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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 15:43:21 -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/2013/May/26/t1369597448kqsbf7r9ztszwpo.htm/, Retrieved Mon, 29 Apr 2024 16:05:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210664, Retrieved Mon, 29 Apr 2024 16:05:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [750 simulaties] [2013-04-19 17:51:17] [434fbce84630be36f597b84053dc4988]
- R P   [Bootstrap Plot - Central Tendency] [Density plot 750 ...] [2013-05-26 16:43:22] [ab781ace6e9bb3bb317e6c6d3622dfa3]
- RM D      [Exponential Smoothing] [] [2013-05-26 19:43:21] [7c79942bdfef66f90cd0e05a66ee0483] [Current]
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Dataseries X:
0,6
0,59
0,61
0,61
0,6
0,6
0,58
0,63
0,65
0,62
0,61
0,67
0,66
0,59
0,54
0,53
0,5
0,5
0,52
0,53
0,54
0,54
0,55
0,52
0,47
0,47
0,44
0,45
0,43
0,41
0,4
0,37
0,37
0,4
0,45
0,4
0,38
0,43
0,53
0,59
0,57
0,61
0,57
0,56
0,53
0,55
0,55
0,58
0,58
0,56
0,52
0,49
0,48
0,46
0,47
0,44
0,45
0,45
0,43
0,44
0,45
0,45
0,45
0,46
0,46
0,45
0,43
0,44
0,47
0,47
0,5
0,51




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210664&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210664&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210664&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.029820328520941
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.029820328520941 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210664&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.029820328520941[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210664&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210664&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
alpha1
beta0.029820328520941
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.610.580.03
40.610.6008946098556280.00910539014437173
50.60.601166135581045-0.00116613558104472
60.60.5911313610349180.00886863896508194
70.580.59139582676239-0.0113958267623904
80.630.5710559994645680.0589440005354319
90.650.6228137289248730.0271862710751267
100.620.643624432459593-0.0236244324595929
110.610.612919944122527-0.00291994412252705
120.670.602832870429530.0671671295704696
130.660.664835816299131-0.00483581629913055
140.590.654691610668424-0.0646916106684235
150.540.582762485585742-0.0427624855857422
160.530.531487294217204-0.00148729421720351
170.50.521442942615039-0.0214429426150392
180.50.4908035070218030.00919649297819697
190.520.4910777494636530.0289222505363466
200.530.5119402204762120.0180597795237878
210.540.5224787690346270.0175212309653727
220.540.5330012578981060.006998742101894
230.550.5332099626868180.0167900373131822
240.520.543710647115376-0.0237106471153758
250.470.513003587828951-0.0430035878289512
260.470.4617212067123130.00827879328768727
270.440.461968083047908-0.0219680830479085
280.450.4313129875944450.0186870124055554
290.430.441870240443453-0.0118702404434531
300.410.421516265973807-0.0115162659738068
310.40.401172847139133-0.00117284713913329
320.370.39113787245214-0.0211378724521396
330.370.3605075341513830.00949246584861702
340.40.3607906026014630.0392093973985375
350.450.3919598397129950.0580401602870049
360.40.443690616360162-0.0436906163601616
370.380.392387747827019-0.0123877478270192
380.430.3720183411171830.057981658882817
390.530.4237473732332580.106252626766742
400.590.5269158614696550.0630841385303451
410.570.58879705120509-0.0187970512050903
420.610.568236516962930.0417634830370704
430.570.609481917747274-0.0394819177472738
440.560.568304553989413-0.00830455398941321
450.530.558056909461229-0.0280569094612291
460.550.5272202432038130.022779756796187
470.550.5478995430351020.00210045696489769
480.580.547962179351840.0320378206481602
490.580.5789175576886630.00108244231133714
500.560.578949836473992-0.0189498364739917
510.520.558384746124919-0.0383847461249194
520.490.517240100385281-0.0272401003852814
530.480.486427791642849-0.00642779164284885
540.460.476236112784395-0.0162361127843949
550.470.4557519465672610.0142480534327388
560.440.466176828201409-0.0261768282014094
570.450.4353962265848070.0146037734151929
580.450.4458317159056940.00416828409430642
590.430.445956015506754-0.0159560155067544
600.440.4254802018824580.0145197981175423
610.450.4359131870323810.0140868129676194
620.450.4463332604228880.00366673957711194
630.450.4464426038016780.00355739619832174
640.460.4465486865249910.0134513134750086
650.460.4569498091118540.00305019088814568
660.450.45704076680619-0.00704076680619037
670.430.44683080882699-0.0168308088269905
680.440.4263289085784960.0136710914215036
690.470.4367365850159250.0332634149840745
700.470.4677285109784790.00227148902152102
710.50.4677962475273320.0322037524726675
720.510.4987565740056740.0112434259943255

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.61 & 0.58 & 0.03 \tabularnewline
4 & 0.61 & 0.600894609855628 & 0.00910539014437173 \tabularnewline
5 & 0.6 & 0.601166135581045 & -0.00116613558104472 \tabularnewline
6 & 0.6 & 0.591131361034918 & 0.00886863896508194 \tabularnewline
7 & 0.58 & 0.59139582676239 & -0.0113958267623904 \tabularnewline
8 & 0.63 & 0.571055999464568 & 0.0589440005354319 \tabularnewline
9 & 0.65 & 0.622813728924873 & 0.0271862710751267 \tabularnewline
10 & 0.62 & 0.643624432459593 & -0.0236244324595929 \tabularnewline
11 & 0.61 & 0.612919944122527 & -0.00291994412252705 \tabularnewline
12 & 0.67 & 0.60283287042953 & 0.0671671295704696 \tabularnewline
13 & 0.66 & 0.664835816299131 & -0.00483581629913055 \tabularnewline
14 & 0.59 & 0.654691610668424 & -0.0646916106684235 \tabularnewline
15 & 0.54 & 0.582762485585742 & -0.0427624855857422 \tabularnewline
16 & 0.53 & 0.531487294217204 & -0.00148729421720351 \tabularnewline
17 & 0.5 & 0.521442942615039 & -0.0214429426150392 \tabularnewline
18 & 0.5 & 0.490803507021803 & 0.00919649297819697 \tabularnewline
19 & 0.52 & 0.491077749463653 & 0.0289222505363466 \tabularnewline
20 & 0.53 & 0.511940220476212 & 0.0180597795237878 \tabularnewline
21 & 0.54 & 0.522478769034627 & 0.0175212309653727 \tabularnewline
22 & 0.54 & 0.533001257898106 & 0.006998742101894 \tabularnewline
23 & 0.55 & 0.533209962686818 & 0.0167900373131822 \tabularnewline
24 & 0.52 & 0.543710647115376 & -0.0237106471153758 \tabularnewline
25 & 0.47 & 0.513003587828951 & -0.0430035878289512 \tabularnewline
26 & 0.47 & 0.461721206712313 & 0.00827879328768727 \tabularnewline
27 & 0.44 & 0.461968083047908 & -0.0219680830479085 \tabularnewline
28 & 0.45 & 0.431312987594445 & 0.0186870124055554 \tabularnewline
29 & 0.43 & 0.441870240443453 & -0.0118702404434531 \tabularnewline
30 & 0.41 & 0.421516265973807 & -0.0115162659738068 \tabularnewline
31 & 0.4 & 0.401172847139133 & -0.00117284713913329 \tabularnewline
32 & 0.37 & 0.39113787245214 & -0.0211378724521396 \tabularnewline
33 & 0.37 & 0.360507534151383 & 0.00949246584861702 \tabularnewline
34 & 0.4 & 0.360790602601463 & 0.0392093973985375 \tabularnewline
35 & 0.45 & 0.391959839712995 & 0.0580401602870049 \tabularnewline
36 & 0.4 & 0.443690616360162 & -0.0436906163601616 \tabularnewline
37 & 0.38 & 0.392387747827019 & -0.0123877478270192 \tabularnewline
38 & 0.43 & 0.372018341117183 & 0.057981658882817 \tabularnewline
39 & 0.53 & 0.423747373233258 & 0.106252626766742 \tabularnewline
40 & 0.59 & 0.526915861469655 & 0.0630841385303451 \tabularnewline
41 & 0.57 & 0.58879705120509 & -0.0187970512050903 \tabularnewline
42 & 0.61 & 0.56823651696293 & 0.0417634830370704 \tabularnewline
43 & 0.57 & 0.609481917747274 & -0.0394819177472738 \tabularnewline
44 & 0.56 & 0.568304553989413 & -0.00830455398941321 \tabularnewline
45 & 0.53 & 0.558056909461229 & -0.0280569094612291 \tabularnewline
46 & 0.55 & 0.527220243203813 & 0.022779756796187 \tabularnewline
47 & 0.55 & 0.547899543035102 & 0.00210045696489769 \tabularnewline
48 & 0.58 & 0.54796217935184 & 0.0320378206481602 \tabularnewline
49 & 0.58 & 0.578917557688663 & 0.00108244231133714 \tabularnewline
50 & 0.56 & 0.578949836473992 & -0.0189498364739917 \tabularnewline
51 & 0.52 & 0.558384746124919 & -0.0383847461249194 \tabularnewline
52 & 0.49 & 0.517240100385281 & -0.0272401003852814 \tabularnewline
53 & 0.48 & 0.486427791642849 & -0.00642779164284885 \tabularnewline
54 & 0.46 & 0.476236112784395 & -0.0162361127843949 \tabularnewline
55 & 0.47 & 0.455751946567261 & 0.0142480534327388 \tabularnewline
56 & 0.44 & 0.466176828201409 & -0.0261768282014094 \tabularnewline
57 & 0.45 & 0.435396226584807 & 0.0146037734151929 \tabularnewline
58 & 0.45 & 0.445831715905694 & 0.00416828409430642 \tabularnewline
59 & 0.43 & 0.445956015506754 & -0.0159560155067544 \tabularnewline
60 & 0.44 & 0.425480201882458 & 0.0145197981175423 \tabularnewline
61 & 0.45 & 0.435913187032381 & 0.0140868129676194 \tabularnewline
62 & 0.45 & 0.446333260422888 & 0.00366673957711194 \tabularnewline
63 & 0.45 & 0.446442603801678 & 0.00355739619832174 \tabularnewline
64 & 0.46 & 0.446548686524991 & 0.0134513134750086 \tabularnewline
65 & 0.46 & 0.456949809111854 & 0.00305019088814568 \tabularnewline
66 & 0.45 & 0.45704076680619 & -0.00704076680619037 \tabularnewline
67 & 0.43 & 0.44683080882699 & -0.0168308088269905 \tabularnewline
68 & 0.44 & 0.426328908578496 & 0.0136710914215036 \tabularnewline
69 & 0.47 & 0.436736585015925 & 0.0332634149840745 \tabularnewline
70 & 0.47 & 0.467728510978479 & 0.00227148902152102 \tabularnewline
71 & 0.5 & 0.467796247527332 & 0.0322037524726675 \tabularnewline
72 & 0.51 & 0.498756574005674 & 0.0112434259943255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210664&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]0.61[/C][C]0.58[/C][C]0.03[/C][/ROW]
[ROW][C]4[/C][C]0.61[/C][C]0.600894609855628[/C][C]0.00910539014437173[/C][/ROW]
[ROW][C]5[/C][C]0.6[/C][C]0.601166135581045[/C][C]-0.00116613558104472[/C][/ROW]
[ROW][C]6[/C][C]0.6[/C][C]0.591131361034918[/C][C]0.00886863896508194[/C][/ROW]
[ROW][C]7[/C][C]0.58[/C][C]0.59139582676239[/C][C]-0.0113958267623904[/C][/ROW]
[ROW][C]8[/C][C]0.63[/C][C]0.571055999464568[/C][C]0.0589440005354319[/C][/ROW]
[ROW][C]9[/C][C]0.65[/C][C]0.622813728924873[/C][C]0.0271862710751267[/C][/ROW]
[ROW][C]10[/C][C]0.62[/C][C]0.643624432459593[/C][C]-0.0236244324595929[/C][/ROW]
[ROW][C]11[/C][C]0.61[/C][C]0.612919944122527[/C][C]-0.00291994412252705[/C][/ROW]
[ROW][C]12[/C][C]0.67[/C][C]0.60283287042953[/C][C]0.0671671295704696[/C][/ROW]
[ROW][C]13[/C][C]0.66[/C][C]0.664835816299131[/C][C]-0.00483581629913055[/C][/ROW]
[ROW][C]14[/C][C]0.59[/C][C]0.654691610668424[/C][C]-0.0646916106684235[/C][/ROW]
[ROW][C]15[/C][C]0.54[/C][C]0.582762485585742[/C][C]-0.0427624855857422[/C][/ROW]
[ROW][C]16[/C][C]0.53[/C][C]0.531487294217204[/C][C]-0.00148729421720351[/C][/ROW]
[ROW][C]17[/C][C]0.5[/C][C]0.521442942615039[/C][C]-0.0214429426150392[/C][/ROW]
[ROW][C]18[/C][C]0.5[/C][C]0.490803507021803[/C][C]0.00919649297819697[/C][/ROW]
[ROW][C]19[/C][C]0.52[/C][C]0.491077749463653[/C][C]0.0289222505363466[/C][/ROW]
[ROW][C]20[/C][C]0.53[/C][C]0.511940220476212[/C][C]0.0180597795237878[/C][/ROW]
[ROW][C]21[/C][C]0.54[/C][C]0.522478769034627[/C][C]0.0175212309653727[/C][/ROW]
[ROW][C]22[/C][C]0.54[/C][C]0.533001257898106[/C][C]0.006998742101894[/C][/ROW]
[ROW][C]23[/C][C]0.55[/C][C]0.533209962686818[/C][C]0.0167900373131822[/C][/ROW]
[ROW][C]24[/C][C]0.52[/C][C]0.543710647115376[/C][C]-0.0237106471153758[/C][/ROW]
[ROW][C]25[/C][C]0.47[/C][C]0.513003587828951[/C][C]-0.0430035878289512[/C][/ROW]
[ROW][C]26[/C][C]0.47[/C][C]0.461721206712313[/C][C]0.00827879328768727[/C][/ROW]
[ROW][C]27[/C][C]0.44[/C][C]0.461968083047908[/C][C]-0.0219680830479085[/C][/ROW]
[ROW][C]28[/C][C]0.45[/C][C]0.431312987594445[/C][C]0.0186870124055554[/C][/ROW]
[ROW][C]29[/C][C]0.43[/C][C]0.441870240443453[/C][C]-0.0118702404434531[/C][/ROW]
[ROW][C]30[/C][C]0.41[/C][C]0.421516265973807[/C][C]-0.0115162659738068[/C][/ROW]
[ROW][C]31[/C][C]0.4[/C][C]0.401172847139133[/C][C]-0.00117284713913329[/C][/ROW]
[ROW][C]32[/C][C]0.37[/C][C]0.39113787245214[/C][C]-0.0211378724521396[/C][/ROW]
[ROW][C]33[/C][C]0.37[/C][C]0.360507534151383[/C][C]0.00949246584861702[/C][/ROW]
[ROW][C]34[/C][C]0.4[/C][C]0.360790602601463[/C][C]0.0392093973985375[/C][/ROW]
[ROW][C]35[/C][C]0.45[/C][C]0.391959839712995[/C][C]0.0580401602870049[/C][/ROW]
[ROW][C]36[/C][C]0.4[/C][C]0.443690616360162[/C][C]-0.0436906163601616[/C][/ROW]
[ROW][C]37[/C][C]0.38[/C][C]0.392387747827019[/C][C]-0.0123877478270192[/C][/ROW]
[ROW][C]38[/C][C]0.43[/C][C]0.372018341117183[/C][C]0.057981658882817[/C][/ROW]
[ROW][C]39[/C][C]0.53[/C][C]0.423747373233258[/C][C]0.106252626766742[/C][/ROW]
[ROW][C]40[/C][C]0.59[/C][C]0.526915861469655[/C][C]0.0630841385303451[/C][/ROW]
[ROW][C]41[/C][C]0.57[/C][C]0.58879705120509[/C][C]-0.0187970512050903[/C][/ROW]
[ROW][C]42[/C][C]0.61[/C][C]0.56823651696293[/C][C]0.0417634830370704[/C][/ROW]
[ROW][C]43[/C][C]0.57[/C][C]0.609481917747274[/C][C]-0.0394819177472738[/C][/ROW]
[ROW][C]44[/C][C]0.56[/C][C]0.568304553989413[/C][C]-0.00830455398941321[/C][/ROW]
[ROW][C]45[/C][C]0.53[/C][C]0.558056909461229[/C][C]-0.0280569094612291[/C][/ROW]
[ROW][C]46[/C][C]0.55[/C][C]0.527220243203813[/C][C]0.022779756796187[/C][/ROW]
[ROW][C]47[/C][C]0.55[/C][C]0.547899543035102[/C][C]0.00210045696489769[/C][/ROW]
[ROW][C]48[/C][C]0.58[/C][C]0.54796217935184[/C][C]0.0320378206481602[/C][/ROW]
[ROW][C]49[/C][C]0.58[/C][C]0.578917557688663[/C][C]0.00108244231133714[/C][/ROW]
[ROW][C]50[/C][C]0.56[/C][C]0.578949836473992[/C][C]-0.0189498364739917[/C][/ROW]
[ROW][C]51[/C][C]0.52[/C][C]0.558384746124919[/C][C]-0.0383847461249194[/C][/ROW]
[ROW][C]52[/C][C]0.49[/C][C]0.517240100385281[/C][C]-0.0272401003852814[/C][/ROW]
[ROW][C]53[/C][C]0.48[/C][C]0.486427791642849[/C][C]-0.00642779164284885[/C][/ROW]
[ROW][C]54[/C][C]0.46[/C][C]0.476236112784395[/C][C]-0.0162361127843949[/C][/ROW]
[ROW][C]55[/C][C]0.47[/C][C]0.455751946567261[/C][C]0.0142480534327388[/C][/ROW]
[ROW][C]56[/C][C]0.44[/C][C]0.466176828201409[/C][C]-0.0261768282014094[/C][/ROW]
[ROW][C]57[/C][C]0.45[/C][C]0.435396226584807[/C][C]0.0146037734151929[/C][/ROW]
[ROW][C]58[/C][C]0.45[/C][C]0.445831715905694[/C][C]0.00416828409430642[/C][/ROW]
[ROW][C]59[/C][C]0.43[/C][C]0.445956015506754[/C][C]-0.0159560155067544[/C][/ROW]
[ROW][C]60[/C][C]0.44[/C][C]0.425480201882458[/C][C]0.0145197981175423[/C][/ROW]
[ROW][C]61[/C][C]0.45[/C][C]0.435913187032381[/C][C]0.0140868129676194[/C][/ROW]
[ROW][C]62[/C][C]0.45[/C][C]0.446333260422888[/C][C]0.00366673957711194[/C][/ROW]
[ROW][C]63[/C][C]0.45[/C][C]0.446442603801678[/C][C]0.00355739619832174[/C][/ROW]
[ROW][C]64[/C][C]0.46[/C][C]0.446548686524991[/C][C]0.0134513134750086[/C][/ROW]
[ROW][C]65[/C][C]0.46[/C][C]0.456949809111854[/C][C]0.00305019088814568[/C][/ROW]
[ROW][C]66[/C][C]0.45[/C][C]0.45704076680619[/C][C]-0.00704076680619037[/C][/ROW]
[ROW][C]67[/C][C]0.43[/C][C]0.44683080882699[/C][C]-0.0168308088269905[/C][/ROW]
[ROW][C]68[/C][C]0.44[/C][C]0.426328908578496[/C][C]0.0136710914215036[/C][/ROW]
[ROW][C]69[/C][C]0.47[/C][C]0.436736585015925[/C][C]0.0332634149840745[/C][/ROW]
[ROW][C]70[/C][C]0.47[/C][C]0.467728510978479[/C][C]0.00227148902152102[/C][/ROW]
[ROW][C]71[/C][C]0.5[/C][C]0.467796247527332[/C][C]0.0322037524726675[/C][/ROW]
[ROW][C]72[/C][C]0.51[/C][C]0.498756574005674[/C][C]0.0112434259943255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210664&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210664&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
30.610.580.03
40.610.6008946098556280.00910539014437173
50.60.601166135581045-0.00116613558104472
60.60.5911313610349180.00886863896508194
70.580.59139582676239-0.0113958267623904
80.630.5710559994645680.0589440005354319
90.650.6228137289248730.0271862710751267
100.620.643624432459593-0.0236244324595929
110.610.612919944122527-0.00291994412252705
120.670.602832870429530.0671671295704696
130.660.664835816299131-0.00483581629913055
140.590.654691610668424-0.0646916106684235
150.540.582762485585742-0.0427624855857422
160.530.531487294217204-0.00148729421720351
170.50.521442942615039-0.0214429426150392
180.50.4908035070218030.00919649297819697
190.520.4910777494636530.0289222505363466
200.530.5119402204762120.0180597795237878
210.540.5224787690346270.0175212309653727
220.540.5330012578981060.006998742101894
230.550.5332099626868180.0167900373131822
240.520.543710647115376-0.0237106471153758
250.470.513003587828951-0.0430035878289512
260.470.4617212067123130.00827879328768727
270.440.461968083047908-0.0219680830479085
280.450.4313129875944450.0186870124055554
290.430.441870240443453-0.0118702404434531
300.410.421516265973807-0.0115162659738068
310.40.401172847139133-0.00117284713913329
320.370.39113787245214-0.0211378724521396
330.370.3605075341513830.00949246584861702
340.40.3607906026014630.0392093973985375
350.450.3919598397129950.0580401602870049
360.40.443690616360162-0.0436906163601616
370.380.392387747827019-0.0123877478270192
380.430.3720183411171830.057981658882817
390.530.4237473732332580.106252626766742
400.590.5269158614696550.0630841385303451
410.570.58879705120509-0.0187970512050903
420.610.568236516962930.0417634830370704
430.570.609481917747274-0.0394819177472738
440.560.568304553989413-0.00830455398941321
450.530.558056909461229-0.0280569094612291
460.550.5272202432038130.022779756796187
470.550.5478995430351020.00210045696489769
480.580.547962179351840.0320378206481602
490.580.5789175576886630.00108244231133714
500.560.578949836473992-0.0189498364739917
510.520.558384746124919-0.0383847461249194
520.490.517240100385281-0.0272401003852814
530.480.486427791642849-0.00642779164284885
540.460.476236112784395-0.0162361127843949
550.470.4557519465672610.0142480534327388
560.440.466176828201409-0.0261768282014094
570.450.4353962265848070.0146037734151929
580.450.4458317159056940.00416828409430642
590.430.445956015506754-0.0159560155067544
600.440.4254802018824580.0145197981175423
610.450.4359131870323810.0140868129676194
620.450.4463332604228880.00366673957711194
630.450.4464426038016780.00355739619832174
640.460.4465486865249910.0134513134750086
650.460.4569498091118540.00305019088814568
660.450.45704076680619-0.00704076680619037
670.430.44683080882699-0.0168308088269905
680.440.4263289085784960.0136710914215036
690.470.4367365850159250.0332634149840745
700.470.4677285109784790.00227148902152102
710.50.4677962475273320.0322037524726675
720.510.4987565740056740.0112434259943255







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.5090918566625260.4508158158497380.567367897475314
740.5081837133250520.424531102462960.591836324187144
750.5072755699875780.4032994809784930.611251658996664
760.5063674266501050.3845399246257750.628194928674434
770.5054592833126310.3672690565686040.643649510056657
780.5045511399751570.3509905245433660.658111755406948
790.5036429966376830.3354141294534370.671871863821929
800.5027348533002090.3203538066796480.685115899920771
810.5018267099627350.3056824114968530.697971008428617
820.5009185666252610.2913089039452890.710528229305234
830.5000104232877880.2771657223349490.722855124240626
840.4991022799503140.2632012923422690.735003267558359

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.509091856662526 & 0.450815815849738 & 0.567367897475314 \tabularnewline
74 & 0.508183713325052 & 0.42453110246296 & 0.591836324187144 \tabularnewline
75 & 0.507275569987578 & 0.403299480978493 & 0.611251658996664 \tabularnewline
76 & 0.506367426650105 & 0.384539924625775 & 0.628194928674434 \tabularnewline
77 & 0.505459283312631 & 0.367269056568604 & 0.643649510056657 \tabularnewline
78 & 0.504551139975157 & 0.350990524543366 & 0.658111755406948 \tabularnewline
79 & 0.503642996637683 & 0.335414129453437 & 0.671871863821929 \tabularnewline
80 & 0.502734853300209 & 0.320353806679648 & 0.685115899920771 \tabularnewline
81 & 0.501826709962735 & 0.305682411496853 & 0.697971008428617 \tabularnewline
82 & 0.500918566625261 & 0.291308903945289 & 0.710528229305234 \tabularnewline
83 & 0.500010423287788 & 0.277165722334949 & 0.722855124240626 \tabularnewline
84 & 0.499102279950314 & 0.263201292342269 & 0.735003267558359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210664&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]0.509091856662526[/C][C]0.450815815849738[/C][C]0.567367897475314[/C][/ROW]
[ROW][C]74[/C][C]0.508183713325052[/C][C]0.42453110246296[/C][C]0.591836324187144[/C][/ROW]
[ROW][C]75[/C][C]0.507275569987578[/C][C]0.403299480978493[/C][C]0.611251658996664[/C][/ROW]
[ROW][C]76[/C][C]0.506367426650105[/C][C]0.384539924625775[/C][C]0.628194928674434[/C][/ROW]
[ROW][C]77[/C][C]0.505459283312631[/C][C]0.367269056568604[/C][C]0.643649510056657[/C][/ROW]
[ROW][C]78[/C][C]0.504551139975157[/C][C]0.350990524543366[/C][C]0.658111755406948[/C][/ROW]
[ROW][C]79[/C][C]0.503642996637683[/C][C]0.335414129453437[/C][C]0.671871863821929[/C][/ROW]
[ROW][C]80[/C][C]0.502734853300209[/C][C]0.320353806679648[/C][C]0.685115899920771[/C][/ROW]
[ROW][C]81[/C][C]0.501826709962735[/C][C]0.305682411496853[/C][C]0.697971008428617[/C][/ROW]
[ROW][C]82[/C][C]0.500918566625261[/C][C]0.291308903945289[/C][C]0.710528229305234[/C][/ROW]
[ROW][C]83[/C][C]0.500010423287788[/C][C]0.277165722334949[/C][C]0.722855124240626[/C][/ROW]
[ROW][C]84[/C][C]0.499102279950314[/C][C]0.263201292342269[/C][C]0.735003267558359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210664&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210664&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
730.5090918566625260.4508158158497380.567367897475314
740.5081837133250520.424531102462960.591836324187144
750.5072755699875780.4032994809784930.611251658996664
760.5063674266501050.3845399246257750.628194928674434
770.5054592833126310.3672690565686040.643649510056657
780.5045511399751570.3509905245433660.658111755406948
790.5036429966376830.3354141294534370.671871863821929
800.5027348533002090.3203538066796480.685115899920771
810.5018267099627350.3056824114968530.697971008428617
820.5009185666252610.2913089039452890.710528229305234
830.5000104232877880.2771657223349490.722855124240626
840.4991022799503140.2632012923422690.735003267558359



Parameters (Session):
par1 = 40 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')