][C]9[/C][C]31.03[/C][C]31.0619875409892[/C][C]-0.0319875409892383[/C][/ROW]
[ROW][C]10[/C][C]30.74[/C][C]31.0087884257166[/C][C]-0.268788425716629[/C][/ROW]
[ROW][C]11[/C][C]30.83[/C][C]30.7254684647811[/C][C]0.104531535218861[/C][/ROW]
[ROW][C]12[/C][C]30.82[/C][C]30.7284741944327[/C][C]0.0915258055672936[/C][/ROW]
[ROW][C]13[/C][C]30.8[/C][C]30.7443006635404[/C][C]0.0556993364596323[/C][/ROW]
[ROW][C]14[/C][C]30.74[/C][C]30.7483939938821[/C][C]-0.00839399388210538[/C][/ROW]
[ROW][C]15[/C][C]30.71[/C][C]30.7056177135961[/C][C]0.00438228640388871[/C][/ROW]
[ROW][C]16[/C][C]30.58[/C][C]30.6728332643579[/C][C]-0.0928332643579033[/C][/ROW]
[ROW][C]17[/C][C]30.71[/C][C]30.5497709369453[/C][C]0.16022906305469[/C][/ROW]
[ROW][C]18[/C][C]30.7[/C][C]30.6422072911168[/C][C]0.0577927088831665[/C][/ROW]
[ROW][C]19[/C][C]30.7[/C][C]30.6767916286361[/C][C]0.0232083713638715[/C][/ROW]
[ROW][C]20[/C][C]30.72[/C][C]30.692729534753[/C][C]0.0272704652469891[/C][/ROW]
[ROW][C]21[/C][C]30.68[/C][C]30.7180426825034[/C][C]-0.0380426825033666[/C][/ROW]
[ROW][C]22[/C][C]30.78[/C][C]30.6885306262764[/C][C]0.0914693737236156[/C][/ROW]
[ROW][C]23[/C][C]30.84[/C][C]30.7715741003294[/C][C]0.0684258996705722[/C][/ROW]
[ROW][C]24[/C][C]30.8[/C][C]30.8548796968014[/C][C]-0.0548796968013754[/C][/ROW]
[ROW][C]25[/C][C]30.8[/C][C]30.838738107586[/C][C]-0.0387381075859636[/C][/ROW]
[ROW][C]26[/C][C]30.88[/C][C]30.8246149702166[/C][C]0.0553850297833804[/C][/ROW]
[ROW][C]27[/C][C]30.87[/C][C]30.8896352369036[/C][C]-0.0196352369035644[/C][/ROW]
[ROW][C]28[/C][C]30.92[/C][C]30.8974454720433[/C][C]0.0225545279566717[/C][/ROW]
[ROW][C]29[/C][C]30.82[/C][C]30.9401869120392[/C][C]-0.120186912039166[/C][/ROW]
[ROW][C]30[/C][C]30.75[/C][C]30.8542347649753[/C][C]-0.104234764975278[/C][/ROW]
[ROW][C]31[/C][C]30.75[/C][C]30.7544798618659[/C][C]-0.00447986186592075[/C][/ROW]
[ROW][C]32[/C][C]30.75[/C][C]30.7234704170976[/C][C]0.0265295829023557[/C][/ROW]
[ROW][C]33[/C][C]30.63[/C][C]30.7205192197625[/C][C]-0.090519219762502[/C][/ROW]
[ROW][C]34[/C][C]30.52[/C][C]30.6139631262368[/C][C]-0.0939631262368152[/C][/ROW]
[ROW][C]35[/C][C]30.58[/C][C]30.4824893612911[/C][C]0.0975106387088722[/C][/ROW]
[ROW][C]36[/C][C]30.6[/C][C]30.5083852571983[/C][C]0.091614742801692[/C][/ROW]
[ROW][C]37[/C][C]30.6[/C][C]30.5520993740872[/C][C]0.0479006259128099[/C][/ROW]
[ROW][C]38[/C][C]30.63[/C][C]30.5766917321628[/C][C]0.053308267837231[/C][/ROW]
[ROW][C]39[/C][C]30.56[/C][C]30.6178379974744[/C][C]-0.0578379974743903[/C][/ROW]
[ROW][C]40[/C][C]30.61[/C][C]30.5673387914222[/C][C]0.0426612085777656[/C][/ROW]
[ROW][C]41[/C][C]30.53[/C][C]30.5973978285107[/C][C]-0.0673978285106678[/C][/ROW]
[ROW][C]42[/C][C]30.6[/C][C]30.5342824501719[/C][C]0.0657175498281255[/C][/ROW]
[ROW][C]43[/C][C]30.6[/C][C]30.5800761559052[/C][C]0.0199238440947624[/C][/ROW]
[ROW][C]44[/C][C]30.63[/C][C]30.5985912317998[/C][C]0.0314087682001905[/C][/ROW]
[ROW][C]45[/C][C]30.66[/C][C]30.6326680544407[/C][C]0.0273319455592684[/C][/ROW]
[ROW][C]46[/C][C]30.34[/C][C]30.6704384113401[/C][C]-0.330438411340126[/C][/ROW]
[ROW][C]47[/C][C]30.32[/C][C]30.3786540838376[/C][C]-0.0586540838375811[/C][/ROW]
[ROW][C]48[/C][C]30.3[/C][C]30.2630422221604[/C][C]0.0369577778396319[/C][/ROW]
[ROW][C]49[/C][C]30.3[/C][C]30.2232017871031[/C][C]0.0767982128969109[/C][/ROW]
[ROW][C]50[/C][C]30.08[/C][C]30.2296414170063[/C][C]-0.149641417006336[/C][/ROW]
[ROW][C]51[/C][C]29.96[/C][C]30.0417517034671[/C][C]-0.0817517034670736[/C][/ROW]
[ROW][C]52[/C][C]29.91[/C][C]29.8817958140179[/C][C]0.0282041859821227[/C][/ROW]
[ROW][C]53[/C][C]29.83[/C][C]29.8055539723085[/C][C]0.0244460276915213[/C][/ROW]
[ROW][C]54[/C][C]29.89[/C][C]29.7325374254374[/C][C]0.157462574562572[/C][/ROW]
[ROW][C]55[/C][C]29.85[/C][C]29.7903367603217[/C][C]0.0596632396782795[/C][/ROW]
[ROW][C]56[/C][C]30.06[/C][C]29.7939775859591[/C][C]0.266022414040894[/C][/ROW]
[ROW][C]57[/C][C]29.83[/C][C]30.0057705293829[/C][C]-0.175770529382874[/C][/ROW]
[ROW][C]58[/C][C]29.95[/C][C]29.866249392136[/C][C]0.0837506078639656[/C][/ROW]
[ROW][C]59[/C][C]30.02[/C][C]29.9284283412304[/C][C]0.0915716587695812[/C][/ROW]
[ROW][C]60[/C][C]30.03[/C][C]30.0180156928953[/C][C]0.0119843071046617[/C][/ROW]
[ROW][C]61[/C][C]30.03[/C][C]30.0547704340191[/C][C]-0.0247704340191177[/C][/ROW]
[ROW][C]62[/C][C]29.96[/C][C]30.0598671647449[/C][C]-0.0998671647449143[/C][/ROW]
[ROW][C]63[/C][C]29.85[/C][C]29.9884821445344[/C][C]-0.138482144534436[/C][/ROW]
[ROW][C]64[/C][C]30.12[/C][C]29.8568994132727[/C][C]0.263100586727337[/C][/ROW]
[ROW][C]65[/C][C]29.91[/C][C]30.0694060433071[/C][C]-0.159406043307055[/C][/ROW]
[ROW][C]66[/C][C]29.9[/C][C]29.948016934298[/C][C]-0.0480169342979586[/C][/ROW]
[ROW][C]67[/C][C]29.92[/C][C]29.8930875035096[/C][C]0.0269124964903753[/C][/ROW]
[ROW][C]68[/C][C]29.89[/C][C]29.8970476726791[/C][C]-0.00704767267914264[/C][/ROW]
[ROW][C]69[/C][C]29.96[/C][C]29.8755509424242[/C][C]0.0844490575757568[/C][/ROW]
[ROW][C]70[/C][C]29.72[/C][C]29.9383211884498[/C][C]-0.218321188449806[/C][/ROW]
[ROW][C]71[/C][C]29.6[/C][C]29.7368871556601[/C][C]-0.136887155660112[/C][/ROW]
[ROW][C]72[/C][C]29.54[/C][C]29.559659860822[/C][C]-0.0196598608220349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204904&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204904&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
331.331.080.220000000000002
431.0631.0766754507936-0.016675450793624
531.0930.90370724889360.1862927511064
631.1130.91741992746050.192580072539457
731.1330.98166240832620.148337591673844
831.131.05047130548030.0495286945197364
931.0331.0619875409892-0.0319875409892383
1030.7431.0087884257166-0.268788425716629
1130.8330.72546846478110.104531535218861
1230.8230.72847419443270.0915258055672936
1330.830.74430066354040.0556993364596323
1430.7430.7483939938821-0.00839399388210538
1530.7130.70561771359610.00438228640388871
1630.5830.6728332643579-0.0928332643579033
1730.7130.54977093694530.16022906305469
1830.730.64220729111680.0577927088831665
1930.730.67679162863610.0232083713638715
2030.7230.6927295347530.0272704652469891
2130.6830.7180426825034-0.0380426825033666
2230.7830.68853062627640.0914693737236156
2330.8430.77157410032940.0684258996705722
2430.830.8548796968014-0.0548796968013754
2530.830.838738107586-0.0387381075859636
2630.8830.82461497021660.0553850297833804
2730.8730.8896352369036-0.0196352369035644
2830.9230.89744547204330.0225545279566717
2930.8230.9401869120392-0.120186912039166
3030.7530.8542347649753-0.104234764975278
3130.7530.7544798618659-0.00447986186592075
3230.7530.72347041709760.0265295829023557
3330.6330.7205192197625-0.090519219762502
3430.5230.6139631262368-0.0939631262368152
3530.5830.48248936129110.0975106387088722
3630.630.50838525719830.091614742801692
3730.630.55209937408720.0479006259128099
3830.6330.57669173216280.053308267837231
3930.5630.6178379974744-0.0578379974743903
4030.6130.56733879142220.0426612085777656
4130.5330.5973978285107-0.0673978285106678
4230.630.53428245017190.0657175498281255
4330.630.58007615590520.0199238440947624
4430.6330.59859123179980.0314087682001905
4530.6630.63266805444070.0273319455592684
4630.3430.6704384113401-0.330438411340126
4730.3230.3786540838376-0.0586540838375811
4830.330.26304222216040.0369577778396319
4930.330.22320178710310.0767982128969109
5030.0830.2296414170063-0.149641417006336
5129.9630.0417517034671-0.0817517034670736
5229.9129.88179581401790.0282041859821227
5329.8329.80555397230850.0244460276915213
5429.8929.73253742543740.157462574562572
5529.8529.79033676032170.0596632396782795
5630.0629.79397758595910.266022414040894
5729.8330.0057705293829-0.175770529382874
5829.9529.8662493921360.0837506078639656
5930.0229.92842834123040.0915716587695812
6030.0330.01801569289530.0119843071046617
6130.0330.0547704340191-0.0247704340191177
6229.9630.0598671647449-0.0998671647449143
6329.8529.9884821445344-0.138482144534436
6430.1229.85689941327270.263100586727337
6529.9130.0694060433071-0.159406043307055
6629.929.948016934298-0.0480169342979586
6729.9229.89308750350960.0269124964903753
6829.8929.8970476726791-0.00704767267914264
6929.9629.87555094242420.0844490575757568
7029.7229.9383211884498-0.218321188449806
7129.629.7368871556601-0.136887155660112
7229.5429.559659860822-0.0196598608220349







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7329.459770852593529.238638692851829.6809030123352
7429.373641796098329.07023622460829.6770473675886
7529.287512739603128.887483556753329.6875419224529
7629.201383683107928.693037375081129.7097299911348
7729.115254626612828.488481841687929.7420274115376
7829.029125570117628.274858289839929.7833928503952
7928.942996513622428.052910952981529.8330820742634
8028.856867457127227.823206503396929.8905284108576
8128.770738400632127.586196956036229.9552798452279
8228.684609344136927.34225543282730.0269632554467
8328.598480287641727.091697936786130.1052626384973
8428.512351231146526.834797404665730.1899050576273

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 29.4597708525935 & 29.2386386928518 & 29.6809030123352 \tabularnewline
74 & 29.3736417960983 & 29.070236224608 & 29.6770473675886 \tabularnewline
75 & 29.2875127396031 & 28.8874835567533 & 29.6875419224529 \tabularnewline
76 & 29.2013836831079 & 28.6930373750811 & 29.7097299911348 \tabularnewline
77 & 29.1152546266128 & 28.4884818416879 & 29.7420274115376 \tabularnewline
78 & 29.0291255701176 & 28.2748582898399 & 29.7833928503952 \tabularnewline
79 & 28.9429965136224 & 28.0529109529815 & 29.8330820742634 \tabularnewline
80 & 28.8568674571272 & 27.8232065033969 & 29.8905284108576 \tabularnewline
81 & 28.7707384006321 & 27.5861969560362 & 29.9552798452279 \tabularnewline
82 & 28.6846093441369 & 27.342255432827 & 30.0269632554467 \tabularnewline
83 & 28.5984802876417 & 27.0916979367861 & 30.1052626384973 \tabularnewline
84 & 28.5123512311465 & 26.8347974046657 & 30.1899050576273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204904&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]29.4597708525935[/C][C]29.2386386928518[/C][C]29.6809030123352[/C][/ROW]
[ROW][C]74[/C][C]29.3736417960983[/C][C]29.070236224608[/C][C]29.6770473675886[/C][/ROW]
[ROW][C]75[/C][C]29.2875127396031[/C][C]28.8874835567533[/C][C]29.6875419224529[/C][/ROW]
[ROW][C]76[/C][C]29.2013836831079[/C][C]28.6930373750811[/C][C]29.7097299911348[/C][/ROW]
[ROW][C]77[/C][C]29.1152546266128[/C][C]28.4884818416879[/C][C]29.7420274115376[/C][/ROW]
[ROW][C]78[/C][C]29.0291255701176[/C][C]28.2748582898399[/C][C]29.7833928503952[/C][/ROW]
[ROW][C]79[/C][C]28.9429965136224[/C][C]28.0529109529815[/C][C]29.8330820742634[/C][/ROW]
[ROW][C]80[/C][C]28.8568674571272[/C][C]27.8232065033969[/C][C]29.8905284108576[/C][/ROW]
[ROW][C]81[/C][C]28.7707384006321[/C][C]27.5861969560362[/C][C]29.9552798452279[/C][/ROW]
[ROW][C]82[/C][C]28.6846093441369[/C][C]27.342255432827[/C][C]30.0269632554467[/C][/ROW]
[ROW][C]83[/C][C]28.5984802876417[/C][C]27.0916979367861[/C][C]30.1052626384973[/C][/ROW]
[ROW][C]84[/C][C]28.5123512311465[/C][C]26.8347974046657[/C][C]30.1899050576273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204904&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204904&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
7329.459770852593529.238638692851829.6809030123352
7429.373641796098329.07023622460829.6770473675886
7529.287512739603128.887483556753329.6875419224529
7629.201383683107928.693037375081129.7097299911348
7729.115254626612828.488481841687929.7420274115376
7829.029125570117628.274858289839929.7833928503952
7928.942996513622428.052910952981529.8330820742634
8028.856867457127227.823206503396929.8905284108576
8128.770738400632127.586196956036229.9552798452279
8228.684609344136927.34225543282730.0269632554467
8328.598480287641727.091697936786130.1052626384973
8428.512351231146526.834797404665730.1899050576273



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')