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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 30 May 2008 06:35:20 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/30/t1212151364u4d7pwj76xtijz8.htm/, Retrieved Tue, 14 May 2024 23:23:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13543, Retrieved Tue, 14 May 2024 23:23:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact235
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [evolutie prijzen ...] [2008-05-30 12:35:20] [e120e668935a0d64689fc62dff0df290] [Current]
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Dataseries X:
2,9
2,9
2,9
2,9
2,9
2,9
2,9
2,9
2,95
2,96
2,96
2,96
2,96
2,96
2,96
2,96
2,96
2,96
2,96
2,96
3,04
3,04
3,04
3,04
3,04
3,04
3,04
3,04
3,04
3,03
3,03
3,03
3,15
3,15
3,15
3,15
3,15
3,15
3,15
3,15
3,15
3,15
3,15
3,15
3,26
3,26
3,27
3,27
3,27
3,27
3,27
3,27
3,27
3,27
3,27
3,27
3,32
3,32
3,32
3,32
3,32
3,32
3,32
3,32
3,32
3,32
3,32
3,33
3,41
3,42
3,42
3,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13543&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13543&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.973951087962422
beta0.0274509287970910
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.973951087962422 \tabularnewline
beta & 0.0274509287970910 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13543&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]0.973951087962422[/C][/ROW]
[ROW][C]beta[/C][C]0.0274509287970910[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13543&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
alpha0.973951087962422
beta0.0274509287970910
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32.92.90
42.92.90
52.92.90
62.92.90
72.92.90
82.92.90
92.952.90.0500000000000003
102.962.950034347496500.00996565250350345
112.962.96134363900266-0.00134363900266399
122.962.96160231039541-0.00160231039540637
132.962.9615662093542-0.00156620935420149
142.962.96152339500425-0.00152339500424858
152.962.96148155045846-0.00148155045845710
162.962.96144084992501-0.00144084992500959
172.962.96140126735568-0.00140126735568291
182.962.96136277218222-0.00136277218221537
192.962.96132533453587-0.00132533453587103
202.962.9612889253647-0.00128892536470238
213.042.961253516414770.0787464835852316
223.043.0412740362027-0.00127403620270128
233.043.0433244212278-0.00332442122780163
243.043.04328895025989-0.00328895025989473
253.043.04320009335961-0.00320009335960592
263.043.04311222147968-0.0031122214796806
273.043.04302672458892-0.00302672458891662
283.043.04294357539711-0.00294357539710655
293.043.04286271042562-0.00286271042561514
303.033.04278406695029-0.0127840669502941
313.033.03270071444433-0.00270071444433206
323.033.03236584815326-0.00236584815326335
333.153.032293872261040.117706127738959
343.153.15231310270680-0.00231310270680440
353.153.15537763028882-0.00537763028881821
363.153.15531368231713-0.00531368231712515
373.153.15516995066507-0.00516995066506531
383.153.15502798352454-0.00502798352454414
393.153.1548898579615-0.00488985796150088
403.153.15475552537336-0.00475552537335977
413.153.15462488308562-0.00462488308562259
423.153.15449782976037-0.00449782976036772
433.153.15437426680385-0.00437426680384734
443.153.15425409832979-0.00425409832978518
453.263.154137231086030.105862768913966
463.263.26409913887453-0.00409913887452928
473.273.266853932926860.00314606707313914
483.273.27674931600944-0.00674931600944406
493.273.27682663119174-0.00682663119173688
503.273.27664612929887-0.0066461292988742
513.273.27646373742539-0.00646373742539152
523.273.27628617272392-0.0062861727239234
533.273.27611348111038-0.00611348111038312
543.273.27594553349462-0.00594553349462412
553.273.27578219967912-0.00578219967911853
563.273.27562335291844-0.00562335291843619
573.323.275468869945720.0445311300542817
583.323.32535297837686-0.00535297837685977
593.323.32650928863846-0.00650928863845701
603.323.32636537782020-0.00636537782020508
613.323.32619144523719-0.0061914452371874
623.323.32602138085739-0.00602138085739101
633.323.32585596405786-0.00585596405786415
643.323.32569509088347-0.00569509088346587
653.323.32553863714854-0.00553863714854375
663.323.32538648146067-0.00538648146067366
673.323.32523850574572-0.00523850574572116
683.333.325094595172800.00490540482719526
693.413.334961507564930.075038492435072
703.423.41514083571090.0048591642890985
713.423.42709884480234-0.00709884480234191
723.423.42722054419455-0.00722054419454565

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.9 & 2.9 & 0 \tabularnewline
4 & 2.9 & 2.9 & 0 \tabularnewline
5 & 2.9 & 2.9 & 0 \tabularnewline
6 & 2.9 & 2.9 & 0 \tabularnewline
7 & 2.9 & 2.9 & 0 \tabularnewline
8 & 2.9 & 2.9 & 0 \tabularnewline
9 & 2.95 & 2.9 & 0.0500000000000003 \tabularnewline
10 & 2.96 & 2.95003434749650 & 0.00996565250350345 \tabularnewline
11 & 2.96 & 2.96134363900266 & -0.00134363900266399 \tabularnewline
12 & 2.96 & 2.96160231039541 & -0.00160231039540637 \tabularnewline
13 & 2.96 & 2.9615662093542 & -0.00156620935420149 \tabularnewline
14 & 2.96 & 2.96152339500425 & -0.00152339500424858 \tabularnewline
15 & 2.96 & 2.96148155045846 & -0.00148155045845710 \tabularnewline
16 & 2.96 & 2.96144084992501 & -0.00144084992500959 \tabularnewline
17 & 2.96 & 2.96140126735568 & -0.00140126735568291 \tabularnewline
18 & 2.96 & 2.96136277218222 & -0.00136277218221537 \tabularnewline
19 & 2.96 & 2.96132533453587 & -0.00132533453587103 \tabularnewline
20 & 2.96 & 2.9612889253647 & -0.00128892536470238 \tabularnewline
21 & 3.04 & 2.96125351641477 & 0.0787464835852316 \tabularnewline
22 & 3.04 & 3.0412740362027 & -0.00127403620270128 \tabularnewline
23 & 3.04 & 3.0433244212278 & -0.00332442122780163 \tabularnewline
24 & 3.04 & 3.04328895025989 & -0.00328895025989473 \tabularnewline
25 & 3.04 & 3.04320009335961 & -0.00320009335960592 \tabularnewline
26 & 3.04 & 3.04311222147968 & -0.0031122214796806 \tabularnewline
27 & 3.04 & 3.04302672458892 & -0.00302672458891662 \tabularnewline
28 & 3.04 & 3.04294357539711 & -0.00294357539710655 \tabularnewline
29 & 3.04 & 3.04286271042562 & -0.00286271042561514 \tabularnewline
30 & 3.03 & 3.04278406695029 & -0.0127840669502941 \tabularnewline
31 & 3.03 & 3.03270071444433 & -0.00270071444433206 \tabularnewline
32 & 3.03 & 3.03236584815326 & -0.00236584815326335 \tabularnewline
33 & 3.15 & 3.03229387226104 & 0.117706127738959 \tabularnewline
34 & 3.15 & 3.15231310270680 & -0.00231310270680440 \tabularnewline
35 & 3.15 & 3.15537763028882 & -0.00537763028881821 \tabularnewline
36 & 3.15 & 3.15531368231713 & -0.00531368231712515 \tabularnewline
37 & 3.15 & 3.15516995066507 & -0.00516995066506531 \tabularnewline
38 & 3.15 & 3.15502798352454 & -0.00502798352454414 \tabularnewline
39 & 3.15 & 3.1548898579615 & -0.00488985796150088 \tabularnewline
40 & 3.15 & 3.15475552537336 & -0.00475552537335977 \tabularnewline
41 & 3.15 & 3.15462488308562 & -0.00462488308562259 \tabularnewline
42 & 3.15 & 3.15449782976037 & -0.00449782976036772 \tabularnewline
43 & 3.15 & 3.15437426680385 & -0.00437426680384734 \tabularnewline
44 & 3.15 & 3.15425409832979 & -0.00425409832978518 \tabularnewline
45 & 3.26 & 3.15413723108603 & 0.105862768913966 \tabularnewline
46 & 3.26 & 3.26409913887453 & -0.00409913887452928 \tabularnewline
47 & 3.27 & 3.26685393292686 & 0.00314606707313914 \tabularnewline
48 & 3.27 & 3.27674931600944 & -0.00674931600944406 \tabularnewline
49 & 3.27 & 3.27682663119174 & -0.00682663119173688 \tabularnewline
50 & 3.27 & 3.27664612929887 & -0.0066461292988742 \tabularnewline
51 & 3.27 & 3.27646373742539 & -0.00646373742539152 \tabularnewline
52 & 3.27 & 3.27628617272392 & -0.0062861727239234 \tabularnewline
53 & 3.27 & 3.27611348111038 & -0.00611348111038312 \tabularnewline
54 & 3.27 & 3.27594553349462 & -0.00594553349462412 \tabularnewline
55 & 3.27 & 3.27578219967912 & -0.00578219967911853 \tabularnewline
56 & 3.27 & 3.27562335291844 & -0.00562335291843619 \tabularnewline
57 & 3.32 & 3.27546886994572 & 0.0445311300542817 \tabularnewline
58 & 3.32 & 3.32535297837686 & -0.00535297837685977 \tabularnewline
59 & 3.32 & 3.32650928863846 & -0.00650928863845701 \tabularnewline
60 & 3.32 & 3.32636537782020 & -0.00636537782020508 \tabularnewline
61 & 3.32 & 3.32619144523719 & -0.0061914452371874 \tabularnewline
62 & 3.32 & 3.32602138085739 & -0.00602138085739101 \tabularnewline
63 & 3.32 & 3.32585596405786 & -0.00585596405786415 \tabularnewline
64 & 3.32 & 3.32569509088347 & -0.00569509088346587 \tabularnewline
65 & 3.32 & 3.32553863714854 & -0.00553863714854375 \tabularnewline
66 & 3.32 & 3.32538648146067 & -0.00538648146067366 \tabularnewline
67 & 3.32 & 3.32523850574572 & -0.00523850574572116 \tabularnewline
68 & 3.33 & 3.32509459517280 & 0.00490540482719526 \tabularnewline
69 & 3.41 & 3.33496150756493 & 0.075038492435072 \tabularnewline
70 & 3.42 & 3.4151408357109 & 0.0048591642890985 \tabularnewline
71 & 3.42 & 3.42709884480234 & -0.00709884480234191 \tabularnewline
72 & 3.42 & 3.42722054419455 & -0.00722054419454565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13543&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]2.9[/C][C]2.9[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]2.9[/C][C]2.9[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]2.9[/C][C]2.9[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]2.9[/C][C]2.9[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]2.9[/C][C]2.9[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]2.9[/C][C]2.9[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]2.95[/C][C]2.9[/C][C]0.0500000000000003[/C][/ROW]
[ROW][C]10[/C][C]2.96[/C][C]2.95003434749650[/C][C]0.00996565250350345[/C][/ROW]
[ROW][C]11[/C][C]2.96[/C][C]2.96134363900266[/C][C]-0.00134363900266399[/C][/ROW]
[ROW][C]12[/C][C]2.96[/C][C]2.96160231039541[/C][C]-0.00160231039540637[/C][/ROW]
[ROW][C]13[/C][C]2.96[/C][C]2.9615662093542[/C][C]-0.00156620935420149[/C][/ROW]
[ROW][C]14[/C][C]2.96[/C][C]2.96152339500425[/C][C]-0.00152339500424858[/C][/ROW]
[ROW][C]15[/C][C]2.96[/C][C]2.96148155045846[/C][C]-0.00148155045845710[/C][/ROW]
[ROW][C]16[/C][C]2.96[/C][C]2.96144084992501[/C][C]-0.00144084992500959[/C][/ROW]
[ROW][C]17[/C][C]2.96[/C][C]2.96140126735568[/C][C]-0.00140126735568291[/C][/ROW]
[ROW][C]18[/C][C]2.96[/C][C]2.96136277218222[/C][C]-0.00136277218221537[/C][/ROW]
[ROW][C]19[/C][C]2.96[/C][C]2.96132533453587[/C][C]-0.00132533453587103[/C][/ROW]
[ROW][C]20[/C][C]2.96[/C][C]2.9612889253647[/C][C]-0.00128892536470238[/C][/ROW]
[ROW][C]21[/C][C]3.04[/C][C]2.96125351641477[/C][C]0.0787464835852316[/C][/ROW]
[ROW][C]22[/C][C]3.04[/C][C]3.0412740362027[/C][C]-0.00127403620270128[/C][/ROW]
[ROW][C]23[/C][C]3.04[/C][C]3.0433244212278[/C][C]-0.00332442122780163[/C][/ROW]
[ROW][C]24[/C][C]3.04[/C][C]3.04328895025989[/C][C]-0.00328895025989473[/C][/ROW]
[ROW][C]25[/C][C]3.04[/C][C]3.04320009335961[/C][C]-0.00320009335960592[/C][/ROW]
[ROW][C]26[/C][C]3.04[/C][C]3.04311222147968[/C][C]-0.0031122214796806[/C][/ROW]
[ROW][C]27[/C][C]3.04[/C][C]3.04302672458892[/C][C]-0.00302672458891662[/C][/ROW]
[ROW][C]28[/C][C]3.04[/C][C]3.04294357539711[/C][C]-0.00294357539710655[/C][/ROW]
[ROW][C]29[/C][C]3.04[/C][C]3.04286271042562[/C][C]-0.00286271042561514[/C][/ROW]
[ROW][C]30[/C][C]3.03[/C][C]3.04278406695029[/C][C]-0.0127840669502941[/C][/ROW]
[ROW][C]31[/C][C]3.03[/C][C]3.03270071444433[/C][C]-0.00270071444433206[/C][/ROW]
[ROW][C]32[/C][C]3.03[/C][C]3.03236584815326[/C][C]-0.00236584815326335[/C][/ROW]
[ROW][C]33[/C][C]3.15[/C][C]3.03229387226104[/C][C]0.117706127738959[/C][/ROW]
[ROW][C]34[/C][C]3.15[/C][C]3.15231310270680[/C][C]-0.00231310270680440[/C][/ROW]
[ROW][C]35[/C][C]3.15[/C][C]3.15537763028882[/C][C]-0.00537763028881821[/C][/ROW]
[ROW][C]36[/C][C]3.15[/C][C]3.15531368231713[/C][C]-0.00531368231712515[/C][/ROW]
[ROW][C]37[/C][C]3.15[/C][C]3.15516995066507[/C][C]-0.00516995066506531[/C][/ROW]
[ROW][C]38[/C][C]3.15[/C][C]3.15502798352454[/C][C]-0.00502798352454414[/C][/ROW]
[ROW][C]39[/C][C]3.15[/C][C]3.1548898579615[/C][C]-0.00488985796150088[/C][/ROW]
[ROW][C]40[/C][C]3.15[/C][C]3.15475552537336[/C][C]-0.00475552537335977[/C][/ROW]
[ROW][C]41[/C][C]3.15[/C][C]3.15462488308562[/C][C]-0.00462488308562259[/C][/ROW]
[ROW][C]42[/C][C]3.15[/C][C]3.15449782976037[/C][C]-0.00449782976036772[/C][/ROW]
[ROW][C]43[/C][C]3.15[/C][C]3.15437426680385[/C][C]-0.00437426680384734[/C][/ROW]
[ROW][C]44[/C][C]3.15[/C][C]3.15425409832979[/C][C]-0.00425409832978518[/C][/ROW]
[ROW][C]45[/C][C]3.26[/C][C]3.15413723108603[/C][C]0.105862768913966[/C][/ROW]
[ROW][C]46[/C][C]3.26[/C][C]3.26409913887453[/C][C]-0.00409913887452928[/C][/ROW]
[ROW][C]47[/C][C]3.27[/C][C]3.26685393292686[/C][C]0.00314606707313914[/C][/ROW]
[ROW][C]48[/C][C]3.27[/C][C]3.27674931600944[/C][C]-0.00674931600944406[/C][/ROW]
[ROW][C]49[/C][C]3.27[/C][C]3.27682663119174[/C][C]-0.00682663119173688[/C][/ROW]
[ROW][C]50[/C][C]3.27[/C][C]3.27664612929887[/C][C]-0.0066461292988742[/C][/ROW]
[ROW][C]51[/C][C]3.27[/C][C]3.27646373742539[/C][C]-0.00646373742539152[/C][/ROW]
[ROW][C]52[/C][C]3.27[/C][C]3.27628617272392[/C][C]-0.0062861727239234[/C][/ROW]
[ROW][C]53[/C][C]3.27[/C][C]3.27611348111038[/C][C]-0.00611348111038312[/C][/ROW]
[ROW][C]54[/C][C]3.27[/C][C]3.27594553349462[/C][C]-0.00594553349462412[/C][/ROW]
[ROW][C]55[/C][C]3.27[/C][C]3.27578219967912[/C][C]-0.00578219967911853[/C][/ROW]
[ROW][C]56[/C][C]3.27[/C][C]3.27562335291844[/C][C]-0.00562335291843619[/C][/ROW]
[ROW][C]57[/C][C]3.32[/C][C]3.27546886994572[/C][C]0.0445311300542817[/C][/ROW]
[ROW][C]58[/C][C]3.32[/C][C]3.32535297837686[/C][C]-0.00535297837685977[/C][/ROW]
[ROW][C]59[/C][C]3.32[/C][C]3.32650928863846[/C][C]-0.00650928863845701[/C][/ROW]
[ROW][C]60[/C][C]3.32[/C][C]3.32636537782020[/C][C]-0.00636537782020508[/C][/ROW]
[ROW][C]61[/C][C]3.32[/C][C]3.32619144523719[/C][C]-0.0061914452371874[/C][/ROW]
[ROW][C]62[/C][C]3.32[/C][C]3.32602138085739[/C][C]-0.00602138085739101[/C][/ROW]
[ROW][C]63[/C][C]3.32[/C][C]3.32585596405786[/C][C]-0.00585596405786415[/C][/ROW]
[ROW][C]64[/C][C]3.32[/C][C]3.32569509088347[/C][C]-0.00569509088346587[/C][/ROW]
[ROW][C]65[/C][C]3.32[/C][C]3.32553863714854[/C][C]-0.00553863714854375[/C][/ROW]
[ROW][C]66[/C][C]3.32[/C][C]3.32538648146067[/C][C]-0.00538648146067366[/C][/ROW]
[ROW][C]67[/C][C]3.32[/C][C]3.32523850574572[/C][C]-0.00523850574572116[/C][/ROW]
[ROW][C]68[/C][C]3.33[/C][C]3.32509459517280[/C][C]0.00490540482719526[/C][/ROW]
[ROW][C]69[/C][C]3.41[/C][C]3.33496150756493[/C][C]0.075038492435072[/C][/ROW]
[ROW][C]70[/C][C]3.42[/C][C]3.4151408357109[/C][C]0.0048591642890985[/C][/ROW]
[ROW][C]71[/C][C]3.42[/C][C]3.42709884480234[/C][C]-0.00709884480234191[/C][/ROW]
[ROW][C]72[/C][C]3.42[/C][C]3.42722054419455[/C][C]-0.00722054419454565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13543&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13543&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
32.92.90
42.92.90
52.92.90
62.92.90
72.92.90
82.92.90
92.952.90.0500000000000003
102.962.950034347496500.00996565250350345
112.962.96134363900266-0.00134363900266399
122.962.96160231039541-0.00160231039540637
132.962.9615662093542-0.00156620935420149
142.962.96152339500425-0.00152339500424858
152.962.96148155045846-0.00148155045845710
162.962.96144084992501-0.00144084992500959
172.962.96140126735568-0.00140126735568291
182.962.96136277218222-0.00136277218221537
192.962.96132533453587-0.00132533453587103
202.962.9612889253647-0.00128892536470238
213.042.961253516414770.0787464835852316
223.043.0412740362027-0.00127403620270128
233.043.0433244212278-0.00332442122780163
243.043.04328895025989-0.00328895025989473
253.043.04320009335961-0.00320009335960592
263.043.04311222147968-0.0031122214796806
273.043.04302672458892-0.00302672458891662
283.043.04294357539711-0.00294357539710655
293.043.04286271042562-0.00286271042561514
303.033.04278406695029-0.0127840669502941
313.033.03270071444433-0.00270071444433206
323.033.03236584815326-0.00236584815326335
333.153.032293872261040.117706127738959
343.153.15231310270680-0.00231310270680440
353.153.15537763028882-0.00537763028881821
363.153.15531368231713-0.00531368231712515
373.153.15516995066507-0.00516995066506531
383.153.15502798352454-0.00502798352454414
393.153.1548898579615-0.00488985796150088
403.153.15475552537336-0.00475552537335977
413.153.15462488308562-0.00462488308562259
423.153.15449782976037-0.00449782976036772
433.153.15437426680385-0.00437426680384734
443.153.15425409832979-0.00425409832978518
453.263.154137231086030.105862768913966
463.263.26409913887453-0.00409913887452928
473.273.266853932926860.00314606707313914
483.273.27674931600944-0.00674931600944406
493.273.27682663119174-0.00682663119173688
503.273.27664612929887-0.0066461292988742
513.273.27646373742539-0.00646373742539152
523.273.27628617272392-0.0062861727239234
533.273.27611348111038-0.00611348111038312
543.273.27594553349462-0.00594553349462412
553.273.27578219967912-0.00578219967911853
563.273.27562335291844-0.00562335291843619
573.323.275468869945720.0445311300542817
583.323.32535297837686-0.00535297837685977
593.323.32650928863846-0.00650928863845701
603.323.32636537782020-0.00636537782020508
613.323.32619144523719-0.0061914452371874
623.323.32602138085739-0.00602138085739101
633.323.32585596405786-0.00585596405786415
643.323.32569509088347-0.00569509088346587
653.323.32553863714854-0.00553863714854375
663.323.32538648146067-0.00538648146067366
673.323.32523850574572-0.00523850574572116
683.333.325094595172800.00490540482719526
693.413.334961507564930.075038492435072
703.423.41514083571090.0048591642890985
713.423.42709884480234-0.00709884480234191
723.423.42722054419455-0.00722054419454565







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733.427030666858393.378721760323733.47533957339305
743.43387324639623.365530665658693.50221582713371
753.440715825934003.356251574343253.52518007752476
763.447558405471813.348929853954193.54618695698943
773.454400985009613.342802647952043.56599932206719
783.461243564547423.337480326327973.58500680276687
793.468086144085233.332733351593803.60343893657665
803.474928723623033.328413730891493.62144371635457
813.481771303160843.324419882851473.6391227234702
823.488613882698643.320678794259383.6565489711379
833.495456462236453.317136096541943.67377682793096
843.502299041774253.313750155515383.69084792803312

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3.42703066685839 & 3.37872176032373 & 3.47533957339305 \tabularnewline
74 & 3.4338732463962 & 3.36553066565869 & 3.50221582713371 \tabularnewline
75 & 3.44071582593400 & 3.35625157434325 & 3.52518007752476 \tabularnewline
76 & 3.44755840547181 & 3.34892985395419 & 3.54618695698943 \tabularnewline
77 & 3.45440098500961 & 3.34280264795204 & 3.56599932206719 \tabularnewline
78 & 3.46124356454742 & 3.33748032632797 & 3.58500680276687 \tabularnewline
79 & 3.46808614408523 & 3.33273335159380 & 3.60343893657665 \tabularnewline
80 & 3.47492872362303 & 3.32841373089149 & 3.62144371635457 \tabularnewline
81 & 3.48177130316084 & 3.32441988285147 & 3.6391227234702 \tabularnewline
82 & 3.48861388269864 & 3.32067879425938 & 3.6565489711379 \tabularnewline
83 & 3.49545646223645 & 3.31713609654194 & 3.67377682793096 \tabularnewline
84 & 3.50229904177425 & 3.31375015551538 & 3.69084792803312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13543&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]3.42703066685839[/C][C]3.37872176032373[/C][C]3.47533957339305[/C][/ROW]
[ROW][C]74[/C][C]3.4338732463962[/C][C]3.36553066565869[/C][C]3.50221582713371[/C][/ROW]
[ROW][C]75[/C][C]3.44071582593400[/C][C]3.35625157434325[/C][C]3.52518007752476[/C][/ROW]
[ROW][C]76[/C][C]3.44755840547181[/C][C]3.34892985395419[/C][C]3.54618695698943[/C][/ROW]
[ROW][C]77[/C][C]3.45440098500961[/C][C]3.34280264795204[/C][C]3.56599932206719[/C][/ROW]
[ROW][C]78[/C][C]3.46124356454742[/C][C]3.33748032632797[/C][C]3.58500680276687[/C][/ROW]
[ROW][C]79[/C][C]3.46808614408523[/C][C]3.33273335159380[/C][C]3.60343893657665[/C][/ROW]
[ROW][C]80[/C][C]3.47492872362303[/C][C]3.32841373089149[/C][C]3.62144371635457[/C][/ROW]
[ROW][C]81[/C][C]3.48177130316084[/C][C]3.32441988285147[/C][C]3.6391227234702[/C][/ROW]
[ROW][C]82[/C][C]3.48861388269864[/C][C]3.32067879425938[/C][C]3.6565489711379[/C][/ROW]
[ROW][C]83[/C][C]3.49545646223645[/C][C]3.31713609654194[/C][C]3.67377682793096[/C][/ROW]
[ROW][C]84[/C][C]3.50229904177425[/C][C]3.31375015551538[/C][C]3.69084792803312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13543&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13543&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
733.427030666858393.378721760323733.47533957339305
743.43387324639623.365530665658693.50221582713371
753.440715825934003.356251574343253.52518007752476
763.447558405471813.348929853954193.54618695698943
773.454400985009613.342802647952043.56599932206719
783.461243564547423.337480326327973.58500680276687
793.468086144085233.332733351593803.60343893657665
803.474928723623033.328413730891493.62144371635457
813.481771303160843.324419882851473.6391227234702
823.488613882698643.320678794259383.6565489711379
833.495456462236453.317136096541943.67377682793096
843.502299041774253.313750155515383.69084792803312



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')