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Author's title

Double exponential smoothing Indexcijfers Consumptieprijzen visitekaartjes ...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 May 2012 12:32:31 -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/2012/May/14/t1337013235zr24r6hrok455gu.htm/, Retrieved Sun, 05 May 2024 18:11:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166450, Retrieved Sun, 05 May 2024 18:11:48 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Double exponentia...] [2012-05-14 16:32:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
101.15
101.14
101.23
101.11
101.55
101.55
101.55
101.6
101.71
101.81
101.95
102.12
102.11
102.25
102.35
102.42
102.34
102.32
102.39
102.45
102.68
102.77
102.83
102.83
103.21
103.58
102.5
102.68
102.7
102.7
102.73
102.72
102.71
102.91
103.1
103.1
103.39
103.38
103.34
103.33
103.33
103.33
103.48
104.38
105.76
107.37
108.16
111.21
112.77
114.39
114.37
114.52
114.54
114.78
114.83
115.86
117
117.27
117.38
117.83




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166450&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]1 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=166450&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166450&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.960953822848989
beta0.591847004487882
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.960953822848989 \tabularnewline
beta & 0.591847004487882 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166450&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]0.960953822848989[/C][/ROW]
[ROW][C]beta[/C][C]0.591847004487882[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166450&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166450&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
alpha0.960953822848989
beta0.591847004487882
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3101.23101.130.100000000000009
4101.11101.272969146435-0.16296914643533
5101.55101.0705503983310.479449601669316
6101.55101.758147437761-0.208147437760672
7101.55101.666614190734-0.116614190733586
8101.6101.5967172875510.00328271244879375
9101.71101.6439027739660.0660972260344437
10101.81101.7890420877850.0209579122147687
11101.95101.9027241589930.0472758410069929
12102.12102.0685840947980.0514159052024041
13102.11102.267664601778-0.157664601778237
14102.25102.1761586025290.0738413974714547
15102.35102.3491155605140.00088443948637007
16102.42102.452467264847-0.0324672648470283
17102.34102.505304165768-0.165304165767523
18102.32102.336476237564-0.0164762375636087
19102.39102.3012944194210.0887055805788606
20102.45102.4176376742040.0323623257964272
21102.68102.4982433357580.181756664241874
22102.77102.825781914502-0.0557819145024609
23102.83102.893331613436-0.0633316134355653
24102.83102.91760732786-0.0876073278595442
25103.21102.868729616680.341270383319923
26103.58103.4260768945180.153923105482107
27102.5103.890933953502-1.39093395350203
28102.68102.0801782196970.59982178030296
29102.7102.5235880433030.176411956697052
30102.7102.6604526984680.0395473015319965
31102.73102.688288779040.0417112209595416
32102.72102.741927027692-0.0219270276919445
33102.71102.721941132008-0.0119411320076637
34102.91102.7047598497010.20524015029919
35103.1103.0130075499010.0869924500988475
36103.1103.257100551449-0.157100551448764
37103.39103.1772824529190.212717547081496
38103.38103.573822945963-0.193822945963376
39103.34103.469462392917-0.129462392917219
40103.33103.35331922335-0.0233192233502137
41103.33103.3259122182580.00408778174198687
42103.33103.3271669548290.00283304517108718
43103.48103.3288272069240.151172793075773
44104.38103.5590127646430.82098723535745
45105.76104.8997854152130.860214584786732
46107.37106.7674901513180.602509848682445
47108.16108.730222566419-0.570222566418934
48111.21109.2417062464921.96829375350794
49112.77113.312029635721-0.542029635721306
50114.39114.661775510838-0.27177551083787
51114.37116.116654157349-1.74665415734931
52114.52115.160854564283-0.640854564282634
53114.54114.903199204041-0.363199204040825
54114.78114.7057927649550.0742072350445255
55114.83114.97091816349-0.140918163489729
56115.86114.9491725239620.910827476037696
57117116.4561277479430.54387225205744
58117.27117.919776568539-0.649776568539394
59117.38117.866831598749-0.486831598748623
60117.83117.693589765310.136410234689777

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 101.23 & 101.13 & 0.100000000000009 \tabularnewline
4 & 101.11 & 101.272969146435 & -0.16296914643533 \tabularnewline
5 & 101.55 & 101.070550398331 & 0.479449601669316 \tabularnewline
6 & 101.55 & 101.758147437761 & -0.208147437760672 \tabularnewline
7 & 101.55 & 101.666614190734 & -0.116614190733586 \tabularnewline
8 & 101.6 & 101.596717287551 & 0.00328271244879375 \tabularnewline
9 & 101.71 & 101.643902773966 & 0.0660972260344437 \tabularnewline
10 & 101.81 & 101.789042087785 & 0.0209579122147687 \tabularnewline
11 & 101.95 & 101.902724158993 & 0.0472758410069929 \tabularnewline
12 & 102.12 & 102.068584094798 & 0.0514159052024041 \tabularnewline
13 & 102.11 & 102.267664601778 & -0.157664601778237 \tabularnewline
14 & 102.25 & 102.176158602529 & 0.0738413974714547 \tabularnewline
15 & 102.35 & 102.349115560514 & 0.00088443948637007 \tabularnewline
16 & 102.42 & 102.452467264847 & -0.0324672648470283 \tabularnewline
17 & 102.34 & 102.505304165768 & -0.165304165767523 \tabularnewline
18 & 102.32 & 102.336476237564 & -0.0164762375636087 \tabularnewline
19 & 102.39 & 102.301294419421 & 0.0887055805788606 \tabularnewline
20 & 102.45 & 102.417637674204 & 0.0323623257964272 \tabularnewline
21 & 102.68 & 102.498243335758 & 0.181756664241874 \tabularnewline
22 & 102.77 & 102.825781914502 & -0.0557819145024609 \tabularnewline
23 & 102.83 & 102.893331613436 & -0.0633316134355653 \tabularnewline
24 & 102.83 & 102.91760732786 & -0.0876073278595442 \tabularnewline
25 & 103.21 & 102.86872961668 & 0.341270383319923 \tabularnewline
26 & 103.58 & 103.426076894518 & 0.153923105482107 \tabularnewline
27 & 102.5 & 103.890933953502 & -1.39093395350203 \tabularnewline
28 & 102.68 & 102.080178219697 & 0.59982178030296 \tabularnewline
29 & 102.7 & 102.523588043303 & 0.176411956697052 \tabularnewline
30 & 102.7 & 102.660452698468 & 0.0395473015319965 \tabularnewline
31 & 102.73 & 102.68828877904 & 0.0417112209595416 \tabularnewline
32 & 102.72 & 102.741927027692 & -0.0219270276919445 \tabularnewline
33 & 102.71 & 102.721941132008 & -0.0119411320076637 \tabularnewline
34 & 102.91 & 102.704759849701 & 0.20524015029919 \tabularnewline
35 & 103.1 & 103.013007549901 & 0.0869924500988475 \tabularnewline
36 & 103.1 & 103.257100551449 & -0.157100551448764 \tabularnewline
37 & 103.39 & 103.177282452919 & 0.212717547081496 \tabularnewline
38 & 103.38 & 103.573822945963 & -0.193822945963376 \tabularnewline
39 & 103.34 & 103.469462392917 & -0.129462392917219 \tabularnewline
40 & 103.33 & 103.35331922335 & -0.0233192233502137 \tabularnewline
41 & 103.33 & 103.325912218258 & 0.00408778174198687 \tabularnewline
42 & 103.33 & 103.327166954829 & 0.00283304517108718 \tabularnewline
43 & 103.48 & 103.328827206924 & 0.151172793075773 \tabularnewline
44 & 104.38 & 103.559012764643 & 0.82098723535745 \tabularnewline
45 & 105.76 & 104.899785415213 & 0.860214584786732 \tabularnewline
46 & 107.37 & 106.767490151318 & 0.602509848682445 \tabularnewline
47 & 108.16 & 108.730222566419 & -0.570222566418934 \tabularnewline
48 & 111.21 & 109.241706246492 & 1.96829375350794 \tabularnewline
49 & 112.77 & 113.312029635721 & -0.542029635721306 \tabularnewline
50 & 114.39 & 114.661775510838 & -0.27177551083787 \tabularnewline
51 & 114.37 & 116.116654157349 & -1.74665415734931 \tabularnewline
52 & 114.52 & 115.160854564283 & -0.640854564282634 \tabularnewline
53 & 114.54 & 114.903199204041 & -0.363199204040825 \tabularnewline
54 & 114.78 & 114.705792764955 & 0.0742072350445255 \tabularnewline
55 & 114.83 & 114.97091816349 & -0.140918163489729 \tabularnewline
56 & 115.86 & 114.949172523962 & 0.910827476037696 \tabularnewline
57 & 117 & 116.456127747943 & 0.54387225205744 \tabularnewline
58 & 117.27 & 117.919776568539 & -0.649776568539394 \tabularnewline
59 & 117.38 & 117.866831598749 & -0.486831598748623 \tabularnewline
60 & 117.83 & 117.69358976531 & 0.136410234689777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166450&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]101.23[/C][C]101.13[/C][C]0.100000000000009[/C][/ROW]
[ROW][C]4[/C][C]101.11[/C][C]101.272969146435[/C][C]-0.16296914643533[/C][/ROW]
[ROW][C]5[/C][C]101.55[/C][C]101.070550398331[/C][C]0.479449601669316[/C][/ROW]
[ROW][C]6[/C][C]101.55[/C][C]101.758147437761[/C][C]-0.208147437760672[/C][/ROW]
[ROW][C]7[/C][C]101.55[/C][C]101.666614190734[/C][C]-0.116614190733586[/C][/ROW]
[ROW][C]8[/C][C]101.6[/C][C]101.596717287551[/C][C]0.00328271244879375[/C][/ROW]
[ROW][C]9[/C][C]101.71[/C][C]101.643902773966[/C][C]0.0660972260344437[/C][/ROW]
[ROW][C]10[/C][C]101.81[/C][C]101.789042087785[/C][C]0.0209579122147687[/C][/ROW]
[ROW][C]11[/C][C]101.95[/C][C]101.902724158993[/C][C]0.0472758410069929[/C][/ROW]
[ROW][C]12[/C][C]102.12[/C][C]102.068584094798[/C][C]0.0514159052024041[/C][/ROW]
[ROW][C]13[/C][C]102.11[/C][C]102.267664601778[/C][C]-0.157664601778237[/C][/ROW]
[ROW][C]14[/C][C]102.25[/C][C]102.176158602529[/C][C]0.0738413974714547[/C][/ROW]
[ROW][C]15[/C][C]102.35[/C][C]102.349115560514[/C][C]0.00088443948637007[/C][/ROW]
[ROW][C]16[/C][C]102.42[/C][C]102.452467264847[/C][C]-0.0324672648470283[/C][/ROW]
[ROW][C]17[/C][C]102.34[/C][C]102.505304165768[/C][C]-0.165304165767523[/C][/ROW]
[ROW][C]18[/C][C]102.32[/C][C]102.336476237564[/C][C]-0.0164762375636087[/C][/ROW]
[ROW][C]19[/C][C]102.39[/C][C]102.301294419421[/C][C]0.0887055805788606[/C][/ROW]
[ROW][C]20[/C][C]102.45[/C][C]102.417637674204[/C][C]0.0323623257964272[/C][/ROW]
[ROW][C]21[/C][C]102.68[/C][C]102.498243335758[/C][C]0.181756664241874[/C][/ROW]
[ROW][C]22[/C][C]102.77[/C][C]102.825781914502[/C][C]-0.0557819145024609[/C][/ROW]
[ROW][C]23[/C][C]102.83[/C][C]102.893331613436[/C][C]-0.0633316134355653[/C][/ROW]
[ROW][C]24[/C][C]102.83[/C][C]102.91760732786[/C][C]-0.0876073278595442[/C][/ROW]
[ROW][C]25[/C][C]103.21[/C][C]102.86872961668[/C][C]0.341270383319923[/C][/ROW]
[ROW][C]26[/C][C]103.58[/C][C]103.426076894518[/C][C]0.153923105482107[/C][/ROW]
[ROW][C]27[/C][C]102.5[/C][C]103.890933953502[/C][C]-1.39093395350203[/C][/ROW]
[ROW][C]28[/C][C]102.68[/C][C]102.080178219697[/C][C]0.59982178030296[/C][/ROW]
[ROW][C]29[/C][C]102.7[/C][C]102.523588043303[/C][C]0.176411956697052[/C][/ROW]
[ROW][C]30[/C][C]102.7[/C][C]102.660452698468[/C][C]0.0395473015319965[/C][/ROW]
[ROW][C]31[/C][C]102.73[/C][C]102.68828877904[/C][C]0.0417112209595416[/C][/ROW]
[ROW][C]32[/C][C]102.72[/C][C]102.741927027692[/C][C]-0.0219270276919445[/C][/ROW]
[ROW][C]33[/C][C]102.71[/C][C]102.721941132008[/C][C]-0.0119411320076637[/C][/ROW]
[ROW][C]34[/C][C]102.91[/C][C]102.704759849701[/C][C]0.20524015029919[/C][/ROW]
[ROW][C]35[/C][C]103.1[/C][C]103.013007549901[/C][C]0.0869924500988475[/C][/ROW]
[ROW][C]36[/C][C]103.1[/C][C]103.257100551449[/C][C]-0.157100551448764[/C][/ROW]
[ROW][C]37[/C][C]103.39[/C][C]103.177282452919[/C][C]0.212717547081496[/C][/ROW]
[ROW][C]38[/C][C]103.38[/C][C]103.573822945963[/C][C]-0.193822945963376[/C][/ROW]
[ROW][C]39[/C][C]103.34[/C][C]103.469462392917[/C][C]-0.129462392917219[/C][/ROW]
[ROW][C]40[/C][C]103.33[/C][C]103.35331922335[/C][C]-0.0233192233502137[/C][/ROW]
[ROW][C]41[/C][C]103.33[/C][C]103.325912218258[/C][C]0.00408778174198687[/C][/ROW]
[ROW][C]42[/C][C]103.33[/C][C]103.327166954829[/C][C]0.00283304517108718[/C][/ROW]
[ROW][C]43[/C][C]103.48[/C][C]103.328827206924[/C][C]0.151172793075773[/C][/ROW]
[ROW][C]44[/C][C]104.38[/C][C]103.559012764643[/C][C]0.82098723535745[/C][/ROW]
[ROW][C]45[/C][C]105.76[/C][C]104.899785415213[/C][C]0.860214584786732[/C][/ROW]
[ROW][C]46[/C][C]107.37[/C][C]106.767490151318[/C][C]0.602509848682445[/C][/ROW]
[ROW][C]47[/C][C]108.16[/C][C]108.730222566419[/C][C]-0.570222566418934[/C][/ROW]
[ROW][C]48[/C][C]111.21[/C][C]109.241706246492[/C][C]1.96829375350794[/C][/ROW]
[ROW][C]49[/C][C]112.77[/C][C]113.312029635721[/C][C]-0.542029635721306[/C][/ROW]
[ROW][C]50[/C][C]114.39[/C][C]114.661775510838[/C][C]-0.27177551083787[/C][/ROW]
[ROW][C]51[/C][C]114.37[/C][C]116.116654157349[/C][C]-1.74665415734931[/C][/ROW]
[ROW][C]52[/C][C]114.52[/C][C]115.160854564283[/C][C]-0.640854564282634[/C][/ROW]
[ROW][C]53[/C][C]114.54[/C][C]114.903199204041[/C][C]-0.363199204040825[/C][/ROW]
[ROW][C]54[/C][C]114.78[/C][C]114.705792764955[/C][C]0.0742072350445255[/C][/ROW]
[ROW][C]55[/C][C]114.83[/C][C]114.97091816349[/C][C]-0.140918163489729[/C][/ROW]
[ROW][C]56[/C][C]115.86[/C][C]114.949172523962[/C][C]0.910827476037696[/C][/ROW]
[ROW][C]57[/C][C]117[/C][C]116.456127747943[/C][C]0.54387225205744[/C][/ROW]
[ROW][C]58[/C][C]117.27[/C][C]117.919776568539[/C][C]-0.649776568539394[/C][/ROW]
[ROW][C]59[/C][C]117.38[/C][C]117.866831598749[/C][C]-0.486831598748623[/C][/ROW]
[ROW][C]60[/C][C]117.83[/C][C]117.69358976531[/C][C]0.136410234689777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166450&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166450&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
3101.23101.130.100000000000009
4101.11101.272969146435-0.16296914643533
5101.55101.0705503983310.479449601669316
6101.55101.758147437761-0.208147437760672
7101.55101.666614190734-0.116614190733586
8101.6101.5967172875510.00328271244879375
9101.71101.6439027739660.0660972260344437
10101.81101.7890420877850.0209579122147687
11101.95101.9027241589930.0472758410069929
12102.12102.0685840947980.0514159052024041
13102.11102.267664601778-0.157664601778237
14102.25102.1761586025290.0738413974714547
15102.35102.3491155605140.00088443948637007
16102.42102.452467264847-0.0324672648470283
17102.34102.505304165768-0.165304165767523
18102.32102.336476237564-0.0164762375636087
19102.39102.3012944194210.0887055805788606
20102.45102.4176376742040.0323623257964272
21102.68102.4982433357580.181756664241874
22102.77102.825781914502-0.0557819145024609
23102.83102.893331613436-0.0633316134355653
24102.83102.91760732786-0.0876073278595442
25103.21102.868729616680.341270383319923
26103.58103.4260768945180.153923105482107
27102.5103.890933953502-1.39093395350203
28102.68102.0801782196970.59982178030296
29102.7102.5235880433030.176411956697052
30102.7102.6604526984680.0395473015319965
31102.73102.688288779040.0417112209595416
32102.72102.741927027692-0.0219270276919445
33102.71102.721941132008-0.0119411320076637
34102.91102.7047598497010.20524015029919
35103.1103.0130075499010.0869924500988475
36103.1103.257100551449-0.157100551448764
37103.39103.1772824529190.212717547081496
38103.38103.573822945963-0.193822945963376
39103.34103.469462392917-0.129462392917219
40103.33103.35331922335-0.0233192233502137
41103.33103.3259122182580.00408778174198687
42103.33103.3271669548290.00283304517108718
43103.48103.3288272069240.151172793075773
44104.38103.5590127646430.82098723535745
45105.76104.8997854152130.860214584786732
46107.37106.7674901513180.602509848682445
47108.16108.730222566419-0.570222566418934
48111.21109.2417062464921.96829375350794
49112.77113.312029635721-0.542029635721306
50114.39114.661775510838-0.27177551083787
51114.37116.116654157349-1.74665415734931
52114.52115.160854564283-0.640854564282634
53114.54114.903199204041-0.363199204040825
54114.78114.7057927649550.0742072350445255
55114.83114.97091816349-0.140918163489729
56115.86114.9491725239620.910827476037696
57117116.4561277479430.54387225205744
58117.27117.919776568539-0.649776568539394
59117.38117.866831598749-0.486831598748623
60117.83117.693589765310.136410234689777







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61118.196836189428117.195626348919119.198046029938
62118.568998677046116.739232983593120.398764370499
63118.941161164663116.15510508386121.727217245466
64119.31332365228115.454164361597123.172482942963
65119.685486139898114.646682746412124.724289533383
66120.057648627515113.741012860257126.374284394773
67120.429811115132112.743938030461128.115684199803
68120.801973602749111.661059867273129.942887338226
69121.174136090367110.49708803099131.851184149744
70121.546298577984109.256046733088133.83655042288
71121.918461065601107.941422728586135.895499402617
72122.290623553219106.55627331683138.024973789607

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 118.196836189428 & 117.195626348919 & 119.198046029938 \tabularnewline
62 & 118.568998677046 & 116.739232983593 & 120.398764370499 \tabularnewline
63 & 118.941161164663 & 116.15510508386 & 121.727217245466 \tabularnewline
64 & 119.31332365228 & 115.454164361597 & 123.172482942963 \tabularnewline
65 & 119.685486139898 & 114.646682746412 & 124.724289533383 \tabularnewline
66 & 120.057648627515 & 113.741012860257 & 126.374284394773 \tabularnewline
67 & 120.429811115132 & 112.743938030461 & 128.115684199803 \tabularnewline
68 & 120.801973602749 & 111.661059867273 & 129.942887338226 \tabularnewline
69 & 121.174136090367 & 110.49708803099 & 131.851184149744 \tabularnewline
70 & 121.546298577984 & 109.256046733088 & 133.83655042288 \tabularnewline
71 & 121.918461065601 & 107.941422728586 & 135.895499402617 \tabularnewline
72 & 122.290623553219 & 106.55627331683 & 138.024973789607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166450&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]61[/C][C]118.196836189428[/C][C]117.195626348919[/C][C]119.198046029938[/C][/ROW]
[ROW][C]62[/C][C]118.568998677046[/C][C]116.739232983593[/C][C]120.398764370499[/C][/ROW]
[ROW][C]63[/C][C]118.941161164663[/C][C]116.15510508386[/C][C]121.727217245466[/C][/ROW]
[ROW][C]64[/C][C]119.31332365228[/C][C]115.454164361597[/C][C]123.172482942963[/C][/ROW]
[ROW][C]65[/C][C]119.685486139898[/C][C]114.646682746412[/C][C]124.724289533383[/C][/ROW]
[ROW][C]66[/C][C]120.057648627515[/C][C]113.741012860257[/C][C]126.374284394773[/C][/ROW]
[ROW][C]67[/C][C]120.429811115132[/C][C]112.743938030461[/C][C]128.115684199803[/C][/ROW]
[ROW][C]68[/C][C]120.801973602749[/C][C]111.661059867273[/C][C]129.942887338226[/C][/ROW]
[ROW][C]69[/C][C]121.174136090367[/C][C]110.49708803099[/C][C]131.851184149744[/C][/ROW]
[ROW][C]70[/C][C]121.546298577984[/C][C]109.256046733088[/C][C]133.83655042288[/C][/ROW]
[ROW][C]71[/C][C]121.918461065601[/C][C]107.941422728586[/C][C]135.895499402617[/C][/ROW]
[ROW][C]72[/C][C]122.290623553219[/C][C]106.55627331683[/C][C]138.024973789607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166450&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166450&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
61118.196836189428117.195626348919119.198046029938
62118.568998677046116.739232983593120.398764370499
63118.941161164663116.15510508386121.727217245466
64119.31332365228115.454164361597123.172482942963
65119.685486139898114.646682746412124.724289533383
66120.057648627515113.741012860257126.374284394773
67120.429811115132112.743938030461128.115684199803
68120.801973602749111.661059867273129.942887338226
69121.174136090367110.49708803099131.851184149744
70121.546298577984109.256046733088133.83655042288
71121.918461065601107.941422728586135.895499402617
72122.290623553219106.55627331683138.024973789607



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')