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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 05:07:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t135573890447psjpibe7ozdld.htm/, Retrieved Sat, 20 Apr 2024 10:35:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200741, Retrieved Sat, 20 Apr 2024 10:35:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 10:07:44] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
0.9
0.9
0.9
0.9
0.9
0.91
0.91
0.91
0.91
0.91
0.92
0.92
0.92
0.92
0.92
0.93
0.93
0.93
0.93
0.93
0.92
0.93
0.93
0.93
0.94
0.95
0.95
0.96
0.97
0.97
0.97
0.98
0.98
0.98
0.98
0.98
0.98
1
1.01
1.01
1.02
1.02
1.02
1.02
1.03
1.03
1.03
1.03
1.03
1.04
1.05
1.05
1.05
1.05
1.06
1.06
1.06
1.06
1.06
1.06
1.06
1.07
1.08
1.09
1.09
1.09
1.09
1.09
1.09
1.09
1.09
1.09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200741&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200741&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200741&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0597923238698339
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0597923238698339 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200741&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]0.0597923238698339[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200741&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200741&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
beta0.0597923238698339
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
30.90.90
40.90.90
50.90.90
60.910.90.01
70.910.910597923238698-0.000597923238698339
80.910.910562172018761-0.000562172018760743
90.910.910528558447344-0.000528558447344452
100.910.910496954709477-0.000496954709476749
110.920.9104672406325390.00953275936746101
120.920.921037226468012-0.00103722646801152
130.920.92097520828711-0.00097520828710973
140.920.920916898317366-0.000916898317366299
150.920.920862074836219-0.000862074836218696
160.930.9208105293784110.00918947062158859
170.930.93135998918201-0.00135998918200986
180.930.93127867226838-0.00127867226837963
190.930.931202217481985-0.00120221748198523
200.930.931130334104941-0.00113033410494046
210.920.931062748802057-0.0110627488020567
220.930.9204012813427940.00959871865720652
230.930.930975211037481-0.000975211037480661
240.930.930916900903286-0.000916900903286111
250.940.930862077267520.0091379227324796
260.950.9414084549030380.00859154509696169
270.950.951922163350018-0.00192216335001805
280.960.9518072327364630.0081927672635369
290.970.9622970973300750.00770290266992535
300.970.972757671781253-0.00275767178125264
310.970.972592784176981-0.00259278417698128
320.980.9724377555857470.00756224441425335
330.980.982889919752946-0.0028899197529465
340.980.982717124735121-0.00271712473512054
350.980.982554661532963-0.00255466153296346
360.980.982401912383207-0.00240191238320664
370.980.982258296460083-0.00225829646008302
3810.9821232676667480.0178767323332524
391.011.003192159036150.00680784096384812
401.011.01359921566792-0.00359921566791654
411.021.013384010199020.006615989800977
421.021.02377959560392-0.0037795956039226
431.021.02355360479948-0.00355360479947597
441.021.0233411265104-0.00334112651040019
451.031.0231413527920.00685864720799967
461.031.03355144724717-0.00355144724716983
471.031.03333909796316-0.00333909796316045
481.031.03313944553631-0.00313944553631407
491.031.03295173079204-0.00295173079203503
501.041.032775239948540.00722476005145878
511.051.043207225141420.0067927748585801
521.051.05361338093574-0.00361338093573904
531.051.05339732849256-0.00339732849256413
541.051.05319419432704-0.0031941943270446
551.061.053003206025340.00699679397466135
561.061.06342156059672-0.00342156059672227
571.061.06321697753738-0.0032169775373827
581.061.06302462697459-0.0030246269745855
591.061.06284377749894-0.00284377749893561
601.061.06267374143371-0.00267374143370547
611.061.06251387221996-0.00251387221995736
621.071.062363561958010.00763643804198577
631.081.072820162334630.00717983766536756
641.091.083249461513650.0067505384863471
651.091.09365309189712-0.00365309189712448
661.091.09343466504329-0.00343466504328527
671.091.09322929843863-0.00322929843863284
681.091.09303621118052-0.00303621118051778
691.091.09285466905827-0.00285466905827492
701.091.0926839817614-0.0026839817614015
711.091.09252350025466-0.00252350025466308
721.091.09237261431015-0.00237261431015057

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.9 & 0.9 & 0 \tabularnewline
4 & 0.9 & 0.9 & 0 \tabularnewline
5 & 0.9 & 0.9 & 0 \tabularnewline
6 & 0.91 & 0.9 & 0.01 \tabularnewline
7 & 0.91 & 0.910597923238698 & -0.000597923238698339 \tabularnewline
8 & 0.91 & 0.910562172018761 & -0.000562172018760743 \tabularnewline
9 & 0.91 & 0.910528558447344 & -0.000528558447344452 \tabularnewline
10 & 0.91 & 0.910496954709477 & -0.000496954709476749 \tabularnewline
11 & 0.92 & 0.910467240632539 & 0.00953275936746101 \tabularnewline
12 & 0.92 & 0.921037226468012 & -0.00103722646801152 \tabularnewline
13 & 0.92 & 0.92097520828711 & -0.00097520828710973 \tabularnewline
14 & 0.92 & 0.920916898317366 & -0.000916898317366299 \tabularnewline
15 & 0.92 & 0.920862074836219 & -0.000862074836218696 \tabularnewline
16 & 0.93 & 0.920810529378411 & 0.00918947062158859 \tabularnewline
17 & 0.93 & 0.93135998918201 & -0.00135998918200986 \tabularnewline
18 & 0.93 & 0.93127867226838 & -0.00127867226837963 \tabularnewline
19 & 0.93 & 0.931202217481985 & -0.00120221748198523 \tabularnewline
20 & 0.93 & 0.931130334104941 & -0.00113033410494046 \tabularnewline
21 & 0.92 & 0.931062748802057 & -0.0110627488020567 \tabularnewline
22 & 0.93 & 0.920401281342794 & 0.00959871865720652 \tabularnewline
23 & 0.93 & 0.930975211037481 & -0.000975211037480661 \tabularnewline
24 & 0.93 & 0.930916900903286 & -0.000916900903286111 \tabularnewline
25 & 0.94 & 0.93086207726752 & 0.0091379227324796 \tabularnewline
26 & 0.95 & 0.941408454903038 & 0.00859154509696169 \tabularnewline
27 & 0.95 & 0.951922163350018 & -0.00192216335001805 \tabularnewline
28 & 0.96 & 0.951807232736463 & 0.0081927672635369 \tabularnewline
29 & 0.97 & 0.962297097330075 & 0.00770290266992535 \tabularnewline
30 & 0.97 & 0.972757671781253 & -0.00275767178125264 \tabularnewline
31 & 0.97 & 0.972592784176981 & -0.00259278417698128 \tabularnewline
32 & 0.98 & 0.972437755585747 & 0.00756224441425335 \tabularnewline
33 & 0.98 & 0.982889919752946 & -0.0028899197529465 \tabularnewline
34 & 0.98 & 0.982717124735121 & -0.00271712473512054 \tabularnewline
35 & 0.98 & 0.982554661532963 & -0.00255466153296346 \tabularnewline
36 & 0.98 & 0.982401912383207 & -0.00240191238320664 \tabularnewline
37 & 0.98 & 0.982258296460083 & -0.00225829646008302 \tabularnewline
38 & 1 & 0.982123267666748 & 0.0178767323332524 \tabularnewline
39 & 1.01 & 1.00319215903615 & 0.00680784096384812 \tabularnewline
40 & 1.01 & 1.01359921566792 & -0.00359921566791654 \tabularnewline
41 & 1.02 & 1.01338401019902 & 0.006615989800977 \tabularnewline
42 & 1.02 & 1.02377959560392 & -0.0037795956039226 \tabularnewline
43 & 1.02 & 1.02355360479948 & -0.00355360479947597 \tabularnewline
44 & 1.02 & 1.0233411265104 & -0.00334112651040019 \tabularnewline
45 & 1.03 & 1.023141352792 & 0.00685864720799967 \tabularnewline
46 & 1.03 & 1.03355144724717 & -0.00355144724716983 \tabularnewline
47 & 1.03 & 1.03333909796316 & -0.00333909796316045 \tabularnewline
48 & 1.03 & 1.03313944553631 & -0.00313944553631407 \tabularnewline
49 & 1.03 & 1.03295173079204 & -0.00295173079203503 \tabularnewline
50 & 1.04 & 1.03277523994854 & 0.00722476005145878 \tabularnewline
51 & 1.05 & 1.04320722514142 & 0.0067927748585801 \tabularnewline
52 & 1.05 & 1.05361338093574 & -0.00361338093573904 \tabularnewline
53 & 1.05 & 1.05339732849256 & -0.00339732849256413 \tabularnewline
54 & 1.05 & 1.05319419432704 & -0.0031941943270446 \tabularnewline
55 & 1.06 & 1.05300320602534 & 0.00699679397466135 \tabularnewline
56 & 1.06 & 1.06342156059672 & -0.00342156059672227 \tabularnewline
57 & 1.06 & 1.06321697753738 & -0.0032169775373827 \tabularnewline
58 & 1.06 & 1.06302462697459 & -0.0030246269745855 \tabularnewline
59 & 1.06 & 1.06284377749894 & -0.00284377749893561 \tabularnewline
60 & 1.06 & 1.06267374143371 & -0.00267374143370547 \tabularnewline
61 & 1.06 & 1.06251387221996 & -0.00251387221995736 \tabularnewline
62 & 1.07 & 1.06236356195801 & 0.00763643804198577 \tabularnewline
63 & 1.08 & 1.07282016233463 & 0.00717983766536756 \tabularnewline
64 & 1.09 & 1.08324946151365 & 0.0067505384863471 \tabularnewline
65 & 1.09 & 1.09365309189712 & -0.00365309189712448 \tabularnewline
66 & 1.09 & 1.09343466504329 & -0.00343466504328527 \tabularnewline
67 & 1.09 & 1.09322929843863 & -0.00322929843863284 \tabularnewline
68 & 1.09 & 1.09303621118052 & -0.00303621118051778 \tabularnewline
69 & 1.09 & 1.09285466905827 & -0.00285466905827492 \tabularnewline
70 & 1.09 & 1.0926839817614 & -0.0026839817614015 \tabularnewline
71 & 1.09 & 1.09252350025466 & -0.00252350025466308 \tabularnewline
72 & 1.09 & 1.09237261431015 & -0.00237261431015057 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200741&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]0.9[/C][C]0.9[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.9[/C][C]0.9[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.9[/C][C]0.9[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.91[/C][C]0.9[/C][C]0.01[/C][/ROW]
[ROW][C]7[/C][C]0.91[/C][C]0.910597923238698[/C][C]-0.000597923238698339[/C][/ROW]
[ROW][C]8[/C][C]0.91[/C][C]0.910562172018761[/C][C]-0.000562172018760743[/C][/ROW]
[ROW][C]9[/C][C]0.91[/C][C]0.910528558447344[/C][C]-0.000528558447344452[/C][/ROW]
[ROW][C]10[/C][C]0.91[/C][C]0.910496954709477[/C][C]-0.000496954709476749[/C][/ROW]
[ROW][C]11[/C][C]0.92[/C][C]0.910467240632539[/C][C]0.00953275936746101[/C][/ROW]
[ROW][C]12[/C][C]0.92[/C][C]0.921037226468012[/C][C]-0.00103722646801152[/C][/ROW]
[ROW][C]13[/C][C]0.92[/C][C]0.92097520828711[/C][C]-0.00097520828710973[/C][/ROW]
[ROW][C]14[/C][C]0.92[/C][C]0.920916898317366[/C][C]-0.000916898317366299[/C][/ROW]
[ROW][C]15[/C][C]0.92[/C][C]0.920862074836219[/C][C]-0.000862074836218696[/C][/ROW]
[ROW][C]16[/C][C]0.93[/C][C]0.920810529378411[/C][C]0.00918947062158859[/C][/ROW]
[ROW][C]17[/C][C]0.93[/C][C]0.93135998918201[/C][C]-0.00135998918200986[/C][/ROW]
[ROW][C]18[/C][C]0.93[/C][C]0.93127867226838[/C][C]-0.00127867226837963[/C][/ROW]
[ROW][C]19[/C][C]0.93[/C][C]0.931202217481985[/C][C]-0.00120221748198523[/C][/ROW]
[ROW][C]20[/C][C]0.93[/C][C]0.931130334104941[/C][C]-0.00113033410494046[/C][/ROW]
[ROW][C]21[/C][C]0.92[/C][C]0.931062748802057[/C][C]-0.0110627488020567[/C][/ROW]
[ROW][C]22[/C][C]0.93[/C][C]0.920401281342794[/C][C]0.00959871865720652[/C][/ROW]
[ROW][C]23[/C][C]0.93[/C][C]0.930975211037481[/C][C]-0.000975211037480661[/C][/ROW]
[ROW][C]24[/C][C]0.93[/C][C]0.930916900903286[/C][C]-0.000916900903286111[/C][/ROW]
[ROW][C]25[/C][C]0.94[/C][C]0.93086207726752[/C][C]0.0091379227324796[/C][/ROW]
[ROW][C]26[/C][C]0.95[/C][C]0.941408454903038[/C][C]0.00859154509696169[/C][/ROW]
[ROW][C]27[/C][C]0.95[/C][C]0.951922163350018[/C][C]-0.00192216335001805[/C][/ROW]
[ROW][C]28[/C][C]0.96[/C][C]0.951807232736463[/C][C]0.0081927672635369[/C][/ROW]
[ROW][C]29[/C][C]0.97[/C][C]0.962297097330075[/C][C]0.00770290266992535[/C][/ROW]
[ROW][C]30[/C][C]0.97[/C][C]0.972757671781253[/C][C]-0.00275767178125264[/C][/ROW]
[ROW][C]31[/C][C]0.97[/C][C]0.972592784176981[/C][C]-0.00259278417698128[/C][/ROW]
[ROW][C]32[/C][C]0.98[/C][C]0.972437755585747[/C][C]0.00756224441425335[/C][/ROW]
[ROW][C]33[/C][C]0.98[/C][C]0.982889919752946[/C][C]-0.0028899197529465[/C][/ROW]
[ROW][C]34[/C][C]0.98[/C][C]0.982717124735121[/C][C]-0.00271712473512054[/C][/ROW]
[ROW][C]35[/C][C]0.98[/C][C]0.982554661532963[/C][C]-0.00255466153296346[/C][/ROW]
[ROW][C]36[/C][C]0.98[/C][C]0.982401912383207[/C][C]-0.00240191238320664[/C][/ROW]
[ROW][C]37[/C][C]0.98[/C][C]0.982258296460083[/C][C]-0.00225829646008302[/C][/ROW]
[ROW][C]38[/C][C]1[/C][C]0.982123267666748[/C][C]0.0178767323332524[/C][/ROW]
[ROW][C]39[/C][C]1.01[/C][C]1.00319215903615[/C][C]0.00680784096384812[/C][/ROW]
[ROW][C]40[/C][C]1.01[/C][C]1.01359921566792[/C][C]-0.00359921566791654[/C][/ROW]
[ROW][C]41[/C][C]1.02[/C][C]1.01338401019902[/C][C]0.006615989800977[/C][/ROW]
[ROW][C]42[/C][C]1.02[/C][C]1.02377959560392[/C][C]-0.0037795956039226[/C][/ROW]
[ROW][C]43[/C][C]1.02[/C][C]1.02355360479948[/C][C]-0.00355360479947597[/C][/ROW]
[ROW][C]44[/C][C]1.02[/C][C]1.0233411265104[/C][C]-0.00334112651040019[/C][/ROW]
[ROW][C]45[/C][C]1.03[/C][C]1.023141352792[/C][C]0.00685864720799967[/C][/ROW]
[ROW][C]46[/C][C]1.03[/C][C]1.03355144724717[/C][C]-0.00355144724716983[/C][/ROW]
[ROW][C]47[/C][C]1.03[/C][C]1.03333909796316[/C][C]-0.00333909796316045[/C][/ROW]
[ROW][C]48[/C][C]1.03[/C][C]1.03313944553631[/C][C]-0.00313944553631407[/C][/ROW]
[ROW][C]49[/C][C]1.03[/C][C]1.03295173079204[/C][C]-0.00295173079203503[/C][/ROW]
[ROW][C]50[/C][C]1.04[/C][C]1.03277523994854[/C][C]0.00722476005145878[/C][/ROW]
[ROW][C]51[/C][C]1.05[/C][C]1.04320722514142[/C][C]0.0067927748585801[/C][/ROW]
[ROW][C]52[/C][C]1.05[/C][C]1.05361338093574[/C][C]-0.00361338093573904[/C][/ROW]
[ROW][C]53[/C][C]1.05[/C][C]1.05339732849256[/C][C]-0.00339732849256413[/C][/ROW]
[ROW][C]54[/C][C]1.05[/C][C]1.05319419432704[/C][C]-0.0031941943270446[/C][/ROW]
[ROW][C]55[/C][C]1.06[/C][C]1.05300320602534[/C][C]0.00699679397466135[/C][/ROW]
[ROW][C]56[/C][C]1.06[/C][C]1.06342156059672[/C][C]-0.00342156059672227[/C][/ROW]
[ROW][C]57[/C][C]1.06[/C][C]1.06321697753738[/C][C]-0.0032169775373827[/C][/ROW]
[ROW][C]58[/C][C]1.06[/C][C]1.06302462697459[/C][C]-0.0030246269745855[/C][/ROW]
[ROW][C]59[/C][C]1.06[/C][C]1.06284377749894[/C][C]-0.00284377749893561[/C][/ROW]
[ROW][C]60[/C][C]1.06[/C][C]1.06267374143371[/C][C]-0.00267374143370547[/C][/ROW]
[ROW][C]61[/C][C]1.06[/C][C]1.06251387221996[/C][C]-0.00251387221995736[/C][/ROW]
[ROW][C]62[/C][C]1.07[/C][C]1.06236356195801[/C][C]0.00763643804198577[/C][/ROW]
[ROW][C]63[/C][C]1.08[/C][C]1.07282016233463[/C][C]0.00717983766536756[/C][/ROW]
[ROW][C]64[/C][C]1.09[/C][C]1.08324946151365[/C][C]0.0067505384863471[/C][/ROW]
[ROW][C]65[/C][C]1.09[/C][C]1.09365309189712[/C][C]-0.00365309189712448[/C][/ROW]
[ROW][C]66[/C][C]1.09[/C][C]1.09343466504329[/C][C]-0.00343466504328527[/C][/ROW]
[ROW][C]67[/C][C]1.09[/C][C]1.09322929843863[/C][C]-0.00322929843863284[/C][/ROW]
[ROW][C]68[/C][C]1.09[/C][C]1.09303621118052[/C][C]-0.00303621118051778[/C][/ROW]
[ROW][C]69[/C][C]1.09[/C][C]1.09285466905827[/C][C]-0.00285466905827492[/C][/ROW]
[ROW][C]70[/C][C]1.09[/C][C]1.0926839817614[/C][C]-0.0026839817614015[/C][/ROW]
[ROW][C]71[/C][C]1.09[/C][C]1.09252350025466[/C][C]-0.00252350025466308[/C][/ROW]
[ROW][C]72[/C][C]1.09[/C][C]1.09237261431015[/C][C]-0.00237261431015057[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200741&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200741&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
30.90.90
40.90.90
50.90.90
60.910.90.01
70.910.910597923238698-0.000597923238698339
80.910.910562172018761-0.000562172018760743
90.910.910528558447344-0.000528558447344452
100.910.910496954709477-0.000496954709476749
110.920.9104672406325390.00953275936746101
120.920.921037226468012-0.00103722646801152
130.920.92097520828711-0.00097520828710973
140.920.920916898317366-0.000916898317366299
150.920.920862074836219-0.000862074836218696
160.930.9208105293784110.00918947062158859
170.930.93135998918201-0.00135998918200986
180.930.93127867226838-0.00127867226837963
190.930.931202217481985-0.00120221748198523
200.930.931130334104941-0.00113033410494046
210.920.931062748802057-0.0110627488020567
220.930.9204012813427940.00959871865720652
230.930.930975211037481-0.000975211037480661
240.930.930916900903286-0.000916900903286111
250.940.930862077267520.0091379227324796
260.950.9414084549030380.00859154509696169
270.950.951922163350018-0.00192216335001805
280.960.9518072327364630.0081927672635369
290.970.9622970973300750.00770290266992535
300.970.972757671781253-0.00275767178125264
310.970.972592784176981-0.00259278417698128
320.980.9724377555857470.00756224441425335
330.980.982889919752946-0.0028899197529465
340.980.982717124735121-0.00271712473512054
350.980.982554661532963-0.00255466153296346
360.980.982401912383207-0.00240191238320664
370.980.982258296460083-0.00225829646008302
3810.9821232676667480.0178767323332524
391.011.003192159036150.00680784096384812
401.011.01359921566792-0.00359921566791654
411.021.013384010199020.006615989800977
421.021.02377959560392-0.0037795956039226
431.021.02355360479948-0.00355360479947597
441.021.0233411265104-0.00334112651040019
451.031.0231413527920.00685864720799967
461.031.03355144724717-0.00355144724716983
471.031.03333909796316-0.00333909796316045
481.031.03313944553631-0.00313944553631407
491.031.03295173079204-0.00295173079203503
501.041.032775239948540.00722476005145878
511.051.043207225141420.0067927748585801
521.051.05361338093574-0.00361338093573904
531.051.05339732849256-0.00339732849256413
541.051.05319419432704-0.0031941943270446
551.061.053003206025340.00699679397466135
561.061.06342156059672-0.00342156059672227
571.061.06321697753738-0.0032169775373827
581.061.06302462697459-0.0030246269745855
591.061.06284377749894-0.00284377749893561
601.061.06267374143371-0.00267374143370547
611.061.06251387221996-0.00251387221995736
621.071.062363561958010.00763643804198577
631.081.072820162334630.00717983766536756
641.091.083249461513650.0067505384863471
651.091.09365309189712-0.00365309189712448
661.091.09343466504329-0.00343466504328527
671.091.09322929843863-0.00322929843863284
681.091.09303621118052-0.00303621118051778
691.091.09285466905827-0.00285466905827492
701.091.0926839817614-0.0026839817614015
711.091.09252350025466-0.00252350025466308
721.091.09237261431015-0.00237261431015057







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.09223075018691.081979989148341.10248151122546
741.09446150037381.07952504836641.1093979523812
751.09669225056071.077855854297991.1155286468234
761.09892300074761.076540728460711.12130527303449
771.10115375093451.07541821522391.1268892866451
781.10338450112141.074408369305821.13236063293698
791.10561525130831.073465403768431.13776509884817
801.10784600149521.072560613897691.14313138909271
811.11007675168211.071674861204291.14847864215991
821.1123075018691.070794806533811.15382019720418
831.11453825205591.069910839436081.15916566467571
841.11676900224281.069015858097331.16452214638827

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.0922307501869 & 1.08197998914834 & 1.10248151122546 \tabularnewline
74 & 1.0944615003738 & 1.0795250483664 & 1.1093979523812 \tabularnewline
75 & 1.0966922505607 & 1.07785585429799 & 1.1155286468234 \tabularnewline
76 & 1.0989230007476 & 1.07654072846071 & 1.12130527303449 \tabularnewline
77 & 1.1011537509345 & 1.0754182152239 & 1.1268892866451 \tabularnewline
78 & 1.1033845011214 & 1.07440836930582 & 1.13236063293698 \tabularnewline
79 & 1.1056152513083 & 1.07346540376843 & 1.13776509884817 \tabularnewline
80 & 1.1078460014952 & 1.07256061389769 & 1.14313138909271 \tabularnewline
81 & 1.1100767516821 & 1.07167486120429 & 1.14847864215991 \tabularnewline
82 & 1.112307501869 & 1.07079480653381 & 1.15382019720418 \tabularnewline
83 & 1.1145382520559 & 1.06991083943608 & 1.15916566467571 \tabularnewline
84 & 1.1167690022428 & 1.06901585809733 & 1.16452214638827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200741&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]1.0922307501869[/C][C]1.08197998914834[/C][C]1.10248151122546[/C][/ROW]
[ROW][C]74[/C][C]1.0944615003738[/C][C]1.0795250483664[/C][C]1.1093979523812[/C][/ROW]
[ROW][C]75[/C][C]1.0966922505607[/C][C]1.07785585429799[/C][C]1.1155286468234[/C][/ROW]
[ROW][C]76[/C][C]1.0989230007476[/C][C]1.07654072846071[/C][C]1.12130527303449[/C][/ROW]
[ROW][C]77[/C][C]1.1011537509345[/C][C]1.0754182152239[/C][C]1.1268892866451[/C][/ROW]
[ROW][C]78[/C][C]1.1033845011214[/C][C]1.07440836930582[/C][C]1.13236063293698[/C][/ROW]
[ROW][C]79[/C][C]1.1056152513083[/C][C]1.07346540376843[/C][C]1.13776509884817[/C][/ROW]
[ROW][C]80[/C][C]1.1078460014952[/C][C]1.07256061389769[/C][C]1.14313138909271[/C][/ROW]
[ROW][C]81[/C][C]1.1100767516821[/C][C]1.07167486120429[/C][C]1.14847864215991[/C][/ROW]
[ROW][C]82[/C][C]1.112307501869[/C][C]1.07079480653381[/C][C]1.15382019720418[/C][/ROW]
[ROW][C]83[/C][C]1.1145382520559[/C][C]1.06991083943608[/C][C]1.15916566467571[/C][/ROW]
[ROW][C]84[/C][C]1.1167690022428[/C][C]1.06901585809733[/C][C]1.16452214638827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200741&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200741&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
731.09223075018691.081979989148341.10248151122546
741.09446150037381.07952504836641.1093979523812
751.09669225056071.077855854297991.1155286468234
761.09892300074761.076540728460711.12130527303449
771.10115375093451.07541821522391.1268892866451
781.10338450112141.074408369305821.13236063293698
791.10561525130831.073465403768431.13776509884817
801.10784600149521.072560613897691.14313138909271
811.11007675168211.071674861204291.14847864215991
821.1123075018691.070794806533811.15382019720418
831.11453825205591.069910839436081.15916566467571
841.11676900224281.069015858097331.16452214638827



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')