Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 16:38:35 -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/28/t1338237593dttofpozj08oekw.htm/, Retrieved Thu, 02 May 2024 04:01:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167878, Retrieved Thu, 02 May 2024 04:01:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-28 20:38:35] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
Dataseries X:
2,58
2,59
2,6
2,6
2,61
2,62
2,64
2,65
2,66
2,67
2,68
2,69
2,69
2,71
2,72
2,73
2,73
2,74
2,74
2,74
2,74
2,74
2,75
2,75
2,75
2,75
2,77
2,78
2,79
2,8
2,82
2,83
2,84
2,87
2,89
2,9
2,9
2,91
2,92
2,92
2,92
2,92
2,94
2,95
2,95
2,97
2,99
3
3
3,01
3,03
3,03
3,04
3,04
3,05
3,05
3,09
3,09
3,09
3,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'AstonUniversity' @ aston.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 & 12 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167878&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]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167878&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 time12 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99801135679491
beta0.00177219161837201
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99801135679491 \tabularnewline
beta & 0.00177219161837201 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167878&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]0.99801135679491[/C][/ROW]
[ROW][C]beta[/C][C]0.00177219161837201[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167878&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
alpha0.99801135679491
beta0.00177219161837201
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32.62.64.44089209850063e-16
42.62.61-0.00999999999999979
52.612.61000219975844-2.1997584354061e-06
62.622.619982313810281.76861897225322e-05
72.642.629982305545210.0100176944547909
82.652.649980137065941.98629340579792e-05
92.662.66000005431658-5.43165841193627e-08
102.672.67000009382882-9.38288216012495e-08
112.682.68000009374145-9.37414452728547e-08
122.692.69000009357547-9.35754744801898e-08
132.692.70000009340964-0.0100000934096398
142.712.700002293002540.00999770699746483
152.722.71998020713071.97928693044247e-05
162.732.73000008464883-8.46488297234771e-08
172.732.74000012402841-0.0100001240284056
182.742.74000232364579-2.32364578733879e-06
192.742.74998243747823-0.00998243747823446
202.742.74998462875244-0.009984628752437
212.742.74996697362311-0.00996697362310783
222.742.74994931025241-0.00994931025241375
232.752.749931678105966.83218940413788e-05
242.752.75991187744856-0.00991187744856337
252.752.75991419369004-0.00991419369003665
262.752.75989666338542-0.00989666338541895
272.772.759879124618380.0101208753816207
282.782.779857217337890.000142782662114094
292.792.789877312739210.000122687260793786
302.82.799877569694740.000122430305256493
312.822.809877786744220.0101222132557788
322.832.829875803572020.000124196427983669
332.842.839895905722410.00010409427758562
342.872.849896129806570.02010387019343
352.892.879891914447140.0101080855528561
362.92.899929670337357.03296626456407e-05
372.92.90994975624218-0.00994975624217842
382.912.909952084808814.7915191193848e-05
392.922.919932287753486.77122465213564e-05
402.922.92993236814464-0.00993236814463971
412.922.9299346876812-0.00993468768119898
422.922.92991712113608-0.0099171211360809
432.942.929899546114020.0101004538859835
442.952.949877602642590.000122397357408488
452.952.95989766191712-0.00989766191711805
462.972.959900082568320.0100999174316798
472.992.979878177912350.0101218220876542
4832.999896036488170.000103963511833172
4933.00991614231142-0.00991614231142357
503.013.009918530369528.14696304756168e-05
513.033.019898792779140.0101012072208548
523.033.03989673277159-0.00989673277159309
533.043.039918997510848.10024891646499e-05
543.043.04989929862187-0.00989929862186578
553.053.049901637313489.83626865194154e-05
563.053.05988192950313-0.00988192950312605
573.093.059884298897190.0301157011028077
583.093.09985802253848-0.009858022538479
593.093.09992008044967-0.00992008044966708
603.13.09990265853829.73414618048452e-05

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.6 & 2.6 & 4.44089209850063e-16 \tabularnewline
4 & 2.6 & 2.61 & -0.00999999999999979 \tabularnewline
5 & 2.61 & 2.61000219975844 & -2.1997584354061e-06 \tabularnewline
6 & 2.62 & 2.61998231381028 & 1.76861897225322e-05 \tabularnewline
7 & 2.64 & 2.62998230554521 & 0.0100176944547909 \tabularnewline
8 & 2.65 & 2.64998013706594 & 1.98629340579792e-05 \tabularnewline
9 & 2.66 & 2.66000005431658 & -5.43165841193627e-08 \tabularnewline
10 & 2.67 & 2.67000009382882 & -9.38288216012495e-08 \tabularnewline
11 & 2.68 & 2.68000009374145 & -9.37414452728547e-08 \tabularnewline
12 & 2.69 & 2.69000009357547 & -9.35754744801898e-08 \tabularnewline
13 & 2.69 & 2.70000009340964 & -0.0100000934096398 \tabularnewline
14 & 2.71 & 2.70000229300254 & 0.00999770699746483 \tabularnewline
15 & 2.72 & 2.7199802071307 & 1.97928693044247e-05 \tabularnewline
16 & 2.73 & 2.73000008464883 & -8.46488297234771e-08 \tabularnewline
17 & 2.73 & 2.74000012402841 & -0.0100001240284056 \tabularnewline
18 & 2.74 & 2.74000232364579 & -2.32364578733879e-06 \tabularnewline
19 & 2.74 & 2.74998243747823 & -0.00998243747823446 \tabularnewline
20 & 2.74 & 2.74998462875244 & -0.009984628752437 \tabularnewline
21 & 2.74 & 2.74996697362311 & -0.00996697362310783 \tabularnewline
22 & 2.74 & 2.74994931025241 & -0.00994931025241375 \tabularnewline
23 & 2.75 & 2.74993167810596 & 6.83218940413788e-05 \tabularnewline
24 & 2.75 & 2.75991187744856 & -0.00991187744856337 \tabularnewline
25 & 2.75 & 2.75991419369004 & -0.00991419369003665 \tabularnewline
26 & 2.75 & 2.75989666338542 & -0.00989666338541895 \tabularnewline
27 & 2.77 & 2.75987912461838 & 0.0101208753816207 \tabularnewline
28 & 2.78 & 2.77985721733789 & 0.000142782662114094 \tabularnewline
29 & 2.79 & 2.78987731273921 & 0.000122687260793786 \tabularnewline
30 & 2.8 & 2.79987756969474 & 0.000122430305256493 \tabularnewline
31 & 2.82 & 2.80987778674422 & 0.0101222132557788 \tabularnewline
32 & 2.83 & 2.82987580357202 & 0.000124196427983669 \tabularnewline
33 & 2.84 & 2.83989590572241 & 0.00010409427758562 \tabularnewline
34 & 2.87 & 2.84989612980657 & 0.02010387019343 \tabularnewline
35 & 2.89 & 2.87989191444714 & 0.0101080855528561 \tabularnewline
36 & 2.9 & 2.89992967033735 & 7.03296626456407e-05 \tabularnewline
37 & 2.9 & 2.90994975624218 & -0.00994975624217842 \tabularnewline
38 & 2.91 & 2.90995208480881 & 4.7915191193848e-05 \tabularnewline
39 & 2.92 & 2.91993228775348 & 6.77122465213564e-05 \tabularnewline
40 & 2.92 & 2.92993236814464 & -0.00993236814463971 \tabularnewline
41 & 2.92 & 2.9299346876812 & -0.00993468768119898 \tabularnewline
42 & 2.92 & 2.92991712113608 & -0.0099171211360809 \tabularnewline
43 & 2.94 & 2.92989954611402 & 0.0101004538859835 \tabularnewline
44 & 2.95 & 2.94987760264259 & 0.000122397357408488 \tabularnewline
45 & 2.95 & 2.95989766191712 & -0.00989766191711805 \tabularnewline
46 & 2.97 & 2.95990008256832 & 0.0100999174316798 \tabularnewline
47 & 2.99 & 2.97987817791235 & 0.0101218220876542 \tabularnewline
48 & 3 & 2.99989603648817 & 0.000103963511833172 \tabularnewline
49 & 3 & 3.00991614231142 & -0.00991614231142357 \tabularnewline
50 & 3.01 & 3.00991853036952 & 8.14696304756168e-05 \tabularnewline
51 & 3.03 & 3.01989879277914 & 0.0101012072208548 \tabularnewline
52 & 3.03 & 3.03989673277159 & -0.00989673277159309 \tabularnewline
53 & 3.04 & 3.03991899751084 & 8.10024891646499e-05 \tabularnewline
54 & 3.04 & 3.04989929862187 & -0.00989929862186578 \tabularnewline
55 & 3.05 & 3.04990163731348 & 9.83626865194154e-05 \tabularnewline
56 & 3.05 & 3.05988192950313 & -0.00988192950312605 \tabularnewline
57 & 3.09 & 3.05988429889719 & 0.0301157011028077 \tabularnewline
58 & 3.09 & 3.09985802253848 & -0.009858022538479 \tabularnewline
59 & 3.09 & 3.09992008044967 & -0.00992008044966708 \tabularnewline
60 & 3.1 & 3.0999026585382 & 9.73414618048452e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167878&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]2.6[/C][C]2.6[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]4[/C][C]2.6[/C][C]2.61[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]5[/C][C]2.61[/C][C]2.61000219975844[/C][C]-2.1997584354061e-06[/C][/ROW]
[ROW][C]6[/C][C]2.62[/C][C]2.61998231381028[/C][C]1.76861897225322e-05[/C][/ROW]
[ROW][C]7[/C][C]2.64[/C][C]2.62998230554521[/C][C]0.0100176944547909[/C][/ROW]
[ROW][C]8[/C][C]2.65[/C][C]2.64998013706594[/C][C]1.98629340579792e-05[/C][/ROW]
[ROW][C]9[/C][C]2.66[/C][C]2.66000005431658[/C][C]-5.43165841193627e-08[/C][/ROW]
[ROW][C]10[/C][C]2.67[/C][C]2.67000009382882[/C][C]-9.38288216012495e-08[/C][/ROW]
[ROW][C]11[/C][C]2.68[/C][C]2.68000009374145[/C][C]-9.37414452728547e-08[/C][/ROW]
[ROW][C]12[/C][C]2.69[/C][C]2.69000009357547[/C][C]-9.35754744801898e-08[/C][/ROW]
[ROW][C]13[/C][C]2.69[/C][C]2.70000009340964[/C][C]-0.0100000934096398[/C][/ROW]
[ROW][C]14[/C][C]2.71[/C][C]2.70000229300254[/C][C]0.00999770699746483[/C][/ROW]
[ROW][C]15[/C][C]2.72[/C][C]2.7199802071307[/C][C]1.97928693044247e-05[/C][/ROW]
[ROW][C]16[/C][C]2.73[/C][C]2.73000008464883[/C][C]-8.46488297234771e-08[/C][/ROW]
[ROW][C]17[/C][C]2.73[/C][C]2.74000012402841[/C][C]-0.0100001240284056[/C][/ROW]
[ROW][C]18[/C][C]2.74[/C][C]2.74000232364579[/C][C]-2.32364578733879e-06[/C][/ROW]
[ROW][C]19[/C][C]2.74[/C][C]2.74998243747823[/C][C]-0.00998243747823446[/C][/ROW]
[ROW][C]20[/C][C]2.74[/C][C]2.74998462875244[/C][C]-0.009984628752437[/C][/ROW]
[ROW][C]21[/C][C]2.74[/C][C]2.74996697362311[/C][C]-0.00996697362310783[/C][/ROW]
[ROW][C]22[/C][C]2.74[/C][C]2.74994931025241[/C][C]-0.00994931025241375[/C][/ROW]
[ROW][C]23[/C][C]2.75[/C][C]2.74993167810596[/C][C]6.83218940413788e-05[/C][/ROW]
[ROW][C]24[/C][C]2.75[/C][C]2.75991187744856[/C][C]-0.00991187744856337[/C][/ROW]
[ROW][C]25[/C][C]2.75[/C][C]2.75991419369004[/C][C]-0.00991419369003665[/C][/ROW]
[ROW][C]26[/C][C]2.75[/C][C]2.75989666338542[/C][C]-0.00989666338541895[/C][/ROW]
[ROW][C]27[/C][C]2.77[/C][C]2.75987912461838[/C][C]0.0101208753816207[/C][/ROW]
[ROW][C]28[/C][C]2.78[/C][C]2.77985721733789[/C][C]0.000142782662114094[/C][/ROW]
[ROW][C]29[/C][C]2.79[/C][C]2.78987731273921[/C][C]0.000122687260793786[/C][/ROW]
[ROW][C]30[/C][C]2.8[/C][C]2.79987756969474[/C][C]0.000122430305256493[/C][/ROW]
[ROW][C]31[/C][C]2.82[/C][C]2.80987778674422[/C][C]0.0101222132557788[/C][/ROW]
[ROW][C]32[/C][C]2.83[/C][C]2.82987580357202[/C][C]0.000124196427983669[/C][/ROW]
[ROW][C]33[/C][C]2.84[/C][C]2.83989590572241[/C][C]0.00010409427758562[/C][/ROW]
[ROW][C]34[/C][C]2.87[/C][C]2.84989612980657[/C][C]0.02010387019343[/C][/ROW]
[ROW][C]35[/C][C]2.89[/C][C]2.87989191444714[/C][C]0.0101080855528561[/C][/ROW]
[ROW][C]36[/C][C]2.9[/C][C]2.89992967033735[/C][C]7.03296626456407e-05[/C][/ROW]
[ROW][C]37[/C][C]2.9[/C][C]2.90994975624218[/C][C]-0.00994975624217842[/C][/ROW]
[ROW][C]38[/C][C]2.91[/C][C]2.90995208480881[/C][C]4.7915191193848e-05[/C][/ROW]
[ROW][C]39[/C][C]2.92[/C][C]2.91993228775348[/C][C]6.77122465213564e-05[/C][/ROW]
[ROW][C]40[/C][C]2.92[/C][C]2.92993236814464[/C][C]-0.00993236814463971[/C][/ROW]
[ROW][C]41[/C][C]2.92[/C][C]2.9299346876812[/C][C]-0.00993468768119898[/C][/ROW]
[ROW][C]42[/C][C]2.92[/C][C]2.92991712113608[/C][C]-0.0099171211360809[/C][/ROW]
[ROW][C]43[/C][C]2.94[/C][C]2.92989954611402[/C][C]0.0101004538859835[/C][/ROW]
[ROW][C]44[/C][C]2.95[/C][C]2.94987760264259[/C][C]0.000122397357408488[/C][/ROW]
[ROW][C]45[/C][C]2.95[/C][C]2.95989766191712[/C][C]-0.00989766191711805[/C][/ROW]
[ROW][C]46[/C][C]2.97[/C][C]2.95990008256832[/C][C]0.0100999174316798[/C][/ROW]
[ROW][C]47[/C][C]2.99[/C][C]2.97987817791235[/C][C]0.0101218220876542[/C][/ROW]
[ROW][C]48[/C][C]3[/C][C]2.99989603648817[/C][C]0.000103963511833172[/C][/ROW]
[ROW][C]49[/C][C]3[/C][C]3.00991614231142[/C][C]-0.00991614231142357[/C][/ROW]
[ROW][C]50[/C][C]3.01[/C][C]3.00991853036952[/C][C]8.14696304756168e-05[/C][/ROW]
[ROW][C]51[/C][C]3.03[/C][C]3.01989879277914[/C][C]0.0101012072208548[/C][/ROW]
[ROW][C]52[/C][C]3.03[/C][C]3.03989673277159[/C][C]-0.00989673277159309[/C][/ROW]
[ROW][C]53[/C][C]3.04[/C][C]3.03991899751084[/C][C]8.10024891646499e-05[/C][/ROW]
[ROW][C]54[/C][C]3.04[/C][C]3.04989929862187[/C][C]-0.00989929862186578[/C][/ROW]
[ROW][C]55[/C][C]3.05[/C][C]3.04990163731348[/C][C]9.83626865194154e-05[/C][/ROW]
[ROW][C]56[/C][C]3.05[/C][C]3.05988192950313[/C][C]-0.00988192950312605[/C][/ROW]
[ROW][C]57[/C][C]3.09[/C][C]3.05988429889719[/C][C]0.0301157011028077[/C][/ROW]
[ROW][C]58[/C][C]3.09[/C][C]3.09985802253848[/C][C]-0.009858022538479[/C][/ROW]
[ROW][C]59[/C][C]3.09[/C][C]3.09992008044967[/C][C]-0.00992008044966708[/C][/ROW]
[ROW][C]60[/C][C]3.1[/C][C]3.0999026585382[/C][C]9.73414618048452e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167878&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167878&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
32.62.64.44089209850063e-16
42.62.61-0.00999999999999979
52.612.61000219975844-2.1997584354061e-06
62.622.619982313810281.76861897225322e-05
72.642.629982305545210.0100176944547909
82.652.649980137065941.98629340579792e-05
92.662.66000005431658-5.43165841193627e-08
102.672.67000009382882-9.38288216012495e-08
112.682.68000009374145-9.37414452728547e-08
122.692.69000009357547-9.35754744801898e-08
132.692.70000009340964-0.0100000934096398
142.712.700002293002540.00999770699746483
152.722.71998020713071.97928693044247e-05
162.732.73000008464883-8.46488297234771e-08
172.732.74000012402841-0.0100001240284056
182.742.74000232364579-2.32364578733879e-06
192.742.74998243747823-0.00998243747823446
202.742.74998462875244-0.009984628752437
212.742.74996697362311-0.00996697362310783
222.742.74994931025241-0.00994931025241375
232.752.749931678105966.83218940413788e-05
242.752.75991187744856-0.00991187744856337
252.752.75991419369004-0.00991419369003665
262.752.75989666338542-0.00989666338541895
272.772.759879124618380.0101208753816207
282.782.779857217337890.000142782662114094
292.792.789877312739210.000122687260793786
302.82.799877569694740.000122430305256493
312.822.809877786744220.0101222132557788
322.832.829875803572020.000124196427983669
332.842.839895905722410.00010409427758562
342.872.849896129806570.02010387019343
352.892.879891914447140.0101080855528561
362.92.899929670337357.03296626456407e-05
372.92.90994975624218-0.00994975624217842
382.912.909952084808814.7915191193848e-05
392.922.919932287753486.77122465213564e-05
402.922.92993236814464-0.00993236814463971
412.922.9299346876812-0.00993468768119898
422.922.92991712113608-0.0099171211360809
432.942.929899546114020.0101004538859835
442.952.949877602642590.000122397357408488
452.952.95989766191712-0.00989766191711805
462.972.959900082568320.0100999174316798
472.992.979878177912350.0101218220876542
4832.999896036488170.000103963511833172
4933.00991614231142-0.00991614231142357
503.013.009918530369528.14696304756168e-05
513.033.019898792779140.0101012072208548
523.033.03989673277159-0.00989673277159309
533.043.039918997510848.10024891646499e-05
543.043.04989929862187-0.00989929862186578
553.053.049901637313489.83626865194154e-05
563.053.05988192950313-0.00988192950312605
573.093.059884298897190.0301157011028077
583.093.09985802253848-0.009858022538479
593.093.09992008044967-0.00992008044966708
603.13.09990265853829.73414618048452e-05







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
613.109882909624853.093010328578153.12675549067154
623.119766012827133.095907204203723.14362482145053
633.129649116029413.100411995817773.15888623624104
643.139532219231693.105747827564983.1733166108984
653.149415322433973.111613572526393.18721707234155
663.159298425636253.117854819293233.20074203197928
673.169181528838533.12437988229183.21398317538527
683.179064632040823.131129059060923.22700020502071
693.18894773524313.138060908277353.23983456220885
703.198830838445383.145145278752123.25251639813864
713.208713941647663.152359426115983.26506845717934
723.218597044849943.159685694131913.27750839556797

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 3.10988290962485 & 3.09301032857815 & 3.12675549067154 \tabularnewline
62 & 3.11976601282713 & 3.09590720420372 & 3.14362482145053 \tabularnewline
63 & 3.12964911602941 & 3.10041199581777 & 3.15888623624104 \tabularnewline
64 & 3.13953221923169 & 3.10574782756498 & 3.1733166108984 \tabularnewline
65 & 3.14941532243397 & 3.11161357252639 & 3.18721707234155 \tabularnewline
66 & 3.15929842563625 & 3.11785481929323 & 3.20074203197928 \tabularnewline
67 & 3.16918152883853 & 3.1243798822918 & 3.21398317538527 \tabularnewline
68 & 3.17906463204082 & 3.13112905906092 & 3.22700020502071 \tabularnewline
69 & 3.1889477352431 & 3.13806090827735 & 3.23983456220885 \tabularnewline
70 & 3.19883083844538 & 3.14514527875212 & 3.25251639813864 \tabularnewline
71 & 3.20871394164766 & 3.15235942611598 & 3.26506845717934 \tabularnewline
72 & 3.21859704484994 & 3.15968569413191 & 3.27750839556797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167878&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]3.10988290962485[/C][C]3.09301032857815[/C][C]3.12675549067154[/C][/ROW]
[ROW][C]62[/C][C]3.11976601282713[/C][C]3.09590720420372[/C][C]3.14362482145053[/C][/ROW]
[ROW][C]63[/C][C]3.12964911602941[/C][C]3.10041199581777[/C][C]3.15888623624104[/C][/ROW]
[ROW][C]64[/C][C]3.13953221923169[/C][C]3.10574782756498[/C][C]3.1733166108984[/C][/ROW]
[ROW][C]65[/C][C]3.14941532243397[/C][C]3.11161357252639[/C][C]3.18721707234155[/C][/ROW]
[ROW][C]66[/C][C]3.15929842563625[/C][C]3.11785481929323[/C][C]3.20074203197928[/C][/ROW]
[ROW][C]67[/C][C]3.16918152883853[/C][C]3.1243798822918[/C][C]3.21398317538527[/C][/ROW]
[ROW][C]68[/C][C]3.17906463204082[/C][C]3.13112905906092[/C][C]3.22700020502071[/C][/ROW]
[ROW][C]69[/C][C]3.1889477352431[/C][C]3.13806090827735[/C][C]3.23983456220885[/C][/ROW]
[ROW][C]70[/C][C]3.19883083844538[/C][C]3.14514527875212[/C][C]3.25251639813864[/C][/ROW]
[ROW][C]71[/C][C]3.20871394164766[/C][C]3.15235942611598[/C][C]3.26506845717934[/C][/ROW]
[ROW][C]72[/C][C]3.21859704484994[/C][C]3.15968569413191[/C][C]3.27750839556797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167878&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167878&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
613.109882909624853.093010328578153.12675549067154
623.119766012827133.095907204203723.14362482145053
633.129649116029413.100411995817773.15888623624104
643.139532219231693.105747827564983.1733166108984
653.149415322433973.111613572526393.18721707234155
663.159298425636253.117854819293233.20074203197928
673.169181528838533.12437988229183.21398317538527
683.179064632040823.131129059060923.22700020502071
693.18894773524313.138060908277353.23983456220885
703.198830838445383.145145278752123.25251639813864
713.208713941647663.152359426115983.26506845717934
723.218597044849943.159685694131913.27750839556797



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')